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Old page wikitext, before the edit (old_wikitext) | '{{Short description|Overview of ancient Greek music theory}}
{{about|the music theory and musical intervals used in ancient Greece|a discussion of the cultural aspects and history of ancient Greek music|Music of ancient Greece}}
The '''musical system of ancient Greece''' evolved over a period of more than 500 years from simple [[scale (music)|scales]] of [[tetrachord]]s, or divisions of the [[perfect fourth]], into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals.{{sfn|Chalmers|1993|loc=ch. 6, p. 99}}
Any discussion of the [[music of ancient Greece]], theoretical, philosophical or aesthetic, is fraught with two problems: there are few examples of written music, and there are many, sometimes fragmentary, theoretical and philosophical accounts. The empirical research of scholars like Richard Crocker,{{sfn|Crocker|1963}}{{sfn|Crocker|1964}}{{sfn|Crocker|1966}} C. André Barbera,{{sfn|Barbera|1977}}{{sfn|Barbera|1984}} and John Chalmers{{sfn|Chalmers|1993}} has made it possible to look at the ancient Greek systems as a whole without regard to the tastes of any one ancient theorist. The primary genera they examine are those of Pythagoras and the [[Pythagoreanism|Pythagorean school]], [[Archytas]], [[Aristoxenus|Aristoxenos]], and [[Ptolemy]] (including his versions of the genera of [[Didymus the Musician|Didymos]] and [[Eratosthenes]]).{{sfn|Chalmers|1993|loc=ch. 5, pp. 48–51}}
==Overview of the first complete tone system==
As an initial introduction to the principal names and divisions of the Ancient Greek tone system we will give a depiction of the "perfect system" or '''systema teleion''', which was elaborated in its entirety by about the turn of the 5th to 4th century [[BCE]].
The following diagram reproduces information from Chalmer. It shows the common ancient ''harmoniai'', the ''tonoi'' in all ''genera'', and the system as a whole in one complete map.
[[File:Systema-teleion-english.png|center|Depiction of the ancient Greek Tone system]]
The central three columns of the diagram show, first the modern note-names, then the two systems of symbols used in ancient Greece: the vocalic (favoured by singers) and instrumental (favoured by instrumentalists). The modern note-names are given in the [[Helmholtz pitch notation]], and the Greek note symbols are as given in the work of {{ill|Egert Pöhlmann|de}}.{{sfn|Pöhlmann|1970}} The pitches of the notes in modern notation are conventional, going back to the time of a publication by {{ill|Johann Friedrich Bellermann|de}} in 1840; in practice the pitches would have been somewhat lower.{{sfn|Pöhlmann and West|2001|loc=7}}
The section spanned by a blue brace is the range of the central [[octave]]. The range is approximately what we today depict as follows:
[[Image:ancient-greek-middle-octave.png|thumb|center|600px|The central octave of the ancient Greek system]]
Greek theorists conceived of scales as descending from higher pitch to lower (the opposite of modern practice).
The earliest Greek scales were [[tetrachord]]s, which were series of four descending tones, with the top and bottom tones being a fourth apart in modern terms. The sub-intervals of the tetrachord were unequal, with the largest intervals always at the top, and the smallest at the bottom. The 'characteristic interval' of a tetrachord is its largest one.
The '''Greater Perfect System''' (''systema teleion meizon'') was composed of four stacked tetrachords called (from lowest to highest) the ''Hypaton'', ''Meson'', ''Diezeugmenon'' and '' Hyperbolaion'' tetrachords. These are shown on the right hand side of the diagram. Octaves were composed from two stacked tetrachords connected by one common tone, the ''synaphe''.
At the position of the ''paramese'', the continuity of the system encounters a boundary (at b-flat, b). To retain the logic of the internal divisions of the tetrachords and avoid the ''Meson'' being forced into three whole tone steps (b–a–g–f), an interstitial note, the ''diazeuxis'' ('dividing'), was introduced between the ''paramese'' and ''mese''. This procedure gives its name to the tetrachord ''diezeugmenon'', which means the 'divided'.
To bridge the inconsistency of the ''diazeuxis'', the system allowed moving the ''nete'' one step up, permitting the construction of the ''Synemmenon'' ('conjunct') tetrachord – shown at the far left of the diagram.
The use of the ''Synemmenon'' tetrachord effected a modulation of the system, hence the name ''systema metabolon'', the modulating system, also called the '''Lesser Perfect System'''. This was considered apart, built of three stacked tetrachords — the ''Hypaton'', ''Meson'' and ''Synemmenon''. The first two of these are the same as the first two tetrachords of the Greater Perfect System, with a third tetrachord placed above the ''Meson''. When all these are considered together, with the ''Synemmenon'' tetrachord placed between the ''Meson'' and ''Diezeugmenon'' tetrachords, they make up the '''Immutable''' (or Unmodulating) '''System''' (systema ametabolon). The lowest tone does not belong to the system of tetrachords, as is reflected in its name, the ''Proslambanomenos'', the adjoined.
In sum, it is clear that the Ancient Greeks conceived of a unified system with the tetrachord as the basic structure, but the octave as the principle of unification.
Below we elaborate the mathematics that led to the logic of the system of tetrachords just described. <!-- The inclusion of the synemmenon tetrachord recalls the well-known medieval practice of avoiding four-tone groups of three whole-tone steps ([[tritone]]), which form an augmented fourth. Medieval music theory demanded the avoidance of the tritone in music practice – but included it in the sound system. It was the other way around with the ancient Greeks. The practice of music allowed a wide range of tolerance – even if the music was thus removed from the Pythagorean ideal. -->
==The Pythagoreans==
{{Main|Pythagorean interval}}
After the discovery of the fundamental intervals (octave, fourth and fifth), the first systematic divisions of the octave we know of were those of [[Pythagoras]] to whom was often attributed the discovery that the frequency of a vibrating string is inversely proportional to its length. [[Pythagoras]] construed the intervals arithmetically, allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2 (see also [[Pythagorean interval|Pythagorean Interval]] and [[Pythagorean tuning|Pythagorean Tuning]]).
The earliest such description of a scale is found in Philolaus fr. B6. [[Philolaus]] recognizes that, if we go up the interval of a fourth from any given note, and then up the interval of a fifth, the final note is an octave above the first note. Thus, the octave is made up of a fourth and a fifth. ... Philolaus's scale thus consisted of the following intervals: 9:8, 9:8, 256:243 [these three intervals take us up a fourth], 9:8, 9:8, 9:8, 256:243 [these four intervals make up a fifth and complete the octave from our starting note]. This scale is known as the Pythagorean diatonic and is the scale that [[Plato]] adopted in the construction of the [[Anima mundi|world soul]] in the ''Timaeus'' (36a-b).{{sfn|Huffman|2011}}
The next notable Pythagorean theorist we know of is [[Archytas]], contemporary and friend of Plato, who explained the use of arithmetic, geometric and harmonic means in tuning musical instruments. [[Euclid]] further developed Archytas's theory in his ''The Division of the Canon'' (''Katatomē kanonos'', the Latin ''Sectio Canonis''). He elaborated the acoustics with reference to the frequency of vibrations (or movements).{{sfn|Levin|1990}}
Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio (octave 2:1, fourth 4:3, fifth 3:2, 9:8).{{sfn|Huffman|2011}}{{sfn|Barker|1984–89|loc=2:46–52}}
Archytas was also the first ancient Greek theorist to provide ratios for all 3 [[Genus (music)|genera]].{{sfn|Chalmers|1993|loc=ch. 6, p. 99}} The three genera of [[tetrachord]]s recognized by Archytas have the following ratios:
*The enharmonic – 5:4, 36:35, and 28:27
*The chromatic – 32:27, 243:224, and 28:27;
*The diatonic – 9:8, 8:7, and 28:27.{{sfn|Huffman|2011}}
These three tunings appear to have corresponded to the actual musical practice of his day.{{sfn|Barker|1984–89|loc=2:46–52}}
The [[Genus (music)|genera]] arose after the framing interval of the tetrachord was fixed, because the two internal notes (called ''lichanoi'' and ''parhypate'') still had variable tunings. Tetrachords were classified into genera depending on the position of the ''lichanos'' (thus the name ''lichanos'', which means "the indicator"). For instance a ''lichanos'' that is a [[minor third]] from the bottom and a [[major second]] from the top, defines the genus [[Diatonic genus|diatonic]]. The other two genera, [[Chromatic genus|chromatic]] and [[Enharmonic genus|enharmonic]], were defined in similar fashion.{{sfn|Chalmers|1993|loc=ch. 5, p. 47}}
More generally, three ''genera'' of seven octave ''species'' can be recognized, depending on the positioning of the interposed tones in the component [[tetrachord]]s:
*The diatonic genus is composed of tones and semitones,
*the chromatic genus is composed of semitones and a minor third,
*the enharmonic genus consists of a major third and two quarter-tones or diesis.{{sfn|Cleonides|1965|loc=35–36}}
Within these basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two "shades" (''chroai''), respectively .{{sfn|Cleonides|1965|loc=39–40}}{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}
The elaboration of tetrachords was also accompanied by penta- and hexachords. The joining of a tetrachord and a pentachord yields an octachord, i.e. the complete seven-tone scale plus a higher octave of the base note. However, this was also produced by joining two tetrachords, which were linked by means of an intermediary or shared note. The final evolution of the system did not end with the octave as such but with the ''Systema teleion'', a set of five tetrachords linked by conjunction and disjunction<!--define --> into arrays of tones spanning two octaves, as explained above.{{sfn|Chalmers|1993|loc=ch. 6, p. 99}}
==The system of Aristoxenus==
Having elaborated the ''Systema teleion'', we will now examine the most significant individual system, that of [[Aristoxenos]], which influenced much classification well into the Middle Ages.
Aristoxenus was a disciple of [[Aristotle]] who flourished in the 4th century BC. He introduced a radically different model for creating scales, and the nature of his scales deviated sharply from his predecessors. His system was based on seven "[[octave species]]" named after Greek regions and ethnicities – Dorian, Lydian, etc. This association of the ethnic names with the octave species appears to have preceded Aristoxenus,{{sfn|Mathiesen|2001a|loc=6(iii)(d)}} and the same system of names was revived in the [[Renaissance]] as names of musical [[mode (music)|modes]] according to the harmonic theory of that time, which was however quite different to that of the ancient Greeks. Thus the names Dorian, Lydian etc. should not be taken to imply a historical continuity between the systems.
In contrast to Archytas who distinguished his "genera" only by moving the ''lichanoi'', Aristoxenus varied both ''lichanoi'' and ''parhypate'' in considerable ranges.{{sfn|Chalmers|1993|loc=ch. 5, p. 48}} Instead of using discrete ratios to place the intervals in his scales, Aristoxenus used continuously variable quantities: as a result he obtained scales of thirteen notes to an octave, and considerably different qualities of consonance.{{sfn|Chalmers|1993|loc=ch. 3, pp. 17–22}}
The octave species in the [[Aristoxenus|Aristoxenian]] tradition were:{{sfn|Barbera|1984|loc=240}}{{sfn|Mathiesen|2001a|loc=6(iii)(d)}}
* [[Mixolydian mode#Greek Mixolydian|Mixolydian]]: ''hypate hypaton–paramese'' (b–b′)
* [[Lydian mode|Lydian]]: ''parhypate hypaton–trite diezeugmenon'' (c′–c″)
* [[Phrygian mode#Ancient Greek Phrygian mode|Phrygian]]: ''lichanos hypaton–paranete diezeugmenon'' (d′–d″)
* [[Dorian mode|Dorian]]: ''hypate meson–nete diezeugmenon'' (e′–e″)
* [[Hypolydian mode|Hypolydian]]: ''parhypate meson–trite hyperbolaion'' (f′–f″)
* [[Hypophrygian mode|Hypophrygian]]: ''lichanos meson–paranete hyperbolaion'' (g′–g″)
* Common, [[Locrian mode|Locrian]], or [[Hypodorian mode|Hypodorian]]: ''mese–nete hyperbolaion'' or ''proslambanomenos–mese'' (a′–a″ or a–a′)
These names are derived from:
*an Ancient Greek subgroup ([[Dorians]]),
*a small region in central Greece ([[Locris]]),
*certain neighboring (non-Greek) peoples from [[Asia Minor]] ([[Lydia]], [[Phrygia]]).
*The prefixes ''myxo'' and ''hypo'' were added to these to form associated scales above and below.
===Aristoxenian ''tonoi''===
The term ''tonos'' (pl. ''tonoi'') was used in four senses, for it could designate a note, an interval, a region of the voice, and a pitch.{{sfn|Cleonides|1965|loc=44}}
The ancient writer [[Cleonides]] attributes thirteen ''tonoi'' to Aristoxenus, which represent a transposition of the tones of the Pythagorean system into a more uniform progressive scale over the range of an octave.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}
According to Cleonides,{{sfn|Cleonides|1965|loc=44}} these transpositional ''tonoi'' were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen. In fact, Aristoxenus criticized the application of these names by the earlier theorists, whom he called the "Harmonicists".{{sfn|Mathiesen|2001a|loc=6(iii)(d)}}
According to the interpretation of at least two modern authorities, in the Aristoxenian ''tonoi'' the Hypodorian is the lowest, and the Mixolydian is next-to-highest: the reverse of the case of the octave species.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}{{sfn|Solomon|1984|loc=250}} The nominal base pitches are as follows (in descending order, after Mathiesen; Solomon uses the octave between '''A''' and '''a''' instead):
{| class="wikitable"
|-
! f
| Hypermixolydian || also called Hyperphrygian
|-
! e
| High Mixolydian || also called Hyperiastian
|-
! e{{sup|{{music|♭}}}}
| Low Mixolydian || also called Hyperdorian
|-
! d
| High Lydian ||
|-
! c{{sup|{{music|♯}}}}
| Low Lydian || also called Aeolian
|-
! c
| High Phrygian ||
|-
! B
| Low Phrygian || also called Iastian
|-
! B{{sup|{{music|♭}}}}
| Dorian ||
|-
! A
| High Hypolydian ||
|-
! G{{sup|{{music|♯}}}} (and A{{sup|{{music|♭}}}}?)
| Low Hypolydian || also called Hypoaeolian
|-
! G
| High Hypophrygian ||
|-
! F{{sup|{{music|♯}}}}
| Low Hypophrygian
| also called Hypoiastian
|-
! F
| Hypodorian ||
|}
==The octave species in all genera {{anchor|octave_species_anchor}}==
{{Main|Octave species}}
Based on the above, it can be seen that the Aristochene system of tones and octave species can be combined with the Pythagorean system of "genera" to produce a more complete system in which each octave species of thirteen tones (Dorian, Lydian, etc.) can be declined into a system of seven tones by selecting particular tones and semitones to form genera (Diatonic, Chromatic, and Enharmonic).
The order of the [[octave species]] names in the following table are the original Greek ones, followed by later alternatives (Greek and other). The species and notation are built around the template of the Dorian.
===Diatonic {{anchor|diatonic_species_anchor}}===
{| class="wikitable" style="text-align:center"
|-
! Tonic
! Name
! Mese
|-
| (A)
| (Hypermixolydian, Hyperphrygian, Locrian)
| (d)
|-
| B
| Mixolydian, Hyperdorian
| e
|-
| c
| Lydian
| f
|-
| d
| Phrygian
| g
|-
| e
| Dorian
| a
|-
| f
| Hypolydian
| b
|-
| g
| Hypophrygian, Ionian
| c′
|-
| a
| Hypodorian, Aeolian
| d′
|-
|}
===Chromatic {{anchor|chromatic_species_anchor}}===
{| class="wikitable" style="text-align:center;"
|-
! Tonic
! Name
! Mese
|-
| (A)
| (Hypermixolydian, Hyperphrygian, Locrian)
| (d{{sup|{{music|♭}}}})
|-
| B
| Mixolydian, Hyperdorian
| e
|-
| c
| Lydian
| f
|-
| d{{sup|{{music|♭}}}}
| Phrygian
| g{{sup|{{music|♭}}}}
|-
| e
| Dorian
| a
|-
| f
| Hypolydian
| b
|-
| g{{sup|{{music|♭}}}}
| Hypophrygian, Ionian
| c′
|-
| a
| Hypodorian, Aeolian
| d′{{sup|{{music|♭}}}}
|-
|}
===Enharmonic{{anchor|enharmonic_species_anchor}}===
{| class="wikitable" style="text-align:center;"
|-
! Tonic
! Name
! Mese
|-
| (A)
| (Hypermixolydian, Hyperphrygian, Locrian)
| (d{{sup|{{music|𝄫}}}})
|-
| B
| Mixolydian, Hyperdorian
| e
|-
| c{{sup|{{music|-}}}}
| Lydian
| f{{sup|{{music|-}}}}
|-
| d{{sup|{{music|𝄫}}}}
| Phrygian
| g{{sup|{{music|𝄫}}}}
|-
| e
| Dorian
| a
|-
| f{{sup|{{music|-}}}}
| Hypolydian
| b
|-
| g{{sup|{{music|𝄫}}}}
| Hypophrygian, Ionian
| c′{{sup|{{music|-}}}}
|-
| a
| Hypodorian, Aeolian
| d′{{sup|{{music|𝄫}}}}
|}
==The oldest ''harmoniai'' in three genera {{anchor|harmoiai_anchor}}==
In the notation above and below, the standard double-flat symbol {{music|𝄫}} is used to accommodate as far as possible the modern musical convention that demands every note in a scale to have a distinct, sequential letter; so interpret {{music|𝄫}} only as meaning the immediate prior letter in the alphabet.{{sfn|Chalmers|1993|loc=ch. 6, p. 109}} This is a complication unnecessary in Greek notation, which had distinct symbols for each half-flat, flat, or natural note.
The superscript symbol {{music|-}} after a letter indicates an approximately half-flattened version of the named note; the exact degree of flattening intended depending on which of several tunings was used. Hence a three-tone falling-pitch sequence '''d''', '''d{{sup|{{music|-}}}}''', '''d{{sup|{{music|♭}}}}''', with the second note, '''d{{sup|{{music|-}}}}''', about {{frac|1|2}}-flat (a [[quarter-tone]] flat) from the first note, '''d''', and the same '''d{{sup|{{music|-}}}}''' about {{frac|1|2}}-sharp (a quarter-tone sharp) from the following '''d{{sup|{{music|♭}}}}'''.
The ('''d''') listed first for the Dorian is the ''Proslambanómenos'', which was appended as it was, and falls outside of the linked-tetrachord scheme.
These tables are a depiction of [[Aristides Quintilianus]]'s enharmonic ''harmoniai'', the diatonic of Henderson{{sfn|Henderson|1942}} and Chalmers{{sfn|Chalmers|1993}} chromatic versions. Chalmers, from whom they originate, states:
{{blockquote|In the enharmonic and chromatic forms of some of the harmoniai, it has been necessary to use both a '''d''' and either a '''d{{sup|{{music|♭}}}}''' or '''d{{sup|{{music|𝄫}}}}''' because of the non-heptatonic nature of these scales. '''C''' and '''F''' are synonyms for '''d{{sup|{{music|𝄫}}}}''' and '''g{{sup|{{music|𝄫}}}}''' [respectively]. The appropriate tunings for these scales are those of Archytas{{sfn|Mountford|1923}} and Pythagoras.{{sfn|Chalmers|1993|loc=ch. 6, p. 109}}}}
The superficial resemblance of these octave species with the church [[mode (music)|modes]] is misleading: The conventional representation as a section (such as '''C D E F''' followed by '''D E F G''') is incorrect. The species were re-tunings of the central octave such that the sequences of intervals (the cyclical modes divided by ratios defined by genus) corresponded to the notes of the Perfect Immutable System as depicted above.{{sfn|Chalmers|1993|loc=ch. 6, p. 106}}
===Dorian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| (d) e f{{sup|{{music|-}}}} g{{sup|{{music|bb}}}} a b c′{{sup|{{music|-}}}} d′{{sup|{{music|𝄫}}}} e′
|-
| Chromatic
| (d) e f g{{sup|{{music|♭}}}} a b c′ d′{{sup|{{music|♭}}}} e′
|-
| Diatonic
| (d) e f g a b c′ d′ e′
|}
===Phrygian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| d e f{{sup|{{music|-}}}} g{{sup|{{music|𝄫}}}} a b c′{{sup|{{music|-}}}} d′{{sup|{{music|𝄫}}}} d′
|-
| Chromatic
| d e f g{{sup|{{music|♭}}}} a b c′ d′{{sup|{{music|♭}}}} d′
|-
| Diatonic
| d e f g a b c′ d′
|}
===Lydian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| f{{sup|{{music|-}}}} g{{sup|{{music|𝄫}}}} a b c′{{sup|{{music|-}}}} d′{{sup|{{music|𝄫}}}} e′ f′{{sup|{{music|-}}}}
|-
| Chromatic
| f g a b c′ d′{{sup|{{music|♭}}}} e′ f′
|-
| Diatonic
| f g a b c′ d′ e′ f′
|}
===Mixolydian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| B c{{sup|{{music|-}}}} d{{sup|{{music|𝄫}}}} d e f{{sup|{{music|-}}}} g{{sup|{{music|𝄫}}}} b
|-
| Chromatic
| B c d{{sup|{{music|♭}}}} d e f{{sup|{{music|-}}}} g{{sup|{{music|♭}}}} b
|-
| Diatonic
| B c d e f(g) (a) b
|}
===Syntonolydian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| B c{{sup|{{music|-}}}} d{{sup|{{music|𝄫}}}} e g
|-
| Chromatic
| B c d{{sup|{{music|♭}}}} e g
|-
| 1st Diatonic
| c d e f g
|-
| 2nd Diatonic
| B c d e g
|}
===Ionian (Iastian)===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| B c{{sup|{{music|-}}}} d{{sup|{{music|𝄫}}}} e g a
|-
| Chromatic
| B c d{{sup|{{music|♭}}}} e g a
|-
| 1st Diatonic
| c e f g
|-
| 2nd Diatonic
| B c d e g a
|}
==Ptolemy and the Alexandrians==
In marked contrast to his predecessors, [[Ptolemy]]'s scales employed a division of the ''pyknon'' in the ratio of 1:2, melodic, in place of equal divisions.{{sfn|Chalmers|1993|loc=ch. 2, p. 10}} Ptolemy, in his ''Harmonics'', ii.3–11, construed the ''tonoi'' differently, presenting all seven octave species within a fixed octave, through chromatic inflection of the scale degrees (comparable to the modern conception of building all seven modal scales on a single tonic). In Ptolemy's system, therefore there are only seven ''tonoi''.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}{{sfn|Mathiesen|2001c}} Ptolemy preserved Archytas's tunings in his ''Harmonics'' as well as transmitting the tunings of [[Eratosthenes]] and [[Didymos (music theorist)|Didymos]] and providing his own ratios and scales.{{sfn|Chalmers|1993|loc=ch. 6, p. 99}}
==''Harmoniai''==
In music theory the Greek word ''harmonia'' can signify the enharmonic genus of tetrachord, the seven octave species, or a style of music associated with one of the ethnic types or the ''tonoi'' named by them.{{sfn|Mathiesen|2001b}}
Particularly in the earliest surviving writings, ''harmonia'' is regarded not as a scale, but as the epitome of the stylised singing of a particular district or people or occupation.{{sfn|Winnington-Ingram|1936|loc=3}} When the late 6th-century poet [[Lasus of Hermione]] referred to the Aeolian ''harmonia'', for example, he was more likely thinking of a [[Melody type|melodic style]] characteristic of Greeks speaking the Aeolic dialect than of a scale pattern.{{sfn|Anderson and Mathiesen|2001}}
In the ''[[Republic (Plato)|Republic]]'', [[Plato]] uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}
The philosophical writings of Plato and [[Aristotle]] (c. 350 [[BCE]]) include sections that describe the effect of different ''harmoniai'' on mood and character formation (see below on ethos). For example, in the ''Republic'' (iii.10–11) Plato describes the music a person is exposed to as molding the person's character, which he discusses as particularly relevant for the proper education of the guardians of his ideal State. Aristotle in the ''Politics'' (viii:1340a:40–1340b:5):
{{blockquote|But melodies themselves do contain imitations of character. This is perfectly clear, for the ''harmoniai'' have quite distinct natures from one another, so that those who hear them are differently affected and do not respond in the same way to each. To some, such as the one called Mixolydian, they respond with more grief and anxiety, to others, such as the relaxed ''harmoniai'', with more mellowness of mind, and to one another with a special degree of moderation and firmness, Dorian being apparently the only one of the ''harmoniai'' to have this effect, while Phrygian creates ecstatic excitement. These points have been well expressed by those who have thought deeply about this kind of education; for they cull the evidence for what they say from the facts themselves.{{sfn|Barker|1984–89|loc=1:175–176}}}}
Aristotle remarks further: {{blockquote |sign=|source=| From what has been said it is evident what an influence music has over the disposition of the mind, and how variously it can fascinate it—and if it can do this, most certainly it is what youth ought to be instructed in.{{sfn|Aristotle|1912|loc=book 8, ch. 5}})}}
==Ethos==
The ancient Greeks have used the word ''ethos'' (ἔθος or ἦθος), in this context best rendered by "character" (in the sense of patterns of being and behaviour, but not necessarily with "moral" implications), to describe the ways music can convey, foster, and even generate emotional or mental states. Beyond this general description, there is no unified "Greek ethos theory" but "many different views, sometimes sharply opposed."{{sfn|Anderson and Mathiesen|2001}} Ethos is attributed to the ''tonoi'' or ''harmoniai'' or modes (for instance, Plato, in the ''Republic'' (iii: 398d–399a), attributes "virility" to the "[[Dorian mode|Dorian]]," and "relaxedness" to the "[[Lydian mode|Lydian]]" mode), instruments (especially the [[aulos]] and the [[cithara]], but also others), rhythms, and sometimes even the [[Genus (music)|genus]] and individual tones. The most comprehensive treatment of musical ethos is provided by [[Aristides Quintilianus]] in his book ''On Music'', with the original conception of assigning ethos to the various musical parameters according to the general categories of male and female. [[Aristoxenus]] was the first Greek theorist to point out that ethos does not only reside in the individual parameters but also in the musical piece as a whole (cited in Pseudo-Plutarch, ''De Musica'' 32: 1142d ff; see also Aristides Quintilianus 1.12). The Greeks were interested in musical ethos particularly in the context of education (so Plato in his ''Republic'' and Aristotle in his eighth book of his ''Politics''), with implications for the well-being of the State. Many other ancient authors refer to what we nowadays would call psychological effect of music and draw judgments for the appropriateness (or value) of particular musical features or styles, while others, in particular [[Philodemus]] (in his fragmentary work ''De musica'') and [[Sextus Empiricus]] (in his sixth book of his work ''Adversus mathematicos''), deny that music possesses any influence on the human person apart from generating pleasure. These different views anticipate in some way the modern debate in [[Philosophy of music|music philosophy]] whether music on its own or [[absolute music]], independent of text, is able to [[Music and emotion|elicit emotions]] on the listener or musician.{{sfn|Kramarz|2016}}
==Melos==
Cleonides describes "melic" composition, "the employment of the materials subject to harmonic practice with due regard to the requirements of each of the subjects under consideration"{{sfn|Cleonides|1965|loc=35}}—which, together with the scales, ''tonoi'', and ''harmoniai'' resemble elements found in medieval modal theory.{{sfn|Mathiesen|2001a|loc=6(iii)}} According to Aristides Quintilianus (''On Music'', i.12), melic composition is subdivided into three classes: dithyrambic, nomic, and tragic. These parallel his three classes of rhythmic composition: systaltic, diastaltic and hesychastic. Each of these broad classes of melic composition may contain various subclasses, such as erotic, comic and panegyric, and any composition might be elevating (diastaltic), depressing (systaltic), or soothing (hesychastic).{{sfn|Mathiesen|2001a|loc=4}}
The classification of the ''requirements'' we have from [[Proclus]] ''Useful Knowledge'' as preserved by [[Photios I of Constantinople|Photios]]{{Citation needed|date=November 2009}}:
* for the gods—[[hymn]], [[prosodion]], [[paean]], [[dithyramb]], nomos, adonidia, iobakchos, and [[Hyporchema|hyporcheme]];
* for humans—[[Encomium|encomion]], [[epinikion]], [[skolion]], [[erotica]], [[epithalamia]], [[hymenaios]], sillos, threnos, and epikedeion;
* for the gods and humans—partheneion, daphnephorika, tripodephorika, oschophorika, and eutika
According to Mathiesen:
{{blockquote | Such pieces of music were called melos, which in its perfect form (teleion melos) comprised not only the melody and the text (including its elements of rhythm and diction) but also stylized dance movement. Melic and rhythmic composition (respectively, melopoiïa and rhuthmopoiïa) were the processes of selecting and applying the various components of melos and rhythm to create a complete work.{{sfn|Mathiesen|1999|loc=25}}}}
==Unicode==
{{Main|Ancient Greek Musical Notation|l1=Ancient Greek Musical Notation (Unicode block)}}
Music symbols of ancient Greece were added to the [[Unicode]] Standard in March 2005 with the release of version 4.1.
