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:

Example 20–1 Joseph Haydn, String Quartet in G major (Op. 17, No. 5 Hob.III 29), III. Adagio, mm. 1-14.

example_20-1

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.

\[\hat7\]

20.2 Construction: vii^o7 in minor and vii^ø7 in major

In Chapter 16 we discussed the diminished leading-tone triad: vii^o. 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 vii^o is in root position.

Example 20–2.

example_20-2

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 (vii^o7 in minor and vii^ø7 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:

Example 20–3.

example_20-3a

example_20-3b

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.

\[\hat7\]

Example 20–4.

example_20-4

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:

Example 20–5.

example_20-5

Unlike the vii^o6 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.

Exercise 20–1a:

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.)

activity_20-1a

Answer

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

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

Exercise 20–1b:

Question

activity_20-1b

Answer

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

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

Exercise 20–1c:

Question

activity_20-1c

Answer

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

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

Exercise 20–1d:

Question

activity_20-1d

Answer

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

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

\[\hat6\]

20.3 Resolving a vii^o7 chord

\[\hat7\]

Example 20–6.

example_20-6

\[\hat4\]

\[\hat2\]

The following example shows a typical resolution of a vii^o7 chord to i in C minor:

Example 20–7.

example_20-7

In Example 20–7, the bass (B§) forms a diminished fifth with the tenor (F). As vii^o7 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.

\[\hat1\]

\[\hat6\]

Example 20–8.

example_20-8

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:

Example 20–9.

example_20-9

\[\hat6\]

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

Example 20–10. Ludwig van Beethoven, Piano Sonata No. 8 [“Pathétique”] (Op. 13), III. Rondo, mm. 1–8.

a. original:

example_20-10a

b. reduction:

example_20-10b

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:

Example 20–11. Louise Reichardt, “Durch die bunten Rosenhecken,” mm. 1-8.

a. original:

example_20-11a

b. reduction:

example_20-11b

\[\hat2\]

Activity 20-2

Activity 20–2

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

Exercise 20–2a:

Question

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

activity_20-2a

Hint

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

Answer

Follow-up question

Resolve the fully-diminished seventh chord:

activity_20-2a

Hint

Remember to resolve all tendency tones in the usual manner.

Answer

activity_20-2a_answer2

Exercise 20–2b:

Question

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

activity_20-2b

Hint

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

Answer

Follow-up question

Resolve the fully-diminished seventh chord:

activity_20-2b

Hint

Remember to resolve all tendency tones in the usual manner.

Answer

activity_20-2b_answer2

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

Exercise 20–2c:

Question

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

activity_20-2c

Hint

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

Answer

cadential 6/4 or auxiliary 6/4

Follow-up question

Resolve the fully-diminished seventh chord:

activity_20-2c

Hint

Remember to resolve all tendency tones in the usual manner.

Answer

activity_20-2c_answer2

Exercise 20–2d:

Question

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

activity_20-2d

Hint

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

Answer

Follow-up question

Resolve the fully-diminished seventh chord:

activity_20-2d

Hint

Remember to resolve all tendency tones in the usual manner.

Answer

activity_20-2d_answer2

20.4 Resolving a vii^ø7 chord

\[\hat4\]

Example 20–12.

example_20-12

\[\hat2\]

Example 20–13.

example_20-13

\[\hat2\]

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.

Exercise 20–3a:

Question

Identify the tritones in the vii^o7 chord:

activity_20-3a

Hint

\[\hat7\]

Answer

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

Follow-up question

Now resolve the vii^o7 to i.

Answer

activity_20-3a_answer

Exercise 20–3b:

Question

Identify the tritones in the vii^o7 chord:

activity_20-3b

Hint

\[\hat7\]

Answer

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

Follow-up question

Now resolve the vii^o7 to i.

Answer

activity_20-3b_answer

Exercise 20–3c:

Question

Identify the tritone in the vii^ø7 chord:

activity_20-3c

Hint

\[\hat7\]

Answer

C# and G form a diminished fifth.

Follow-up question

Now resolve the vii^ø7 to I.

Answer

activity_20-3c_answer

Exercise 20–3d:

Question

Identify the tritone in the vii^ø7 chord:

activity_20-3d

Hint

\[\hat7\]

Answer

D and Ab form a diminished fifth.

Follow-up question

Now resolve the vii^ø7 to I.

Answer

activity_20-3d_answer

20.5 vii^o7 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 vii^ø7 chords, which typically appear only in major-key contexts, vii^o7 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:

Example 20–14.

example_20-14

\[\hat6\]

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

Example 20–15. Frédéric Chopin, Mazurkas (Op. 17), mm. 1–8.

example_20-15

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

\[\hat6\]

Exercise 20–4a:

Question

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

activity_20-4a

Hint

Remember to raise the leading tone in minor.

Answer

activity_20-4a_answer

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

Exercise 20–4b:

Question

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

activity_20-4b

Hint

\[\hat6\]

Answer

activity_20-4b_answer

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

Exercise 20–4c:

Question

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

activity_20-4c

Hint

Remember to raise the leading tone in minor.

Answer

activity_20-4d_answer

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

Exercise 20–4d:

Question

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

Hint

\[\hat6\]

Answer

activity_20-4d_answer

(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:

Example 20–16.

example_20-16

\[\hat7\]

Notice the similarity between the V7 and vii^o4/3 chords in m. 8 of the following excerpt:

Example 20–17 Carlota Ferrari, 6 Melodie, 5. “Son figliuola d’una fata,” mm. 6-9.

a. original:

example_20-17a

b. reduction:

example_20-17b

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 vii^o4/3 (F).

20.7 Summary

\[\hat7\]

20.1 Introduction

20.2 Construction: viio7 in minor and viiø7 in major

Exercise 20–1a:

Question

Exercise 20–1b:

Question

Exercise 20–1c:

Question

Exercise 20–1d:

Question

20.3 Resolving a viio7 chord

Exercise 20–2a:

Question

Follow-up question

Exercise 20–2b:

Question

Follow-up question

Exercise 20–2c:

Question

Follow-up question

Exercise 20–2d:

Question

Follow-up question

20.4 Resolving a viiø7 chord

Exercise 20–3a:

Question

Follow-up question

Exercise 20–3b:

Question

Follow-up question

Exercise 20–3c:

Question

Follow-up question

Exercise 20–3d:

Question

Follow-up question

20.5 viio7 chords in major keys

Exercise 20–4a:

Question

Exercise 20–4b:

Question

Exercise 20–4c:

Question

Exercise 20–4d:

Question

20.6 Diminished-seventh chords as dominant substitutes

20.7 Summary

20.2 Construction: vii^o7 in minor and vii^ø7 in major

20.3 Resolving a vii^o7 chord

20.4 Resolving a vii^ø7 chord

20.5 vii^o7 chords in major keys