Jump to content

Diminished third: Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous edit
Content deleted Content added
VisualWikitext
Hyacinth (talk | contribs)
176,976 edits
m cents_24T_equal_temperament = 200|
m Misleading
 
(44 intermediate revisions by 24 users not shown)
Line 4: Line 4:
complement = [[augmented sixth]]|
complement = [[augmented sixth]]|
other_names = -|
other_names = -|
abbreviation = d3|
abbreviation = d3<ref name="B&S"/>|
semitones = 2|
semitones = 2|
interval_class = 2|
interval_class = 2|
just_interval = 144:125,<ref name="Haluska">Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxvi. {{ISBN|0-8247-4714-3}}. Classic diminished third.</ref> 256:225,<ref>Haluska, ibid. Diminished third.</ref> 65536:59049|
just_interval = 144:125, 8:7|
cents_equal_temperament = 200|
cents_equal_temperament = 200|
cents_24T_equal_temperament = 200|
cents_24T_equal_temperament = |
cents_just_intonation = 245
cents_just_intonation = 245, 223, 180
}}
}}


[[File:Diminished third on C.png|thumb|right|Diminished third {{Audio|Major second on C.mid|Play}}.]]
In music, a '''diminished third''' ({{Audio|Major second on C.mid|Play}}) is the interval produced by flattening a [[minor third]] by a [[chromatic semitone]]. In [[equal temperament]] it is [[enharmonic]] with the [[major second]], both having a value of 200 [[cent (music)|cent]]s. However in [[meantone temperament|meantone]] tunings with fifths flatter than the 700 cents of equal temperament, the diminished third is wider than the major second. In [[19 equal temperament]] it is in fact enharmonically equivalent to an [[augmented second]], both having a value of 262.6 cents. In
In [[classical music]] from [[Western culture]], a '''diminished third''' ({{Audio|Major second on C.mid|Play}}) is the [[interval (music)|musical interval]] produced by [[Diminution|narrowing]] a [[minor third]] by a [[chromatic semitone]].<ref name="B&S">Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. {{ISBN|978-0-07-294262-0}}.</ref><ref>Hoffmann, F.A. (1881). ''Music: Its Theory & Practice'', p.89-90. Thurgate & Sonsasaetd. Digitized August 16, 2007.</ref> For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A{{Music|sharp}} to C, and from A to C{{Music|b}} are diminished thirds, two semitones wide. Being diminished, it is considered a [[consonance and dissonance|dissonant]] interval.<ref>Benward & Saker (2003), p.92.</ref>
⚫
[[31 equal temperament]] it has a more typical value of 232.3 cents. In a twelve-note keyboard tuned in a meantone tuning from E{{music|flat}} to G{{music|sharp}}, the dimininished third appears between C{{music|sharp}} and E{{music|flat}}, and again between G{{music|sharp}} and B{{music|flat}}.


In [[septimal meantone temperament]] the diminished third is considered to approximate the interval of a [[septimal major second]] ({{Audio|Septimal major second on C.mid|play}}), with ratio 8/7, and in any meantone tuning in the vicinity of [[quarter-comma meantone]], such as 31-equal temperament, it will come close to that value; for instance in 31-equal temperament the diminished third is a cent sharp of 8/7.
In [[12-tone equal temperament]] a diminished third is [[enharmonic]] with the [[major second]], both having a value of 200 [[cent (music)|cent]]s. However, in [[meantone temperament|meantone]] tunings with fifths flatter than 700 cents, the diminished third is wider than the major second. In [[19 equal temperament]] it is in fact enharmonically equivalent to an [[augmented second]], both having a value of 252.6 cents. In
⚫
[[31 equal temperament]] it has a more typical value of 232.3 cents. In a twelve-note keyboard tuned in a meantone tuning from E{{Music|flat}} to G{{Music|sharp}}, the dimininished third appears between C{{Music|sharp}} and E{{Music|flat}}, and again between G{{Music|sharp}} and B{{Music|flat}}.


In superpythagorean tunings, the diminished third is narrower than the major second. In the special case of [[17 equal temperament]], the chromatic semitone and diminished third are in fact represented by the same interval of 141.18 cents, which allows the minor third to be evenly divided in half. In [[22 equal temperament]], the diminished third is ~ 109 cents while the chromatic semitone is ~ 163 cents and the diatonic semitone is ~ 55 cents.
⚫
The [[complement (music)|complementary interval]] to the diminished third is the [[augmented sixth]], and the numerous chords of [[common practice]] music described as [[augmented sixth chord]]s thereby contain the diminished third as well. For example, a German sixth chord E{{music|flat}}-G-B{{music|flat}}-C{{music|sharp}}-E{{music|flat}}' exhibits a diminished third between C{{music|sharp}} and E{{music|flat}}' which complements the augmented sixth between E{{music|flat}} and C{{music|sharp}}.


