Second inversion

<score lang="lilypond"> {\override Score.TimeSignature#'stencil = ##f \relative c' {

  \clef treble 
  \time 4/4
  \key c \major

  <d g b>1

} }

</score>

A G-major triad in second inversion

The second inversion of a chord is the voicing of a triad, seventh chord, or ninth chord in which the fifth of the chord is the bass note. In this inversion, the bass note and the root of the chord are a fourth apart which traditionally qualifies as a dissonance. There is therefore a tendency for movement and resolution. In notation form, it may be referred to with a c following the chord position (e.g., Ic. Vc or IVc).Template:Sfn In figured bass, a second-inversion triad is a chord (as in I), while a second-inversion seventh chord is a chord.

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

1. '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

1. '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" } }
  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

There are four types of second-inversion chords: cadential, passing, auxiliary, and bass arpeggiation.

Cadential

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

1. In the first designation, the cadential chord features the progression: I-V-I. Most older harmony textbooks use this label, and it can be traced back to the early 19th century.
2. In the second designation, this chord is not considered an inversion of a tonic triad but as a dissonance resolving to a consonant dominant harmony. This is notated as V-I, in which the is not the inversion of the V chord but a double appoggiatura on the V that resolves down by step to V (that is, V-V). This function is very similar to the resolution of a 4–3 suspension. Several modern textbooks prefer this conception of the cadential , which can also be traced back to the early 19th century.

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). When moving from I to I ⁶, the passing chord V is placed between them – though some prefer VII ⁶ to V – creating stepwise motion in the bass (scale degrees scale degree 1 – scale degree 2 – scale degree 3). It can also be used in the reverse direction: I ⁶-V-I. The important point is that the V chord functions as a passing chord between the two more stable chords. It occurs on the weaker beat between these two chords. The upper 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 chord functions as the harmonization of a neighbor note in the progression, I-IV-I. In this progression, the third and fifth rise a step each and then fall back, creating a harmonization for the scale degrees scale degree 5 – scale degree 6 – scale degree 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 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.

<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

• Root position
• First inversion
• Third inversion
• Fourth inversion

References

Bibliography

Further reading

• Walter Piston, HarmonyTemplate:Full
• Aldwell and Schachter, Harmony and Voice Leading, 3rd EditionTemplate:Full