Second Inversion
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Second Inversion
 {\override Score.TimeSignature#'stencil = ##f
\relative c' {
   \clef treble 
   \time 4/4
   \key c \major

   <d g b>1
} }
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 is referred to with a c following the chord position (For e.g., Ic. Vc or IVc)[] or as a 6
4
chord (as in I6
4
).

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.


{
\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" } }
   }
}

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


{
\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" } }
   }
}

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 I6
4
-V-I, or one of its variation, like I6
4
-V 7-I. In this form, the chord is sometimes referred to as a cadential 6
4
chord. The chord preceding I6
4
is most often a chord that would introduce V as a weak to strong progression, for example, making -II-V into II-I6
4
-V or making IV-V into IV-I6
4
-V.


    {
      \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 "||"
                }
            >>
    >> }

The cadential 6
4
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 6
    4
    chord features the progression: -V-I. Most older harmony textbooks use this label, and it can be traced back to the early 19th century.[1]
  2. In the second designation, this chord is not considered an inversion of a tonic triad[2] but as a dissonance resolving to a consonant dominant harmony.[3] This is notated as -I, in which the 6
    4
    is not the inversion of the V chord but a double appoggiatura on the V that resolves down by step to (that is, -V). This function is very similar to the resolution of a 4-3 suspension. Several modern textbooks prefer this conception of the cadential6
    4
    , which can also be traced back to the early 19th century.[4]

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[5]). When moving from I to I 6, the passing chord V6
4
is placed between them - though some prefer VII 6 to V6
4
- 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-V6
4
-I. The important point is that the V6
4
chord functions as a passing chord between the two more stable chords. It occurs on the weaker beat between these two chords.[5] The upper voices usually move in step (or remain stationary) in this progression.


    {
      \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 "||"
                }
            >>
    >> }

Auxiliary

In a progression with an auxiliary second-inversion chord, the IV6
4
chord functions as the harmonization of a neighbor note in the progression, I-IV6
4
-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.


    {
      \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 "||"
                }
            >>
    >> }

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.[]


    {
      \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 "||"
                }
            >>
    >> }

See also

References

  1. ^ 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
  2. ^ Aldwell, Edward; Schachter, Carl (1989), Harmony and Voice Leading (2nd ed.), San Diego, Toronto: Harcourt Brace Jovanovich, p. 263, ISBN 0-15-531519-6, OCLC 19029983, The chord does not act as an inversion of I 5
    3
    ; it serves neither to extend it nor to substitute for it.
    LCC MT50 A444 1989.
  3. ^ Forte, Allen (1974), Tonal Harmony in Concept and Practice (2nd ed.), NY: Holt, Rinehart and Winston, p. 68, ISBN 0-03-077495-0.
  4. ^ 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).
  5. ^ a b Gauldin, Robert (1997). Harmonic Practice in Tonal Music New York: W.W. Norton & Company, pg 273. ISBN 0-393-97666-1

Further reading

  • Walter Piston, Harmony[full ]
  • Aldwell and Schachter, Harmony and Voice Leading, 3rd Edition[full ]

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