Voice Leading and Diminished Triads Diminished triads are a special case, behaving partly like motion by fifth and partly like motion by second. The prototype is the chord, which resolves to the chord. Strictly speaking, this is motion by second. However, it is generally more convenient to imagine the chord as the three upper notes of a dominant seventh chord – they behave in essentially the same way. A diminished triad should rarely ever appear in root position, because of the diminished fifth that frames it. Instead, it almost always appears in first inversion. And, unlike other triads, doubling the third is the ideal doubling, because it does not participate in the diminished fifth (both tones of which have strong resolution tendencies); one great advantage of this is that there can be a complete triad in the upper three voices, which simplifies voice leading – however, beware of the parallel octaves on the way out! The doubled third must be split so that the two voices move in opposite directions.
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Getting into a diminished triad is generally easier than other triads: since it does not have a perfect fifth, parallel fifths are not a problem – parallel octaves are still an issue, however. As a rule, the best option (as is often true of root motion by second) is usually to move the upper voices together, in the opposite direction from the bass, but other methods are also quite common. The standard resolution of a diminished fifth is inwards by step in both voices. The leading tone, which is the root of the chord, must always resolve upwards, just as it does in dominant chords (but, unlike dominant chords, it is immaterial whether the leading tone appears in the outer voices or the inner voices; it must resolve either way). For the same reason, the chordal fifth should normally step downwards; in part, this is because the diminished fifth would otherwise resolve to a perfect fifth by similar motion (however, it corresponds to the seventh of a dominant seventh chord, which always resolves downward; this is a convenient way to remember this). The chordal third, which is usually doubled, then splits: the one in the bass must resolve by step to the next bass note (be it upwards or downwards – both are common); the other may move to either of the remaining chord tones. This procedure may create doubled thirds, which are allowed in this case (but this tends to be better in the minor key than a major key); however, you must be careful in the resolution to avoid parallel octaves. The other possibility is by skip up to the fifth, which creates a complete chord.
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The most common use of is to fill the gap between and in either direction – as a kind of substitution for the dominant, it rarely moves to any chord other than or its inversions.
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Complete the following progressions, according to the indicated preference:
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Note that the opening chords here have doubled fifths – remember that this is one of the two typical ways of preventing parallel octaves with first-inversion triads.
Augmented Fourths There are two exceptions to the rules given above. First, when the diminished fifth is inverted so that it appears as an augmented fourth, the chordal fifth need not resolve down, since the parallels become fourths, rather than fifths (and there is no prohibition about similar motion to a fourth). However, it is still generally desirable for it to resolve downward unless there is a good reason not to.
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Complete the following progressions by resolving upwards if allowed; cross out the measure if the upwards resolution of is not allowed.
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Third-Progressions
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The second exception also occurs as an exception to the descending seventh of a chord (to which the chord is nearly identical). Recall that the alternation between a tonic and a dominant ( functions as a dominant, even though it doesn’t contain the dominant tone) provides and opportunity for the highly valued – – progression in the soprano. If this third-progression is instead placed in the bass, it can be harmonised by the chord progression – – . Then, the soprano can carry another third-progression, in parallel tenths, as – – . In this harmonisation, the fifth of the diminished triad (which is ) does not progress downward, but upwards. However, since the parallel tenths rising from the tonic is an extremely favoured progression, it is permitted to overrule the expected resolution of the diminished fifth.
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Complete the following progressions using parallel tenths between soprano and bass:
In the Minor Key The leading-tone diminished triad created by the harmonic minor poses no new problems. But there is also a diminished triad on the second scale degree, and while nearly every diminished triad resolves up by step, normally resolves by fifth to . In this progression, the diminished fifth cannot resolve regularly, because the note to which the root should step up does not exist in the subsequent chord; since the root cannot resolve correctly, it becomes that much more important for the fifth to resolve downwards, as expected; the Common-Tone method is not ideal for this (nor is the Tertian Leap, since the third is in the bass must resolve up by step instead of leaping to the new third). The Similar Motion method is ideal (and note that the melodic diminished third is okay here). The Triple-Root method is also possible, but leaves the resulting dominant chord in an awkward voicing. This is another circumstance in which doubling the fifth is a useful compromise.
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Complete the following progressions, using the method indicated:
