Why is V7->i considered a better resolution than others like vi dim->i in a minor scale?

Question

I've seen multiple sources and videos where V7->I (major) and V7->i (minor) are said to be the strongest resolutions. In the case of the minor scale, I hear vi dim->i (where vi is minor of b6) as the better resolution. They both have tritones but vi dim->i has 3 half-step (one down, two up) movements while V7 has 2 half-step (up) movements and 1 full-step (up) movement. Am I missing something? Did I understand this completely wrong?

Any explanation or extra theory is appreciated!

Edit: There has been a bit of focus on the names I have used to describe the chords. While I'm not an expert at theory at all, and while I'm interested in all the naming conventions (and their history), I want to know why one chord-progression sounds "better" to me than another does, and why music-theory videos/sources do not agree with me. I would like to read further answers that tackle the sound or feel of the two progressions.

1. C dim -> E minor and B 7 -> E minor are the progressions I want to compare. Call them however you want to (and correct me if I used the wrong names).

Edit 2: If a mod is reading the comments and the rest of the thread: If no further clarification is possible, I vote to close this post from future answers and comments. If you'd like me to delete the post instead, please let me know. Thanks!

Answer 1

It all depends on how you define the "strongest" resolution. If you're looking for minimal movement between the two chords, then there are chords other than V7 that move more smoothly to I.

But this voice-leading proximity is not what has made V7–I the de facto cadential resolution in Western art music. Rather, it's an outgrowth of several centuries of development: first we had single-line chants that often ended with a 2–1 cadential gesture, and then we had two lines that created an occursus (literally a "meeting") when the two voices moved in contrary motion to end on an octave or a unison (one voiced moved 7–1, the other 2–1). And then down the road composers started harmonizing this with a third voice, and following the rules of counterpoint, there was really only one pitch they could add in to that penultimate pair of 7 and 2: scale-degree 5, thereby creating 5–7–2, the dominant triad.

This is a quick-and-dirty summary of the situation, but I say it to show that V–I and V7–I are not privileged because their voice leading is smoothest. Like biological evolution, there are fits and starts to this developmental process, and when it's all said and done, not everything about the system is maximized for efficiency.

V7–I is the "strongest" resolution only because composers have decided it is so for centuries now. But there's nothing inherently stronger in that resolution than in another resolution that also has a tritone and equal voice leading. It's just that V7–I has been used so much that it has entered our collective cultural understanding as "the" cadence to use.

So no, you're not missing anything. It sounds like your sources are emphasizing smooth voice leading, which is correct. But this smooth voice leading has its limits; we want that smoothness, but not something so smooth that it disrupts the standard V7–I motion.

Answer 2

When I first read this question, I assumed that by vi dim you mean the diminished triad built on the raised sixth degree of the scale (for example, F♯-A-C in A minor). But then I read your description:

vi dim->i has 3 half-step (one down, two up) movements

That implies that you're asking about the chord F-A♭-C♭. But you're not really asking about that chord, because A♭ and C♭ don't resolve up to A and C; they resolve down to G and B♭. You're really asking about the chord F-G♯-B. And that is, as Albrecht Hügli describes, a vii°7 chord, albeit with the fifth omitted. The diminished seventh chord on the raised seventh degree is enharmonically equivalent to the diminished seventh chord on the natural sixth degree, but when resolving to the tonic, the former spelling is proper.

This cadence is indeed very common in the late baroque, but, as others have noted, movement by a descending fifth or ascending fourth in the bass is generally found to be stronger or more final than motion by an ascending half step or descending whole step. This cadence is therefore more likely to be found at intermediate points rather than at the end of a piece.

Answer 3

In addition to Richard's reply I would add that in traditional classical harmony some bass progressions are considered strong and some weaker. The bass descending a 5th - e.g. G descending to C in the key of C or C minor is considered the strongest progression. The diminished chord on the flattened sixth has no such strong bass progression. Now we are a few hundred years away from the Baroque and Classical periods our sense of harmony has changed. Composers started using harmony for the beauty of extended chords rather than just the functional aspects of harmonic progressions.

Answer 4

V7-I or V7-i (as mentioned in other answers) has developed over time as a very strong resolution. There are several intervallic movements happening simultaneously. Most of these evolved over time. (Using octave equivalency), there are simultaneous half and whole step movements to the tonic, 7-8 and 2-1; this comes from the medieval expansion of a major sixth to an octave. Also, the tritone 4-7 is resolved to 3-8 or the 7-4 interval resolves to 1-3 (augmented intervals expand and diminished intervals contract; depending on the chord voicing, either may happen.) In tonal music, root movement by fifths (5 to 1) are considered good; all the above occur at the same time.

Minor chords lack the half-step movement to the third; stylistically this whole step (b7 to 8) isn't as "final" sounding as a half-step movement.

Another point (though probably not as important) is that the V7 chord is the unique diatonic major-minor seventh in a given key and thus identifies that key. Then the tonic chord confirms the key (moving to a non-tonic chord such as V7-vi, a "deceptive" cadence isn't as final sounding again.)

There is nothing wrong with v-i in a piece, it just doesn't signal a cadence. In a minor key, a repeated cycle-of-fifths progression may usefully use both: i-iv-VII-III-VI-ii0-v-i-iv-VII-III-VI-ii0-V7-i allows two harmonically similar phrases but only the second sound cadential.

Answer 5

As far as I understand your question correct you mean with vi dim the dim seventh chord of the 6th degree which is actually the vii dim si,ti,re,fa, and dominant substitution (V7 or Vb9).

This is considered as a rootless V7 chord. The root would be the fifth (=dominant) of the tonic and has a strong tendency to resolve to the tonic.

What I actually played was in E minor: C-F#-C-D# to B-G-B-E as well as B-F#-A-D# to B-G-B-E. I'm still learning theory so I might make mistakes with semantics (saying Ab instead of G# and vice versa)...

Guitarists often use diminished 7th chords as substitutes for dominant 7th chords on the guitar. For example, you can play the typical cadence B-Em as D# dim - Em. In this case, the D# dim chord replaces B7.

This substitution works for a couple of reasons:

D#dim7 has many of the same notes as B: D#dim7 has D#, F#, A, C and B7 has B, D#, F# and A. (With the b9 it will have B, D#, F#, A, C. Notice the three respectively four notes they have in common: D#, F#, A, C. Basically, the D# dim7 chord is like an B7(b9) chord, except that it’s missing the root note B (the dominant) and in your example the fifth of D# dim is omitted.

D# dim contains the leading note of the chord of resolution; the D# is the leading note of E.

Edit:

I can't see a relation of vi dim to i if this iv dim isn't an inversion of an incomplete vii dim7 e.g. A-minor: F,G#,B = 3rd inversion of G#-B-(D)-F ... i.e omitted 5th

My original question was however about the sound of the resolution .

Now I hope to have convinced you that this isn‘t vidim - i but the dominant substitution vii dim ... why the resolution of the dominant substitution sounds stronger in your ear is an opinion based question.

May be in V-i we have just one leading tone (D#-E) but a strong 5th fall (B-E).

In your example C,D#,F#,C we gave 2 leading tones: 2x C-B, D#-E.

Maybe this „stronger“ resolution varies with the instrument and the chord pattern (position and shape on the neck) you are playing.

For further reading (and understanding the theory) you might look up

Cadence-Wikipedia

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