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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!

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    Can you point to an example of a piece that employs this cadence?
    – phoog
    Mar 3 at 15:20
  • or could you write the tones you're playing with vi dim in a-minor or c-minor and tell the resolution of the single notes? Mar 3 at 15:22
  • @AlbrechtHügli In A minor, V7 -> i would be E-B-D-G# going up to A-E-A-C on the same strings on the guitar. Whereas vi dim -> i would be F-B-F-G# going up to A-E-A-C in the same way.
    – Aditya
    Mar 3 at 20:55
  • But this isn‘t vi dim. vi dim is F,Ab,Cb. Yes, F resolves to E, Cb to A? and Ab to ??? Mar 3 at 22:09
  • 3
    @AlbrechtHügli your comment asked for "could you write the tones you're playing with vi dim in a-minor or c-minor and tell the resolution of the single notes?" and hence I specified the corresponding chords in A minor off the top of my head. 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). My original question was however about the sound of the resolution.
    – Aditya
    Mar 3 at 22:31
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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.

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  • Thanks for your explanation! I didn't think of the historical/cultural factor in this cadence. This might be a noob question, but could you clarify what you meant by something so smooth that it disrupts the standard V7 I motion ? Does vi dim -> i fall under this?
    – Aditya
    Mar 3 at 13:05
  • @aditya I basically mean that "something that resolves more smoothly than a V7 isn't automatically better than a V7," and yes, the vi dim would be included in that statement.
    – Richard
    Mar 3 at 13:52
  • Richard, you are discussing the strong V-i function, but you don‘t say anything about vi dim - i. What sense does it make to have a chord like F,Ab,Cb in a-minor. Imho this is a misinterpretation of an incomplete vii dim 7. Mar 3 at 19:07
  • @AlbrechtHügli I didn't address that because it was unclear which scale-degree 6 this diminished chord had as the root. (That's since been addressed in an edit.) The original version of the question highlighted the V7–I aspect a bit more, which is what I tried to answer.
    – Richard
    Mar 4 at 0:59
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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.

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  • 1
    1. A♭ and C♭ don't resolve up to A and C; they resolve down to G and B♭. This point flew over my head, I don't understand why they don't resolve up. Could you point me to a source I can read up on? 2. when resolving to the tonic, the former spelling is proper: Is this even when the bass moves from F up to A? (I am imagining an F-B-F-G# barre chord moving up to A-E-A-C)
    – Aditya
    Mar 3 at 16:04
  • This is because you probably hear F,G#,B, resolving to E, A,C (dim vii7 of Am) and not F, Ab,Cb, . s(. my comment to your question and my answer.) Mar 3 at 16:38
  • @aditya 1. this is perhaps a subject for a different question, and my answer to it would be more historical and based on medieval/renaissance theory than most. A shorter more modern answer is that resolution should involve changing the pitch letter, or, roughly equivalently, sharps resolve upward and flats resolve downward. Motion from A♭ to A will normally be a chromatic alteration that creates an unstable chord rather than a resolution to a stable one. 2. Yes, in functional theory, any dominant-function chord in A minor that includes the leading tone should spell it as G♯ rather than A♭.
    – phoog
    Mar 3 at 17:28
  • @Aditya by contrast, if the final chord is a m7 chord, and some voice moves down a semitone from the leading tone to the minor seventh, then it may make sense to spell the "leading tone" as an A♭, making the chord an F dim chord. But now we're moving well into the realm of jazz theory, because common-practice functional harmony would not have a final cadence on a tonic minor seventh chord. This is probably a good example of one reason for jazz being less concerned about "proper" enharmonic spelling than is classical theory.
    – phoog
    Mar 3 at 17:35
  • @phoog I think I misunderstood your point in your original answer. The diminished seventh chord on the raised seventh degree is enharmonically equivalent to the diminished seventh chord on the natural sixth degree. -- In this case why not call it vi dim instead of vii dim 7? Especially given the fact that the notes F-G#-B make up 75% of vii dim7 but make up the entire vi dim?
    – Aditya
    Mar 3 at 18:43
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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.

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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.

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  • Could you tell us something about the strange progression vi dim - i which sounds better than V7 - i in OP‘s ear? Mar 4 at 6:04
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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

enter link description here

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  • No, I did not talk about vi dim7. I don't see how vi dim is actually a rootless V7, I consider a dim chord on the guitar to have the same root it's based on, at least the way I play it. I understand your point about the 5->1 movement, which is also what Ian Stewart talked about.
    – Aditya
    Mar 3 at 14:20
  • Even though I can't see a relation of vi dim to i if this iv dim isn't an inversion of vii dim - e.g. A-minor - G#-B-(D)-F ... i.e without the 5th... Mar 3 at 15:19
  • I can understand the equivalence between vi dim and vii dim7. But in your original answer you say vi dim is the same as a rootless V7, if I'm right. But vi dim or vii dim7 would be F-G#-B-(D) whereas a rootless V7 would be (E)-B-D-G# in A minor. In this case I don't see how V7 and vi dim are the same. Hence your answer does not clarify my original question about vi dim (vii dim7) -> i and V7 -> i.
    – Aditya
    Mar 3 at 20:33
  • No, I say vi dim is actually vii dim7 without fifth. It doesn‘t make sense to me to apply Roman numbers discussing about leading tones leading nowhere. Where goes Ab in a-minor? Mar 3 at 22:19
  • I have already acknowledged the equivalence between vi dim and vii dim7. Consider those notes however you want, but you still have talked about V7 in your original answer. I suggest you clarify how V7 is the same as vii dim7 or vi dim, or otherwise edit your original answer, since it doesn't respond to my question directly. Either your post does not answer the difference between the two resolutions I asked about, or I am missing a lot of information in order to understand your point.
    – Aditya
    Mar 3 at 22:42

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