==See also==
* [[Alypius of Alexandria]]
* [[Delphic Hymns]]
* [[Seikilos epitaph]]
* [[Mesomedes]]
* [[Oxyrhynchus hymn]]
==References==
{{reflist|18em}}
'''Sources'''
{{div col|colwidth=45em}}
* {{wikicite|ref={{harvid|Anderson and Mathiesen|2001}}|reference=Anderson, Warren, and [[Thomas J. Mathiesen]] (2001). "Ethos". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan.}}
* {{wikicite|ref={{harvid|Aristotle|1912}}|reference=[[Aristotle]] (1912). ''[http://www.gutenberg.org/files/6762/6762-h/6762-h.htm A Treatise on Government]'' [''Politics''], translated by William Ellis. London and Toronto: J. M. Dent; New York: E. P. Dutton.}}
* {{cite journal|last=Barbera|first=C. André|date=Autumn 1977|title=Arithmetic and Geometric Divisions of the Tetrachord|journal=[[Journal of Music Theory]]|volume=21|issue=2|pages=294–323|doi=10.2307/843492|jstor=843492}}
* {{cite journal|last=Barbera|first=C. André|date=Summer 1984|title=Octave Species|journal=[[The Journal of Musicology]]|volume=3|issue=3|pages=229–241|doi=10.2307/763813|jstor=763813}}
* {{wikicite|ref={{harvid|Barker|1984–89}}|reference=[[Andrew Barker (classicist)|Barker, Andrew]] (ed.) (1984–89). ''Greek Musical Writings'', 2 vols. Cambridge and New York: Cambridge University Press. {{ISBN|0-521-23593-6}} (v. 1) {{ISBN|0-521-30220-X}} (v. 2).}}
* {{citation|last=Chalmers|first=John H.|title=Divisions of the Tetrachord: A Prolegomenon to the Construction of Musical Scales|others=edited by Larry Polansky and Carter Scholz, foreword by Lou Harrison|place=Hanover, New Hampshire|publisher=Frog Peak Music|year=1993|url=http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html|isbn=0-945996-04-7}}
* {{wikicite|ref={{harvid|Cleonides|1965}}|reference=[[Cleonides]] (1965). "Harmonic Introduction", translated by [[Oliver Strunk]]. In ''Source Readings in Music History'', vol. 1 (Antiquity and the Middle Ages), edited by Oliver Strunk, 35–46. New York: W. W. Norton.}}
* {{cite journal|last=Crocker|first=Richard L.|date=Winter 1963|title=Pythagorean Mathematics and Music|journal=[[The Journal of Aesthetics and Art Criticism]]|volume=22|issue=2|pages=189–198|doi=10.2307/427754|jstor=427754}}
* {{cite journal|last=Crocker|first=Richard L.|date=Spring 1964|title=Pythagorean Mathematics and Music|journal=[[The Journal of Aesthetics and Art Criticism]]|volume=22|issue=3|pages=325–335|doi=10.2307/427236|jstor=427236}}
* {{cite journal|last=Crocker|first=Richard L.|date=April 1966|title=The Troping Hypothesis|journal=[[The Musical Quarterly]]|volume=52|issue=2|pages=183–203|doi=10.1093/mq/lii.2.183 }}
* {{cite journal|last=Henderson|first=M. I.|date=October 1942|title=The Growth of the Greek ἁρμονιαι|journal=[[The Classical Quarterly]]|volume=36|issue=3–4|pages=94–103}}
* {{wikicite|ref={{harvid|Huffman|2011}}|reference=Huffman, Carl A. (2011). "[http://plato.stanford.edu/entries/archytas/ Archytas]". ''The Stanford Encyclopedia of Philosophy'' (accessed 25 August 2014).}}
* {{citation|last=Kramarz|first=Andreas|year=2016|title=The Power and Value of Music. Its Effect and Ethos in Classical Authors and Contemporary Music Theory|place=New York/Bern|publisher=Peter Lang|isbn=9781433133787}}
* {{citation | last = Levin | first = Flora R. | author-link = Flora Levin | issue = 4 | journal = Hermes | jstor = 4476778 | pages = 430–443 | title = Unity in Euclid's 'Sectio Canonis' | volume = 118 | year = 1990}}
* {{citation|last=Mathiesen|first=Thomas J.|author-link=Thomas J. Mathiesen|title=Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages|series=of Publications of the Center for the History of Music Theory and Literature 2|place=Lincoln|publisher=University of Nebraska Press|year=1999|isbn=9780803230798}}
* {{wikicite|ref={{harvid|Mathiesen|2001a}}|reference=Mathiesen, Thomas J. (2001a). "Greece, §I: Ancient". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan.}}
* {{wikicite|ref={{harvid|Mathiesen|2001b}}|reference=Mathiesen, Thomas J. (2001b). "Harmonia (i)". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.}}
* {{wikicite|ref={{harvid|Mathiesen|2001c}}|reference=Mathiesen, Thomas J. (2001c). "Tonos". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.}}
* {{wikicite|ref={{harvid|Mountford|1923}}|reference=Mountford, James Frederick. (1923). The Musical Scales of Plato's Republic. ''[[The Classical Quarterly]]'' 17:125-136.}}
* {{citation|last=Pöhlmann|first=Egert|title=Denkmäler altgriechischer Musik|series=Erlanger Beiträge zur Sprach- und Kunstwissenschaft 31|place=Nuremberg|publisher=Hans Carl Verlag|year=1970|issn=0425-2268}}
* {{wikicite|ref={{harvid|Pöhlmann and West|2001}}|reference={{ill|Egert Pöhlmann|de|Pöhlmann, Egert}}, and [[Martin Litchfield West|Martin L. West]]. 2001. ''Documents of Ancient Greek Music: The Extant Melodies and Fragments'', edited and transcribed with commentary by Egert Pöhlmann and Martin L. West. Oxford: Clarendon Press. {{ISBN|0-19-815223-X}}.}}
* {{cite journal|last=Solomon|first=Jon|date=Summer 1984|title=Towards a History of Tonoi|journal=[[The Journal of Musicology]]|volume=3|issue=3|pages=242–251|doi=10.2307/763814|jstor=763814}}
* {{citation|last=Winnington-Ingram|first=Reginald P.|year=1936|title=Mode in Ancient Greek Music|place=London|publisher=Cambridge University Press}}
{{div col end}}
==Further reading==
{{div col|colwidth=45em}}
* {{ill|Johann Friedrich Bellermann|de|lt=Bellermann, Johann Friedrich}} (1840). ''[https://books.google.com/books?id=PssqAAAAYAAJ Die Hymnen des Dionysius und Mesomedes: Text und Melodieen nach Handschriften und den alten Ausgaben bearbeitet von Dr. Friedrich Bellermann]''. Berlin: Albert Förstner.
* Jan, Karl von (ed.) (1895). ''Musici scriptores graeci: Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat''. Bibliotheca scriptorum graecorum et romanorum Teubneriana. Leipzig: B. G. Teubner.
* {{citation|last=Jowett|first=Benjamin|author-link=Benjamin Jowett|year=1937|title=The Dialogues of Plato|type=2 vols.|translator=Benjamin Jowett|edition=3rd|place=New York|publisher=Random House|ref=none}}
* [[Thomas J. Mathiesen|Mathiesen, Thomas J.]] (2001d). "Alypius [Alupios]". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan Publishers.
* Meibom, Marcus (ed.) (1652). ''Antiquae musicae auctores septem: Graece et latine'', 2 vols. Amsterdam: Apud Ludovicum Elzevirium. Facsimile reprint in Monuments of Music and Music Literature in Facsimile, Second Series: Music Literature 51. New York: Broude Bros., 1977. {{ISBN|9780845022511}}.
* {{cite journal|last=Winnington-Ingram|first=Reginald P.|year=1932|title=Aristoxenus and the Intervals of Greek Music|journal=[[The Classical Quarterly]]|volume=26|issue=3–4|pages=195–208|doi=10.1017/s0009838800014415|s2cid=170375844 |ref=none}}
* Winnington-Ingram, Reginald P. (1954). "Greek Music (Ancient)". ''[[Grove's Dictionary of Music and Musicians]]'', fifth edition, edited by [[Eric Blom]]. New York: St. Martin's Press.
{{div col end}}
==External links==
* Elsie Hamilton, [http://www.nakedlight.co.uk/pdf/articles/a-002.pdf booklet on the modes of ancient Greece] {{Webarchive|url=https://web.archive.org/web/20081121100923/http://www.nakedlight.co.uk/pdf/articles/a-002.pdf |date=2008-11-21 }}, with detailed examples of the construction of Aolus (reed pipe instruments) and monochord, which might help reconstruct the intervals and modes of the Greeks
* Nikolaos Ioannidis musician, composer, has attempted to [http://homoecumenicus.com/ioannidis_music_ancient_greeks.htm reconstruct ancient Greek music] from a combination of the ancient texts (to be performed) and his knowledge of Greek music.
* A mid-19th century, 1902 edition, Henry S. Macran, [https://archive.org/stream/aristoxenouharm00arisgoog ''The Harmonics of Aristoxenus'']. The Barbera translation cited above is more up to date.
* Joe Monzo (2004). [http://www.tonalsoft.com/monzo/aristoxenus/aristoxenus.aspx Analysis of Aristoxenus]. Full of interesting and insightful mathematical analysis. There are some original hypotheses outlined.
* [[Robert Erickson]], American composer and academic, [http://www.ex-tempore.org/ARCHYTAS/ARCHYTAS.html Analysis of Archytas], something of a complement to the above Aristoxenus but, dealing with the earlier and arithmetically precise Archytas:. An incidental note. Erickson is keen to demonstrate that Archytas tuning system not only corresponds with Platos Harmonia, but also with the practice of musicians. Erickson mentions the ease of tuning with the Lyre.
* Austrian Academy of Sciences [http://www.oeaw.ac.at/kal/agm/ examples of instruments and compositions]
*[http://www.kerylos.fr/index_en.php Ensemble Kérylos], a music group led by scholar [[Annie Bélis]], dedicated to the recreation of ancient Greek and Roman music and playing scores written on inscriptions and papyri.
{{Musical notation}}
{{Ancient Greece topics}}
{{Modes}}
{{DEFAULTSORT:Musical Mode}}
[[Category:Ancient Greek music]]
[[Category:Ancient Greek music theory]]
[[Category:Melody types]]
[[Category:Modes (music)| ]]
[[Category:Musical tuning]]' |
New page wikitext, after the edit (new_wikitext) | '{{Short description|Overview of ancient Greek music theory}}
{{about|the music theory and musical intervals used in ancient Greece|a discussion of the cultural aspects and history of ancient Greek music|Music of ancient Greece}}
The '''musical system of ancient Greece''' evolved over a period of more than 500 years from simple [[scale (music)|scales]] of [[tetrachord]]s, or divisions of the [[perfect fourth]], into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals.{{sfn|Chalmers|1993|loc=ch. 6, p. 99}}
Any discussion of the [[music of ancient Greece]], theoretical, philosophical or aesthetic, is fraught with two problems: there are few examples of written music, and there are many, sometimes fragmentary, theoretical and philosophical accounts. The empirical research of scholars like Richard Crocker,{{sfn|Crocker|1963}}{{sfn|Crocker|1964}}{{sfn|Crocker|1966}} C. André Barbera,{{sfn|Barbera|1977}}{{sfn|Barbera|1984}} and John Chalmers{{sfn|Chalmers|1993}} has made it possible to look at the ancient Greek systems as a whole without regard to the tastes of any one ancient theorist. The primary genera they examine are those of Pythagoras and the [[Pythagoreanism|Pythagorean school]], [[Archytas]], [[Aristoxenus|Aristoxenos]], and [[Ptolemy]] (including his versions of the genera of [[Didymus the Musician|Didymos]] and [[Eratosthenes]]).{{sfn|Chalmers|1993|loc=ch. 5, pp. 48–51}}
==Overview of the first complete tone system==
As an initial introduction to the principal names and divisions of the Ancient Greek tone system we will give a depiction of the "perfect system" or '''systema teleion''', which was elaborated in its entirety by about the turn of the 5th to 4th century [[BCE]].
The following diagram reproduces information from Chalmer. It shows the common ancient ''harmoniai'', the ''tonoi'' in all ''genera'', and the system as a whole in one complete map.
[[File:Systema-teleion-english.png|center|Depiction of the ancient Greek Tone system]]
The central three columns of the diagram show, first the modern note-names, then the two systems of symbols used in ancient Greece: the vocalic (favoured by singers) and instrumental (favoured by instrumentalists). The modern note-names are given in the [[Helmholtz pitch notation]], and the Greek note symbols are as given in the work of {{ill|Egert Pöhlmann|de}}.{{sfn|Pöhlmann|1970}} The pitches of the notes in modern notation are conventional, going back to the time of a publication by {{ill|Johann Friedrich Bellermann|de}} in 1840; in practice the pitches would have been somewhat lower.{{sfn|Pöhlmann and West|2001|loc=7}}
The section spanned by a blue brace is the range of the central [[octave]]. The range is approximately what we today depict as follows:
[[Image:ancient-greek-middle-octave.png|thumb|center|600px|The central octave of the ancient Greek system]]
Greek theorists conceived of scales as descending from higher pitch to lower (the opposite of modern practice).
The earliest Greek scales were [[tetrachord]]s, which were series of four descending tones, with the top and bottom tones being a fourth apart in modern terms. The sub-intervals of the tetrachord were unequal, with the largest intervals always at the top, and the smallest at the bottom. The 'characteristic interval' of a tetrachord is its largest one.
The '''Greater Perfect System''' (''systema teleion meizon'') was composed of four stacked tetrachords called (from lowest to highest) the ''Hypaton'', ''Meson'', ''Diezeugmenon'' and '' Hyperbolaion'' tetrachords. These are shown on the right hand side of the diagram. Octaves were composed from two stacked tetrachords connected by one common tone, the ''synaphe''.
At the position of the ''paramese'', the continuity of the system encounters a boundary (at b-flat, b). To retain the logic of the internal divisions of the tetrachords and avoid the ''Meson'' being forced into three whole tone steps (b–a–g–f), an interstitial note, the ''diazeuxis'' ('dividing'), was introduced between the ''paramese'' and ''mese''. This procedure gives its name to the tetrachord ''diezeugmenon'', which means the 'divided'.
To bridge the inconsistency of the ''diazeuxis'', the system allowed moving the ''nete'' one step up, permitting the construction of the ''Synemmenon'' ('conjunct') tetrachord – shown at the far left of the diagram.
The use of the ''Synemmenon'' tetrachord effected a modulation of the system, hence the name ''systema metabolon'', the modulating system, also called the '''Lesser Perfect System'''. This was considered apart, built of three stacked tetrachords — the ''Hypaton'', ''Meson'' and ''Synemmenon''. The first two of these are the same as the first two tetrachords of the Greater Perfect System, with a third tetrachord placed above the ''Meson''. When all these are considered together, with the ''Synemmenon'' tetrachord placed between the ''Meson'' and ''Diezeugmenon'' tetrachords, they make up the '''Immutable''' (or Unmodulating) '''System''' (systema ametabolon). The lowest tone does not belong to the system of tetrachords, as is reflected in its name, the ''Proslambanomenos'', the adjoined.
In sum, it is clear that the Ancient Greeks conceived of a unified system with the tetrachord as the basic structure, but the octave as the principle of unification.
Below we elaborate the mathematics that led to the logic of the system of tetrachords just described. <!-- The inclusion of the synemmenon tetrachord recalls the well-known medieval practice of avoiding four-tone groups of three whole-tone steps ([[tritone]]), which form an augmented fourth. Medieval music theory demanded the avoidance of the tritone in music practice – but included it in the sound system. It was the other way around with the ancient Greeks. The practice of music allowed a wide range of tolerance – even if the music was thus removed from the Pythagorean ideal. -->
==The Pythagoreans==
{{Main|Pythagorean interval}}
After the discovery of the fundamental intervals (octave, fourth and fifth), the first systematic divisions of the octave we know of were those of [[Pythagoras]] to whom was often attributed the discovery that the frequency of a vibrating string is inversely proportional to its length. [[Pythagoras]] construed the intervals arithmetically, allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2 (see also [[Pythagorean interval|Pythagorean Interval]] and [[Pythagorean tuning|Pythagorean Tuning]]).
The earliest such description of a scale is found in Philolaus fr. B6. [[Philolaus]] recognizes that, if we go up the interval of a fourth from any given note, and then up the interval of a fifth, the final note is an octave above the first note. Thus, the octave is made up of a fourth and a fifth. ... Philolaus's scale thus consisted of the following intervals: 9:8, 9:8, 256:243 [these three intervals take us up a fourth], 9:8, 9:8, 9:8, 256:243 [these four intervals make up a fifth and complete the octave from our starting note]. This scale is known as the Pythagorean diatonic and is the scale that [[Plato]] adopted in the construction of the [[Anima mundi|world soul]] in the ''Timaeus'' (36a-b).{{sfn|Huffman|2011}}
The next notable Pythagorean theorist we know of is [[Archytas]], contemporary and friend of Plato, who explained the use of arithmetic, geometric and harmonic means in tuning musical instruments. [[Euclid]] further developed Archytas's theory in his ''The Division of the Canon'' (''Katatomē kanonos'', the Latin ''Sectio Canonis''). He elaborated the acoustics with reference to the frequency of vibrations (or movements).{{sfn|Levin|1990}}
Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio (octave 2:1, fourth 4:3, fifth 3:2, 9:8).{{sfn|Huffman|2011}}{{sfn|Barker|1984–89|loc=2:46–52}}
Archytas was also the first ancient Greek theorist to provide ratios for all 3 [[Genus (music)|genera]].{{sfn|Chalmers|1993|loc=ch. 6, p. 99}} The three genera of [[tetrachord]]s recognized by Archytas have the following ratios:
*The enharmonic – 5:4, 36:35, and 28:27
*The chromatic – 32:27, 243:224, and 28:27;
*The diatonic – 9:8, 8:7, and 28:27.{{sfn|Huffman|2011}}
These three tunings appear to have corresponded to the actual musical practice of his day.{{sfn|Barker|1984–89|loc=2:46–52}}
The [[Genus (music)|genera]] arose after the framing interval of the tetrachord was fixed, because the two internal notes (called ''lichanoi'' and ''parhypate'') still had variable tunings. Tetrachords were classified into genera depending on the position of the ''lichanos'' (thus the name ''lichanos'', which means "the indicator"). For instance a ''lichanos'' that is a [[minor third]] from the bottom and a [[major second]] from the top, defines the genus [[Diatonic genus|diatonic]]. The other two genera, [[Chromatic genus|chromatic]] and [[Enharmonic genus|enharmonic]], were defined in similar fashion.{{sfn|Chalmers|1993|loc=ch. 5, p. 47}}
More generally, three ''genera'' of seven octave ''species'' can be recognized, depending on the positioning of the interposed tones in the component [[tetrachord]]s:
*The diatonic genus is composed of tones and semitones,
*the chromatic genus is composed of semitones and a minor third,
*the enharmonic genus consists of a major third and two quarter-tones or diesis.{{sfn|Cleonides|1965|loc=35–36}}
Within these basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two "shades" (''chroai''), respectively .{{sfn|Cleonides|1965|loc=39–40}}{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}
The elaboration of tetrachords was also accompanied by penta- and hexachords. The joining of a tetrachord and a pentachord yields an octachord, i.e. the complete seven-tone scale plus a higher octave of the base note. However, this was also produced by joining two tetrachords, which were linked by means of an intermediary or shared note. The final evolution of the system did not end with the octave as such but with the ''Systema teleion'', a set of five tetrachords linked by conjunction and disjunction<!--define --> into arrays of tones spanning two octaves, as explained above.{{sfn|Chalmers|1993|loc=ch. 6, p. 99}}
==The system of Aristoxenus==
Having elaborated the ''Systema teleion'', we will now examine the most significant individual system, that of [[Aristoxenos]], which influenced much classification well into the Middle Ages.
Aristoxenus was a disciple of [[Aristotle]] who flourished in the 4th century BC. He introduced a radically different model for creating scales, and the nature of his scales deviated sharply from his predecessors. His system was based on seven "[[octave species]]" named after Greek regions and ethnicities – Dorian, Lydian, etc. This association of the ethnic names with the octave species appears to have preceded Aristoxenus,{{sfn|Mathiesen|2001a|loc=6(iii)(d)}} and the same system of names was revived in the [[Renaissance]] as names of musical [[mode (music)|modes]] according to the harmonic theory of that time, which was however quite different from that of the ancient Greeks. Thus the names Dorian, Lydian etc. should not be taken to imply a historical continuity between the systems.
In contrast to Archytas who distinguished his "genera" only by moving the ''lichanoi'', Aristoxenus varied both ''lichanoi'' and ''parhypate'' in considerable ranges.{{sfn|Chalmers|1993|loc=ch. 5, p. 48}} Instead of using discrete ratios to place the intervals in his scales, Aristoxenus used continuously variable quantities: as a result he obtained scales of thirteen notes to an octave, and considerably different qualities of consonance.{{sfn|Chalmers|1993|loc=ch. 3, pp. 17–22}}
The octave species in the [[Aristoxenus|Aristoxenian]] tradition were:{{sfn|Barbera|1984|loc=240}}{{sfn|Mathiesen|2001a|loc=6(iii)(d)}}
* [[Mixolydian mode#Greek Mixolydian|Mixolydian]]: ''hypate hypaton–paramese'' (b–b′)
* [[Lydian mode|Lydian]]: ''parhypate hypaton–trite diezeugmenon'' (c′–c″)
* [[Phrygian mode#Ancient Greek Phrygian mode|Phrygian]]: ''lichanos hypaton–paranete diezeugmenon'' (d′–d″)
* [[Dorian mode|Dorian]]: ''hypate meson–nete diezeugmenon'' (e′–e″)
* [[Hypolydian mode|Hypolydian]]: ''parhypate meson–trite hyperbolaion'' (f′–f″)
* [[Hypophrygian mode|Hypophrygian]]: ''lichanos meson–paranete hyperbolaion'' (g′–g″)
* Common, [[Locrian mode|Locrian]], or [[Hypodorian mode|Hypodorian]]: ''mese–nete hyperbolaion'' or ''proslambanomenos–mese'' (a′–a″ or a–a′)
These names are derived from:
*an Ancient Greek subgroup ([[Dorians]]),
*a small region in central Greece ([[Locris]]),
*certain neighboring (non-Greek) peoples from [[Asia Minor]] ([[Lydia]], [[Phrygia]]).
*The prefixes ''myxo'' and ''hypo'' were added to these to form associated scales above and below.
===Aristoxenian ''tonoi''===
The term ''tonos'' (pl. ''tonoi'') was used in four senses, for it could designate a note, an interval, a region of the voice, and a pitch.{{sfn|Cleonides|1965|loc=44}}
The ancient writer [[Cleonides]] attributes thirteen ''tonoi'' to Aristoxenus, which represent a transposition of the tones of the Pythagorean system into a more uniform progressive scale over the range of an octave.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}
According to Cleonides,{{sfn|Cleonides|1965|loc=44}} these transpositional ''tonoi'' were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen. In fact, Aristoxenus criticized the application of these names by the earlier theorists, whom he called the "Harmonicists".{{sfn|Mathiesen|2001a|loc=6(iii)(d)}}
According to the interpretation of at least two modern authorities, in the Aristoxenian ''tonoi'' the Hypodorian is the lowest, and the Mixolydian is next-to-highest: the reverse of the case of the octave species.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}{{sfn|Solomon|1984|loc=250}} The nominal base pitches are as follows (in descending order, after Mathiesen; Solomon uses the octave between '''A''' and '''a''' instead):
{| class="wikitable"
|-
! f
| Hypermixolydian || also called Hyperphrygian
|-
! e
| High Mixolydian || also called Hyperiastian
|-
! e{{sup|{{music|♭}}}}
| Low Mixolydian || also called Hyperdorian
|-
! d
| High Lydian ||
|-
! c{{sup|{{music|♯}}}}
| Low Lydian || also called Aeolian
|-
! c
| High Phrygian ||
|-
! B
| Low Phrygian || also called Iastian
|-
! B{{sup|{{music|♭}}}}
| Dorian ||
|-
! A
| High Hypolydian ||
|-
! G{{sup|{{music|♯}}}} (and A{{sup|{{music|♭}}}}?)
| Low Hypolydian || also called Hypoaeolian
|-
! G
| High Hypophrygian ||
|-
! F{{sup|{{music|♯}}}}
| Low Hypophrygian
| also called Hypoiastian
|-
! F
| Hypodorian ||
|}
==The octave species in all genera {{anchor|octave_species_anchor}}==
{{Main|Octave species}}
Based on the above, it can be seen that the Aristochene system of tones and octave species can be combined with the Pythagorean system of "genera" to produce a more complete system in which each octave species of thirteen tones (Dorian, Lydian, etc.) can be declined into a system of seven tones by selecting particular tones and semitones to form genera (Diatonic, Chromatic, and Enharmonic).
The order of the [[octave species]] names in the following table are the original Greek ones, followed by later alternatives (Greek and other). The species and notation are built around the template of the Dorian.
===Diatonic {{anchor|diatonic_species_anchor}}===
{| class="wikitable" style="text-align:center"
|-
! Tonic
! Name
! Mese
|-
| (A)
| (Hypermixolydian, Hyperphrygian, Locrian)
| (d)
|-
| B
| Mixolydian, Hyperdorian
| e
|-
| c
| Lydian
| f
|-
| d
| Phrygian
| g
|-
| e
| Dorian
| a
|-
| f
| Hypolydian
| b
|-
| g
| Hypophrygian, Ionian
| c′
|-
| a
| Hypodorian, Aeolian
| d′
|-
|}
===Chromatic {{anchor|chromatic_species_anchor}}===
{| class="wikitable" style="text-align:center;"
|-
! Tonic
! Name
! Mese
|-
| (A)
| (Hypermixolydian, Hyperphrygian, Locrian)
| (d{{sup|{{music|♭}}}})
|-
| B
| Mixolydian, Hyperdorian
| e
|-
| c
| Lydian
| f
|-
| d{{sup|{{music|♭}}}}
| Phrygian
| g{{sup|{{music|♭}}}}
|-
| e
| Dorian
| a
|-
| f
| Hypolydian
| b
|-
| g{{sup|{{music|♭}}}}
| Hypophrygian, Ionian
| c′
|-
| a
| Hypodorian, Aeolian
| d′{{sup|{{music|♭}}}}
|-
|}
===Enharmonic{{anchor|enharmonic_species_anchor}}===
{| class="wikitable" style="text-align:center;"
|-
! Tonic
! Name
! Mese
|-
| (A)
| (Hypermixolydian, Hyperphrygian, Locrian)
| (d{{sup|{{music|𝄫}}}})
|-
| B
| Mixolydian, Hyperdorian
| e
|-
| c{{sup|{{music|-}}}}
| Lydian
| f{{sup|{{music|-}}}}
|-
| d{{sup|{{music|𝄫}}}}
| Phrygian
| g{{sup|{{music|𝄫}}}}
|-
| e
| Dorian
| a
|-
| f{{sup|{{music|-}}}}
| Hypolydian
| b
|-
| g{{sup|{{music|𝄫}}}}
| Hypophrygian, Ionian
| c′{{sup|{{music|-}}}}
|-
| a
| Hypodorian, Aeolian
| d′{{sup|{{music|𝄫}}}}
|}
==The oldest ''harmoniai'' in three genera {{anchor|harmoiai_anchor}}==
In the notation above and below, the standard double-flat symbol {{music|𝄫}} is used to accommodate as far as possible the modern musical convention that demands every note in a scale to have a distinct, sequential letter; so interpret {{music|𝄫}} only as meaning the immediate prior letter in the alphabet.{{sfn|Chalmers|1993|loc=ch. 6, p. 109}} This is a complication unnecessary in Greek notation, which had distinct symbols for each half-flat, flat, or natural note.
