# 2.10: Fully-diminished Seventh Chords

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# 20.1 Introduction

Consider the particularly dissonant chord on the downbeat of m. 2 in the following excerpt:

This sonority, a fully-diminished seventh chord built on the leading tone of G minor, is comprised of two interlocking tritones, both of which resolve in the manner described in Chapter 16. The tritone between F# and C resolves inward to a third and the tritone between the A and Eb does the same. The chord reappears in mm. 3–4, though here the members have been rearranged. Each chord member resolves in the same way, but now the tritone between F# and C has been inverted and resolves outward to a sixth. The effect of these two chords is striking, but the voice-leading smooth and consistent with that seen in most tonal Western art music.

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# 20.2 Construction: viio7 in minor and viiø7 in major

In Chapter 16 we discussed the diminished leading-tone triad: viio. There, we examined why the tritone between the root and fifth of the chord requires special attention. The chord usually appears in first inversion precisely to avoid the dissonant interval sounding against the bass when viio is in root position.

As Example 20–2 demonstrates, placing the chord in first inversion ensures that the upper voices are consonant with the bass. The diminished fifth is between the alto and soprano, concealed within the upper voices. It is therefore best understood as a resultant interval formed by avoiding dissonances that involve the bass.

Leading-tone seventh chords (viio7 in minor and viiø7 in major) are even more dissonant than the triads on which they are based. The following example shows leading-tone seventh chords in both C minor and C major:

Both of these chords add a dissonant seventh to an already dissonant triad. In a minor key, the chordal seventh above a leading-tone triad forms a diminished seventh above the root. (See Example 18–16a.) This is a fully-diminished seventh chord. The prefix “fully-” refers to the fact that the chord is constructed of a diminished triad and a diminished seventh.

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As Example 20–4 demonstrates, every member of the chord forms a tritone with some other member. Regardless of the chord’s position, then, one of the tritones inevitably involves the bass:

Unlike the viio6 chord, where the single tritone can be hidden between upper voices, one of the two tritones in a fully-diminished chord will be accentuated by the bass and, as we will discuss momentarily, must be treated with care.

Activity 20-1

Activity 20–1

Identify the diminished fifths and augmented fourths in the following inverted fully-diminished seventh chords.

### Question

Which two pitches form the tritone between the root and fifth of the following fully-diminished seventh chord? Which two voices form the tritone between the third and seventh? (Keep in mind that a tritone may appear as a diminished fifth or in inversion as an augmented fourth.)

Tritone between root and fifth: G# (tenor) and D (alto)

Tritone between third and seventh: B (bass) and F (soprano)

### Question

Which two pitches form the tritone between the root and fifth of the following fully-diminished seventh chord? Which two voices form the tritone between the third and seventh? (Keep in mind that a tritone may appear as a diminished fifth or in inversion as an augmented fourth.)

Tritone between root and fifth: A# (soprano) and E (bass)

Tritone between third and seventh: C# (alto) and G (tenor)

### Question

Which two pitches form the tritone between the root and fifth of the following fully-diminished seventh chord? Which two voices form the tritone between the third and seventh? (Keep in mind that a tritone may appear as a diminished fifth or in inversion as an augmented fourth.)

Tritone between root and fifth: B§ (tenor) and F (bass)

Tritone between third and seventh: D (alto) and Ab (soprano)

### Question

Which two pitches form the tritone between the root and fifth of the following fully-diminished seventh chord? Which two voices form the tritone between the third and seventh? (Keep in mind that a tritone may appear as a diminished fifth or in inversion as an augmented fourth.)

Tritone between root and fifth: C# (tenor) and G (alto)

Tritone between third and seventh: E (bass) and Bb (soprano)

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# 20.3 Resolving a viio7 chord

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The following example shows a typical resolution of a viio7 chord to i in C minor:

In Example 20–7, the bass (B§) forms a diminished fifth with the tenor (F). As viio7 resolves to i, we can see this tritone contracting to a minor third (C and Eb). Likewise, the augmented fourth between the alto and soprano (Ab and D) expands to form a minor sixth (G and Eb). Note the resulting doubled third in the tonic, which is common after fully-diminished leading-tone chords. Typically, contrary motion of this sort is the favored method of resolving tritones. Composers will occasionally resolve a tritone using similar motion, but will frequently restrict such a progression to the upper voices.

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Note that in Example 20–8 the augmented fourth formed by the alto and soprano now resolves with similar motion to a perfect fourth.

Fully-diminished seventh chords resolve similarly in any position:

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Now consider the following example (Example 20–10b provides a reduction of mm. 5–6):

In m. 5 we encounter a fully-diminished seventh chord in second inversion. Looking at the left-hand part, we see that all of the voices resolve as expected. Both of the tritones appear as augmented fourths and expand outward by contrary motion to sixths: F and B§ move in contrary motion to Eb and C while Ab and D do the same, to G and Eb.

