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Working through "Guide to practical harmony" of Tchaikovsky in chapter 9 about the inversions of diminished and augmented triads, we read that the first inversion of the diminished triad is consonant because the respective intervals between bass and the upper voices are all consonant.

Indeed in chord: D - B - D - F (major scale) we have major sixth (to B) and minor third (to F) from the bass voice. So we consider it to be a consonant chord, and we use the appropriate rules (and do not comply with the rules of dissonance being supported by consonances, resolution and so on).

The question is: why do we discard the diminished fifth between tenor and soprano (B - F)? Are the dissonances in upper voices considered to be less "dissonant" (sorry) as opposed to dissonances with the bass in common practice music?

An extreme example (+ a small question): What if we have a chord where two of upper voices form a minor and major third with a bass (which will be by a definition from the book a consonant chord, but is strongly dissonant). Is the catch here, that we are not diatonic anymore, or because it is not a triad?

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You're exactly right: we're more concerned with dissonances created with the bass and any upper voice than we are with dissonances created in the inner voices.

This is why diminished triads are basically always in first inversion; if they were in root position or second inversion, the bass would form a tritone with an upper voice. But in first inversion, that tritone is hidden in the upper voices.

Incidentally, it's why we can have fully diminished seventh chords in any inversion. Since it's a symmetrical chord, there's always going to be a tritone formed with whatever bass pitch you choose. So we just collectively realized we were screwed no matter what and allowed all inversions :-)

As for your final question, the logic breaks down because the pitches don't form a triad or seventh chord. But we see some of this logic already when we have, for instance, a V43 chord: the upper voices are consonance with the bass, but there's a dissonant second (or seventh) hidden in the upper voices.

  • Thanks Richard! But do the chords in such a position that upper voices form a dissonant interval between each other really sound more "stable" than if they form it with a bass (from a common practice period perspective). – NickQuant Sep 16 at 21:26
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    @NickQuant Fair question, but it's so hard to answer (with our modern ears) how these chords were perceived historically. This instance is especially hard to hear, since triadic structures are really slow developments from very early polyphonic music. Musicians back then certainly seemed to hear things this way. I think it's less an instance of us hearing it the same way and just being able to understand their perspective. – Richard Sep 16 at 21:34
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    Why are V6/5 chords so common, then, if their bass notes always produce tritones with their upper notes? – Dekkadeci Sep 16 at 23:27
  • @Dekkadeci As I was writing this answer, I knew someone would have this question :-) I admit I don't have a great answer, it's just the answer I typically hear and read in textbooks. Schenkerian theorists would insist that the seventh is really just a passing tone, and therefore perhaps the tritone is just incidental? – Richard Sep 16 at 23:29
  • @Dekkadeci are they common in Tchaikovsky? My first reaction to the question was "of course a first inversion diminished triad is dissonant, what on earth are you taking about?" But I mostly do baroque music, where V6/5 chords are terribly common, as are V4/2 chords, and, like diminished chords, are invariably used for their dissonance and are treated as dissonant. – phoog Sep 17 at 14:23

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