The superscript symbol {{music|-}} after a letter indicates an approximately half-flattened version of the named note; the exact degree of flattening intended depending on which of several tunings was used. Hence a three-tone falling-pitch sequence '''d''', '''d{{sup|{{music|-}}}}''', '''d{{sup|{{music|♭}}}}''', with the second note, '''d{{sup|{{music|-}}}}''', about {{frac|1|2}}-flat (a [[quarter-tone]] flat) from the first note, '''d''', and the same '''d{{sup|{{music|-}}}}''' about {{frac|1|2}}-sharp (a quarter-tone sharp) from the following '''d{{sup|{{music|♭}}}}'''.
The ('''d''') listed first for the Dorian is the ''Proslambanómenos'', which was appended as it was, and falls outside of the linked-tetrachord scheme.
These tables are a depiction of [[Aristides Quintilianus]]'s enharmonic ''harmoniai'', the diatonic of Henderson{{sfn|Henderson|1942}} and Chalmers{{sfn|Chalmers|1993}} chromatic versions. Chalmers, from whom they originate, states:
{{blockquote|In the enharmonic and chromatic forms of some of the harmoniai, it has been necessary to use both a '''d''' and either a '''d{{sup|{{music|♭}}}}''' or '''d{{sup|{{music|𝄫}}}}''' because of the non-heptatonic nature of these scales. '''C''' and '''F''' are synonyms for '''d{{sup|{{music|𝄫}}}}''' and '''g{{sup|{{music|𝄫}}}}''' [respectively]. The appropriate tunings for these scales are those of Archytas{{sfn|Mountford|1923}} and Pythagoras.{{sfn|Chalmers|1993|loc=ch. 6, p. 109}}}}
The superficial resemblance of these octave species with the church [[mode (music)|modes]] is misleading: The conventional representation as a section (such as '''C D E F''' followed by '''D E F G''') is incorrect. The species were re-tunings of the central octave such that the sequences of intervals (the cyclical modes divided by ratios defined by genus) corresponded to the notes of the Perfect Immutable System as depicted above.{{sfn|Chalmers|1993|loc=ch. 6, p. 106}}
===Dorian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| (d) e f{{sup|{{music|-}}}} g{{sup|{{music|bb}}}} a b c′{{sup|{{music|-}}}} d′{{sup|{{music|𝄫}}}} e′
|-
| Chromatic
| (d) e f g{{sup|{{music|♭}}}} a b c′ d′{{sup|{{music|♭}}}} e′
|-
| Diatonic
| (d) e f g a b c′ d′ e′
|}
===Phrygian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| d e f{{sup|{{music|-}}}} g{{sup|{{music|𝄫}}}} a b c′{{sup|{{music|-}}}} d′{{sup|{{music|𝄫}}}} d′
|-
| Chromatic
| d e f g{{sup|{{music|♭}}}} a b c′ d′{{sup|{{music|♭}}}} d′
|-
| Diatonic
| d e f g a b c′ d′
|}
===Lydian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| f{{sup|{{music|-}}}} g{{sup|{{music|𝄫}}}} a b c′{{sup|{{music|-}}}} d′{{sup|{{music|𝄫}}}} e′ f′{{sup|{{music|-}}}}
|-
| Chromatic
| f g a b c′ d′{{sup|{{music|♭}}}} e′ f′
|-
| Diatonic
| f g a b c′ d′ e′ f′
|}
===Mixolydian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| B c{{sup|{{music|-}}}} d{{sup|{{music|𝄫}}}} d e f{{sup|{{music|-}}}} g{{sup|{{music|𝄫}}}} b
|-
| Chromatic
| B c d{{sup|{{music|♭}}}} d e f{{sup|{{music|-}}}} g{{sup|{{music|♭}}}} b
|-
| Diatonic
| B c d e f(g) (a) b
|}
===Syntonolydian===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| B c{{sup|{{music|-}}}} d{{sup|{{music|𝄫}}}} e g
|-
| Chromatic
| B c d{{sup|{{music|♭}}}} e g
|-
| 1st Diatonic
| c d e f g
|-
| 2nd Diatonic
| B c d e g
|}
===Ionian (Iastian)===
{| class="wikitable"
|-
! Genus
! Tones
|-
| Enharmonic
| B c{{sup|{{music|-}}}} d{{sup|{{music|𝄫}}}} e g a
|-
| Chromatic
| B c d{{sup|{{music|♭}}}} e g a
|-
| 1st Diatonic
| c e f g
|-
| 2nd Diatonic
| B c d e g a
|}
==Ptolemy and the Alexandrians==
In marked contrast to his predecessors, [[Ptolemy]]'s scales employed a division of the ''pyknon'' in the ratio of 1:2, melodic, in place of equal divisions.{{sfn|Chalmers|1993|loc=ch. 2, p. 10}} Ptolemy, in his ''Harmonics'', ii.3–11, construed the ''tonoi'' differently, presenting all seven octave species within a fixed octave, through chromatic inflection of the scale degrees (comparable to the modern conception of building all seven modal scales on a single tonic). In Ptolemy's system, therefore there are only seven ''tonoi''.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}{{sfn|Mathiesen|2001c}} Ptolemy preserved Archytas's tunings in his ''Harmonics'' as well as transmitting the tunings of [[Eratosthenes]] and [[Didymos (music theorist)|Didymos]] and providing his own ratios and scales.{{sfn|Chalmers|1993|loc=ch. 6, p. 99}}
==''Harmoniai''==
In music theory the Greek word ''harmonia'' can signify the enharmonic genus of tetrachord, the seven octave species, or a style of music associated with one of the ethnic types or the ''tonoi'' named by them.{{sfn|Mathiesen|2001b}}
Particularly in the earliest surviving writings, ''harmonia'' is regarded not as a scale, but as the epitome of the stylised singing of a particular district or people or occupation.{{sfn|Winnington-Ingram|1936|loc=3}} When the late 6th-century poet [[Lasus of Hermione]] referred to the Aeolian ''harmonia'', for example, he was more likely thinking of a [[Melody type|melodic style]] characteristic of Greeks speaking the Aeolic dialect than of a scale pattern.{{sfn|Anderson and Mathiesen|2001}}
In the ''[[Republic (Plato)|Republic]]'', [[Plato]] uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc.{{sfn|Mathiesen|2001a|loc=6(iii)(e)}}
The philosophical writings of Plato and [[Aristotle]] (c. 350 [[BCE]]) include sections that describe the effect of different ''harmoniai'' on mood and character formation (see below on ethos). For example, in the ''Republic'' (iii.10–11) Plato describes the music a person is exposed to as molding the person's character, which he discusses as particularly relevant for the proper education of the guardians of his ideal State. Aristotle in the ''Politics'' (viii:1340a:40–1340b:5):
{{blockquote|But melodies themselves do contain imitations of character. This is perfectly clear, for the ''harmoniai'' have quite distinct natures from one another, so that those who hear them are differently affected and do not respond in the same way to each. To some, such as the one called Mixolydian, they respond with more grief and anxiety, to others, such as the relaxed ''harmoniai'', with more mellowness of mind, and to one another with a special degree of moderation and firmness, Dorian being apparently the only one of the ''harmoniai'' to have this effect, while Phrygian creates ecstatic excitement. These points have been well expressed by those who have thought deeply about this kind of education; for they cull the evidence for what they say from the facts themselves.{{sfn|Barker|1984–89|loc=1:175–176}}}}
Aristotle remarks further: {{blockquote |sign=|source=| From what has been said it is evident what an influence music has over the disposition of the mind, and how variously it can fascinate it—and if it can do this, most certainly it is what youth ought to be instructed in.{{sfn|Aristotle|1912|loc=book 8, ch. 5}})}}
==Ethos==
The ancient Greeks have used the word ''ethos'' (ἔθος or ἦθος), in this context best rendered by "character" (in the sense of patterns of being and behaviour, but not necessarily with "moral" implications), to describe the ways music can convey, foster, and even generate emotional or mental states. Beyond this general description, there is no unified "Greek ethos theory" but "many different views, sometimes sharply opposed."{{sfn|Anderson and Mathiesen|2001}} Ethos is attributed to the ''tonoi'' or ''harmoniai'' or modes (for instance, Plato, in the ''Republic'' (iii: 398d–399a), attributes "virility" to the "[[Dorian mode|Dorian]]," and "relaxedness" to the "[[Lydian mode|Lydian]]" mode), instruments (especially the [[aulos]] and the [[cithara]], but also others), rhythms, and sometimes even the [[Genus (music)|genus]] and individual tones. The most comprehensive treatment of musical ethos is provided by [[Aristides Quintilianus]] in his book ''On Music'', with the original conception of assigning ethos to the various musical parameters according to the general categories of male and female. [[Aristoxenus]] was the first Greek theorist to point out that ethos does not only reside in the individual parameters but also in the musical piece as a whole (cited in Pseudo-Plutarch, ''De Musica'' 32: 1142d ff; see also Aristides Quintilianus 1.12). The Greeks were interested in musical ethos particularly in the context of education (so Plato in his ''Republic'' and Aristotle in his eighth book of his ''Politics''), with implications for the well-being of the State. Many other ancient authors refer to what we nowadays would call psychological effect of music and draw judgments for the appropriateness (or value) of particular musical features or styles, while others, in particular [[Philodemus]] (in his fragmentary work ''De musica'') and [[Sextus Empiricus]] (in his sixth book of his work ''Adversus mathematicos''), deny that music possesses any influence on the human person apart from generating pleasure. These different views anticipate in some way the modern debate in [[Philosophy of music|music philosophy]] whether music on its own or [[absolute music]], independent of text, is able to [[Music and emotion|elicit emotions]] on the listener or musician.{{sfn|Kramarz|2016}}
==Melos==
Cleonides describes "melic" composition, "the employment of the materials subject to harmonic practice with due regard to the requirements of each of the subjects under consideration"{{sfn|Cleonides|1965|loc=35}}—which, together with the scales, ''tonoi'', and ''harmoniai'' resemble elements found in medieval modal theory.{{sfn|Mathiesen|2001a|loc=6(iii)}} According to Aristides Quintilianus (''On Music'', i.12), melic composition is subdivided into three classes: dithyrambic, nomic, and tragic. These parallel his three classes of rhythmic composition: systaltic, diastaltic and hesychastic. Each of these broad classes of melic composition may contain various subclasses, such as erotic, comic and panegyric, and any composition might be elevating (diastaltic), depressing (systaltic), or soothing (hesychastic).{{sfn|Mathiesen|2001a|loc=4}}
The classification of the ''requirements'' we have from [[Proclus]] ''Useful Knowledge'' as preserved by [[Photios I of Constantinople|Photios]]{{Citation needed|date=November 2009}}:
* for the gods—[[hymn]], [[prosodion]], [[paean]], [[dithyramb]], nomos, adonidia, iobakchos, and [[Hyporchema|hyporcheme]];
* for humans—[[Encomium|encomion]], [[epinikion]], [[skolion]], [[erotica]], [[epithalamia]], [[hymenaios]], sillos, threnos, and epikedeion;
* for the gods and humans—partheneion, daphnephorika, tripodephorika, oschophorika, and eutika
According to Mathiesen:
{{blockquote | Such pieces of music were called melos, which in its perfect form (teleion melos) comprised not only the melody and the text (including its elements of rhythm and diction) but also stylized dance movement. Melic and rhythmic composition (respectively, melopoiïa and rhuthmopoiïa) were the processes of selecting and applying the various components of melos and rhythm to create a complete work.{{sfn|Mathiesen|1999|loc=25}}}}
==Unicode==
{{Main|Ancient Greek Musical Notation|l1=Ancient Greek Musical Notation (Unicode block)}}
Music symbols of ancient Greece were added to the [[Unicode]] Standard in March 2005 with the release of version 4.1.
==See also==
* [[Alypius of Alexandria]]
* [[Delphic Hymns]]
* [[Seikilos epitaph]]
* [[Mesomedes]]
* [[Oxyrhynchus hymn]]
==References==
{{reflist|18em}}
'''Sources'''
{{div col|colwidth=45em}}
* {{wikicite|ref={{harvid|Anderson and Mathiesen|2001}}|reference=Anderson, Warren, and [[Thomas J. Mathiesen]] (2001). "Ethos". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan.}}
* {{wikicite|ref={{harvid|Aristotle|1912}}|reference=[[Aristotle]] (1912). ''[http://www.gutenberg.org/files/6762/6762-h/6762-h.htm A Treatise on Government]'' [''Politics''], translated by William Ellis. London and Toronto: J. M. Dent; New York: E. P. Dutton.}}
* {{cite journal|last=Barbera|first=C. André|date=Autumn 1977|title=Arithmetic and Geometric Divisions of the Tetrachord|journal=[[Journal of Music Theory]]|volume=21|issue=2|pages=294–323|doi=10.2307/843492|jstor=843492}}
* {{cite journal|last=Barbera|first=C. André|date=Summer 1984|title=Octave Species|journal=[[The Journal of Musicology]]|volume=3|issue=3|pages=229–241|doi=10.2307/763813|jstor=763813}}
* {{wikicite|ref={{harvid|Barker|1984–89}}|reference=[[Andrew Barker (classicist)|Barker, Andrew]] (ed.) (1984–89). ''Greek Musical Writings'', 2 vols. Cambridge and New York: Cambridge University Press. {{ISBN|0-521-23593-6}} (v. 1) {{ISBN|0-521-30220-X}} (v. 2).}}
* {{citation|last=Chalmers|first=John H.|title=Divisions of the Tetrachord: A Prolegomenon to the Construction of Musical Scales|others=edited by Larry Polansky and Carter Scholz, foreword by Lou Harrison|place=Hanover, New Hampshire|publisher=Frog Peak Music|year=1993|url=http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html|isbn=0-945996-04-7}}
* {{wikicite|ref={{harvid|Cleonides|1965}}|reference=[[Cleonides]] (1965). "Harmonic Introduction", translated by [[Oliver Strunk]]. In ''Source Readings in Music History'', vol. 1 (Antiquity and the Middle Ages), edited by Oliver Strunk, 35–46. New York: W. W. Norton.}}
* {{cite journal|last=Crocker|first=Richard L.|date=Winter 1963|title=Pythagorean Mathematics and Music|journal=[[The Journal of Aesthetics and Art Criticism]]|volume=22|issue=2|pages=189–198|doi=10.2307/427754|jstor=427754}}
* {{cite journal|last=Crocker|first=Richard L.|date=Spring 1964|title=Pythagorean Mathematics and Music|journal=[[The Journal of Aesthetics and Art Criticism]]|volume=22|issue=3|pages=325–335|doi=10.2307/427236|jstor=427236}}
* {{cite journal|last=Crocker|first=Richard L.|date=April 1966|title=The Troping Hypothesis|journal=[[The Musical Quarterly]]|volume=52|issue=2|pages=183–203|doi=10.1093/mq/lii.2.183 }}
* {{cite journal|last=Henderson|first=M. I.|date=October 1942|title=The Growth of the Greek ἁρμονιαι|journal=[[The Classical Quarterly]]|volume=36|issue=3–4|pages=94–103}}
* {{wikicite|ref={{harvid|Huffman|2011}}|reference=Huffman, Carl A. (2011). "[http://plato.stanford.edu/entries/archytas/ Archytas]". ''The Stanford Encyclopedia of Philosophy'' (accessed 25 August 2014).}}
* {{citation|last=Kramarz|first=Andreas|year=2016|title=The Power and Value of Music. Its Effect and Ethos in Classical Authors and Contemporary Music Theory|place=New York/Bern|publisher=Peter Lang|isbn=9781433133787}}
* {{citation | last = Levin | first = Flora R. | author-link = Flora Levin | issue = 4 | journal = Hermes | jstor = 4476778 | pages = 430–443 | title = Unity in Euclid's 'Sectio Canonis' | volume = 118 | year = 1990}}
* {{citation|last=Mathiesen|first=Thomas J.|author-link=Thomas J. Mathiesen|title=Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages|series=of Publications of the Center for the History of Music Theory and Literature 2|place=Lincoln|publisher=University of Nebraska Press|year=1999|isbn=9780803230798}}
* {{wikicite|ref={{harvid|Mathiesen|2001a}}|reference=Mathiesen, Thomas J. (2001a). "Greece, §I: Ancient". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan.}}
* {{wikicite|ref={{harvid|Mathiesen|2001b}}|reference=Mathiesen, Thomas J. (2001b). "Harmonia (i)". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.}}
* {{wikicite|ref={{harvid|Mathiesen|2001c}}|reference=Mathiesen, Thomas J. (2001c). "Tonos". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.}}
* {{wikicite|ref={{harvid|Mountford|1923}}|reference=Mountford, James Frederick. (1923). The Musical Scales of Plato's Republic. ''[[The Classical Quarterly]]'' 17:125-136.}}
* {{citation|last=Pöhlmann|first=Egert|title=Denkmäler altgriechischer Musik|series=Erlanger Beiträge zur Sprach- und Kunstwissenschaft 31|place=Nuremberg|publisher=Hans Carl Verlag|year=1970|issn=0425-2268}}
* {{wikicite|ref={{harvid|Pöhlmann and West|2001}}|reference={{ill|Egert Pöhlmann|de|Pöhlmann, Egert}}, and [[Martin Litchfield West|Martin L. West]]. 2001. ''Documents of Ancient Greek Music: The Extant Melodies and Fragments'', edited and transcribed with commentary by Egert Pöhlmann and Martin L. West. Oxford: Clarendon Press. {{ISBN|0-19-815223-X}}.}}
* {{cite journal|last=Solomon|first=Jon|date=Summer 1984|title=Towards a History of Tonoi|journal=[[The Journal of Musicology]]|volume=3|issue=3|pages=242–251|doi=10.2307/763814|jstor=763814}}
* {{citation|last=Winnington-Ingram|first=Reginald P.|year=1936|title=Mode in Ancient Greek Music|place=London|publisher=Cambridge University Press}}
{{div col end}}
==Further reading==
{{div col|colwidth=45em}}
* {{ill|Johann Friedrich Bellermann|de|lt=Bellermann, Johann Friedrich}} (1840). ''[https://books.google.com/books?id=PssqAAAAYAAJ Die Hymnen des Dionysius und Mesomedes: Text und Melodieen nach Handschriften und den alten Ausgaben bearbeitet von Dr. Friedrich Bellermann]''. Berlin: Albert Förstner.
* Jan, Karl von (ed.) (1895). ''Musici scriptores graeci: Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat''. Bibliotheca scriptorum graecorum et romanorum Teubneriana. Leipzig: B. G. Teubner.
* {{citation|last=Jowett|first=Benjamin|author-link=Benjamin Jowett|year=1937|title=The Dialogues of Plato|type=2 vols.|translator=Benjamin Jowett|edition=3rd|place=New York|publisher=Random House|ref=none}}
* [[Thomas J. Mathiesen|Mathiesen, Thomas J.]] (2001d). "Alypius [Alupios]". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan Publishers.
* Meibom, Marcus (ed.) (1652). ''Antiquae musicae auctores septem: Graece et latine'', 2 vols. Amsterdam: Apud Ludovicum Elzevirium. Facsimile reprint in Monuments of Music and Music Literature in Facsimile, Second Series: Music Literature 51. New York: Broude Bros., 1977. {{ISBN|9780845022511}}.
* {{cite journal|last=Winnington-Ingram|first=Reginald P.|year=1932|title=Aristoxenus and the Intervals of Greek Music|journal=[[The Classical Quarterly]]|volume=26|issue=3–4|pages=195–208|doi=10.1017/s0009838800014415|s2cid=170375844 |ref=none}}
* Winnington-Ingram, Reginald P. (1954). "Greek Music (Ancient)". ''[[Grove's Dictionary of Music and Musicians]]'', fifth edition, edited by [[Eric Blom]]. New York: St. Martin's Press.
{{div col end}}
==External links==
* Elsie Hamilton, [http://www.nakedlight.co.uk/pdf/articles/a-002.pdf booklet on the modes of ancient Greece] {{Webarchive|url=https://web.archive.org/web/20081121100923/http://www.nakedlight.co.uk/pdf/articles/a-002.pdf |date=2008-11-21 }}, with detailed examples of the construction of Aolus (reed pipe instruments) and monochord, which might help reconstruct the intervals and modes of the Greeks
* Nikolaos Ioannidis musician, composer, has attempted to [http://homoecumenicus.com/ioannidis_music_ancient_greeks.htm reconstruct ancient Greek music] from a combination of the ancient texts (to be performed) and his knowledge of Greek music.
* A mid-19th century, 1902 edition, Henry S. Macran, [https://archive.org/stream/aristoxenouharm00arisgoog ''The Harmonics of Aristoxenus'']. The Barbera translation cited above is more up to date.
* Joe Monzo (2004). [http://www.tonalsoft.com/monzo/aristoxenus/aristoxenus.aspx Analysis of Aristoxenus]. Full of interesting and insightful mathematical analysis. There are some original hypotheses outlined.
* [[Robert Erickson]], American composer and academic, [http://www.ex-tempore.org/ARCHYTAS/ARCHYTAS.html Analysis of Archytas], something of a complement to the above Aristoxenus but, dealing with the earlier and arithmetically precise Archytas:. An incidental note. Erickson is keen to demonstrate that Archytas tuning system not only corresponds with Platos Harmonia, but also with the practice of musicians. Erickson mentions the ease of tuning with the Lyre.
* Austrian Academy of Sciences [http://www.oeaw.ac.at/kal/agm/ examples of instruments and compositions]
*[http://www.kerylos.fr/index_en.php Ensemble Kérylos], a music group led by scholar [[Annie Bélis]], dedicated to the recreation of ancient Greek and Roman music and playing scores written on inscriptions and papyri.
{{Musical notation}}
{{Ancient Greece topics}}
{{Modes}}
{{DEFAULTSORT:Musical Mode}}
[[Category:Ancient Greek music]]
[[Category:Ancient Greek music theory]]
[[Category:Melody types]]
[[Category:Modes (music)| ]]
[[Category:Musical tuning]]' |
Unified diff of changes made by edit (edit_diff) | '@@ -66,5 +66,5 @@
Having elaborated the ''Systema teleion'', we will now examine the most significant individual system, that of [[Aristoxenos]], which influenced much classification well into the Middle Ages.
-Aristoxenus was a disciple of [[Aristotle]] who flourished in the 4th century BC. He introduced a radically different model for creating scales, and the nature of his scales deviated sharply from his predecessors. His system was based on seven "[[octave species]]" named after Greek regions and ethnicities – Dorian, Lydian, etc. This association of the ethnic names with the octave species appears to have preceded Aristoxenus,{{sfn|Mathiesen|2001a|loc=6(iii)(d)}} and the same system of names was revived in the [[Renaissance]] as names of musical [[mode (music)|modes]] according to the harmonic theory of that time, which was however quite different to that of the ancient Greeks. Thus the names Dorian, Lydian etc. should not be taken to imply a historical continuity between the systems.
+Aristoxenus was a disciple of [[Aristotle]] who flourished in the 4th century BC. He introduced a radically different model for creating scales, and the nature of his scales deviated sharply from his predecessors. His system was based on seven "[[octave species]]" named after Greek regions and ethnicities – Dorian, Lydian, etc. This association of the ethnic names with the octave species appears to have preceded Aristoxenus,{{sfn|Mathiesen|2001a|loc=6(iii)(d)}} and the same system of names was revived in the [[Renaissance]] as names of musical [[mode (music)|modes]] according to the harmonic theory of that time, which was however quite different from that of the ancient Greeks. Thus the names Dorian, Lydian etc. should not be taken to imply a historical continuity between the systems.