A very similar resolution may be found in the following excerpt:

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Activity 20-2

Activity 20–2

Resolve the following fully-diminished seventh chords according to the voice leading procedures outlined above.

### Question

To what chord would the following fully-diminished seventh in first inversion normally resolve to?

Hint

Which chord member is in the bass? To where does this pitch normally resolve?

i6

### Follow-up question

Resolve the fully-diminished seventh chord:

Hint

Remember to resolve all tendency tones in the usual manner.

### Question

To what chord would the following fully-diminished seventh in second inversion normally resolve to?

Hint

Which chord member is in the bass? To where does this pitch normally resolve?

i6

### Follow-up question

Resolve the fully-diminished seventh chord:

Hint

Remember to resolve all tendency tones in the usual manner.

(Alternatively, C# in the alto may resolve to B).

### Question

To what chord would the following fully-diminished seventh in third inversion normally resolve to?

Hint

Which chord member is in the bass? To where does this pitch normally resolve?

### Follow-up question

Resolve the fully-diminished seventh chord:

Hint

Remember to resolve all tendency tones in the usual manner.

### Question

To what chord would the following fully-diminished seventh in root position normally resolve to?

Hint

Which chord member is in the bass? To where does this pitch normally resolve?

I

### Follow-up question

Resolve the fully-diminished seventh chord:

Hint

Remember to resolve all tendency tones in the usual manner.

# 20.4 Resolving a viiø7 chord

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Activity 20-3

Activity 20–3

In this activity, you will be presented with a series of fully-diminished and half-diminished seventh chords. For each exercise you will be asked to identify the tritones and then resolve the chord to the tonic triad.

### Question

Identify the tritones in the viio7 chord:

Hint

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G# and D form a diminished fifth, while B and F also form a diminished fifth.

### Follow-up question

Now resolve the viio7 to i.

### Question

Identify the tritones in the viio7 chord:

Hint

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C# and G form a diminished fifth, while Bb and E form augmented fourth.

### Follow-up question

Now resolve the viio7 to i.

### Question

Identify the tritone in the viiø7 chord:

Hint

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C# and G form a diminished fifth.

### Follow-up question

Now resolve the viiø7 to I.

### Question

Identify the tritone in the viiø7 chord:

Hint

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D and Ab form a diminished fifth.

### Follow-up question

Now resolve the viiø7 to I.

# 20.5 viio7 chords in major keys

The sound of a fully-diminished leading-tone chord is both striking and immediately recognizable, a characteristic that composers will often exploit even when the chord does not belong to the key at hand. Unlike viiø7 chords, which typically appear only in major-key contexts, viio7 chords are commonly encountered in both major and minor. The following example shows the construction of the chord in C major and in C minor:

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The following example is in Ab major and includes several prominent fully-diminished leading tone sevenths:

The leading-tone chords on the downbeats of the opening bars in this excerpt all include Fb instead of F§. Combined with the suspended Cs in the right hand, these borrowed tones enhance the peculiar, dissonant character of the passage.

Activity 20-4

Activity 20–4

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### Question

Build a root position fully-diminished leading tone seventh chord in D minor.

Hint

Remember to raise the leading tone in minor.

(Answers may vary, provided C# is in the bass with E, G, Bb in the upper voices.)

### Question

Build a root position fully-diminished leading tone seventh chord in F major.

Hint

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(Answers may vary, provided E is in the bass with G, Bb,Db in the upper voices.)

### Question

Build a root position fully-diminished leading tone seventh chord in E minor.

Hint

Remember to raise the leading tone in minor.

(Answers may vary, provided D# is in the bass with F#, A, C in the upper voices.)

### Question

Build a root position fully-diminished leading tone seventh chord in G major.

Hint

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(Answers may vary, provided F# is in the bass with A, C, Eb in the upper voices.)

# 20.6 Diminished-seventh chords as dominant substitutes

As its name indicates, the leading-tone seventh chord includes the leading tone as its root. As discussed in Chapter 19, the leading tone is an important member of the dominant seventh chord. The similarity between these two chords, however, does not end here. The following example compares dominant seventh chords with fully-diminished leading-tone chords in both C major and C minor:

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Notice the similarity between the V7 and viio4/3 chords in m. 8 of the following excerpt:

In the first half of m. 8 we see a dominant seventh chord with pitch classes E, G#, B, and D. In the second half of the same measure, after beat three, the D is transferred down an octave while the G# and B are held in place. The root of the V7 chord (E) steps up to form the seventh of the viio4/3 (F).

# 20.7 Summary

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This page titled 2.10: Fully-diminished Seventh Chords is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Andre Mount & Lee Rothfarb (Milne Library Publishing) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.