Dissonances with bass versus in upper voices. 4-part harmony

Question

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?

Answer 1

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.

Answer 2

This is constructed from memories of readings in music history, so it might not be historically accurate.

Theorists in the early late Middle Ages were concerned with intervals rather than chords per se. There were three classes of intervals: perfect intervals, unison, octave, fifth, abd fourth (but see comment infra); imperfect, all major and minor thirds and sixths; and dissonance, all seconds, sevenths, augmented intervals, diminished intervals, and the tritone (could be subsumed as augmented or diminished). The fourth was sometimes treats as dissonant under some circumstances. There were only 12 intervals without considering enharmonics, but in practice, enharmonics were treated as I equivalent (they still are).

Thicker textures were being composed suing 3 or more different notes so the idea of chords as Sui generics arose rather than only analysing these as unions of intervals. Based on practice theorists started analyzing chords.

Sometimes triads were analyzed as containing 3 intervak, sometimes the 2 intervals over the bass were used. Only major and minor chords and their first inversion gave all consonant intervals. Th 6-4 chord has a fourth against the bass and was considered dissonant (still is, but with different analysys). One effect was to make first inversion diminished triads consonant.

Mostly treating triads as basic structures leads to fewer things to analyze than checking out all intervals whereas 4-note chords are always dissonant. CPP harmony analyzes 4-note chords but allows some unprepared dissonance. Unresolved dissonance are not wrong, just unresolved.