In contrast to Archytas who distinguished his "genera" only by moving the ''lichanoi'', Aristoxenus varied both ''lichanoi'' and ''parhypate'' in considerable ranges.{{sfn|Chalmers|1993|loc=ch. 5, p. 48}} Instead of using discrete ratios to place the intervals in his scales, Aristoxenus used continuously variable quantities: as a result he obtained scales of thirteen notes to an octave, and considerably different qualities of consonance.{{sfn|Chalmers|1993|loc=ch. 3, pp. 17–22}}
' |
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Parsed HTML source of the new revision (new_html) | '<div class="mw-parser-output"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Overview of ancient Greek music theory</div>
<style data-mw-deduplicate="TemplateStyles:r1033289096">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the music theory and musical intervals used in ancient Greece. For a discussion of the cultural aspects and history of ancient Greek music, see <a href="/enwiki/wiki/Music_of_ancient_Greece" title="Music of ancient Greece">Music of ancient Greece</a>.</div>
<p>The <b>musical system of ancient Greece</b> evolved over a period of more than 500 years from simple <a href="/enwiki/wiki/Scale_(music)" title="Scale (music)">scales</a> of <a href="/enwiki/wiki/Tetrachord" title="Tetrachord">tetrachords</a>, or divisions of the <a href="/enwiki/wiki/Perfect_fourth" title="Perfect fourth">perfect fourth</a>, into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals.<sup id="cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._6,_p._99-1">[1]</a></sup>
</p><p>Any discussion of the <a href="/enwiki/wiki/Music_of_ancient_Greece" title="Music of ancient Greece">music of ancient Greece</a>, theoretical, philosophical or aesthetic, is fraught with two problems: there are few examples of written music, and there are many, sometimes fragmentary, theoretical and philosophical accounts. The empirical research of scholars like Richard Crocker,<sup id="cite_ref-FOOTNOTECrocker1963_2-0" class="reference"><a href="#cite_note-FOOTNOTECrocker1963-2">[2]</a></sup><sup id="cite_ref-FOOTNOTECrocker1964_3-0" class="reference"><a href="#cite_note-FOOTNOTECrocker1964-3">[3]</a></sup><sup id="cite_ref-FOOTNOTECrocker1966_4-0" class="reference"><a href="#cite_note-FOOTNOTECrocker1966-4">[4]</a></sup> C. André Barbera,<sup id="cite_ref-FOOTNOTEBarbera1977_5-0" class="reference"><a href="#cite_note-FOOTNOTEBarbera1977-5">[5]</a></sup><sup id="cite_ref-FOOTNOTEBarbera1984_6-0" class="reference"><a href="#cite_note-FOOTNOTEBarbera1984-6">[6]</a></sup> and John Chalmers<sup id="cite_ref-FOOTNOTEChalmers1993_7-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993-7">[7]</a></sup> has made it possible to look at the ancient Greek systems as a whole without regard to the tastes of any one ancient theorist. The primary genera they examine are those of Pythagoras and the <a href="/enwiki/wiki/Pythagoreanism" title="Pythagoreanism">Pythagorean school</a>, <a href="/enwiki/wiki/Archytas" title="Archytas">Archytas</a>, <a href="/enwiki/wiki/Aristoxenus" title="Aristoxenus">Aristoxenos</a>, and <a href="/enwiki/wiki/Ptolemy" title="Ptolemy">Ptolemy</a> (including his versions of the genera of <a href="/enwiki/wiki/Didymus_the_Musician" title="Didymus the Musician">Didymos</a> and <a href="/enwiki/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a>).<sup id="cite_ref-FOOTNOTEChalmers1993ch._5,_pp._48–51_8-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._5,_pp._48–51-8">[8]</a></sup>
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Overview_of_the_first_complete_tone_system"><span class="tocnumber">1</span> <span class="toctext">Overview of the first complete tone system</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#The_Pythagoreans"><span class="tocnumber">2</span> <span class="toctext">The Pythagoreans</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="#The_system_of_Aristoxenus"><span class="tocnumber">3</span> <span class="toctext">The system of Aristoxenus</span></a>
<ul>
<li class="toclevel-2 tocsection-4"><a href="#Aristoxenian_tonoi"><span class="tocnumber">3.1</span> <span class="toctext">Aristoxenian <i>tonoi</i></span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-5"><a href="#The_octave_species_in_all_genera"><span class="tocnumber">4</span> <span class="toctext">The octave species in all genera</span></a>
<ul>
<li class="toclevel-2 tocsection-6"><a href="#Diatonic"><span class="tocnumber">4.1</span> <span class="toctext">Diatonic</span></a></li>
<li class="toclevel-2 tocsection-7"><a href="#Chromatic"><span class="tocnumber">4.2</span> <span class="toctext">Chromatic</span></a></li>
<li class="toclevel-2 tocsection-8"><a href="#Enharmonic"><span class="tocnumber">4.3</span> <span class="toctext">Enharmonic</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-9"><a href="#The_oldest_harmoniai_in_three_genera"><span class="tocnumber">5</span> <span class="toctext">The oldest <i>harmoniai</i> in three genera</span></a>
<ul>
<li class="toclevel-2 tocsection-10"><a href="#Dorian"><span class="tocnumber">5.1</span> <span class="toctext">Dorian</span></a></li>
<li class="toclevel-2 tocsection-11"><a href="#Phrygian"><span class="tocnumber">5.2</span> <span class="toctext">Phrygian</span></a></li>
<li class="toclevel-2 tocsection-12"><a href="#Lydian"><span class="tocnumber">5.3</span> <span class="toctext">Lydian</span></a></li>
<li class="toclevel-2 tocsection-13"><a href="#Mixolydian"><span class="tocnumber">5.4</span> <span class="toctext">Mixolydian</span></a></li>
<li class="toclevel-2 tocsection-14"><a href="#Syntonolydian"><span class="tocnumber">5.5</span> <span class="toctext">Syntonolydian</span></a></li>
<li class="toclevel-2 tocsection-15"><a href="#Ionian_(Iastian)"><span class="tocnumber">5.6</span> <span class="toctext">Ionian (Iastian)</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-16"><a href="#Ptolemy_and_the_Alexandrians"><span class="tocnumber">6</span> <span class="toctext">Ptolemy and the Alexandrians</span></a></li>
<li class="toclevel-1 tocsection-17"><a href="#Harmoniai"><span class="tocnumber">7</span> <span class="toctext"><i>Harmoniai</i></span></a></li>
<li class="toclevel-1 tocsection-18"><a href="#Ethos"><span class="tocnumber">8</span> <span class="toctext">Ethos</span></a></li>
<li class="toclevel-1 tocsection-19"><a href="#Melos"><span class="tocnumber">9</span> <span class="toctext">Melos</span></a></li>
<li class="toclevel-1 tocsection-20"><a href="#Unicode"><span class="tocnumber">10</span> <span class="toctext">Unicode</span></a></li>
<li class="toclevel-1 tocsection-21"><a href="#See_also"><span class="tocnumber">11</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-22"><a href="#References"><span class="tocnumber">12</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-23"><a href="#Further_reading"><span class="tocnumber">13</span> <span class="toctext">Further reading</span></a></li>
<li class="toclevel-1 tocsection-24"><a href="#External_links"><span class="tocnumber">14</span> <span class="toctext">External links</span></a></li>
</ul>
</div>
<h2><span class="mw-headline" id="Overview_of_the_first_complete_tone_system">Overview of the first complete tone system</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=1" title="Edit section: Overview of the first complete tone system">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>As an initial introduction to the principal names and divisions of the Ancient Greek tone system we will give a depiction of the "perfect system" or <b>systema teleion</b>, which was elaborated in its entirety by about the turn of the 5th to 4th century <a href="/enwiki/wiki/BCE" class="mw-redirect" title="BCE">BCE</a>.
</p><p>The following diagram reproduces information from Chalmer. It shows the common ancient <i>harmoniai</i>, the <i>tonoi</i> in all <i>genera</i>, and the system as a whole in one complete map.
</p>
<div class="center"><div class="floatnone"><a href="/enwiki/wiki/File:Systema-teleion-english.png" class="image" title="Depiction of the ancient Greek Tone system"><img alt="Depiction of the ancient Greek Tone system" src="/upwiki/wikipedia/commons/b/bf/Systema-teleion-english.png" decoding="async" width="571" height="495" data-file-width="571" data-file-height="495" /></a></div></div>
<p>The central three columns of the diagram show, first the modern note-names, then the two systems of symbols used in ancient Greece: the vocalic (favoured by singers) and instrumental (favoured by instrumentalists). The modern note-names are given in the <a href="/enwiki/wiki/Helmholtz_pitch_notation" title="Helmholtz pitch notation">Helmholtz pitch notation</a>, and the Greek note symbols are as given in the work of <a href="/enwiki/w/index.php?title=Egert_P%C3%B6hlmann&action=edit&redlink=1" class="new" title="Egert Pöhlmann (page does not exist)">Egert Pöhlmann</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Egert_P%C3%B6hlmann" class="extiw" title="de:Egert Pöhlmann">de</a>]</span>.<sup id="cite_ref-FOOTNOTEPöhlmann1970_9-0" class="reference"><a href="#cite_note-FOOTNOTEPöhlmann1970-9">[9]</a></sup> The pitches of the notes in modern notation are conventional, going back to the time of a publication by <a href="/enwiki/w/index.php?title=Johann_Friedrich_Bellermann&action=edit&redlink=1" class="new" title="Johann Friedrich Bellermann (page does not exist)">Johann Friedrich Bellermann</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Johann_Friedrich_Bellermann" class="extiw" title="de:Johann Friedrich Bellermann">de</a>]</span> in 1840; in practice the pitches would have been somewhat lower.<sup id="cite_ref-FOOTNOTEPöhlmann_and_West20017_10-0" class="reference"><a href="#cite_note-FOOTNOTEPöhlmann_and_West20017-10">[10]</a></sup>
</p><p>The section spanned by a blue brace is the range of the central <a href="/enwiki/wiki/Octave" title="Octave">octave</a>. The range is approximately what we today depict as follows:
</p>
<div class="center"><div class="thumb tnone"><div class="thumbinner" style="width:311px;"><a href="/enwiki/wiki/File:Ancient-greek-middle-octave.png" class="image"><img src="/upwiki/wikipedia/en/3/33/Ancient-greek-middle-octave.png" decoding="async" width="309" height="54" class="thumbimage" data-file-width="309" data-file-height="54" /></a> <div class="thumbcaption"><div class="magnify"><a href="/enwiki/wiki/File:Ancient-greek-middle-octave.png" class="internal" title="Enlarge"></a></div>The central octave of the ancient Greek system</div></div></div></div>
<p>Greek theorists conceived of scales as descending from higher pitch to lower (the opposite of modern practice).
</p><p>The earliest Greek scales were <a href="/enwiki/wiki/Tetrachord" title="Tetrachord">tetrachords</a>, which were series of four descending tones, with the top and bottom tones being a fourth apart in modern terms. The sub-intervals of the tetrachord were unequal, with the largest intervals always at the top, and the smallest at the bottom. The 'characteristic interval' of a tetrachord is its largest one.
</p><p>The <b>Greater Perfect System</b> (<i>systema teleion meizon</i>) was composed of four stacked tetrachords called (from lowest to highest) the <i>Hypaton</i>, <i>Meson</i>, <i>Diezeugmenon</i> and <i> Hyperbolaion</i> tetrachords. These are shown on the right hand side of the diagram. Octaves were composed from two stacked tetrachords connected by one common tone, the <i>synaphe</i>.
</p><p>At the position of the <i>paramese</i>, the continuity of the system encounters a boundary (at b-flat, b). To retain the logic of the internal divisions of the tetrachords and avoid the <i>Meson</i> being forced into three whole tone steps (b–a–g–f), an interstitial note, the <i>diazeuxis</i> ('dividing'), was introduced between the <i>paramese</i> and <i>mese</i>. This procedure gives its name to the tetrachord <i>diezeugmenon</i>, which means the 'divided'.
</p><p>To bridge the inconsistency of the <i>diazeuxis</i>, the system allowed moving the <i>nete</i> one step up, permitting the construction of the <i>Synemmenon</i> ('conjunct') tetrachord – shown at the far left of the diagram.
</p><p>The use of the <i>Synemmenon</i> tetrachord effected a modulation of the system, hence the name <i>systema metabolon</i>, the modulating system, also called the <b>Lesser Perfect System</b>. This was considered apart, built of three stacked tetrachords — the <i>Hypaton</i>, <i>Meson</i> and <i>Synemmenon</i>. The first two of these are the same as the first two tetrachords of the Greater Perfect System, with a third tetrachord placed above the <i>Meson</i>. When all these are considered together, with the <i>Synemmenon</i> tetrachord placed between the <i>Meson</i> and <i>Diezeugmenon</i> tetrachords, they make up the <b>Immutable</b> (or Unmodulating) <b>System</b> (systema ametabolon). The lowest tone does not belong to the system of tetrachords, as is reflected in its name, the <i>Proslambanomenos</i>, the adjoined.
</p><p>In sum, it is clear that the Ancient Greeks conceived of a unified system with the tetrachord as the basic structure, but the octave as the principle of unification.
</p><p>Below we elaborate the mathematics that led to the logic of the system of tetrachords just described.
</p>
<h2><span class="mw-headline" id="The_Pythagoreans">The Pythagoreans</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=2" title="Edit section: The Pythagoreans">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/enwiki/wiki/Pythagorean_interval" title="Pythagorean interval">Pythagorean interval</a></div>
<p>After the discovery of the fundamental intervals (octave, fourth and fifth), the first systematic divisions of the octave we know of were those of <a href="/enwiki/wiki/Pythagoras" title="Pythagoras">Pythagoras</a> to whom was often attributed the discovery that the frequency of a vibrating string is inversely proportional to its length. <a href="/enwiki/wiki/Pythagoras" title="Pythagoras">Pythagoras</a> construed the intervals arithmetically, allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2 (see also <a href="/enwiki/wiki/Pythagorean_interval" title="Pythagorean interval">Pythagorean Interval</a> and <a href="/enwiki/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean Tuning</a>).
</p><p>The earliest such description of a scale is found in Philolaus fr. B6. <a href="/enwiki/wiki/Philolaus" title="Philolaus">Philolaus</a> recognizes that, if we go up the interval of a fourth from any given note, and then up the interval of a fifth, the final note is an octave above the first note. Thus, the octave is made up of a fourth and a fifth. ... Philolaus's scale thus consisted of the following intervals: 9:8, 9:8, 256:243 [these three intervals take us up a fourth], 9:8, 9:8, 9:8, 256:243 [these four intervals make up a fifth and complete the octave from our starting note]. This scale is known as the Pythagorean diatonic and is the scale that <a href="/enwiki/wiki/Plato" title="Plato">Plato</a> adopted in the construction of the <a href="/enwiki/wiki/Anima_mundi" title="Anima mundi">world soul</a> in the <i>Timaeus</i> (36a-b).<sup id="cite_ref-FOOTNOTEHuffman2011_11-0" class="reference"><a href="#cite_note-FOOTNOTEHuffman2011-11">[11]</a></sup>
</p><p>The next notable Pythagorean theorist we know of is <a href="/enwiki/wiki/Archytas" title="Archytas">Archytas</a>, contemporary and friend of Plato, who explained the use of arithmetic, geometric and harmonic means in tuning musical instruments. <a href="/enwiki/wiki/Euclid" title="Euclid">Euclid</a> further developed Archytas's theory in his <i>The Division of the Canon</i> (<i>Katatomē kanonos</i>, the Latin <i>Sectio Canonis</i>). He elaborated the acoustics with reference to the frequency of vibrations (or movements).<sup id="cite_ref-FOOTNOTELevin1990_12-0" class="reference"><a href="#cite_note-FOOTNOTELevin1990-12">[12]</a></sup>
</p><p>Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio (octave 2:1, fourth 4:3, fifth 3:2, 9:8).<sup id="cite_ref-FOOTNOTEHuffman2011_11-1" class="reference"><a href="#cite_note-FOOTNOTEHuffman2011-11">[11]</a></sup><sup id="cite_ref-FOOTNOTEBarker1984–892:46–52_13-0" class="reference"><a href="#cite_note-FOOTNOTEBarker1984–892:46–52-13">[13]</a></sup>
</p><p>Archytas was also the first ancient Greek theorist to provide ratios for all 3 <a href="/enwiki/wiki/Genus_(music)" title="Genus (music)">genera</a>.<sup id="cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-1" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._6,_p._99-1">[1]</a></sup> The three genera of <a href="/enwiki/wiki/Tetrachord" title="Tetrachord">tetrachords</a> recognized by Archytas have the following ratios:
</p>
<ul><li>The enharmonic – 5:4, 36:35, and 28:27</li>
<li>The chromatic – 32:27, 243:224, and 28:27;</li>
<li>The diatonic – 9:8, 8:7, and 28:27.<sup id="cite_ref-FOOTNOTEHuffman2011_11-2" class="reference"><a href="#cite_note-FOOTNOTEHuffman2011-11">[11]</a></sup></li></ul>
<p>These three tunings appear to have corresponded to the actual musical practice of his day.<sup id="cite_ref-FOOTNOTEBarker1984–892:46–52_13-1" class="reference"><a href="#cite_note-FOOTNOTEBarker1984–892:46–52-13">[13]</a></sup>
</p><p>The <a href="/enwiki/wiki/Genus_(music)" title="Genus (music)">genera</a> arose after the framing interval of the tetrachord was fixed, because the two internal notes (called <i>lichanoi</i> and <i>parhypate</i>) still had variable tunings. Tetrachords were classified into genera depending on the position of the <i>lichanos</i> (thus the name <i>lichanos</i>, which means "the indicator"). For instance a <i>lichanos</i> that is a <a href="/enwiki/wiki/Minor_third" title="Minor third">minor third</a> from the bottom and a <a href="/enwiki/wiki/Major_second" title="Major second">major second</a> from the top, defines the genus <a href="/enwiki/wiki/Diatonic_genus" class="mw-redirect" title="Diatonic genus">diatonic</a>. The other two genera, <a href="/enwiki/wiki/Chromatic_genus" class="mw-redirect" title="Chromatic genus">chromatic</a> and <a href="/enwiki/wiki/Enharmonic_genus" class="mw-redirect" title="Enharmonic genus">enharmonic</a>, were defined in similar fashion.<sup id="cite_ref-FOOTNOTEChalmers1993ch._5,_p._47_14-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._5,_p._47-14">[14]</a></sup>
</p><p>More generally, three <i>genera</i> of seven octave <i>species</i> can be recognized, depending on the positioning of the interposed tones in the component <a href="/enwiki/wiki/Tetrachord" title="Tetrachord">tetrachords</a>:
</p>
<ul><li>The diatonic genus is composed of tones and semitones,</li>
<li>the chromatic genus is composed of semitones and a minor third,</li>
<li>the enharmonic genus consists of a major third and two quarter-tones or diesis.<sup id="cite_ref-FOOTNOTECleonides196535–36_15-0" class="reference"><a href="#cite_note-FOOTNOTECleonides196535–36-15">[15]</a></sup></li></ul>
<p>Within these basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two "shades" (<i>chroai</i>), respectively .<sup id="cite_ref-FOOTNOTECleonides196539–40_16-0" class="reference"><a href="#cite_note-FOOTNOTECleonides196539–40-16">[16]</a></sup><sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-0" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(e)-17">[17]</a></sup>
</p><p>The elaboration of tetrachords was also accompanied by penta- and hexachords. The joining of a tetrachord and a pentachord yields an octachord, i.e. the complete seven-tone scale plus a higher octave of the base note. However, this was also produced by joining two tetrachords, which were linked by means of an intermediary or shared note. The final evolution of the system did not end with the octave as such but with the <i>Systema teleion</i>, a set of five tetrachords linked by conjunction and disjunction into arrays of tones spanning two octaves, as explained above.<sup id="cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-2" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._6,_p._99-1">[1]</a></sup>
</p>
<h2><span class="mw-headline" id="The_system_of_Aristoxenus">The system of Aristoxenus</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=3" title="Edit section: The system of Aristoxenus">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Having elaborated the <i>Systema teleion</i>, we will now examine the most significant individual system, that of <a href="/enwiki/wiki/Aristoxenos" class="mw-redirect" title="Aristoxenos">Aristoxenos</a>, which influenced much classification well into the Middle Ages.
</p><p>Aristoxenus was a disciple of <a href="/enwiki/wiki/Aristotle" title="Aristotle">Aristotle</a> who flourished in the 4th century BC. He introduced a radically different model for creating scales, and the nature of his scales deviated sharply from his predecessors. His system was based on seven "<a href="/enwiki/wiki/Octave_species" title="Octave species">octave species</a>" named after Greek regions and ethnicities – Dorian, Lydian, etc. This association of the ethnic names with the octave species appears to have preceded Aristoxenus,<sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(d)_18-0" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(d)-18">[18]</a></sup> and the same system of names was revived in the <a href="/enwiki/wiki/Renaissance" title="Renaissance">Renaissance</a> as names of musical <a href="/enwiki/wiki/Mode_(music)" title="Mode (music)">modes</a> according to the harmonic theory of that time, which was however quite different from that of the ancient Greeks. Thus the names Dorian, Lydian etc. should not be taken to imply a historical continuity between the systems.
</p><p>In contrast to Archytas who distinguished his "genera" only by moving the <i>lichanoi</i>, Aristoxenus varied both <i>lichanoi</i> and <i>parhypate</i> in considerable ranges.<sup id="cite_ref-FOOTNOTEChalmers1993ch._5,_p._48_19-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._5,_p._48-19">[19]</a></sup> Instead of using discrete ratios to place the intervals in his scales, Aristoxenus used continuously variable quantities: as a result he obtained scales of thirteen notes to an octave, and considerably different qualities of consonance.<sup id="cite_ref-FOOTNOTEChalmers1993ch._3,_pp._17–22_20-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._3,_pp._17–22-20">[20]</a></sup>
</p><p>The octave species in the <a href="/enwiki/wiki/Aristoxenus" title="Aristoxenus">Aristoxenian</a> tradition were:<sup id="cite_ref-FOOTNOTEBarbera1984240_21-0" class="reference"><a href="#cite_note-FOOTNOTEBarbera1984240-21">[21]</a></sup><sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(d)_18-1" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(d)-18">[18]</a></sup>
</p>
<ul><li><a href="/enwiki/wiki/Mixolydian_mode#Greek_Mixolydian" title="Mixolydian mode">Mixolydian</a>: <i>hypate hypaton–paramese</i> (b–b′)</li>
<li><a href="/enwiki/wiki/Lydian_mode" title="Lydian mode">Lydian</a>: <i>parhypate hypaton–trite diezeugmenon</i> (c′–c″)</li>
<li><a href="/enwiki/wiki/Phrygian_mode#Ancient_Greek_Phrygian_mode" title="Phrygian mode">Phrygian</a>: <i>lichanos hypaton–paranete diezeugmenon</i> (d′–d″)</li>
<li><a href="/enwiki/wiki/Dorian_mode" title="Dorian mode">Dorian</a>: <i>hypate meson–nete diezeugmenon</i> (e′–e″)</li>
<li><a href="/enwiki/wiki/Hypolydian_mode" title="Hypolydian mode">Hypolydian</a>: <i>parhypate meson–trite hyperbolaion</i> (f′–f″)</li>
<li><a href="/enwiki/wiki/Hypophrygian_mode" title="Hypophrygian mode">Hypophrygian</a>: <i>lichanos meson–paranete hyperbolaion</i> (g′–g″)</li>
<li>Common, <a href="/enwiki/wiki/Locrian_mode" title="Locrian mode">Locrian</a>, or <a href="/enwiki/wiki/Hypodorian_mode" title="Hypodorian mode">Hypodorian</a>: <i>mese–nete hyperbolaion</i> or <i>proslambanomenos–mese</i> (a′–a″ or a–a′)</li></ul>
<p>These names are derived from:
</p>
<ul><li>an Ancient Greek subgroup (<a href="/enwiki/wiki/Dorians" title="Dorians">Dorians</a>),</li>
<li>a small region in central Greece (<a href="/enwiki/wiki/Locris" title="Locris">Locris</a>),</li>
<li>certain neighboring (non-Greek) peoples from <a href="/enwiki/wiki/Asia_Minor" class="mw-redirect" title="Asia Minor">Asia Minor</a> (<a href="/enwiki/wiki/Lydia" title="Lydia">Lydia</a>, <a href="/enwiki/wiki/Phrygia" title="Phrygia">Phrygia</a>).</li>
<li>The prefixes <i>myxo</i> and <i>hypo</i> were added to these to form associated scales above and below.</li></ul>
<h3><span class="mw-headline" id="Aristoxenian_tonoi">Aristoxenian <i>tonoi</i></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=4" title="Edit section: Aristoxenian tonoi">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>The term <i>tonos</i> (pl. <i>tonoi</i>) was used in four senses, for it could designate a note, an interval, a region of the voice, and a pitch.<sup id="cite_ref-FOOTNOTECleonides196544_22-0" class="reference"><a href="#cite_note-FOOTNOTECleonides196544-22">[22]</a></sup>
</p><p>The ancient writer <a href="/enwiki/wiki/Cleonides" title="Cleonides">Cleonides</a> attributes thirteen <i>tonoi</i> to Aristoxenus, which represent a transposition of the tones of the Pythagorean system into a more uniform progressive scale over the range of an octave.<sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-1" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(e)-17">[17]</a></sup>
</p><p>According to Cleonides,<sup id="cite_ref-FOOTNOTECleonides196544_22-1" class="reference"><a href="#cite_note-FOOTNOTECleonides196544-22">[22]</a></sup> these transpositional <i>tonoi</i> were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen. In fact, Aristoxenus criticized the application of these names by the earlier theorists, whom he called the "Harmonicists".<sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(d)_18-2" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(d)-18">[18]</a></sup>
</p><p>According to the interpretation of at least two modern authorities, in the Aristoxenian <i>tonoi</i> the Hypodorian is the lowest, and the Mixolydian is next-to-highest: the reverse of the case of the octave species.<sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-2" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(e)-17">[17]</a></sup><sup id="cite_ref-FOOTNOTESolomon1984250_23-0" class="reference"><a href="#cite_note-FOOTNOTESolomon1984250-23">[23]</a></sup> The nominal base pitches are as follows (in descending order, after Mathiesen; Solomon uses the octave between <b>A</b> and <b>a</b> instead):
</p>
<table class="wikitable">
<tbody><tr>
<th>f
</th>
<td>Hypermixolydian</td>
<td>also called Hyperphrygian
</td></tr>
<tr>
<th>e
</th>
<td>High Mixolydian</td>
<td>also called Hyperiastian
</td></tr>
<tr>
<th>e<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>
</th>
<td>Low Mixolydian</td>
<td>also called Hyperdorian
</td></tr>
<tr>
<th>d
</th>
<td>High Lydian</td>
<td>
</td></tr>
<tr>
<th>c<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span></sup>
</th>
<td>Low Lydian</td>
<td>also called Aeolian
</td></tr>
<tr>
<th>c
</th>
<td>High Phrygian</td>
<td>
</td></tr>
<tr>
<th>B
</th>
<td>Low Phrygian</td>
<td>also called Iastian
</td></tr>
<tr>
<th>B<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>
</th>
<td>Dorian</td>
<td>
</td></tr>
<tr>
<th>A
</th>
<td>High Hypolydian</td>
<td>
</td></tr>
<tr>
<th>G<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span></sup> (and A<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>?)
</th>
<td>Low Hypolydian</td>
<td>also called Hypoaeolian
</td></tr>
<tr>
<th>G
</th>
<td>High Hypophrygian</td>
<td>
</td></tr>
<tr>
<th>F<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-sharp">♯</span></span></sup>
</th>
<td>Low Hypophrygian
</td>
<td>also called Hypoiastian
</td></tr>
<tr>
<th>F
</th>
<td>Hypodorian</td>
<td>
</td></tr></tbody></table>
<h2><span class="mw-headline" id="The_octave_species_in_all_genera">The octave species in all genera <span class="anchor" id="octave_species_anchor"></span></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=5" title="Edit section: The octave species in all genera">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/enwiki/wiki/Octave_species" title="Octave species">Octave species</a></div>
<p>Based on the above, it can be seen that the Aristochene system of tones and octave species can be combined with the Pythagorean system of "genera" to produce a more complete system in which each octave species of thirteen tones (Dorian, Lydian, etc.) can be declined into a system of seven tones by selecting particular tones and semitones to form genera (Diatonic, Chromatic, and Enharmonic).
</p><p>The order of the <a href="/enwiki/wiki/Octave_species" title="Octave species">octave species</a> names in the following table are the original Greek ones, followed by later alternatives (Greek and other). The species and notation are built around the template of the Dorian.
</p>
<h3><span class="mw-headline" id="Diatonic">Diatonic <span class="anchor" id="diatonic_species_anchor"></span></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=6" title="Edit section: Diatonic">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable" style="text-align:center">
<tbody><tr>
<th>Tonic
</th>
<th>Name
</th>
<th>Mese
</th></tr>
<tr>
<td>(A)
</td>
<td>(Hypermixolydian, Hyperphrygian, Locrian)
</td>
<td>(d)
</td></tr>
<tr>
<td>B
</td>
<td>Mixolydian, Hyperdorian
</td>
<td>e
</td></tr>
<tr>
<td>c
</td>
<td>Lydian
</td>
<td>f
</td></tr>
<tr>
<td>d
</td>
<td>Phrygian
</td>
<td>g
</td></tr>
<tr>
<td>e
</td>
<td>Dorian
</td>
<td>a
</td></tr>
<tr>
<td>f
</td>
<td>Hypolydian
</td>
<td>b
</td></tr>
<tr>
<td>g
</td>
<td>Hypophrygian, Ionian
</td>
<td>c′
</td></tr>
<tr>
<td>a
</td>
<td>Hypodorian, Aeolian
</td>
<td>d′
</td></tr>
</tbody></table>
<h3><span class="mw-headline" id="Chromatic">Chromatic <span class="anchor" id="chromatic_species_anchor"></span></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=7" title="Edit section: Chromatic">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable" style="text-align:center;">
<tbody><tr>
<th>Tonic
</th>
<th>Name
</th>
<th>Mese
</th></tr>
<tr>
<td>(A)
</td>
<td>(Hypermixolydian, Hyperphrygian, Locrian)
</td>
<td>(d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>)
</td></tr>
<tr>
<td>B
</td>
<td>Mixolydian, Hyperdorian
</td>
<td>e
</td></tr>
<tr>
<td>c
</td>
<td>Lydian
</td>
<td>f
</td></tr>
<tr>
<td>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>
</td>
<td>Phrygian
</td>
<td>g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>
</td></tr>
<tr>
<td>e
</td>
<td>Dorian
</td>
<td>a
</td></tr>
<tr>
<td>f
</td>
<td>Hypolydian
</td>
<td>b
</td></tr>
<tr>
<td>g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>
</td>
<td>Hypophrygian, Ionian
</td>
<td>c′
</td></tr>
<tr>
<td>a
</td>
<td>Hypodorian, Aeolian
</td>
<td>d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup>
</td></tr>
</tbody></table>
<h3><span class="mw-headline" id="Enharmonic">Enharmonic<span class="anchor" id="enharmonic_species_anchor"></span></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=8" title="Edit section: Enharmonic">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable" style="text-align:center;">
<tbody><tr>
<th>Tonic
</th>
<th>Name
</th>
<th>Mese
</th></tr>
<tr>
<td>(A)
</td>
<td>(Hypermixolydian, Hyperphrygian, Locrian)
</td>
<td>(d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup>)
</td></tr>
<tr>
<td>B
</td>
<td>Mixolydian, Hyperdorian
</td>
<td>e
</td></tr>
<tr>
<td>c<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup>
</td>
<td>Lydian
</td>
<td>f<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup>
</td></tr>
<tr>
<td>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup>
</td>
<td>Phrygian
</td>
<td>g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup>
</td></tr>
<tr>
<td>e
</td>
<td>Dorian
</td>
<td>a
</td></tr>
<tr>
<td>f<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup>
</td>
<td>Hypolydian
</td>
<td>b
</td></tr>
<tr>
<td>g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup>
</td>
<td>Hypophrygian, Ionian
</td>
<td>c′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup>
</td></tr>
<tr>
<td>a
</td>
<td>Hypodorian, Aeolian
</td>
<td>d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup>
</td></tr></tbody></table>
<h2><span class="mw-headline" id="The_oldest_harmoniai_in_three_genera">The oldest <i>harmoniai</i> in three genera <span class="anchor" id="harmoiai_anchor"></span></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=9" title="Edit section: The oldest harmoniai in three genera">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>In the notation above and below, the standard double-flat symbol <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span> is used to accommodate as far as possible the modern musical convention that demands every note in a scale to have a distinct, sequential letter; so interpret <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span> only as meaning the immediate prior letter in the alphabet.<sup id="cite_ref-FOOTNOTEChalmers1993ch._6,_p._109_24-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._6,_p._109-24">[24]</a></sup> This is a complication unnecessary in Greek notation, which had distinct symbols for each half-flat, flat, or natural note.