In [[septimal meantone temperament]] the diminished third is considered to approximate the interval of a [[septimal major second]] ({{Audio|Septimal major second on C.mid|play}}), with ratio 8/7, and in any meantone tuning in the vicinity of [[quarter-comma meantone]], such as 31-equal temperament, it will come close to that value; for instance in 31-equal temperament the diminished third is a cent sharp of 8/7.
⚫
==See also==


⚫
The [[complement (music)|complementary interval]] to the diminished third is the [[augmented sixth]], and the numerous chords of [[common practice]] music described as [[augmented sixth chord]]s thereby contain the diminished third as well. For example, a German sixth chord E{{Music|flat}}-G-B{{Music|flat}}-C{{Music|sharp}}-E{{Music|flat}}' exhibits a diminished third between C{{Music|sharp}} and E{{Music|flat}}' which complements the augmented sixth between E{{Music|flat}} and C{{Music|sharp}}.

The '''just diminished third''' arises in the extended C major scale between F{{music|#}} and A{{music|b}},<ref>Paul, Oscar (1885). ''[https://books.google.com/books?id=4WEJAQAAMAAJ&q=musical+interval+%22pythagorean+major+third%22 A manual of harmony for use in music-schools and seminaries and for self-instruction]'', p.165. Theodore Baker, trans. G. Schirmer.</ref> {{audio|Just diminished third in scale.mid|Play}} and between B and D{{music|b}}.

⚫
==See also==
*[[List of meantone intervals]]
*[[List of meantone intervals]]


==References==
{{Diatonic intervals}}
{{Reflist}}


[[Category:Intervals]]
{{Intervals}}


{{DEFAULTSORT:Diminished Third}}
[[et:Vähendatud terts]]
[[Category:Diminished intervals]]
[[Category:Thirds (music)]]

Latest revision as of 11:51, 27 June 2024

diminished third
Inverseaugmented sixth
Name
Other names-
Abbreviationd3[1]
Size
Semitones2
Interval class2
Just interval144:125,[2] 256:225,[3] 65536:59049
Cents
12-Tone equal temperament200
Just intonation245, 223, 180
Diminished third Playⓘ.

In classical music from Western culture, a diminished third (Playⓘ) is the musical interval produced by narrowing a minor third by a chromatic semitone.[1][4] For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A♯ to C, and from A to C♭ are diminished thirds, two semitones wide. Being diminished, it is considered a dissonant interval.[5]

In 12-tone equal temperament a diminished third is enharmonic with the major second, both having a value of 200 cents. However, in meantone tunings with fifths flatter than 700 cents, the diminished third is wider than the major second. In 19 equal temperament it is in fact enharmonically equivalent to an augmented second, both having a value of 252.6 cents. In 31 equal temperament it has a more typical value of 232.3 cents. In a twelve-note keyboard tuned in a meantone tuning from E♭ to G♯, the dimininished third appears between C♯ and E♭, and again between G♯ and B♭.

In superpythagorean tunings, the diminished third is narrower than the major second. In the special case of 17 equal temperament, the chromatic semitone and diminished third are in fact represented by the same interval of 141.18 cents, which allows the minor third to be evenly divided in half. In 22 equal temperament, the diminished third is ~ 109 cents while the chromatic semitone is ~ 163 cents and the diatonic semitone is ~ 55 cents.

In septimal meantone temperament the diminished third is considered to approximate the interval of a septimal major second (playⓘ), with ratio 8/7, and in any meantone tuning in the vicinity of quarter-comma meantone, such as 31-equal temperament, it will come close to that value; for instance in 31-equal temperament the diminished third is a cent sharp of 8/7.

The complementary interval to the diminished third is the augmented sixth, and the numerous chords of common practice music described as augmented sixth chords thereby contain the diminished third as well. For example, a German sixth chord E♭-G-B♭-C♯-E♭' exhibits a diminished third between C♯ and E♭' which complements the augmented sixth between E♭ and C♯.

The just diminished third arises in the extended C major scale between F♯ and A♭,[6] Playⓘ and between B and D♭.

See also

[edit]

References

[edit]
  1. ^ a b Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0.
  2. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0-8247-4714-3. Classic diminished third.
  3. ^ Haluska, ibid. Diminished third.
  4. ^ Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sonsasaetd. Digitized August 16, 2007.
  5. ^ Benward & Saker (2003), p.92.
  6. ^ Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction, p.165. Theodore Baker, trans. G. Schirmer.
Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Diminished_third&oldid=1231266707"