3.5 Seventh-chord inversions and figures

3.5 Seventh-chord inversions and figures

A seventh chord can keep exactly the same four pitches while its bass changes, so the ear may hear a new bass line without hearing a new harmony. Seventh-chord inversion identifies which chord member is in the bass; figured bass records the intervals above that bass note.

PIT-2.D.1: Seventh chords have the potential for a third inversion in which the chordal seventh appears in the bass.

The inversion map

For a seventh chord, the figure names the intervals above the bass. The Roman numeral identifies the chord’s root and scale-degree function; the Arabic figures identify its inversion.

Bass position	Chord member in bass	Standard figure	Example using $G^7 = G$–$B$–$D$–$F$
Root position	Root	$7$ or omitted in some contexts	Bass $G$: $V^7$
First inversion	Third	$6/5$	Bass $B$: $V^{6/5}$
Second inversion	Fifth	$4/3$	Bass $D$: $V^{4/3}$
Third inversion	Seventh	$4/2$ or $2$	Bass $F$: $V^{4/2}$

Read the bass before reading the figure

The fastest reliable procedure is: identify the bass pitch, read the figure, build the chord above that bass, then determine the chord root and Roman numeral. Do not assume that the lowest note is the root.

Suppose the bass note is $F$ with the figure $4/2$ in the key of $C$ major. The intervals above $F$ must be a fourth, sixth, and second: $B$, $D$, and $G$. The complete sonority is $F$–$G$–$B$–$D$, which rearranges to $G$–$B$–$D$–$F$. Therefore the analysis is $V^{4/2}$: a dominant seventh chord in third inversion.

A bass note with figure $6$ is different. In the ordinary diatonic context, $6$ indicates a first-inversion triad, not a seventh chord. Thus, in a minor key, a bass $B\flat$ with figure $6$ can represent $i^6$: the tonic triad with its third in the bass. The missing $3$ is conventionally understood in a simple triadic figure.

Why $6/5$ means first inversion

For a seventh chord in first inversion, the bass is the chordal third. From that bass, the remaining chord members normally form the intervals $3$, $5$, and $6$, producing the compact figure $6/5$.

For example, if the chord is $A$–$C$–$E\flat$–$G$, then $A$ is the root. With $A$ in the bass, the chord is root position and should be represented by $7$. To create first inversion, place $C$ in the bass: $C$–$E\flat$–$G$–$A$. The resulting analysis is $A^{6/5}$, because $C$ is the third of the A seventh chord.

Misconception check: A figure $6/5$ does not mean “the bass note is the root.” It means the bass is the third of a seventh chord.

A complete Roman-numeral example

Consider this progression in $A$ minor:

$$I - I^6 - ii^7 - ii^{6/5} - V^7 - V^{4/2} - i$$

The first two sonorities may contain related tonic pitches but differ in bass placement. Likewise, $ii^7$ and $ii^{6/5}$ can contain the same four chord members while the bass changes from the root to the third. In harmonic dictation, listen for whether the harmony changes or whether only its inversion changes.

A useful listening question is: “Can I rearrange the notes of the second sonority into the same chord as the first?” If yes, the chord may be unchanged in a new inversion. If the pitch collection or function changes, the Roman numeral changes as well.

Sing the dominant seventh in every inversion

In $C$ major, the dominant seventh is $G$–$B$–$D$–$F$. Practice its arpeggio by rote in four bass arrangements:

$$G-B-D-F \quad (V^7)$$

$$B-D-F-G \quad (V^{6/5})$$

$$D-F-G-B \quad (V^{4/3})$$

$$F-G-B-D \quad (V^{4/2})$$

Singing these patterns makes inversion an audible event rather than a memorized symbol. It also supports melodic dictation: melodies may outline tonic and dominant triads, while compound meter changes how those arpeggiated pitches are grouped rhythmically.

Third-related dissonance

A seventh chord can contain a third-related dissonance: two chord members separated by a third may sound unstable when heard within the complete seventh-chord sonority. The added seventh changes the chord’s color and often creates a need for resolution, especially in dominant-function harmony.

This is why a seventh chord should not be treated as “just a triad with one extra note.” Its inversion changes the bass support, its figure changes, and its dissonant tendency may become more or less prominent depending on register and context.

Retrieval check

A bass note $D$ with figure $4/3$ appears in a $G$-dominant seventh chord. Name the inversion and the Roman numeral. Then answer: if the next sonority contains the same four pitches but puts $B$ in the bass, has the chord necessarily changed?

Answer: $D$ is the fifth of $G$–$B$–$D$–$F$, so the chord is $V^{4/3}$, a second-inversion dominant seventh. Moving the bass to $B$ produces $V^{6/5}$; the inversion changes, but the chord may remain the same.