</p><p>The superscript symbol <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span> after a letter indicates an approximately half-flattened version of the named note; the exact degree of flattening intended depending on which of several tunings was used. Hence a three-tone falling-pitch sequence <b>d</b>, <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup></b>, <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup></b>, with the second note, <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup></b>, about <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac" role="math"><span class="num">1</span>⁄<span class="den">2</span></span>-flat (a <a href="/enwiki/wiki/Quarter-tone" class="mw-redirect" title="Quarter-tone">quarter-tone</a> flat) from the first note, <b>d</b>, and the same <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup></b> about <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac" role="math"><span class="num">1</span>⁄<span class="den">2</span></span>-sharp (a quarter-tone sharp) from the following <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup></b>.
</p><p>The (<b>d</b>) listed first for the Dorian is the <i>Proslambanómenos</i>, which was appended as it was, and falls outside of the linked-tetrachord scheme.
</p><p>These tables are a depiction of <a href="/enwiki/wiki/Aristides_Quintilianus" title="Aristides Quintilianus">Aristides Quintilianus</a>'s enharmonic <i>harmoniai</i>, the diatonic of Henderson<sup id="cite_ref-FOOTNOTEHenderson1942_25-0" class="reference"><a href="#cite_note-FOOTNOTEHenderson1942-25">[25]</a></sup> and Chalmers<sup id="cite_ref-FOOTNOTEChalmers1993_7-1" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993-7">[7]</a></sup> chromatic versions. Chalmers, from whom they originate, states:
</p>
<style data-mw-deduplicate="TemplateStyles:r996844942">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 40px}.mw-parser-output .templatequote .templatequotecite{line-height:1.5em;text-align:left;padding-left:1.6em;margin-top:0}</style><blockquote class="templatequote"><p>In the enharmonic and chromatic forms of some of the harmoniai, it has been necessary to use both a <b>d</b> and either a <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup></b> or <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup></b> because of the non-heptatonic nature of these scales. <b>C</b> and <b>F</b> are synonyms for <b>d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup></b> and <b>g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup></b> [respectively]. The appropriate tunings for these scales are those of Archytas<sup id="cite_ref-FOOTNOTEMountford1923_26-0" class="reference"><a href="#cite_note-FOOTNOTEMountford1923-26">[26]</a></sup> and Pythagoras.<sup id="cite_ref-FOOTNOTEChalmers1993ch._6,_p._109_24-1" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._6,_p._109-24">[24]</a></sup></p></blockquote>
<p>The superficial resemblance of these octave species with the church <a href="/enwiki/wiki/Mode_(music)" title="Mode (music)">modes</a> is misleading: The conventional representation as a section (such as <b>C D E F</b> followed by <b>D E F G</b>) is incorrect. The species were re-tunings of the central octave such that the sequences of intervals (the cyclical modes divided by ratios defined by genus) corresponded to the notes of the Perfect Immutable System as depicted above.<sup id="cite_ref-FOOTNOTEChalmers1993ch._6,_p._106_27-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._6,_p._106-27">[27]</a></sup>
</p>
<h3><span class="mw-headline" id="Dorian">Dorian</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=10" title="Edit section: Dorian">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable">
<tbody><tr>
<th>Genus
</th>
<th>Tones
</th></tr>
<tr>
<td>Enharmonic
</td>
<td>(d) e f<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> a b c′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> e′
</td></tr>
<tr>
<td>Chromatic
</td>
<td>(d) e f g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> a b c′ d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> e′
</td></tr>
<tr>
<td>Diatonic
</td>
<td>(d) e f g a b c′ d′ e′
</td></tr></tbody></table>
<h3><span class="mw-headline" id="Phrygian">Phrygian</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=11" title="Edit section: Phrygian">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable">
<tbody><tr>
<th>Genus
</th>
<th>Tones
</th></tr>
<tr>
<td>Enharmonic
</td>
<td>d e f<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> a b c′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> d′
</td></tr>
<tr>
<td>Chromatic
</td>
<td>d e f g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> a b c′ d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> d′
</td></tr>
<tr>
<td>Diatonic
</td>
<td>d e f g a b c′ d′
</td></tr></tbody></table>
<h3><span class="mw-headline" id="Lydian">Lydian</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=12" title="Edit section: Lydian">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable">
<tbody><tr>
<th>Genus
</th>
<th>Tones
</th></tr>
<tr>
<td>Enharmonic
</td>
<td>f<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> a b c′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> e′ f′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup>
</td></tr>
<tr>
<td>Chromatic
</td>
<td>f g a b c′ d′<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> e′ f′
</td></tr>
<tr>
<td>Diatonic
</td>
<td>f g a b c′ d′ e′ f′
</td></tr></tbody></table>
<h3><span class="mw-headline" id="Mixolydian">Mixolydian</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=13" title="Edit section: Mixolydian">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable">
<tbody><tr>
<th>Genus
</th>
<th>Tones
</th></tr>
<tr>
<td>Enharmonic
</td>
<td>B c<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> d e f<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> b
</td></tr>
<tr>
<td>Chromatic
</td>
<td>B c d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> d e f<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> g<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> b
</td></tr>
<tr>
<td>Diatonic
</td>
<td>B c d e f(g) (a) b
</td></tr></tbody></table>
<h3><span class="mw-headline" id="Syntonolydian">Syntonolydian</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=14" title="Edit section: Syntonolydian">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable">
<tbody><tr>
<th>Genus
</th>
<th>Tones
</th></tr>
<tr>
<td>Enharmonic
</td>
<td>B c<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> e g
</td></tr>
<tr>
<td>Chromatic
</td>
<td>B c d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> e g
</td></tr>
<tr>
<td>1st Diatonic
</td>
<td>c d e f g
</td></tr>
<tr>
<td>2nd Diatonic
</td>
<td>B c d e g
</td></tr></tbody></table>
<h3><span id="Ionian_.28Iastian.29"></span><span class="mw-headline" id="Ionian_(Iastian)">Ionian (Iastian)</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=15" title="Edit section: Ionian (Iastian)">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<table class="wikitable">
<tbody><tr>
<th>Genus
</th>
<th>Tones
</th></tr>
<tr>
<td>Enharmonic
</td>
<td>B c<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;">-</span></sup> d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><a href="/enwiki/wiki/File:Doubleflat.svg" class="image" title="double flat"><img alt="double flat" src="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/8px-Doubleflat.svg.png" decoding="async" width="8" height="12" srcset="/upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/12px-Doubleflat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/23/Doubleflat.svg/16px-Doubleflat.svg.png 2x" data-file-width="133" data-file-height="200" /></a></span></sup> e g a
</td></tr>
<tr>
<td>Chromatic
</td>
<td>B c d<sup><span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span></sup> e g a
</td></tr>
<tr>
<td>1st Diatonic
</td>
<td>c e f g
</td></tr>
<tr>
<td>2nd Diatonic
</td>
<td>B c d e g a
</td></tr></tbody></table>
<h2><span class="mw-headline" id="Ptolemy_and_the_Alexandrians">Ptolemy and the Alexandrians</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=16" title="Edit section: Ptolemy and the Alexandrians">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>In marked contrast to his predecessors, <a href="/enwiki/wiki/Ptolemy" title="Ptolemy">Ptolemy</a>'s scales employed a division of the <i>pyknon</i> in the ratio of 1:2, melodic, in place of equal divisions.<sup id="cite_ref-FOOTNOTEChalmers1993ch._2,_p._10_28-0" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._2,_p._10-28">[28]</a></sup> Ptolemy, in his <i>Harmonics</i>, ii.3–11, construed the <i>tonoi</i> differently, presenting all seven octave species within a fixed octave, through chromatic inflection of the scale degrees (comparable to the modern conception of building all seven modal scales on a single tonic). In Ptolemy's system, therefore there are only seven <i>tonoi</i>.<sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-3" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(e)-17">[17]</a></sup><sup id="cite_ref-FOOTNOTEMathiesen2001c_29-0" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001c-29">[29]</a></sup> Ptolemy preserved Archytas's tunings in his <i>Harmonics</i> as well as transmitting the tunings of <a href="/enwiki/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> and <a href="/enwiki/wiki/Didymos_(music_theorist)" class="mw-redirect" title="Didymos (music theorist)">Didymos</a> and providing his own ratios and scales.<sup id="cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-3" class="reference"><a href="#cite_note-FOOTNOTEChalmers1993ch._6,_p._99-1">[1]</a></sup>
</p>
<h2><span class="mw-headline" id="Harmoniai"><i>Harmoniai</i></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=17" title="Edit section: Harmoniai">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>In music theory the Greek word <i>harmonia</i> can signify the enharmonic genus of tetrachord, the seven octave species, or a style of music associated with one of the ethnic types or the <i>tonoi</i> named by them.<sup id="cite_ref-FOOTNOTEMathiesen2001b_30-0" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001b-30">[30]</a></sup>
</p><p>Particularly in the earliest surviving writings, <i>harmonia</i> is regarded not as a scale, but as the epitome of the stylised singing of a particular district or people or occupation.<sup id="cite_ref-FOOTNOTEWinnington-Ingram19363_31-0" class="reference"><a href="#cite_note-FOOTNOTEWinnington-Ingram19363-31">[31]</a></sup> When the late 6th-century poet <a href="/enwiki/wiki/Lasus_of_Hermione" title="Lasus of Hermione">Lasus of Hermione</a> referred to the Aeolian <i>harmonia</i>, for example, he was more likely thinking of a <a href="/enwiki/wiki/Melody_type" title="Melody type">melodic style</a> characteristic of Greeks speaking the Aeolic dialect than of a scale pattern.<sup id="cite_ref-FOOTNOTEAnderson_and_Mathiesen2001_32-0" class="reference"><a href="#cite_note-FOOTNOTEAnderson_and_Mathiesen2001-32">[32]</a></sup>
</p><p>In the <i><a href="/enwiki/wiki/Republic_(Plato)" title="Republic (Plato)">Republic</a></i>, <a href="/enwiki/wiki/Plato" title="Plato">Plato</a> uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc.<sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-4" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)(e)-17">[17]</a></sup>
</p><p>The philosophical writings of Plato and <a href="/enwiki/wiki/Aristotle" title="Aristotle">Aristotle</a> (c. 350 <a href="/enwiki/wiki/BCE" class="mw-redirect" title="BCE">BCE</a>) include sections that describe the effect of different <i>harmoniai</i> on mood and character formation (see below on ethos). For example, in the <i>Republic</i> (iii.10–11) Plato describes the music a person is exposed to as molding the person's character, which he discusses as particularly relevant for the proper education of the guardians of his ideal State. Aristotle in the <i>Politics</i> (viii:1340a:40–1340b:5):
</p>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996844942"><blockquote class="templatequote"><p>But melodies themselves do contain imitations of character. This is perfectly clear, for the <i>harmoniai</i> have quite distinct natures from one another, so that those who hear them are differently affected and do not respond in the same way to each. To some, such as the one called Mixolydian, they respond with more grief and anxiety, to others, such as the relaxed <i>harmoniai</i>, with more mellowness of mind, and to one another with a special degree of moderation and firmness, Dorian being apparently the only one of the <i>harmoniai</i> to have this effect, while Phrygian creates ecstatic excitement. These points have been well expressed by those who have thought deeply about this kind of education; for they cull the evidence for what they say from the facts themselves.<sup id="cite_ref-FOOTNOTEBarker1984–891:175–176_33-0" class="reference"><a href="#cite_note-FOOTNOTEBarker1984–891:175–176-33">[33]</a></sup></p></blockquote><p>
Aristotle remarks further: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996844942"></p><blockquote class="templatequote"><p> From what has been said it is evident what an influence music has over the disposition of the mind, and how variously it can fascinate it—and if it can do this, most certainly it is what youth ought to be instructed in.<sup id="cite_ref-FOOTNOTEAristotle1912book_8,_ch._5_34-0" class="reference"><a href="#cite_note-FOOTNOTEAristotle1912book_8,_ch._5-34">[34]</a></sup>)</p></blockquote>
<h2><span class="mw-headline" id="Ethos">Ethos</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=18" title="Edit section: Ethos">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>The ancient Greeks have used the word <i>ethos</i> (ἔθος or ἦθος), in this context best rendered by "character" (in the sense of patterns of being and behaviour, but not necessarily with "moral" implications), to describe the ways music can convey, foster, and even generate emotional or mental states. Beyond this general description, there is no unified "Greek ethos theory" but "many different views, sometimes sharply opposed."<sup id="cite_ref-FOOTNOTEAnderson_and_Mathiesen2001_32-1" class="reference"><a href="#cite_note-FOOTNOTEAnderson_and_Mathiesen2001-32">[32]</a></sup> Ethos is attributed to the <i>tonoi</i> or <i>harmoniai</i> or modes (for instance, Plato, in the <i>Republic</i> (iii: 398d–399a), attributes "virility" to the "<a href="/enwiki/wiki/Dorian_mode" title="Dorian mode">Dorian</a>," and "relaxedness" to the "<a href="/enwiki/wiki/Lydian_mode" title="Lydian mode">Lydian</a>" mode), instruments (especially the <a href="/enwiki/wiki/Aulos" title="Aulos">aulos</a> and the <a href="/enwiki/wiki/Cithara" class="mw-redirect" title="Cithara">cithara</a>, but also others), rhythms, and sometimes even the <a href="/enwiki/wiki/Genus_(music)" title="Genus (music)">genus</a> and individual tones. The most comprehensive treatment of musical ethos is provided by <a href="/enwiki/wiki/Aristides_Quintilianus" title="Aristides Quintilianus">Aristides Quintilianus</a> in his book <i>On Music</i>, with the original conception of assigning ethos to the various musical parameters according to the general categories of male and female. <a href="/enwiki/wiki/Aristoxenus" title="Aristoxenus">Aristoxenus</a> was the first Greek theorist to point out that ethos does not only reside in the individual parameters but also in the musical piece as a whole (cited in Pseudo-Plutarch, <i>De Musica</i> 32: 1142d ff; see also Aristides Quintilianus 1.12). The Greeks were interested in musical ethos particularly in the context of education (so Plato in his <i>Republic</i> and Aristotle in his eighth book of his <i>Politics</i>), with implications for the well-being of the State. Many other ancient authors refer to what we nowadays would call psychological effect of music and draw judgments for the appropriateness (or value) of particular musical features or styles, while others, in particular <a href="/enwiki/wiki/Philodemus" title="Philodemus">Philodemus</a> (in his fragmentary work <i>De musica</i>) and <a href="/enwiki/wiki/Sextus_Empiricus" title="Sextus Empiricus">Sextus Empiricus</a> (in his sixth book of his work <i>Adversus mathematicos</i>), deny that music possesses any influence on the human person apart from generating pleasure. These different views anticipate in some way the modern debate in <a href="/enwiki/wiki/Philosophy_of_music" title="Philosophy of music">music philosophy</a> whether music on its own or <a href="/enwiki/wiki/Absolute_music" title="Absolute music">absolute music</a>, independent of text, is able to <a href="/enwiki/wiki/Music_and_emotion" title="Music and emotion">elicit emotions</a> on the listener or musician.<sup id="cite_ref-FOOTNOTEKramarz2016_35-0" class="reference"><a href="#cite_note-FOOTNOTEKramarz2016-35">[35]</a></sup>
</p>
<h2><span class="mw-headline" id="Melos">Melos</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=19" title="Edit section: Melos">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Cleonides describes "melic" composition, "the employment of the materials subject to harmonic practice with due regard to the requirements of each of the subjects under consideration"<sup id="cite_ref-FOOTNOTECleonides196535_36-0" class="reference"><a href="#cite_note-FOOTNOTECleonides196535-36">[36]</a></sup>—which, together with the scales, <i>tonoi</i>, and <i>harmoniai</i> resemble elements found in medieval modal theory.<sup id="cite_ref-FOOTNOTEMathiesen2001a6(iii)_37-0" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a6(iii)-37">[37]</a></sup> According to Aristides Quintilianus (<i>On Music</i>, i.12), melic composition is subdivided into three classes: dithyrambic, nomic, and tragic. These parallel his three classes of rhythmic composition: systaltic, diastaltic and hesychastic. Each of these broad classes of melic composition may contain various subclasses, such as erotic, comic and panegyric, and any composition might be elevating (diastaltic), depressing (systaltic), or soothing (hesychastic).<sup id="cite_ref-FOOTNOTEMathiesen2001a4_38-0" class="reference"><a href="#cite_note-FOOTNOTEMathiesen2001a4-38">[38]</a></sup>
</p><p>The classification of the <i>requirements</i> we have from <a href="/enwiki/wiki/Proclus" title="Proclus">Proclus</a> <i>Useful Knowledge</i> as preserved by <a href="/enwiki/wiki/Photios_I_of_Constantinople" title="Photios I of Constantinople">Photios</a><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/enwiki/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2009)">citation needed</span></a></i>]</sup>:
</p>
<ul><li>for the gods—<a href="/enwiki/wiki/Hymn" title="Hymn">hymn</a>, <a href="/enwiki/wiki/Prosodion" title="Prosodion">prosodion</a>, <a href="/enwiki/wiki/Paean" title="Paean">paean</a>, <a href="/enwiki/wiki/Dithyramb" title="Dithyramb">dithyramb</a>, nomos, adonidia, iobakchos, and <a href="/enwiki/wiki/Hyporchema" title="Hyporchema">hyporcheme</a>;</li>
<li>for humans—<a href="/enwiki/wiki/Encomium" title="Encomium">encomion</a>, <a href="/enwiki/wiki/Epinikion" title="Epinikion">epinikion</a>, <a href="/enwiki/wiki/Skolion" title="Skolion">skolion</a>, <a href="/enwiki/wiki/Erotica" title="Erotica">erotica</a>, <a href="/enwiki/wiki/Epithalamia" class="mw-redirect" title="Epithalamia">epithalamia</a>, <a href="/enwiki/wiki/Hymenaios" class="mw-redirect" title="Hymenaios">hymenaios</a>, sillos, threnos, and epikedeion;</li>
<li>for the gods and humans—partheneion, daphnephorika, tripodephorika, oschophorika, and eutika</li></ul>
<p>According to Mathiesen:
</p>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996844942"><blockquote class="templatequote"><p> Such pieces of music were called melos, which in its perfect form (teleion melos) comprised not only the melody and the text (including its elements of rhythm and diction) but also stylized dance movement. Melic and rhythmic composition (respectively, melopoiïa and rhuthmopoiïa) were the processes of selecting and applying the various components of melos and rhythm to create a complete work.<sup id="cite_ref-FOOTNOTEMathiesen199925_39-0" class="reference"><a href="#cite_note-FOOTNOTEMathiesen199925-39">[39]</a></sup></p></blockquote>
<h2><span class="mw-headline" id="Unicode">Unicode</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=20" title="Edit section: Unicode">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1033289096"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/enwiki/wiki/Ancient_Greek_Musical_Notation" title="Ancient Greek Musical Notation">Ancient Greek Musical Notation (Unicode block)</a></div>
<p>Music symbols of ancient Greece were added to the <a href="/enwiki/wiki/Unicode" title="Unicode">Unicode</a> Standard in March 2005 with the release of version 4.1.
