View source for Second inversion

{{Image frame|content=<score lang="lilypond"> {\override Score.TimeSignature#'stencil = ##f
\relative c' {
   \clef treble 
   \time 4/4
   \key c \major

   <d g b>1
} }
</score>|width=120|caption=A G-major triad in second inversion}}
{{F major chord inversions}}

The '''second [[Inverted chord|inversion]]''' of a [[Chord (music)|chord]] is the [[Voicing (music)|voicing]] of a [[Triad (music)|triad]], [[seventh chord]], or [[ninth chord]] in which the [[fifth (chord)|fifth]] of the chord is the [[bass note]]. In this inversion, the bass note and the [[root (music)|root]] of the chord are a [[perfect fourth|fourth]] apart which traditionally qualifies as a [[dissonance (music)|dissonance]]. There is therefore a tendency for movement and resolution. In notation form, it is referred to with a c following the chord position (For e.g., Ic. Vc  or IVc).{{citation needed|date=March 2014}} In [[figured bass]], a second-inversion triad is a {{music|64}} chord (as in I{{music|64}}), while a second-inversion seventh chord is a {{music|43 chord}} chord.

{{Quote|Inversions are not restricted to the same number of tones as the original chord, nor to any fixed order of tones except with regard to the interval between the root, or its octave, and the bass note, hence, great variety results.<ref>Hubbard, William Lines (1908). The American History and Encyclopedia of Music, Vol. 10: ''[https://books.google.com/books?id=cfgg5POKoNsC&pg=PA103 Musical Dictionary]'', p.103. Irving Squire: London. {{pre-ISBN}}. {{HathiTrust |htid=ucw.ark:/13960/t7fr0b61n |title=Also}}</ref>}}

Note that any voicing above the bass is allowed. A second inversion chord must have the fifth [[chord factor]] in the bass, but it may have any arrangement of the root and third above that, including doubled notes, compound intervals, and omission (G-C-E, G-C-E-G', G-E-G-C'-E', etc.)

== Examples ==
In the second inversion of a C-[[major triad]], the bass is G — the fifth of the triad — with the root and third stacked above it, forming the intervals of a fourth and a sixth above the inverted bass of G, respectively.

:<score lang="lilypond" vorbis="1">
{
\override Score.TimeSignature
#'stencil = ##f
\override Score.SpacingSpanner.strict-note-spacing = ##t
\set Score.proportionalNotationDuration = #(ly:make-moment 1/4)
\time 4/4 
\relative c' { 
   <c e g>1^\markup { \column { "Root" "position" } }
   <e g c>1^\markup { \column { "First" "inversion" } }
   \once \override NoteHead.color = #blue  <g c e>1^\markup { \column { "Second" "inversion" } }
   }
}
</score>

In the second inversion of a G [[dominant seventh chord]], the bass note is D, the fifth of the seventh chord.

:<score lang="lilypond" vorbis="1">
{
\override Score.TimeSignature
#'stencil = ##f
\override Score.SpacingSpanner.strict-note-spacing = ##t
\set Score.proportionalNotationDuration = #(ly:make-moment 1/4)
\time 4/4 
\relative c' { 
   <g b d f>1^\markup { \column { "Root" "position" } }
   <b d f g>1^\markup { \column { "First" "inversion" } }
   \once \override NoteHead.color = #blue <d f g b>1^\markup { \column { "Second" "inversion" } }
   <f g b d>1^\markup { \column { "Third" "inversion" } }
   }
}
</score>

==Types==
{{Unreferenced section|date=October 2018}}
There are four types of second-inversion chords: [[cadence (music)|cadential]], [[passing tone|passing]], [[Auxiliary note|auxiliary]], and bass [[arpeggiation]].

=== Cadential ===
{{redirect|Six-four|the time signature|Sextuple metre}}{{anchor|Cadential six-four chord}}{{anchor|Cadential six-four}}

[[Cadence (music)|Cadential]] second-inversion chords are typically used in the [[Chord progression|authentic cadence]] I{{music|64}}-V-I, or one of its variation, like I{{music|64}}-V{{music|7 chord}}-I. In this form, the chord is sometimes referred to as a ''cadential {{music|64}}'' chord. The chord preceding I{{music|64}} is most often a chord that would introduce V as a weak to strong progression, for example, making -II-V into II-I{{music|64}}-V or making IV-V into IV-I{{music|64}}-V.

:<score vorbis="1" lang="lilypond">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c'' {
                \stemUp \clef treble \key c \major \time 4/4
                c1 b c
                }
            \new Voice \relative c'' {
                \stemDown
                g1 g g
                }
            >>
        \new Staff <<
            \new Voice \relative c' {
                \stemUp \clef bass \key c \major \time 4/4
                e1 d e
                }
            \new Voice \relative c' {
                \stemDown
                g1 g c, \bar "||"
                }
            >>
    >> }
</score>

The cadential {{music|64}}  can be analyzed in two ways: the first labels it as a second-inversion chord, while the second treats it instead as part of a horizontal progression involving [[voice leading]] above a stationary bass.