</p>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=21" title="Edit section: See also">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li><a href="/enwiki/wiki/Alypius_of_Alexandria" title="Alypius of Alexandria">Alypius of Alexandria</a></li>
<li><a href="/enwiki/wiki/Delphic_Hymns" title="Delphic Hymns">Delphic Hymns</a></li>
<li><a href="/enwiki/wiki/Seikilos_epitaph" title="Seikilos epitaph">Seikilos epitaph</a></li>
<li><a href="/enwiki/wiki/Mesomedes" title="Mesomedes">Mesomedes</a></li>
<li><a href="/enwiki/wiki/Oxyrhynchus_hymn" title="Oxyrhynchus hymn">Oxyrhynchus hymn</a></li></ul>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=22" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<style data-mw-deduplicate="TemplateStyles:r1011085734">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 18em;">
<ol class="references">
<li id="cite_note-FOOTNOTEChalmers1993ch._6,_p._99-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChalmers1993ch._6,_p._99_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 6, p. 99.</span>
</li>
<li id="cite_note-FOOTNOTECrocker1963-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECrocker1963_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCrocker1963">Crocker 1963</a>.</span>
</li>
<li id="cite_note-FOOTNOTECrocker1964-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECrocker1964_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCrocker1964">Crocker 1964</a>.</span>
</li>
<li id="cite_note-FOOTNOTECrocker1966-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECrocker1966_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCrocker1966">Crocker 1966</a>.</span>
</li>
<li id="cite_note-FOOTNOTEBarbera1977-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBarbera1977_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBarbera1977">Barbera 1977</a>.</span>
</li>
<li id="cite_note-FOOTNOTEBarbera1984-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBarbera1984_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBarbera1984">Barbera 1984</a>.</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEChalmers1993_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChalmers1993_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>.</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993ch._5,_pp._48–51-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChalmers1993ch._5,_pp._48–51_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 5, pp. 48–51.</span>
</li>
<li id="cite_note-FOOTNOTEPöhlmann1970-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPöhlmann1970_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPöhlmann1970">Pöhlmann 1970</a>.</span>
</li>
<li id="cite_note-FOOTNOTEPöhlmann_and_West20017-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEPöhlmann_and_West20017_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFPöhlmann_and_West2001">Pöhlmann and West 2001</a>, 7.</span>
</li>
<li id="cite_note-FOOTNOTEHuffman2011-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEHuffman2011_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHuffman2011_11-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEHuffman2011_11-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFHuffman2011">Huffman 2011</a>.</span>
</li>
<li id="cite_note-FOOTNOTELevin1990-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTELevin1990_12-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLevin1990">Levin 1990</a>.</span>
</li>
<li id="cite_note-FOOTNOTEBarker1984–892:46–52-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEBarker1984–892:46–52_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEBarker1984–892:46–52_13-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFBarker1984–89">Barker 1984–89</a>, 2:46–52.</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993ch._5,_p._47-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChalmers1993ch._5,_p._47_14-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 5, p. 47.</span>
</li>
<li id="cite_note-FOOTNOTECleonides196535–36-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECleonides196535–36_15-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCleonides1965">Cleonides 1965</a>, 35–36.</span>
</li>
<li id="cite_note-FOOTNOTECleonides196539–40-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECleonides196539–40_16-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCleonides1965">Cleonides 1965</a>, 39–40.</span>
</li>
<li id="cite_note-FOOTNOTEMathiesen2001a6(iii)(e)-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(e)_17-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFMathiesen2001a">Mathiesen 2001a</a>, 6(iii)(e).</span>
</li>
<li id="cite_note-FOOTNOTEMathiesen2001a6(iii)(d)-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(d)_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(d)_18-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)(d)_18-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFMathiesen2001a">Mathiesen 2001a</a>, 6(iii)(d).</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993ch._5,_p._48-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChalmers1993ch._5,_p._48_19-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 5, p. 48.</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993ch._3,_pp._17–22-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChalmers1993ch._3,_pp._17–22_20-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 3, pp. 17–22.</span>
</li>
<li id="cite_note-FOOTNOTEBarbera1984240-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBarbera1984240_21-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBarbera1984">Barbera 1984</a>, 240.</span>
</li>
<li id="cite_note-FOOTNOTECleonides196544-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTECleonides196544_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTECleonides196544_22-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFCleonides1965">Cleonides 1965</a>, 44.</span>
</li>
<li id="cite_note-FOOTNOTESolomon1984250-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESolomon1984250_23-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSolomon1984">Solomon 1984</a>, 250.</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993ch._6,_p._109-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEChalmers1993ch._6,_p._109_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEChalmers1993ch._6,_p._109_24-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 6, p. 109.</span>
</li>
<li id="cite_note-FOOTNOTEHenderson1942-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHenderson1942_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHenderson1942">Henderson 1942</a>.</span>
</li>
<li id="cite_note-FOOTNOTEMountford1923-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMountford1923_26-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMountford1923">Mountford 1923</a>.</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993ch._6,_p._106-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChalmers1993ch._6,_p._106_27-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 6, p. 106.</span>
</li>
<li id="cite_note-FOOTNOTEChalmers1993ch._2,_p._10-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChalmers1993ch._2,_p._10_28-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChalmers1993">Chalmers 1993</a>, ch. 2, p. 10.</span>
</li>
<li id="cite_note-FOOTNOTEMathiesen2001c-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMathiesen2001c_29-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMathiesen2001c">Mathiesen 2001c</a>.</span>
</li>
<li id="cite_note-FOOTNOTEMathiesen2001b-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMathiesen2001b_30-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMathiesen2001b">Mathiesen 2001b</a>.</span>
</li>
<li id="cite_note-FOOTNOTEWinnington-Ingram19363-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWinnington-Ingram19363_31-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWinnington-Ingram1936">Winnington-Ingram 1936</a>, 3.</span>
</li>
<li id="cite_note-FOOTNOTEAnderson_and_Mathiesen2001-32"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEAnderson_and_Mathiesen2001_32-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEAnderson_and_Mathiesen2001_32-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFAnderson_and_Mathiesen2001">Anderson and Mathiesen 2001</a>.</span>
</li>
<li id="cite_note-FOOTNOTEBarker1984–891:175–176-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBarker1984–891:175–176_33-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBarker1984–89">Barker 1984–89</a>, 1:175–176.</span>
</li>
<li id="cite_note-FOOTNOTEAristotle1912book_8,_ch._5-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEAristotle1912book_8,_ch._5_34-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAristotle1912">Aristotle 1912</a>, book 8, ch. 5.</span>
</li>
<li id="cite_note-FOOTNOTEKramarz2016-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKramarz2016_35-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKramarz2016">Kramarz 2016</a>.</span>
</li>
<li id="cite_note-FOOTNOTECleonides196535-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTECleonides196535_36-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFCleonides1965">Cleonides 1965</a>, 35.</span>
</li>
<li id="cite_note-FOOTNOTEMathiesen2001a6(iii)-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMathiesen2001a6(iii)_37-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMathiesen2001a">Mathiesen 2001a</a>, 6(iii).</span>
</li>
<li id="cite_note-FOOTNOTEMathiesen2001a4-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMathiesen2001a4_38-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMathiesen2001a">Mathiesen 2001a</a>, 4.</span>
</li>
<li id="cite_note-FOOTNOTEMathiesen199925-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMathiesen199925_39-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMathiesen1999">Mathiesen 1999</a>, 25.</span>
</li>
</ol></div>
<p><b>Sources</b>
</p>
<style data-mw-deduplicate="TemplateStyles:r1147244281">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="div-col" style="column-width: 45em;">
<ul><li><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><cite class="citation wikicite" id="CITEREFAnderson_and_Mathiesen2001">Anderson, Warren, and <a href="/enwiki/wiki/Thomas_J._Mathiesen" title="Thomas J. Mathiesen">Thomas J. Mathiesen</a> (2001). "Ethos". <i><a href="/enwiki/wiki/The_New_Grove_Dictionary_of_Music_and_Musicians" title="The New Grove Dictionary of Music and Musicians">The New Grove Dictionary of Music and Musicians</a></i>, second edition, edited by <a href="/enwiki/wiki/Stanley_Sadie" title="Stanley Sadie">Stanley Sadie</a> and <a href="/enwiki/wiki/John_Tyrrell_(musicologist)" title="John Tyrrell (musicologist)">John Tyrrell</a>. London: Macmillan.</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFAristotle1912"><a href="/enwiki/wiki/Aristotle" title="Aristotle">Aristotle</a> (1912). <i><a rel="nofollow" class="external text" href="http://www.gutenberg.org/files/6762/6762-h/6762-h.htm">A Treatise on Government</a></i> [<i>Politics</i>], translated by William Ellis. London and Toronto: J. M. Dent; New York: E. P. Dutton.</cite></li>
<li><style data-mw-deduplicate="TemplateStyles:r1133582631">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("/upwiki/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("/upwiki/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("/upwiki/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("/upwiki/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFBarbera1977" class="citation journal cs1">Barbera, C. André (Autumn 1977). "Arithmetic and Geometric Divisions of the Tetrachord". <i><a href="/enwiki/wiki/Journal_of_Music_Theory" title="Journal of Music Theory">Journal of Music Theory</a></i>. <b>21</b> (2): 294–323. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F843492">10.2307/843492</a>. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/843492">843492</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Music+Theory&rft.atitle=Arithmetic+and+Geometric+Divisions+of+the+Tetrachord&rft.ssn=fall&rft.volume=21&rft.issue=2&rft.pages=294-323&rft.date=1977&rft_id=info%3Adoi%2F10.2307%2F843492&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F843492%23id-name%3DJSTOR&rft.aulast=Barbera&rft.aufirst=C.+Andr%C3%A9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFBarbera1984" class="citation journal cs1">Barbera, C. André (Summer 1984). "Octave Species". <i><a href="/enwiki/wiki/The_Journal_of_Musicology" title="The Journal of Musicology">The Journal of Musicology</a></i>. <b>3</b> (3): 229–241. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F763813">10.2307/763813</a>. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/763813">763813</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Musicology&rft.atitle=Octave+Species&rft.ssn=summer&rft.volume=3&rft.issue=3&rft.pages=229-241&rft.date=1984&rft_id=info%3Adoi%2F10.2307%2F763813&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F763813%23id-name%3DJSTOR&rft.aulast=Barbera&rft.aufirst=C.+Andr%C3%A9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFBarker1984–89"><a href="/enwiki/wiki/Andrew_Barker_(classicist)" title="Andrew Barker (classicist)">Barker, Andrew</a> (ed.) (1984–89). <i>Greek Musical Writings</i>, 2 vols. Cambridge and New York: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/0-521-23593-6" title="Special:BookSources/0-521-23593-6">0-521-23593-6</a> (v. 1) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/0-521-30220-X" title="Special:BookSources/0-521-30220-X">0-521-30220-X</a> (v. 2).</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFChalmers1993" class="citation cs2">Chalmers, John H. (1993), <a rel="nofollow" class="external text" href="http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html"><i>Divisions of the Tetrachord: A Prolegomenon to the Construction of Musical Scales</i></a>, edited by Larry Polansky and Carter Scholz, foreword by Lou Harrison, Hanover, New Hampshire: Frog Peak Music, <a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/0-945996-04-7" title="Special:BookSources/0-945996-04-7"><bdi>0-945996-04-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Divisions+of+the+Tetrachord%3A+A+Prolegomenon+to+the+Construction+of+Musical+Scales&rft.place=Hanover%2C+New+Hampshire&rft.pub=Frog+Peak+Music&rft.date=1993&rft.isbn=0-945996-04-7&rft.aulast=Chalmers&rft.aufirst=John+H.&rft_id=http%3A%2F%2Feamusic.dartmouth.edu%2F~larry%2Fpublished_articles%2Fdivisions_of_the_tetrachord%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
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<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFCrocker1963" class="citation journal cs1">Crocker, Richard L. (Winter 1963). "Pythagorean Mathematics and Music". <i><a href="/enwiki/wiki/The_Journal_of_Aesthetics_and_Art_Criticism" title="The Journal of Aesthetics and Art Criticism">The Journal of Aesthetics and Art Criticism</a></i>. <b>22</b> (2): 189–198. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F427754">10.2307/427754</a>. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/427754">427754</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Aesthetics+and+Art+Criticism&rft.atitle=Pythagorean+Mathematics+and+Music&rft.ssn=winter&rft.volume=22&rft.issue=2&rft.pages=189-198&rft.date=1963&rft_id=info%3Adoi%2F10.2307%2F427754&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F427754%23id-name%3DJSTOR&rft.aulast=Crocker&rft.aufirst=Richard+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFCrocker1964" class="citation journal cs1">Crocker, Richard L. (Spring 1964). "Pythagorean Mathematics and Music". <i><a href="/enwiki/wiki/The_Journal_of_Aesthetics_and_Art_Criticism" title="The Journal of Aesthetics and Art Criticism">The Journal of Aesthetics and Art Criticism</a></i>. <b>22</b> (3): 325–335. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F427236">10.2307/427236</a>. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/427236">427236</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Aesthetics+and+Art+Criticism&rft.atitle=Pythagorean+Mathematics+and+Music&rft.ssn=spring&rft.volume=22&rft.issue=3&rft.pages=325-335&rft.date=1964&rft_id=info%3Adoi%2F10.2307%2F427236&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F427236%23id-name%3DJSTOR&rft.aulast=Crocker&rft.aufirst=Richard+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
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<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFHuffman2011">Huffman, Carl A. (2011). "<a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/archytas/">Archytas</a>". <i>The Stanford Encyclopedia of Philosophy</i> (accessed 25 August 2014).</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFKramarz2016" class="citation cs2">Kramarz, Andreas (2016), <i>The Power and Value of Music. Its Effect and Ethos in Classical Authors and Contemporary Music Theory</i>, New York/Bern: Peter Lang, <a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/9781433133787" title="Special:BookSources/9781433133787"><bdi>9781433133787</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Power+and+Value+of+Music.+Its+Effect+and+Ethos+in+Classical+Authors+and+Contemporary+Music+Theory&rft.place=New+York%2FBern&rft.pub=Peter+Lang&rft.date=2016&rft.isbn=9781433133787&rft.aulast=Kramarz&rft.aufirst=Andreas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFLevin1990" class="citation cs2"><a href="/enwiki/wiki/Flora_Levin" title="Flora Levin">Levin, Flora R.</a> (1990), "Unity in Euclid's 'Sectio Canonis'<span class="cs1-kern-right"></span>", <i>Hermes</i>, <b>118</b> (4): 430–443, <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/4476778">4476778</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Hermes&rft.atitle=Unity+in+Euclid%27s+%27Sectio+Canonis%27&rft.volume=118&rft.issue=4&rft.pages=430-443&rft.date=1990&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F4476778%23id-name%3DJSTOR&rft.aulast=Levin&rft.aufirst=Flora+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFMathiesen1999" class="citation cs2"><a href="/enwiki/wiki/Thomas_J._Mathiesen" title="Thomas J. Mathiesen">Mathiesen, Thomas J.</a> (1999), <i>Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages</i>, of Publications of the Center for the History of Music Theory and Literature 2, Lincoln: University of Nebraska Press, <a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/9780803230798" title="Special:BookSources/9780803230798"><bdi>9780803230798</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Apollo%27s+Lyre%3A+Greek+Music+and+Music+Theory+in+Antiquity+and+the+Middle+Ages&rft.place=Lincoln&rft.series=of+Publications+of+the+Center+for+the+History+of+Music+Theory+and+Literature+2&rft.pub=University+of+Nebraska+Press&rft.date=1999&rft.isbn=9780803230798&rft.aulast=Mathiesen&rft.aufirst=Thomas+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFMathiesen2001a">Mathiesen, Thomas J. (2001a). "Greece, §I: Ancient". <i><a href="/enwiki/wiki/The_New_Grove_Dictionary_of_Music_and_Musicians" title="The New Grove Dictionary of Music and Musicians">The New Grove Dictionary of Music and Musicians</a></i>, second edition, edited by <a href="/enwiki/wiki/Stanley_Sadie" title="Stanley Sadie">Stanley Sadie</a> and <a href="/enwiki/wiki/John_Tyrrell_(musicologist)" title="John Tyrrell (musicologist)">John Tyrrell</a>. London: Macmillan.</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFMathiesen2001b">Mathiesen, Thomas J. (2001b). "Harmonia (i)". <i>The New Grove Dictionary of Music and Musicians</i>, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFMathiesen2001c">Mathiesen, Thomas J. (2001c). "Tonos". <i>The New Grove Dictionary of Music and Musicians</i>, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFMountford1923">Mountford, James Frederick. (1923). The Musical Scales of Plato's Republic. <i><a href="/enwiki/wiki/The_Classical_Quarterly" class="mw-redirect" title="The Classical Quarterly">The Classical Quarterly</a></i> 17:125-136.</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFPöhlmann1970" class="citation cs2">Pöhlmann, Egert (1970), <i>Denkmäler altgriechischer Musik</i>, Erlanger Beiträge zur Sprach- und Kunstwissenschaft 31, Nuremberg: Hans Carl Verlag, <a href="/enwiki/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/issn/0425-2268">0425-2268</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Denkm%C3%A4ler+altgriechischer+Musik&rft.place=Nuremberg&rft.series=Erlanger+Beitr%C3%A4ge+zur+Sprach-+und+Kunstwissenschaft+31&rft.pub=Hans+Carl+Verlag&rft.date=1970&rft.issn=0425-2268&rft.aulast=P%C3%B6hlmann&rft.aufirst=Egert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><cite class="citation wikicite" id="CITEREFPöhlmann_and_West2001"><a href="/enwiki/w/index.php?title=Egert_P%C3%B6hlmann&action=edit&redlink=1" class="new" title="Egert Pöhlmann (page does not exist)">Egert Pöhlmann</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/P%C3%B6hlmann,_Egert" class="extiw" title="de:Pöhlmann, Egert">de</a>]</span>, and <a href="/enwiki/wiki/Martin_Litchfield_West" title="Martin Litchfield West">Martin L. West</a>. 2001. <i>Documents of Ancient Greek Music: The Extant Melodies and Fragments</i>, edited and transcribed with commentary by Egert Pöhlmann and Martin L. West. Oxford: Clarendon Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/0-19-815223-X" title="Special:BookSources/0-19-815223-X">0-19-815223-X</a>.</cite></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFSolomon1984" class="citation journal cs1">Solomon, Jon (Summer 1984). "Towards a History of Tonoi". <i><a href="/enwiki/wiki/The_Journal_of_Musicology" title="The Journal of Musicology">The Journal of Musicology</a></i>. <b>3</b> (3): 242–251. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F763814">10.2307/763814</a>. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/763814">763814</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Musicology&rft.atitle=Towards+a+History+of+Tonoi&rft.ssn=summer&rft.volume=3&rft.issue=3&rft.pages=242-251&rft.date=1984&rft_id=info%3Adoi%2F10.2307%2F763814&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F763814%23id-name%3DJSTOR&rft.aulast=Solomon&rft.aufirst=Jon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite id="CITEREFWinnington-Ingram1936" class="citation cs2">Winnington-Ingram, Reginald P. (1936), <i>Mode in Ancient Greek Music</i>, London: Cambridge University Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mode+in+Ancient+Greek+Music&rft.place=London&rft.pub=Cambridge+University+Press&rft.date=1936&rft.aulast=Winnington-Ingram&rft.aufirst=Reginald+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li></ul>
</div>
<h2><span class="mw-headline" id="Further_reading">Further reading</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=23" title="Edit section: Further reading">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1147244281"><div class="div-col" style="column-width: 45em;">
<ul><li><a href="/enwiki/w/index.php?title=Johann_Friedrich_Bellermann&action=edit&redlink=1" class="new" title="Johann Friedrich Bellermann (page does not exist)">Bellermann, Johann Friedrich</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Johann_Friedrich_Bellermann" class="extiw" title="de:Johann Friedrich Bellermann">de</a>]</span> (1840). <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=PssqAAAAYAAJ">Die Hymnen des Dionysius und Mesomedes: Text und Melodieen nach Handschriften und den alten Ausgaben bearbeitet von Dr. Friedrich Bellermann</a></i>. Berlin: Albert Förstner.</li>
<li>Jan, Karl von (ed.) (1895). <i>Musici scriptores graeci: Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat</i>. Bibliotheca scriptorum graecorum et romanorum Teubneriana. Leipzig: B. G. Teubner.</li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite class="citation cs2"><a href="/enwiki/wiki/Benjamin_Jowett" title="Benjamin Jowett">Jowett, Benjamin</a> (1937), <i>The Dialogues of Plato</i> (2 vols.), translated by Benjamin Jowett (3rd ed.), New York: Random House</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Dialogues+of+Plato&rft.place=New+York&rft.edition=3rd&rft.pub=Random+House&rft.date=1937&rft.aulast=Jowett&rft.aufirst=Benjamin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li><a href="/enwiki/wiki/Thomas_J._Mathiesen" title="Thomas J. Mathiesen">Mathiesen, Thomas J.</a> (2001d). "Alypius [Alupios]". <i><a href="/enwiki/wiki/The_New_Grove_Dictionary_of_Music_and_Musicians" title="The New Grove Dictionary of Music and Musicians">The New Grove Dictionary of Music and Musicians</a></i>, second edition, edited by <a href="/enwiki/wiki/Stanley_Sadie" title="Stanley Sadie">Stanley Sadie</a> and <a href="/enwiki/wiki/John_Tyrrell_(musicologist)" title="John Tyrrell (musicologist)">John Tyrrell</a>. London: Macmillan Publishers.</li>
<li>Meibom, Marcus (ed.) (1652). <i>Antiquae musicae auctores septem: Graece et latine</i>, 2 vols. Amsterdam: Apud Ludovicum Elzevirium. Facsimile reprint in Monuments of Music and Music Literature in Facsimile, Second Series: Music Literature 51. New York: Broude Bros., 1977. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/9780845022511" title="Special:BookSources/9780845022511">9780845022511</a>.</li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1133582631"><cite class="citation journal cs1">Winnington-Ingram, Reginald P. (1932). "Aristoxenus and the Intervals of Greek Music". <i><a href="/enwiki/wiki/The_Classical_Quarterly" class="mw-redirect" title="The Classical Quarterly">The Classical Quarterly</a></i>. <b>26</b> (3–4): 195–208. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Fs0009838800014415">10.1017/s0009838800014415</a>. <a href="/enwiki/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:170375844">170375844</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Classical+Quarterly&rft.atitle=Aristoxenus+and+the+Intervals+of+Greek+Music&rft.volume=26&rft.issue=3%E2%80%934&rft.pages=195-208&rft.date=1932&rft_id=info%3Adoi%2F10.1017%2Fs0009838800014415&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A170375844%23id-name%3DS2CID&rft.aulast=Winnington-Ingram&rft.aufirst=Reginald+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMusical+system+of+ancient+Greece" class="Z3988"></span></li>
<li>Winnington-Ingram, Reginald P. (1954). "Greek Music (Ancient)". <i><a href="/enwiki/wiki/Grove%27s_Dictionary_of_Music_and_Musicians" class="mw-redirect" title="Grove's Dictionary of Music and Musicians">Grove's Dictionary of Music and Musicians</a></i>, fifth edition, edited by <a href="/enwiki/wiki/Eric_Blom" title="Eric Blom">Eric Blom</a>. New York: St. Martin's Press.</li></ul>
</div>
<h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Musical_system_of_ancient_Greece&action=edit&section=24" title="Edit section: External links">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li>Elsie Hamilton, <a rel="nofollow" class="external text" href="http://www.nakedlight.co.uk/pdf/articles/a-002.pdf">booklet on the modes of ancient Greece</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081121100923/http://www.nakedlight.co.uk/pdf/articles/a-002.pdf">Archived</a> 2008-11-21 at the <a href="/enwiki/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, with detailed examples of the construction of Aolus (reed pipe instruments) and monochord, which might help reconstruct the intervals and modes of the Greeks</li>
<li>Nikolaos Ioannidis musician, composer, has attempted to <a rel="nofollow" class="external text" href="http://homoecumenicus.com/ioannidis_music_ancient_greeks.htm">reconstruct ancient Greek music</a> from a combination of the ancient texts (to be performed) and his knowledge of Greek music.</li>
<li>A mid-19th century, 1902 edition, Henry S. Macran, <a rel="nofollow" class="external text" href="https://archive.org/stream/aristoxenouharm00arisgoog"><i>The Harmonics of Aristoxenus</i></a>. The Barbera translation cited above is more up to date.</li>
<li>Joe Monzo (2004). <a rel="nofollow" class="external text" href="http://www.tonalsoft.com/monzo/aristoxenus/aristoxenus.aspx">Analysis of Aristoxenus</a>. Full of interesting and insightful mathematical analysis. There are some original hypotheses outlined.</li>
<li><a href="/enwiki/wiki/Robert_Erickson" title="Robert Erickson">Robert Erickson</a>, American composer and academic, <a rel="nofollow" class="external text" href="http://www.ex-tempore.org/ARCHYTAS/ARCHYTAS.html">Analysis of Archytas</a>, something of a complement to the above Aristoxenus but, dealing with the earlier and arithmetically precise Archytas:. An incidental note. Erickson is keen to demonstrate that Archytas tuning system not only corresponds with Platos Harmonia, but also with the practice of musicians. Erickson mentions the ease of tuning with the Lyre.</li>
<li>Austrian Academy of Sciences <a rel="nofollow" class="external text" href="http://www.oeaw.ac.at/kal/agm/">examples of instruments and compositions</a></li>
<li><a rel="nofollow" class="external text" href="http://www.kerylos.fr/index_en.php">Ensemble Kérylos</a>, a music group led by scholar <a href="/enwiki/wiki/Annie_B%C3%A9lis" title="Annie Bélis">Annie Bélis</a>, dedicated to the recreation of ancient Greek and Roman music and playing scores written on inscriptions and papyri.</li></ul>
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transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Musical_notation" title="Template talk:Musical notation"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Musical_notation&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Musical_notation" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Musical_notation" title="Musical notation">Musical notation</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Staff_(music)" title="Staff (music)">Staff</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Octave#Ottava_alta_and_bassa" title="Octave">8<sup>va</sup></a></li>
<li><a href="/enwiki/wiki/Octave#Ottava_alta_and_bassa" title="Octave">15<sup>ma</sup></a></li>
<li><a href="/enwiki/wiki/Abbreviation_(music)" title="Abbreviation (music)">Abbreviation</a></li>
<li><a href="/enwiki/wiki/Bar_(music)" title="Bar (music)">Bar / barline / measure</a></li>
<li><a href="/enwiki/wiki/Clef" title="Clef">Clef</a></li>
<li><a href="/enwiki/wiki/Da_capo" title="Da capo">Da capo</a></li>
<li><a href="/enwiki/wiki/Dal_segno" title="Dal segno">Dal segno</a></li>
<li><a href="/enwiki/wiki/Key_signature" title="Key signature">Key signature</a></li>
<li><a href="/enwiki/wiki/Ledger_line" title="Ledger line">Ledger line</a></li>
<li><a href="/enwiki/wiki/Mode_(music)" title="Mode (music)">Mode</a></li>
<li><a href="/enwiki/wiki/Ossia" title="Ossia">Ossia</a></li>
<li><a href="/enwiki/wiki/Scale_(music)" title="Scale (music)">Scale</a></li>
<li><a href="/enwiki/wiki/Rehearsal_letter" title="Rehearsal letter">Rehearsal letter</a></li>
<li><a href="/enwiki/wiki/Repeat_sign" title="Repeat sign">Repeat sign</a></li>
<li><a href="/enwiki/wiki/Tempo" title="Tempo">Tempo</a></li>
<li><a href="/enwiki/wiki/Time_signature" title="Time signature">Time signature</a></li>
<li><a href="/enwiki/wiki/Transposition_(music)" title="Transposition (music)">Transposition</a></li>
<li><a href="/enwiki/wiki/Transposing_instrument" title="Transposing instrument">Transposing instrument</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Musical_note" title="Musical note">Musical notes</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Accidental_(music)" title="Accidental (music)">Accidental</a> (<a href="/enwiki/wiki/Flat_(music)" title="Flat (music)">flat</a></li>
<li><a href="/enwiki/wiki/Natural_(music)" title="Natural (music)">natural</a></li>
<li><a href="/enwiki/wiki/Sharp_(music)" title="Sharp (music)">sharp</a>)</li>
<li><a href="/enwiki/wiki/Cue_note" title="Cue note">Cue note</a></li>
<li><a href="/enwiki/wiki/Dotted_note" title="Dotted note">Dotted note</a></li>
<li><a href="/enwiki/wiki/Grace_note" title="Grace note">Grace note</a></li>
<li><a href="/enwiki/wiki/Note_value" title="Note value">Note value</a> (<a href="/enwiki/wiki/Beam_(music)" title="Beam (music)">beam</a></li>
<li><a href="/enwiki/wiki/Notehead" title="Notehead">notehead</a></li>
<li><a href="/enwiki/wiki/Stem_(music)" title="Stem (music)">stem</a>)</li>
<li><a href="/enwiki/wiki/Pitch_(music)" title="Pitch (music)">Pitch</a></li>
<li><a href="/enwiki/wiki/Rest_(music)" title="Rest (music)">Rest</a></li>
<li><a href="/enwiki/wiki/Tacet" title="Tacet">Tacet</a></li>
<li><a href="/enwiki/wiki/Tuplet" title="Tuplet">Tuplet</a></li>
<li><a href="/enwiki/wiki/Tremolo" title="Tremolo">Tremolo</a></li>
<li><a href="/enwiki/wiki/Interval_(music)" title="Interval (music)">Interval</a></li>
<li><a href="/enwiki/wiki/Helmholtz_pitch_notation" title="Helmholtz pitch notation">Helmholtz pitch notation</a></li>
<li><a href="/enwiki/wiki/Letter_notation" title="Letter notation">Letter notation</a></li>
<li><a href="/enwiki/wiki/Scientific_pitch_notation" title="Scientific pitch notation">Scientific pitch notation</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Articulation_(music)" title="Articulation (music)">Articulation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Accent_(music)" title="Accent (music)">Accent</a></li>
<li><a href="/enwiki/wiki/Caesura" title="Caesura">Caesura</a></li>
<li><a href="/enwiki/wiki/Damping_(music)" title="Damping (music)">Damping</a></li>
<li><a href="/enwiki/wiki/Dynamics_(music)" title="Dynamics (music)">Dynamics</a></li>
<li><a href="/enwiki/wiki/Fermata" title="Fermata">Fermata</a></li>
<li><a href="/enwiki/wiki/Fingering_(music)" title="Fingering (music)">Fingering</a></li>
<li><a href="/enwiki/wiki/Legato" title="Legato">Legato</a></li>
<li><a href="/enwiki/wiki/Marcato" title="Marcato">Marcato</a></li>
<li><a href="/enwiki/wiki/Ornament_(music)" title="Ornament (music)">Ornament</a> (<a href="/enwiki/wiki/Appoggiatura" title="Appoggiatura">appoggiatura</a></li>
<li><a href="/enwiki/wiki/Glissando" title="Glissando">glissando</a></li>
<li><a href="/enwiki/wiki/Grace_note" title="Grace note">grace note</a></li>
<li><a href="/enwiki/wiki/Mordent" title="Mordent">mordent</a></li>
<li><a href="/enwiki/wiki/Slide_(musical_ornament)" title="Slide (musical ornament)">slide</a></li>
<li><a href="/enwiki/wiki/Trill_(music)" title="Trill (music)">trill</a>)</li>
<li><a href="/enwiki/wiki/Portato" title="Portato">Portato</a></li>
<li><a href="/enwiki/wiki/Slur_(music)" title="Slur (music)">Slur</a></li>
<li><a href="/enwiki/wiki/Staccato" title="Staccato">Staccato</a></li>
<li><a href="/enwiki/wiki/Tenuto" title="Tenuto">Tenuto</a></li>
<li><a href="/enwiki/wiki/Tie_(music)" title="Tie (music)">Tie</a></li>
<li><a href="/enwiki/wiki/Tonguing" title="Tonguing">Tonguing</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Sheet_music" title="Sheet music">Sheet music</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/History_of_music_publishing" title="History of music publishing">History of music publishing</a></li>
<li><a href="/enwiki/wiki/Music_engraving" title="Music engraving">Music engraving</a></li>
<li><a href="/enwiki/wiki/Music_publisher" title="Music publisher">Music publisher</a></li>
<li><a href="/enwiki/wiki/Scorewriter" title="Scorewriter">Scorewriter</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Alternative</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Braille_music" title="Braille music">Braille music</a></li>
<li><a href="/enwiki/wiki/Chord_chart" title="Chord chart">Chord chart</a></li>
<li><a href="/enwiki/wiki/Chord_diagram_(music)" title="Chord diagram (music)"> Chord diagram</a></li>
<li><a href="/enwiki/wiki/Eye_music" title="Eye music">Eye music</a></li>
<li><a href="/enwiki/wiki/Figured_bass" title="Figured bass">Figured bass</a></li>
<li><a href="/enwiki/wiki/Graphic_notation_(music)" title="Graphic notation (music)">Graphic notation</a></li>
<li><a href="/enwiki/wiki/Lead_sheet" title="Lead sheet">Lead sheet</a></li>
<li><a href="/enwiki/wiki/Nashville_Number_System" title="Nashville Number System">Nashville Number System</a></li>
<li><a href="/enwiki/wiki/Numbered_musical_notation" title="Numbered musical notation">Numbered musical notation</a></li>
<li><a href="/enwiki/wiki/Klavarskribo" title="Klavarskribo">Klavarskribo</a></li>
<li><a href="/enwiki/wiki/Tablature" title="Tablature">Tablature</a> ("Tab")</li>
<li><a href="/enwiki/wiki/Parsons_code" title="Parsons code">Parsons</a></li>
<li><a href="/enwiki/wiki/Percussion_notation" title="Percussion notation">Percussion notation</a></li>
<li><a href="/enwiki/wiki/Simplified_music_notation" title="Simplified music notation">Simplified</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Non-Western<br />and ancient</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a class="mw-selflink selflink">Ancient Greek</a></li>
<li><a href="/enwiki/wiki/Chinese_musical_notation" title="Chinese musical notation">Chinese</a></li>
<li><a href="/enwiki/wiki/Ekphonetic_notation" title="Ekphonetic notation">Ekphonetic</a></li>
<li><a href="/enwiki/wiki/Gamelan_notation" title="Gamelan notation">Gamelan</a></li>
<li><a href="/enwiki/wiki/Kunkunshi" title="Kunkunshi">Kunkunshi</a></li>
<li><a href="/enwiki/wiki/Neume" title="Neume">Neume</a></li>
<li><a href="/enwiki/wiki/Swaralipi" title="Swaralipi">Swaralipi</a></li>
<li><a href="/enwiki/wiki/Shakuhachi_musical_notation" title="Shakuhachi musical notation">Shakuhachi</a></li>
<li><a href="/enwiki/wiki/Znamenny_chant#Notation" title="Znamenny chant">Znamenny</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Mensural_notation" title="Mensural notation">Mensural notation</a></li>
<li><a href="/enwiki/wiki/Music_stand" title="Music stand">Music stand</a></li>
<li><a href="/enwiki/wiki/Absolute_pitch" title="Absolute pitch">Perfect pitch</a></li>
<li><a href="/enwiki/wiki/Sight-reading" title="Sight-reading">Sight-reading</a></li>
<li><a href="/enwiki/wiki/Transcription_(music)" title="Transcription (music)">Transcription</a></li></ul>
</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>
<ul><li><img alt="" src="/upwiki/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" title="List-Class article" width="16" height="16" class="noviewer" srcset="/upwiki/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, /upwiki/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/enwiki/wiki/List_of_musical_symbols" title="List of musical symbols">List of musical symbols</a></li>
<li><img alt="" src="/upwiki/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" title="Category" width="16" height="16" class="noviewer" srcset="/upwiki/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, /upwiki/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/enwiki/wiki/Category:Musical_notation" title="Category:Musical notation">Category:Musical notation</a></li></ul>
</div></td></tr></tbody></table></div>
<div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1061467846"></div><div role="navigation" class="navbox" aria-labelledby="Ancient_Greece" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1063604349"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Ancient_Greece_topics" title="Template:Ancient Greece topics"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Ancient_Greece_topics" title="Template talk:Ancient Greece topics"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Ancient_Greece_topics&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Ancient_Greece" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Ancient_Greece" title="Ancient Greece">Ancient Greece</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>
<ul><li><a href="/enwiki/wiki/Timeline_of_ancient_Greece" title="Timeline of ancient Greece">Timeline</a></li></ul>
</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="HistoryGeography" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/enwiki/wiki/History_of_Greece" title="History of Greece">History</a></li><li><a href="/enwiki/wiki/Regions_of_ancient_Greece" title="Regions of ancient Greece">Geography</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Periods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Cycladic_culture" title="Cycladic culture">Cycladic civilization</a></li>
<li><a href="/enwiki/wiki/Minoan_civilization" title="Minoan civilization">Minoan civilization</a></li>
<li><a href="/enwiki/wiki/Mycenaean_Greece" title="Mycenaean Greece">Mycenaean civilization</a></li>
<li><a href="/enwiki/wiki/Greek_Dark_Ages" title="Greek Dark Ages">Greek Dark Ages</a></li>
<li><a href="/enwiki/wiki/Archaic_Greece" title="Archaic Greece">Archaic period</a></li>
<li><a href="/enwiki/wiki/Classical_Greece" title="Classical Greece">Classical Greece</a></li>
<li><a href="/enwiki/wiki/Hellenistic_Greece" title="Hellenistic Greece">Hellenistic Greece</a></li>
<li><a href="/enwiki/wiki/Roman_Greece" class="mw-redirect" title="Roman Greece">Roman Greece</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Regions_of_ancient_Greece" title="Regions of ancient Greece">Geography</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Aegean_Sea" title="Aegean Sea">Aegean Sea</a></li>
<li><a href="/enwiki/wiki/Aeolis" title="Aeolis">Aeolis</a></li>
<li><a href="/enwiki/wiki/Crete" title="Crete">Crete</a></li>
<li><a href="/enwiki/wiki/Cyrenaica" title="Cyrenaica">Cyrenaica</a></li>
<li><a href="/enwiki/wiki/Cyprus" title="Cyprus">Cyprus</a></li>
<li><a href="/enwiki/wiki/Doric_Hexapolis" title="Doric Hexapolis">Doris</a></li>
<li><a href="/enwiki/wiki/Epirus" title="Epirus">Epirus</a></li>
<li><a href="/enwiki/wiki/Dardanelles" title="Dardanelles">Hellespont</a></li>
<li><a href="/enwiki/wiki/Ionia" title="Ionia">Ionia</a></li>
<li><a href="/enwiki/wiki/Ionian_Sea" title="Ionian Sea">Ionian Sea</a></li>
<li><a href="/enwiki/wiki/Macedonia_(region)" title="Macedonia (region)">Macedonia</a></li>
<li><a href="/enwiki/wiki/Magna_Graecia" title="Magna Graecia">Magna Graecia</a></li>
<li><a href="/enwiki/wiki/Peloponnese" title="Peloponnese">Peloponnesus</a></li>
<li><a href="/enwiki/wiki/Pontus_(region)" title="Pontus (region)">Pontus</a></li>
<li><a href="/enwiki/wiki/Crimea" title="Crimea">Taurica</a></li>
<li><a href="/enwiki/wiki/Colonies_in_antiquity" title="Colonies in antiquity">Ancient Greek colonies</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="City_statesPoliticsMilitary" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/enwiki/wiki/Polis" title="Polis">City states</a></li><li><a href="/enwiki/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Politics</a></li><li><a href="/enwiki/wiki/Ancient_Greek_warfare" title="Ancient Greek warfare">Military</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Polis" title="Polis">City states</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Ancient_Argos" class="mw-redirect" title="Ancient Argos">Argos</a></li>
<li><a href="/enwiki/wiki/Classical_Athens" title="Classical Athens">Athens</a></li>
<li><a href="/enwiki/wiki/Byzantium" title="Byzantium">Byzantion</a></li>
<li><a href="/enwiki/wiki/Chalcis" title="Chalcis">Chalcis</a></li>
<li><a href="/enwiki/wiki/Ancient_Corinth" title="Ancient Corinth">Corinth</a></li>
<li><a href="/enwiki/wiki/Ephesus" title="Ephesus">Ephesus</a></li>
<li><a href="/enwiki/wiki/Miletus" title="Miletus">Miletus</a></li>
<li><a href="/enwiki/wiki/Pergamon" title="Pergamon">Pergamon</a></li>
<li><a href="/enwiki/wiki/Eretria" title="Eretria">Eretria</a></li>
<li><a href="/enwiki/wiki/Corfu" title="Corfu">Kerkyra</a></li>
<li><a href="/enwiki/wiki/Larissa" title="Larissa">Larissa</a></li>
<li><a href="/enwiki/wiki/Megalopolis,_Greece" title="Megalopolis, Greece">Megalopolis</a></li>
<li><a href="/enwiki/wiki/Thebes,_Greece" title="Thebes, Greece">Thebes</a></li>
<li><a href="/enwiki/wiki/Megara" title="Megara">Megara</a></li>
<li><a href="/enwiki/wiki/Rhodes" title="Rhodes">Rhodes</a></li>
<li><a href="/enwiki/wiki/Samos" title="Samos">Samos</a></li>
<li><a href="/enwiki/wiki/Sparta" title="Sparta">Sparta</a></li>
<li><a href="/enwiki/wiki/Lissus_(Crete)" title="Lissus (Crete)">Lissus (Crete)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Kingdoms</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Kingdom_of_Bithynia" title="Kingdom of Bithynia">Bithynia</a></li>
<li><a href="/enwiki/wiki/Kingdom_of_Cappadocia" title="Kingdom of Cappadocia">Cappadocia</a></li>
<li><a href="/enwiki/wiki/Epirus_(ancient_state)" title="Epirus (ancient state)">Epirus</a></li>
<li><a href="/enwiki/wiki/Greco-Bactrian_Kingdom" title="Greco-Bactrian Kingdom">Greco-Bactrian Kingdom</a></li>
<li><a href="/enwiki/wiki/Indo-Greek_Kingdom" title="Indo-Greek Kingdom">Indo-Greek Kingdom</a></li>
<li><a href="/enwiki/wiki/Macedonia_(ancient_kingdom)" title="Macedonia (ancient kingdom)">Macedonia</a></li>
<li><a href="/enwiki/wiki/Kingdom_of_Pergamon" title="Kingdom of Pergamon">Pergamon</a></li>
<li><a href="/enwiki/wiki/Kingdom_of_Pontus" title="Kingdom of Pontus">Pontus</a></li>
<li><a href="/enwiki/wiki/Ptolemaic_Kingdom" title="Ptolemaic Kingdom">Ptolemaic Kingdom</a></li>
<li><a href="/enwiki/wiki/Seleucid_Empire" title="Seleucid Empire">Seleucid Empire</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Federation" title="Federation">Federations</a>/<br /><a href="/enwiki/wiki/Confederation" title="Confederation">Confederations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Doric_Hexapolis" title="Doric Hexapolis">Doric Hexapolis</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1100</span> – c.<span style="white-space:nowrap;"> 560 BC</span>)</li>
<li><a href="/enwiki/wiki/Italiotes#Italiote_League" title="Italiotes">Italiote League</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 800</span>–389 BC)</li>
<li><a href="/enwiki/wiki/Ionian_League" title="Ionian League">Ionian League</a> (c. 650–404 BC)</li>
<li><a href="/enwiki/wiki/Peloponnesian_League" title="Peloponnesian League">Peloponnesian League</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 550</span>–366 BC)</li>
<li><a href="/enwiki/wiki/Amphictyonic_League" class="mw-redirect" title="Amphictyonic League">Amphictyonic League</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 595</span>–279 BC)</li>
<li><a href="/enwiki/wiki/Acarnanian_League" title="Acarnanian League">Acarnanian League</a> (c. 500–31 BC)</li>
<li><a href="/enwiki/wiki/Greco-Persian_Wars" title="Greco-Persian Wars">Hellenic League</a> (499–449 BC)</li>
<li><a href="/enwiki/wiki/Delian_League" title="Delian League">Delian League</a> (478–404 BC)</li>
<li><a href="/enwiki/wiki/Chalcidian_League" title="Chalcidian League">Chalcidian League</a> (430–348 BC)</li>
<li><a href="/enwiki/wiki/Boeotia#Boeotian_League" title="Boeotia">Boeotian League</a> (c. 424–c. 395 BC)</li>
<li><a href="/enwiki/wiki/Aetolian_League" title="Aetolian League">Aetolian League</a> (c. 400–188 BC)</li>
<li><a href="/enwiki/wiki/Second_Athenian_League" title="Second Athenian League">Second Athenian League</a> (378–355 BC)</li>
<li><a href="/enwiki/wiki/Thessalian_League" title="Thessalian League">Thessalian League</a> (374–196 BC)</li>
<li><a href="/enwiki/wiki/Arcadian_League" title="Arcadian League">Arcadian League</a> (370–c. 230 BC)</li>
<li><a href="/enwiki/wiki/Epirote_League" title="Epirote League">Epirote League</a> (370–168 BC)</li>
<li><a href="/enwiki/wiki/League_of_Corinth" title="League of Corinth">League of Corinth</a> (338–322 BC)</li>
<li><a href="/enwiki/wiki/Euboean_League" title="Euboean League">Euboean League</a> (c. 300 BC–c. 300 AD)</li>
<li><a href="/enwiki/wiki/Achaean_League" title="Achaean League">Achaean League</a> (280–146 BC)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Politics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Boule_(ancient_Greece)" title="Boule (ancient Greece)">Boule</a></li>
<li><a href="/enwiki/wiki/Koinon" title="Koinon">Koinon</a></li>
<li><a href="/enwiki/wiki/Proxeny" title="Proxeny">Proxeny</a></li>
<li><a href="/enwiki/wiki/Tagus_(title)" title="Tagus (title)">Tagus</a></li>
<li><a href="/enwiki/wiki/Tyrant" title="Tyrant">Tyrant</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/enwiki/wiki/Athenian_democracy" title="Athenian democracy">Athenian</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Agora" title="Agora">Agora</a></li>
<li><a href="/enwiki/wiki/Areopagus" title="Areopagus">Areopagus</a></li>
<li><a href="/enwiki/wiki/Ecclesia_(ancient_Athens)" class="mw-redirect" title="Ecclesia (ancient Athens)">Ecclesia</a></li>
<li><a href="/enwiki/wiki/Graphe_paranomon" title="Graphe paranomon">Graphe paranomon</a></li>
<li><a href="/enwiki/wiki/Heliaia" title="Heliaia">Heliaia</a></li>
<li><a href="/enwiki/wiki/Ostracism" title="Ostracism">Ostracism</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/enwiki/wiki/Spartan_Constitution" title="Spartan Constitution">Spartan</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Ecclesia_(Sparta)" title="Ecclesia (Sparta)">Ekklesia</a></li>
<li><a href="/enwiki/wiki/Ephor" title="Ephor">Ephor</a></li>
<li><a href="/enwiki/wiki/Gerousia" title="Gerousia">Gerousia</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/enwiki/wiki/Macedonia_(ancient_kingdom)" title="Macedonia (ancient kingdom)">Macedon</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Synedrion" title="Synedrion">Synedrion</a></li>
<li><a href="/enwiki/wiki/Koinon_of_Macedonians" class="mw-redirect" title="Koinon of Macedonians">Koinon</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greek_warfare" title="Ancient Greek warfare">Military</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/List_of_wars_involving_Greece" title="List of wars involving Greece">Wars</a></li>
<li><a href="/enwiki/wiki/Athenian_military" title="Athenian military">Athenian military</a>
<ul><li><a href="/enwiki/wiki/Scythian_archers" title="Scythian archers">Scythian archers</a></li></ul></li>
<li><a href="/enwiki/wiki/Antigonid_Macedonian_army" title="Antigonid Macedonian army">Antigonid Macedonian army</a></li>
<li><a href="/enwiki/wiki/Ancient_Macedonian_army" title="Ancient Macedonian army">Army of Macedon</a></li>
<li><a href="/enwiki/wiki/Ballista" title="Ballista">Ballista</a></li>
<li><a href="/enwiki/wiki/Cretan_archers" title="Cretan archers">Cretan archers</a></li>
<li><a href="/enwiki/wiki/Hellenistic_armies" title="Hellenistic armies">Hellenistic armies</a></li>
<li><a href="/enwiki/wiki/Hippeis" title="Hippeis">Hippeis</a></li>
<li><a href="/enwiki/wiki/Hoplite" title="Hoplite">Hoplite</a></li>
<li><a href="/enwiki/wiki/Companion_cavalry" title="Companion cavalry">Hetairoi</a></li>
<li><a href="/enwiki/wiki/Macedonian_phalanx" title="Macedonian phalanx">Macedonian phalanx</a></li>
<li><a href="/enwiki/wiki/Military_of_Mycenaean_Greece" title="Military of Mycenaean Greece">Military of Mycenaean Greece</a></li>
<li><a href="/enwiki/wiki/Phalanx" title="Phalanx">Phalanx</a></li>
<li><a href="/enwiki/wiki/Peltast" title="Peltast">Peltast</a></li>
<li><a href="/enwiki/wiki/Pezhetairos" title="Pezhetairos">Pezhetairos</a></li>
<li><a href="/enwiki/wiki/Sarissa" title="Sarissa">Sarissa</a></li>
<li><a href="/enwiki/wiki/Sacred_Band_of_Thebes" title="Sacred Band of Thebes">Sacred Band of Thebes</a></li>
<li><a href="/enwiki/wiki/Sciritae" title="Sciritae">Sciritae</a></li>
<li><a href="/enwiki/wiki/Seleucid_army" title="Seleucid army">Seleucid army</a></li>
<li><a href="/enwiki/wiki/Spartan_army" title="Spartan army">Spartan army</a></li>
<li><a href="/enwiki/wiki/Strategos" title="Strategos">Strategos</a></li>
<li><a href="/enwiki/wiki/Toxotai" title="Toxotai">Toxotai</a></li>
<li><a href="/enwiki/wiki/Xiphos" title="Xiphos">Xiphos</a></li>
<li><a href="/enwiki/wiki/Xyston" title="Xyston">Xyston</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="People" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Category:Ancient_Greeks" title="Category:Ancient Greeks">People</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td class="navbox-abovebelow" colspan="2"><div id="List_of_ancient_Greeks"><a href="/enwiki/wiki/List_of_ancient_Greeks" title="List of ancient Greeks">List of ancient Greeks</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Lists_of_rulers_of_Greece#Antiquity" class="mw-redirect" title="Lists of rulers of Greece">Rulers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/List_of_kings_of_Argos" title="List of kings of Argos">Kings of Argos</a></li>
<li><a href="/enwiki/wiki/Eponymous_archon" title="Eponymous archon">Archons of Athens</a></li>
<li><a href="/enwiki/wiki/List_of_kings_of_Athens" title="List of kings of Athens">Kings of Athens</a></li>
<li><a href="/enwiki/wiki/List_of_rulers_of_Commagene" class="mw-redirect" title="List of rulers of Commagene">Kings of Commagene</a></li>
<li><a href="/enwiki/wiki/Diadochi" title="Diadochi">Diadochi</a></li>
<li><a href="/enwiki/wiki/List_of_kings_of_Macedonia" title="List of kings of Macedonia">Kings of Macedonia</a></li>
<li><a href="/enwiki/wiki/List_of_rulers_of_Thrace_and_Dacia" class="mw-redirect" title="List of rulers of Thrace and Dacia">Kings of Paionia</a></li>
<li><a href="/enwiki/wiki/Attalid_dynasty" class="mw-redirect" title="Attalid dynasty">Attalid kings of Pergamon</a></li>
<li><a href="/enwiki/wiki/List_of_kings_of_Pontus" title="List of kings of Pontus">Kings of Pontus</a></li>
<li><a href="/enwiki/wiki/Ptolemaic_dynasty" title="Ptolemaic dynasty">Ptolemaic dynasty</a></li>
<li><a href="/enwiki/wiki/Seleucid_dynasty" title="Seleucid dynasty">Seleucid dynasty</a></li>
<li><a href="/enwiki/wiki/List_of_kings_of_Sparta" title="List of kings of Sparta">Kings of Sparta</a></li>
<li><a href="/enwiki/wiki/List_of_tyrants_of_Syracuse" title="List of tyrants of Syracuse">Tyrants of Syracuse</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Artists & scholars</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/List_of_ancient_Greek_astronomers" title="List of ancient Greek astronomers">Astronomers</a></li>
<li><a href="/enwiki/wiki/List_of_Graeco-Roman_geographers" title="List of Graeco-Roman geographers">Geographers</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_historians" title="List of ancient Greek historians">Historians</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_mathematicians" title="List of ancient Greek mathematicians">Mathematicians</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_philosophers" title="List of ancient Greek philosophers">Philosophers</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_playwrights" title="List of ancient Greek playwrights">Playwrights</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_poets" title="List of ancient Greek poets">Poets</a></li>
<li><a href="/enwiki/wiki/Seven_Sages_of_Greece" title="Seven Sages of Greece">Seven Sages</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_writers" title="List of ancient Greek writers">Writers</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greek_philosophy" title="Ancient Greek philosophy">Philosophers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Anaxagoras" title="Anaxagoras">Anaxagoras</a></li>
<li><a href="/enwiki/wiki/Anaximander" title="Anaximander">Anaximander</a></li>
<li><a href="/enwiki/wiki/Anaximenes_of_Miletus" title="Anaximenes of Miletus">Anaximenes</a></li>
<li><a href="/enwiki/wiki/Antisthenes" title="Antisthenes">Antisthenes</a></li>
<li><a href="/enwiki/wiki/Aristotle" title="Aristotle">Aristotle</a></li>
<li><a href="/enwiki/wiki/Democritus" title="Democritus">Democritus</a></li>
<li><a href="/enwiki/wiki/Diogenes" title="Diogenes">Diogenes of Sinope</a></li>
<li><a href="/enwiki/wiki/Empedocles" title="Empedocles">Empedocles</a></li>
<li><a href="/enwiki/wiki/Epicurus" title="Epicurus">Epicurus</a></li>
<li><a href="/enwiki/wiki/Gorgias" title="Gorgias">Gorgias</a></li>
<li><a href="/enwiki/wiki/Heraclitus" title="Heraclitus">Heraclitus</a></li>
<li><a href="/enwiki/wiki/Hypatia" title="Hypatia">Hypatia</a></li>
<li><a href="/enwiki/wiki/Leucippus" title="Leucippus">Leucippus</a></li>
<li><a href="/enwiki/wiki/Parmenides" title="Parmenides">Parmenides</a></li>
<li><a href="/enwiki/wiki/Plato" title="Plato">Plato</a></li>
<li><a href="/enwiki/wiki/Protagoras" title="Protagoras">Protagoras</a></li>
<li><a href="/enwiki/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li>
<li><a href="/enwiki/wiki/Socrates" title="Socrates">Socrates</a></li>
<li><a href="/enwiki/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales</a></li>
<li><a href="/enwiki/wiki/Zeno_of_Citium" title="Zeno of Citium">Zeno</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greek_literature" title="Ancient Greek literature">Authors</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Aeschylus" title="Aeschylus">Aeschylus</a></li>
<li><a href="/enwiki/wiki/Aesop" title="Aesop">Aesop</a></li>
<li><a href="/enwiki/wiki/Alcaeus_of_Mytilene" title="Alcaeus of Mytilene">Alcaeus</a></li>
<li><a href="/enwiki/wiki/Archilochus" title="Archilochus">Archilochus</a></li>
<li><a href="/enwiki/wiki/Aristophanes" title="Aristophanes">Aristophanes</a></li>
<li><a href="/enwiki/wiki/Bacchylides" title="Bacchylides">Bacchylides</a></li>
<li><a href="/enwiki/wiki/Euripides" title="Euripides">Euripides</a></li>
<li><a href="/enwiki/wiki/Herodotus" title="Herodotus">Herodotus</a></li>
<li><a href="/enwiki/wiki/Hesiod" title="Hesiod">Hesiod</a></li>
<li><a href="/enwiki/wiki/Hipponax" title="Hipponax">Hipponax</a></li>
<li><a href="/enwiki/wiki/Homer" title="Homer">Homer</a></li>
<li><a href="/enwiki/wiki/Ibycus" title="Ibycus">Ibycus</a></li>
<li><a href="/enwiki/wiki/Lucian" title="Lucian">Lucian</a></li>
<li><a href="/enwiki/wiki/Menander" title="Menander">Menander</a></li>
<li><a href="/enwiki/wiki/Mimnermus" title="Mimnermus">Mimnermus</a></li>
<li><a href="/enwiki/wiki/Panyassis" title="Panyassis">Panyassis</a></li>
<li><a href="/enwiki/wiki/Philocles" title="Philocles">Philocles</a></li>
<li><a href="/enwiki/wiki/Pindar" title="Pindar">Pindar</a></li>
<li><a href="/enwiki/wiki/Plutarch" title="Plutarch">Plutarch</a></li>
<li><a href="/enwiki/wiki/Polybius" title="Polybius">Polybius</a></li>
<li><a href="/enwiki/wiki/Sappho" title="Sappho">Sappho</a></li>
<li><a href="/enwiki/wiki/Simonides_of_Ceos" title="Simonides of Ceos">Simonides</a></li>
<li><a href="/enwiki/wiki/Sophocles" title="Sophocles">Sophocles</a></li>
<li><a href="/enwiki/wiki/Stesichorus" title="Stesichorus">Stesichorus</a></li>
<li><a href="/enwiki/wiki/Theognis_of_Megara" title="Theognis of Megara">Theognis</a></li>
<li><a href="/enwiki/wiki/Thucydides" title="Thucydides">Thucydides</a></li>
<li><a href="/enwiki/wiki/Timocreon" title="Timocreon">Timocreon</a></li>