# In the first designation, the cadential {{su|p=6|b=4}} chord features the progression: {{nowrap|I{{su|p=6|b=4}}}}-V-I. Most older harmony textbooks use this label, and it can be traced back to the early 19th century.<ref>[[Gottfried Weber|Weber]], ''Theory of musical composition,'' p. 350, quoted in Beach, D (1967) "The functions of the six-four chord in tonal music", ''Journal of Music Theory'', 11(1), p. 8</ref>
# In the second designation, this chord is ''not'' considered an inversion of a tonic triad<ref>{{Citation|last=Aldwell|first=Edward|title=Harmony and Voice Leading|page=263|year=1989|edition=2nd|place=San Diego, Toronto|publisher=[[Harcourt Brace Jovanovich]]|isbn=0-15-531519-6|oclc=19029983|quote=The chord does not act as an inversion of I {{su|p=5|b=3}}; it serves neither to extend it nor to substitute for it.|last2=Schachter|first2=Carl|author-link=Edward Aldwell|author2-link=Carl Schachter}} {{LCC|MT50 A444 1989}}.</ref> but as a dissonance resolving to a consonant dominant harmony.<ref>{{Citation|last=Forte|first=Allen|title=Tonal Harmony in Concept and Practice|page=68|year=1974|edition=2nd|place=NY|publisher=Holt, Rinehart and Winston|isbn=0-03-077495-0|author-link=Allen Forte}}.</ref> This is notated as {{nowrap|V{{su|p=6–5|b=4–3}}}}-I, in which the {{su|p=6|b=4}} is not the inversion of the V chord but a [[double appoggiatura]] on the V that resolves down by step to {{nowrap|V{{su|p=5|b=3}}}} (that is, {{nowrap|V{{su|p=6|b=4}}}}-V). This function is very similar to the resolution of a 4–3 [[Suspension (music)|suspension]]. Several modern textbooks prefer this conception of the cadential {{su|p=6|b=4}}, which can also be traced back to the early 19th century.<ref>Arnold, F.T. ''The art of accompaniment from a thorough-bass'', Vol. 1, p. 314. {{ISBN|0-486-43188-6}}. quoted in Beach, David (1967). "The functions of the six-four chord in tonal music", p.7, ''Journal of Music Theory'', 11(1).</ref>

=== Passing ===
In a progression with a passing second-inversion chord, the bass passes between two tones a third apart (usually of the same [[Harmonic function (music)|harmonic function]]<ref name="Gauldin">Gauldin, Robert (1997).  ''Harmonic Practice in Tonal Music''  New York: W.W. Norton & Company, pg 273. {{ISBN|0-393-97666-1}}</ref>). When moving from I to I{{music|6 chord}}, the [[passing chord]] V{{music|64}} is placed between them – though some prefer VII{{music|6 chord}} to V{{music|64}} – creating [[Stepwise motion|stepwise]] motion in the bass ([[scale degrees]] {{music|scale|1}} – {{music|scale|2}} – {{music|scale|3}}). It can also be used in the reverse direction: I{{music|6 chord}}-V{{music|64}}-I. The important point is that the V{{music|64}} chord functions as a passing chord between the two more stable chords. It occurs on the weaker beat between these two chords.<ref name="Gauldin" /> The upper [[Voice (music)|voices]] usually move in step (or remain stationary) in this progression.

:<score vorbis="1" lang="lilypond">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c'' {
                \stemUp \clef treble \key c \major \time 4/4
                g1 g g
                }
            \new Voice \relative c' {
                \stemDown
                e1 d c
                }
            >>
        \new Staff <<
            \new Voice \relative c' {
                \stemUp \clef bass \key c \major \time 4/4
                c1 b c
                }
            \new Voice \relative c {
                \stemDown
                c1 d e \bar "||"
                }
            >>
    >> }
</score>

=== Auxiliary (or pedal) ===
In a progression with an auxiliary (or pedal) second-inversion chord, the IV{{music|64}} chord functions as the harmonization of a [[neighbor note]] in the progression, I-IV{{music|64}}-I. In this progression, the third and fifth rise a step each and then fall back, creating a harmonization for the scale degrees {{music|scale|5}} – {{music|scale|6}} – {{music|scale|5}} in the top voice.

:<score vorbis="1" lang="lilypond">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c'' {
                \stemUp \clef treble \key c \major \time 4/4
                g1 a g
                }
            \new Voice \relative c' {
                \stemDown
                e1 f e
                }
            >>
        \new Staff <<
            \new Voice \relative c' {
                \stemUp \clef bass \key c \major \time 4/4
                c1 c c
                }
            \new Voice \relative c {
                \stemDown
                c1 c c \bar "||"
                }
            >>
    >> }
</score>

=== Bass arpeggiation ===
In this progression, the bass [[Arpeggio|arpeggiates]] the root, third, and fifth of the chord. This is just a florid movement but since the fifth is present in the bass, it is referred to as a bass arpeggiation flavour of the second inversion.{{Citation needed|date=October 2018}}

:<score vorbis="1" lang="lilypond">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c'' {
                \stemUp \clef treble \key c \major \time 4/4
                g1 g g
                }
            \new Voice \relative c' {
                \stemDown
                e1 e e
                }
            >>
        \new Staff <<
            \new Voice \relative c' {
                \stemUp \clef bass \key c \major \time 4/4
                c1 c c
                }
            \new Voice \relative c {
                \stemDown
                c1 e g \bar "||"
                }
            >>
    >> }
</score>

==See also==
{{div col}}
*[[Root position]]
*[[First inversion]]
*[[Third inversion]]
*[[Fourth inversion]]
{{div col end}}

==References==
{{reflist}}

==Further reading==
* Walter Piston, Harmony{{full|date=March 2014}}
* Aldwell and Schachter, Harmony and Voice Leading, 3rd Edition{{full|date=March 2014}}
{{Voicing (music)}}

[[Category:Harmony]]
[[Category:Voicing (music)]]
[[Category:Chords]]
[[Category:Chord factors]]