<li><a href="/enwiki/wiki/Tyrtaeus" title="Tyrtaeus">Tyrtaeus</a></li>
<li><a href="/enwiki/wiki/Xenophon" title="Xenophon">Xenophon</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Others</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/List_of_ancient_Athenian_statesmen" class="mw-redirect" title="List of ancient Athenian statesmen">Athenian statesmen</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_lawgivers" title="List of ancient Greek lawgivers">Lawgivers</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Olympic_victors" title="List of ancient Olympic victors">Olympic victors</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_tyrants" title="List of ancient Greek tyrants">Tyrants</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By culture</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/List_of_ancient_Greek_tribes" title="List of ancient Greek tribes">Ancient Greek tribes</a></li>
<li><a href="/enwiki/wiki/List_of_Thracian_Greeks" title="List of Thracian Greeks">Thracian Greeks</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Macedonians" title="List of ancient Macedonians">Ancient Macedonians</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="SocietyCulture" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/enwiki/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Society</a></li><li><a href="/enwiki/wiki/Culture_of_Greece" title="Culture of Greece">Culture</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greece#Politics_and_society" title="Ancient Greece">Society</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Agriculture_in_ancient_Greece" title="Agriculture in ancient Greece">Agriculture</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_calendars" title="Ancient Greek calendars">Calendar</a></li>
<li><a href="/enwiki/wiki/Clothing_in_ancient_Greece" title="Clothing in ancient Greece">Clothing</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_coinage" title="Ancient Greek coinage">Coinage</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_cuisine" title="Ancient Greek cuisine">Cuisine</a></li>
<li><a href="/enwiki/wiki/Economy_of_ancient_Greece" title="Economy of ancient Greece">Economy</a></li>
<li><a href="/enwiki/wiki/Paideia" title="Paideia">Education</a></li>
<li><a href="/enwiki/wiki/Athenian_festivals" title="Athenian festivals">Festivals</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_folklore" title="Ancient Greek folklore">Folklore</a></li>
<li><a href="/enwiki/wiki/Homosexuality_in_ancient_Greece" title="Homosexuality in ancient Greece">Homosexuality</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_law" title="Ancient Greek law">Law</a></li>
<li><a href="/enwiki/wiki/Ancient_Olympic_Games" title="Ancient Olympic Games">Olympic Games</a></li>
<li><a href="/enwiki/wiki/Pederasty_in_ancient_Greece" title="Pederasty in ancient Greece">Pederasty</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_philosophy" title="Ancient Greek philosophy">Philosophy</a></li>
<li><a href="/enwiki/wiki/Prostitution_in_ancient_Greece" title="Prostitution in ancient Greece">Prostitution</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_religion" title="Ancient Greek religion">Religion</a></li>
<li><a href="/enwiki/wiki/Slavery_in_ancient_Greece" title="Slavery in ancient Greece">Slavery</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_warfare" title="Ancient Greek warfare">Warfare</a></li>
<li><a href="/enwiki/wiki/Marriage_in_ancient_Greece" title="Marriage in ancient Greece">Wedding customs</a></li>
<li><a href="/enwiki/wiki/Ancient_Greece_and_wine" title="Ancient Greece and wine">Wine</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greek_art" title="Ancient Greek art">Arts</a> and science</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Ancient_Greek_architecture" title="Ancient Greek architecture">Architecture</a>
<ul><li><a href="/enwiki/wiki/Greek_Revival_architecture" title="Greek Revival architecture">Greek Revival architecture</a></li></ul></li>
<li><a href="/enwiki/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Astronomy</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_literature" title="Ancient Greek literature">Literature</a></li>
<li><a href="/enwiki/wiki/Greek_mathematics" title="Greek mathematics">Mathematics</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_medicine" title="Ancient Greek medicine">Medicine</a></li>
<li><a href="/enwiki/wiki/Music_of_ancient_Greece" title="Music of ancient Greece">Music</a>
<ul><li><a class="mw-selflink selflink">Musical system</a></li></ul></li>
<li><a href="/enwiki/wiki/Pottery_of_ancient_Greece" title="Pottery of ancient Greece">Pottery</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_sculpture" title="Ancient Greek sculpture">Sculpture</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_technology" title="Ancient Greek technology">Technology</a></li>
<li><a href="/enwiki/wiki/Theatre_of_ancient_Greece" title="Theatre of ancient Greece">Theatre</a></li>
<li><a href="/enwiki/wiki/Greco-Buddhist_art" title="Greco-Buddhist art">Greco-Buddhist art</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greek_religion" title="Ancient Greek religion">Religion</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Ancient_Greek_funeral_and_burial_practices" title="Ancient Greek funeral and burial practices">Funeral and burial practices</a></li>
<li><a href="/enwiki/wiki/Greek_mythology" title="Greek mythology">Mythology</a>
<ul><li><a href="/enwiki/wiki/List_of_Greek_mythological_figures" title="List of Greek mythological figures">mythological figures</a></li></ul></li>
<li><a href="/enwiki/wiki/Ancient_Greek_temple" title="Ancient Greek temple">Temple</a></li>
<li><a href="/enwiki/wiki/Twelve_Olympians" title="Twelve Olympians">Twelve Olympians</a></li>
<li><a href="/enwiki/wiki/Greek_underworld" title="Greek underworld">Underworld</a></li>
<li><a href="/enwiki/wiki/Greco-Buddhism" title="Greco-Buddhism">Greco-Buddhism</a></li>
<li><a href="/enwiki/wiki/Greco-Buddhist_monasticism" title="Greco-Buddhist monasticism">Greco-Buddhist monasticism</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;text-align:left;">Sacred places</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Eleusis" class="mw-redirect" title="Eleusis">Eleusis</a></li>
<li><a href="/enwiki/wiki/Delphi" title="Delphi">Delphi</a></li>
<li><a href="/enwiki/wiki/Delos" title="Delos">Delos</a></li>
<li><a href="/enwiki/wiki/Dion,_Pieria" title="Dion, Pieria">Dion</a></li>
<li><a href="/enwiki/wiki/Dodona" title="Dodona">Dodona</a></li>
<li><a href="/enwiki/wiki/Mount_Olympus" title="Mount Olympus">Mount Olympus</a></li>
<li><a href="/enwiki/wiki/Olympia,_Greece" title="Olympia, Greece">Olympia</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Structures</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Athenian_Treasury" title="Athenian Treasury">Athenian Treasury</a></li>
<li><a href="/enwiki/wiki/Lion_Gate" title="Lion Gate">Lion Gate</a></li>
<li><a href="/enwiki/wiki/Long_Walls" title="Long Walls">Long Walls</a></li>
<li><a href="/enwiki/wiki/Philippeion" title="Philippeion">Philippeion</a></li>
<li><a href="/enwiki/wiki/Theatre_of_Dionysus" title="Theatre of Dionysus">Theatre of Dionysus</a></li>
<li><a href="/enwiki/wiki/Tunnel_of_Eupalinos" title="Tunnel of Eupalinos">Tunnel of Eupalinos</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/enwiki/wiki/Ancient_Greek_temple" title="Ancient Greek temple">Temples</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Temple_of_Aphaea" title="Temple of Aphaea">Aphaea</a></li>
<li><a href="/enwiki/wiki/Temple_of_Artemis" title="Temple of Artemis">Artemis</a></li>
<li><a href="/enwiki/wiki/Temple_of_Athena_Nike" title="Temple of Athena Nike">Athena Nike</a></li>
<li><a href="/enwiki/wiki/Erechtheion" title="Erechtheion">Erechtheion</a></li>
<li><a href="/enwiki/wiki/Temple_of_Hephaestus" title="Temple of Hephaestus">Hephaestus</a></li>
<li><a href="/enwiki/wiki/Temple_of_Hera,_Olympia" title="Temple of Hera, Olympia">Hera, Olympia</a></li>
<li><a href="/enwiki/wiki/Parthenon" title="Parthenon">Parthenon</a></li>
<li><a href="/enwiki/wiki/Samothrace_temple_complex" title="Samothrace temple complex">Samothrace</a></li>
<li><a href="/enwiki/wiki/Temple_of_Zeus,_Olympia" title="Temple of Zeus, Olympia">Zeus, Olympia</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Ancient_Greek" title="Ancient Greek">Language</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Proto-Greek_language" title="Proto-Greek language">Proto-Greek</a></li>
<li><a href="/enwiki/wiki/Mycenaean_Greek" title="Mycenaean Greek">Mycenaean</a></li>
<li><a href="/enwiki/wiki/Homeric_Greek" title="Homeric Greek">Homeric</a></li>
<li><a href="/enwiki/wiki/Ancient_Greek_dialects" title="Ancient Greek dialects">Dialects</a>
<ul><li><a href="/enwiki/wiki/Aeolic_Greek" title="Aeolic Greek">Aeolic</a></li>
<li><a href="/enwiki/wiki/Arcadocypriot_Greek" title="Arcadocypriot Greek">Arcadocypriot</a></li>
<li><a href="/enwiki/wiki/Attic_Greek" title="Attic Greek">Attic</a></li>
<li><a href="/enwiki/wiki/Doric_Greek" title="Doric Greek">Doric</a></li>
<li><a href="/enwiki/wiki/Epirote_Greek" title="Epirote Greek">Epirote</a></li>
<li><a href="/enwiki/wiki/Ionic_Greek" title="Ionic Greek">Ionic</a></li>
<li><a href="/enwiki/wiki/Locrian_Greek" title="Locrian Greek">Locrian</a></li>
<li><a href="/enwiki/wiki/Ancient_Macedonian_language" title="Ancient Macedonian language">Macedonian</a></li>
<li><a href="/enwiki/wiki/Pamphylian_Greek" title="Pamphylian Greek">Pamphylian</a></li></ul></li>
<li><a href="/enwiki/wiki/Koine_Greek" title="Koine Greek">Koine</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/History_of_the_Greek_alphabet" title="History of the Greek alphabet">Writing</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Linear_A" title="Linear A">Linear A</a></li>
<li><a href="/enwiki/wiki/Linear_B" title="Linear B">Linear B</a></li>
<li><a href="/enwiki/wiki/Cypriot_syllabary" title="Cypriot syllabary">Cypriot syllabary</a></li>
<li><a href="/enwiki/wiki/Greek_alphabet" title="Greek alphabet">Greek alphabet</a></li>
<li><a href="/enwiki/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li>
<li><a href="/enwiki/wiki/Attic_numerals" title="Attic numerals">Attic numerals</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Greek_colonisation" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/enwiki/wiki/Greek_colonisation" title="Greek colonisation">Greek colonisation</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Magna_Graecia" title="Magna Graecia">South Italy</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Lecce" title="Lecce">Alision</a></li>
<li><a href="/enwiki/wiki/Brindisi" title="Brindisi">Brentesion</a></li>
<li><a href="/enwiki/wiki/Caulonia_(ancient_city)" title="Caulonia (ancient city)">Caulonia</a></li>
<li><a href="/enwiki/wiki/Casabona" title="Casabona">Chone</a></li>
<li><a href="/enwiki/wiki/Crotone" title="Crotone">Croton</a></li>
<li><a href="/enwiki/wiki/Cumae" title="Cumae">Cumae</a></li>
<li><a href="/enwiki/wiki/Velia" title="Velia">Elea</a></li>
<li><a href="/enwiki/wiki/Heraclea_Lucania" title="Heraclea Lucania">Heraclea Lucania</a></li>
<li><a href="/enwiki/wiki/Vibo_Valentia" title="Vibo Valentia">Hipponion</a></li>
<li><a href="/enwiki/wiki/Otranto" title="Otranto">Hydrus</a></li>
<li><a href="/enwiki/wiki/Krimisa" title="Krimisa">Krimisa</a></li>
<li><a href="/enwiki/wiki/La%C3%BCs" title="Laüs">Laüs</a></li>
<li><a href="/enwiki/wiki/Locri" title="Locri">Locri</a></li>
<li><a href="/enwiki/wiki/Medma" title="Medma">Medma</a></li>
<li><a href="/enwiki/wiki/Metapontum" title="Metapontum">Metapontion</a></li>
<li><a href="/enwiki/wiki/Naples" title="Naples">Neápolis</a></li>
<li><a href="/enwiki/wiki/Pandosia_(Lucania)" title="Pandosia (Lucania)">Pandosia (Lucania)</a></li>
<li><a href="/enwiki/wiki/Paestum" title="Paestum">Poseidonia</a></li>
<li><a href="/enwiki/wiki/Policastro_Bussentino" title="Policastro Bussentino">Pixous</a></li>
<li><a href="/enwiki/wiki/Reggio_Calabria" title="Reggio Calabria">Rhegion</a></li>
<li><a href="/enwiki/wiki/Scylletium" title="Scylletium">Scylletium</a></li>
<li><a href="/enwiki/wiki/Siris_(Magna_Graecia)" class="mw-redirect" title="Siris (Magna Graecia)">Siris</a></li>
<li><a href="/enwiki/wiki/Sybaris" title="Sybaris">Sybaris</a></li>
<li><a href="/enwiki/wiki/Sybaris_on_the_Traeis" title="Sybaris on the Traeis">Sybaris on the Traeis</a></li>
<li><a href="/enwiki/wiki/Taranto" title="Taranto">Taras</a></li>
<li><a href="/enwiki/wiki/Terina_(ancient_city)" title="Terina (ancient city)">Terina</a></li>
<li><a href="/enwiki/wiki/Thurii" title="Thurii">Thurii</a></li></ul>
</div></td><td class="noviewer navbox-image" rowspan="8" style="width:1px;padding:0 0 0 2px"><div><a href="/enwiki/wiki/File:Magna_Graecia_ancient_colonies_and_dialects-en.svg" class="image"><img alt="Magna Graecia ancient colonies and dialects-en.svg" src="/upwiki/wikipedia/commons/thumb/4/49/Magna_Graecia_ancient_colonies_and_dialects-en.svg/70px-Magna_Graecia_ancient_colonies_and_dialects-en.svg.png" decoding="async" width="70" height="66" srcset="/upwiki/wikipedia/commons/thumb/4/49/Magna_Graecia_ancient_colonies_and_dialects-en.svg/105px-Magna_Graecia_ancient_colonies_and_dialects-en.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/4/49/Magna_Graecia_ancient_colonies_and_dialects-en.svg/140px-Magna_Graecia_ancient_colonies_and_dialects-en.svg.png 2x" data-file-width="440" data-file-height="414" /></a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Sicily" title="Sicily">Sicily</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Agrigento" title="Agrigento">Akragas</a></li>
<li><a href="/enwiki/wiki/Akrai" title="Akrai">Akrai</a></li>
<li><a href="/enwiki/wiki/Akrillai" title="Akrillai">Akrillai</a></li>
<li><a href="/enwiki/wiki/Apollonia_(Sicily)" title="Apollonia (Sicily)">Apollonia</a></li>
<li><a href="/enwiki/wiki/Caronia" title="Caronia">Calacte</a></li>
<li><a href="/enwiki/wiki/Casmenae" title="Casmenae">Casmenae</a></li>
<li><a href="/enwiki/wiki/Catania" title="Catania">Catana</a></li>
<li><a href="/enwiki/wiki/Gela" title="Gela">Gela</a></li>
<li><a href="/enwiki/wiki/Helorus" title="Helorus">Helorus</a></li>
<li><a href="/enwiki/wiki/Enna" title="Enna">Henna</a></li>
<li><a href="/enwiki/wiki/Heraclea_Minoa" title="Heraclea Minoa">Heraclea Minoa</a></li>
<li><a href="/enwiki/wiki/Himera" title="Himera">Himera</a></li>
<li><a href="/enwiki/wiki/Hybla_Gereatis" title="Hybla Gereatis">Hybla Gereatis</a></li>
<li><a href="/enwiki/wiki/Hybla_Heraea" title="Hybla Heraea">Hybla Heraea</a></li>
<li><a href="/enwiki/wiki/Kamarina,_Sicily" title="Kamarina, Sicily">Kamarina</a></li>
<li><a href="/enwiki/wiki/Lentini" title="Lentini">Leontinoi</a></li>
<li><a href="/enwiki/wiki/Megara_Hyblaea" title="Megara Hyblaea">Megara Hyblaea</a></li>
<li><a href="/enwiki/wiki/Messina" title="Messina">Messana</a></li>
<li><a href="/enwiki/wiki/Naxos_(Sicily)" title="Naxos (Sicily)">Naxos</a></li>
<li><a href="/enwiki/wiki/Segesta" title="Segesta">Segesta</a></li>
<li><a href="/enwiki/wiki/Selinunte" title="Selinunte">Selinous</a></li>
<li><a href="/enwiki/wiki/Syracuse,_Sicily" title="Syracuse, Sicily">Syracuse</a></li>
<li><a href="/enwiki/wiki/Taormina" title="Taormina">Tauromenion</a></li>
<li><a href="/enwiki/wiki/Sciacca" title="Sciacca">Thermae</a></li>
<li><a href="/enwiki/wiki/Tindari" title="Tindari">Tyndaris</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Aeolian_Islands" title="Aeolian Islands">Aeolian Islands</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Salina,_Sicily" title="Salina, Sicily">Didyme</a></li>
<li><a href="/enwiki/wiki/Panarea" title="Panarea">Euonymos</a></li>
<li><a href="/enwiki/wiki/Alicudi" title="Alicudi">Ereikousa</a></li>
<li><a href="/enwiki/wiki/Basiluzzo" title="Basiluzzo">Hycesia</a></li>
<li><a href="/enwiki/wiki/Lipari" title="Lipari">Lipara/Meligounis</a></li>
<li><a href="/enwiki/wiki/Filicudi" title="Filicudi">Phoenicusa</a></li>
<li><a href="/enwiki/wiki/Stromboli" title="Stromboli">Strongyle</a></li>
<li><a href="/enwiki/wiki/Vulcano" title="Vulcano">Therassía</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Cyrenaica" title="Cyrenaica">Cyrenaica</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Bayda,_Libya" title="Bayda, Libya">Balagrae</a></li>
<li><a href="/enwiki/wiki/Barca_(ancient_city)" title="Barca (ancient city)">Barca</a></li>
<li><a href="/enwiki/wiki/Benghazi" title="Benghazi">Berenice</a></li>
<li><a href="/enwiki/wiki/Cyrene,_Libya" title="Cyrene, Libya">Cyrene</a> (<a href="/enwiki/wiki/Apollonia,_Cyrenaica" class="mw-redirect" title="Apollonia, Cyrenaica">Apollonia</a>)</li>
<li><a href="/enwiki/wiki/Ptolemais,_Cyrenaica" title="Ptolemais, Cyrenaica">Ptolemais</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Iberian_Peninsula" title="Iberian Peninsula">Iberian Peninsula</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Lucentum" title="Lucentum">Akra Leuke</a></li>
<li><a href="/enwiki/wiki/Villajoyosa" title="Villajoyosa">Alonis</a></li>
<li><a href="/enwiki/wiki/Emp%C3%BAries" title="Empúries">Emporion</a></li>
<li><a href="/enwiki/wiki/Elche" title="Elche">Helike</a></li>
<li><a href="/enwiki/wiki/D%C3%A9nia" title="Dénia">Hemeroscopion</a></li>
<li><a href="/enwiki/wiki/Aljaraque" title="Aljaraque">Kalathousa</a></li>
<li><a href="/enwiki/wiki/Sant_Mart%C3%AD_d%27Emp%C3%BAries" title="Sant Martí d'Empúries">Kypsela</a></li>
<li><a href="/enwiki/wiki/Mainake_(Greek_settlement)" title="Mainake (Greek settlement)">Mainake</a></li>
<li><a href="/enwiki/wiki/El_Puerto_de_Santa_Mar%C3%ADa" title="El Puerto de Santa María">Menestheus's Limin</a></li>
<li><a href="/enwiki/wiki/Santa_Pola" title="Santa Pola">Illicitanus Limin/Portus Illicitanus</a></li>
<li><a href="/enwiki/wiki/Roses,_Girona" title="Roses, Girona">Rhode</a></li>
<li><a href="/enwiki/wiki/Salou" title="Salou">Salauris</a></li>
<li><a href="/enwiki/wiki/Sagunto" title="Sagunto">Zacynthos</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Illyria" title="Illyria">Illyria</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Aspalathos" class="mw-redirect" title="Aspalathos">Aspalathos</a></li>
<li><a href="/enwiki/wiki/Apollonia_(Illyria)" title="Apollonia (Illyria)">Apollonia</a></li>
<li><a href="/enwiki/wiki/Vlor%C3%AB#Early_history" title="Vlorë">Aulon</a></li>
<li><a href="/enwiki/wiki/Epidamnos" title="Epidamnos">Epidamnos</a></li>
<li><a href="/enwiki/wiki/Epidaurum" title="Epidaurum">Epidauros</a></li>
<li><a href="/enwiki/wiki/Issa_(polis)" class="mw-redirect" title="Issa (polis)">Issa</a></li>
<li><a href="/enwiki/wiki/Melaina_Korkyra" class="mw-redirect" title="Melaina Korkyra">Melaina Korkyra</a></li>
<li><a href="/enwiki/wiki/Nymphaeum_(Illyria)" title="Nymphaeum (Illyria)">Nymphaion</a></li>
<li><a href="/enwiki/wiki/Oricum" title="Oricum">Orikon</a></li>
<li><a href="/enwiki/wiki/Pharos_(polis)" class="mw-redirect" title="Pharos (polis)">Pharos</a></li>
<li><a href="/enwiki/wiki/Tragurion" class="mw-redirect" title="Tragurion">Tragurion</a></li>
<li><a href="/enwiki/wiki/Thronion_(Illyria)" title="Thronion (Illyria)">Thronion</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Black Sea<br />north coast</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Berezan_Island" title="Berezan Island">Borysthenes</a></li>
<li><a href="/enwiki/wiki/Charax,_Crimea" title="Charax, Crimea">Charax</a></li>
<li><a href="/enwiki/wiki/Chersonesus" title="Chersonesus">Chersonesus</a></li>
<li><a href="/enwiki/wiki/Sukhumi" title="Sukhumi">Dioscurias</a></li>
<li><a href="/enwiki/wiki/Yevpatoria" title="Yevpatoria">Eupatoria</a></li>
<li><a href="/enwiki/wiki/Anapa" title="Anapa">Gorgippia</a></li>
<li><a href="/enwiki/wiki/Tmutarakan" title="Tmutarakan">Hermonassa</a></li>
<li><a href="/enwiki/wiki/Kepoi" title="Kepoi">Kepoi</a></li>
<li><a href="/enwiki/wiki/Kimmerikon" title="Kimmerikon">Kimmerikon</a></li>
<li><a href="/enwiki/wiki/Myrmekion" title="Myrmekion">Myrmekion</a></li>
<li><a href="/enwiki/wiki/Nikonion" title="Nikonion">Nikonion</a></li>
<li><a href="/enwiki/wiki/Nymphaion_(Crimea)" title="Nymphaion (Crimea)">Nymphaion</a></li>
<li><a href="/enwiki/wiki/Olbia_(Pontic)" class="mw-redirect" title="Olbia (Pontic)">Olbia</a></li>
<li><a href="/enwiki/wiki/Panticapaeum" title="Panticapaeum">Panticapaion</a></li>
<li><a href="/enwiki/wiki/Phanagoria" title="Phanagoria">Phanagoria</a></li>
<li><a href="/enwiki/wiki/Pitsunda" title="Pitsunda">Pityus</a></li>
<li><a href="/enwiki/wiki/Tanais" title="Tanais">Tanais</a></li>
<li><a href="/enwiki/wiki/Feodosia" title="Feodosia">Theodosia</a></li>
<li><a href="/enwiki/wiki/Tyras" title="Tyras">Tyras</a></li>
<li><a href="/enwiki/wiki/Tyritake" title="Tyritake">Tyritake</a></li>
<li><a href="/enwiki/wiki/Akra_(Crimmerian_Bosporus)" class="mw-redirect" title="Akra (Crimmerian Bosporus)">Akra</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Black Sea<br />south coast</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Balchik" title="Balchik">Dionysopolis</a></li>
<li><a href="/enwiki/wiki/Varna,_Bulgaria" title="Varna, Bulgaria">Odessos</a></li>
<li><a href="/enwiki/wiki/Pomorie" title="Pomorie">Anchialos</a></li>
<li><a href="/enwiki/wiki/Nesebar" title="Nesebar">Mesambria</a></li>
<li><a href="/enwiki/wiki/Sozopol" title="Sozopol">Apollonia</a></li>
<li><a href="/enwiki/wiki/K%C4%B1y%C4%B1k%C3%B6y" title="Kıyıköy">Salmydessus</a></li>
<li><a href="/enwiki/wiki/Heraclea_Pontica" title="Heraclea Pontica">Heraclea</a></li>
<li><a href="/enwiki/wiki/Tium" title="Tium">Tium</a></li>
<li><a href="/enwiki/wiki/Amasra" title="Amasra">Sesamus</a></li>
<li><a href="/enwiki/wiki/Cytorus" title="Cytorus">Cytorus</a></li>
<li><a href="/enwiki/wiki/Abonoteichos" title="Abonoteichos">Abonoteichos</a></li>
<li><a href="/enwiki/wiki/Sinop,_Turkey" title="Sinop, Turkey">Sinope</a></li>
<li><a href="/enwiki/wiki/Zaliche" title="Zaliche">Zaliche</a></li>
<li><a href="/enwiki/wiki/Samsun" title="Samsun">Amisos</a></li>
<li><a href="/enwiki/wiki/%C3%9Cnye" title="Ünye">Oinòe</a></li>
<li><a href="/enwiki/wiki/Fatsa" title="Fatsa">Polemonion</a></li>
<li><a href="/enwiki/wiki/Terme" title="Terme">Thèrmae</a></li>
<li><a href="/enwiki/wiki/Ordu" title="Ordu">Cotyora</a></li>
<li><a href="/enwiki/wiki/Giresun" title="Giresun">Kerasous</a></li>
<li><a href="/enwiki/wiki/Tripolis_(Pontus)" title="Tripolis (Pontus)">Tripolis</a></li>
<li><a href="/enwiki/wiki/Trabzon" title="Trabzon">Trapezous</a></li>
<li><a href="/enwiki/wiki/Rize" title="Rize">Rhizos</a></li>
<li><a href="/enwiki/wiki/Pazar,_Rize" title="Pazar, Rize">Athina</a></li>
<li><a href="/enwiki/wiki/Batumi" title="Batumi">Bathus</a></li>
<li><a href="/enwiki/wiki/Phasis_(town)" title="Phasis (town)">Phasis</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Lists" style="font-size:114%;margin:0 4em">Lists</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/List_of_ancient_Greek_cities" title="List of ancient Greek cities">Cities</a>
<ul><li><a href="/enwiki/wiki/List_of_cities_in_ancient_Epirus" title="List of cities in ancient Epirus">in Epirus</a></li></ul></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greeks" title="List of ancient Greeks">People</a></li>
<li><a href="/enwiki/wiki/List_of_Greek_place_names" title="List of Greek place names">Place names</a></li>
<li><a href="/enwiki/wiki/List_of_stoae" title="List of stoae">Stoae</a></li>
<li><a href="/enwiki/wiki/List_of_Ancient_Greek_temples" title="List of Ancient Greek temples">Temples</a></li>
<li><a href="/enwiki/wiki/List_of_ancient_Greek_theatres" title="List of ancient Greek theatres">Theatres</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>
<ul><li><img alt="" src="/upwiki/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" title="Category" width="16" height="16" class="noviewer" srcset="/upwiki/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, /upwiki/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/enwiki/wiki/Category:Ancient_Greece" title="Category:Ancient Greece">Category</a></li>
<li><a href="/enwiki/wiki/File:Symbol_portal_class.svg" class="image" title="Portal"><img alt="" src="/upwiki/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="noviewer" srcset="/upwiki/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, /upwiki/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a> <a href="/enwiki/wiki/Portal:Ancient_Greece" title="Portal:Ancient Greece">Portal</a></li>
<li><img alt="" src="/upwiki/wikipedia/commons/thumb/4/41/Global_thinking.svg/10px-Global_thinking.svg.png" decoding="async" title="Outline" width="10" height="16" class="noviewer" srcset="/upwiki/wikipedia/commons/thumb/4/41/Global_thinking.svg/15px-Global_thinking.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/4/41/Global_thinking.svg/21px-Global_thinking.svg.png 2x" data-file-width="130" data-file-height="200" /> <a href="/enwiki/wiki/Outline_of_ancient_Greece" title="Outline of ancient Greece">Outline</a></li></ul>
</div></td></tr></tbody></table></div>
<div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1061467846"></div><div role="navigation" class="navbox" aria-labelledby="Modes_in_Western_music" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1063604349"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Modes" title="Template:Modes"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Modes" title="Template talk:Modes"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Modes&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Modes_in_Western_music" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Mode_(music)" title="Mode (music)">Modes in Western music</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Gregorian_mode" title="Gregorian mode">Gregorian</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/enwiki/wiki/Authentic_mode" class="mw-redirect" title="Authentic mode">Authentic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Dorian_mode" title="Dorian mode">Dorian</a></li>
<li><a href="/enwiki/wiki/Phrygian_mode" title="Phrygian mode">Phrygian</a></li>
<li><a href="/enwiki/wiki/Lydian_mode" title="Lydian mode">Lydian</a></li>
<li><a href="/enwiki/wiki/Mixolydian_mode" title="Mixolydian mode">Mixolydian</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/enwiki/wiki/Plagal_mode" class="mw-redirect" title="Plagal mode">Plagal</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Hypodorian_mode" title="Hypodorian mode">Hypodorian</a></li>
<li><a href="/enwiki/wiki/Hypophrygian_mode" title="Hypophrygian mode">Hypophrygian</a></li>
<li><a href="/enwiki/wiki/Hypolydian_mode" title="Hypolydian mode">Hypolydian</a></li>
<li><a href="/enwiki/wiki/Mixolydian_mode" title="Mixolydian mode">Hypomixolydian</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Ionian_mode" title="Ionian mode">Ionian</a></li>
<li><a href="/enwiki/wiki/Hypoionian_mode" title="Hypoionian mode">Hypoionian</a></li>
<li><a href="/enwiki/wiki/Aeolian_mode" title="Aeolian mode">Aeolian</a></li>
<li><a href="/enwiki/wiki/Hypoaeolian_mode" title="Hypoaeolian mode">Hypoaeolian</a></li>
<li><a href="/enwiki/wiki/Locrian_mode" title="Locrian mode">Locrian</a></li>
<li><a href="/enwiki/wiki/Hypolocrian_mode" title="Hypolocrian mode">Hypolocrian</a></li>
<li><a href="/enwiki/wiki/Reciting_tone" title="Reciting tone">Reciting tone</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Diatonic_scale" title="Diatonic scale">Diatonic</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Ionian_mode" title="Ionian mode">Ionian (I)</a></li>
<li><a href="/enwiki/wiki/Dorian_mode" title="Dorian mode">Dorian (II)</a></li>
<li><a href="/enwiki/wiki/Phrygian_mode" title="Phrygian mode">Phrygian (III)</a></li>
<li><a href="/enwiki/wiki/Lydian_mode" title="Lydian mode">Lydian (IV)</a></li>
<li><a href="/enwiki/wiki/Mixolydian_mode" title="Mixolydian mode"> Mixolydian (V)</a></li>
<li><a href="/enwiki/wiki/Aeolian_mode" title="Aeolian mode">Aeolian (VI)</a></li>
<li><a href="/enwiki/wiki/Locrian_mode" title="Locrian mode"> Locrian (VII)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Jazz_minor_scale" title="Jazz minor scale">Jazz minor</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/enwiki/wiki/Jazz_minor_scale" title="Jazz minor scale">Jazz minor (I)</a></li>
<li><a href="/enwiki/wiki/Dorian_%E2%99%AD2_scale" title="Dorian ♭2 scale">Dorian <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>2 (II)</a></li>
<li><a href="/enwiki/wiki/Lydian_augmented_scale" title="Lydian augmented scale">Lydian Augmented (III)</a></li>
<li><a href="/enwiki/wiki/Acoustic_scale" title="Acoustic scale">Lydian Dominant (IV)</a></li>
<li><a href="/enwiki/wiki/Aeolian_dominant_scale" title="Aeolian dominant scale">Mixolydian <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-flat">♭</span></span>6 (V)</a></li>
<li><a href="/enwiki/wiki/Half_diminished_scale" title="Half diminished scale">Locrian <span class="music-symbol" style="font-family: Arial Unicode MS, Lucida Sans Unicode;"><span class="music-natural">♮</span></span>2 (VI)</a></li>
<li><a href="/enwiki/wiki/Altered_scale" title="Altered scale"> Altered (VII)</a></li></ul>
</div></td></tr></tbody></table></div></div>' |
Whether or not the change was made through a Tor exit node (tor_exit_node) | false |
Unix timestamp of change (timestamp) | '1687735057' |