Diminished major seventh chord function

Question

I know that a diminished chord can function as a rootless dominant 7 b9 however i was curious as to how the diminished maj 7 chord functions. In the key of c a C dim maj 7 is spelled C Eb Gb B. Does this function as a B7 b9 with b9 in the bass? As a C dim with a B in the bass would be root position B7 b9 (if c is placed on top)

Answer 1

In the key of c a C dim maj 7 is spelled C Eb Gb B...

...Does this function as a B7 b9 with b9 in the bass?

There is a related question regarding ninth chords and inversions: How do you write a dominant ninth in fourth inversion?

Basically, you can't just re-arrange the tones and haphazardly omit tones to force it into something contrary to the obvious: it's a diminished triad with a major seventh. It doesn't sound like a dominant ninth chord in isolation.

To really say what the function is you need to know the next chord. But, putting it in C major provides some context where it does resemble a common tone diminished seventh chord, but instead of C Eb Gb Bbb the B is natural. A common tone diminished seventh chord often is just an embellishment of the tonic chord. So, the Eb and Gb would move up to E and G natural of a C triad. This diminished major seventh chord could have the B natural move up to C with more or less the same embellishing effect.

I know that a diminished chord can function as a rootless dominant 7 b9

That's a common harmony theory explanation. I think the point is to give viio7 a hypothetical root from V, because otherwise the symmetry of viio7 allows all four tones to be possible roots. But, you can sidestep that issue by focusing on the voice leading/scale degree perspective. In both V7 and viio7 scale tones TI and FA resolve to DO and MI respectively. Those two movements are the real heart of dominant function. Also, in the fully diminished seventh chord the diminished seventh steps down to the fifth of the tonic (scale degree ♭^6 to ^5) which is another important voice leading aspect. From this perspective the "rootless" notion of viio7 isn't important. Instead of looking for a hypothetical root for a V chord, we just need to know what is the leading tone. FWIW, the dominant functioning diminished seventh chord is often called the leading tone diminished seventh chord.

This has bearing on your question.

On the one hand, if C diminished major seven is supposed to be a dominant, its root C should be a leading tone and move like TI to DO. The TI and FA voice leading would then be C and Gb moving to Db and F. Deciding how to handle the B isn't clear, but that doesn't have direct bearing on the dominant function.

On the other hand, you might be able to get close to the B7b9 dominant idea with a bit of enharmonic re-spelling and using the leading tone diminished seventh chord. If B7b9 is the dominant, and the leading tone will be D#, and the target tonic will be Em. Accordingly, re-spell the chord enharmonically from C Eb Gb b to C D# F# B.

The full, root position viio7 leading to Em is D# F# A C. Resolution would be D# up to E, A down to G, C down to B.

Our chord in question isn't full and root position. It's 3rd inversion and missing A. C is the bass and the A is "altered" up to Ax/B - C D# F# Ax. It would "resolve" to B E G B. I put altered and resolve in quotes, because this harmony seems abnormal. But, it does have a leading tone resolution and scale degree ^6 resolving down to ^5. Of course, when you re-spell the chord this way to make the dominant function more clear, it becomes a sort of diminished seventh chord instead of a diminished major seventh.

So, decided what the next chord is and then spell this diminished chord in a way to make the function (embellishment versus dominant, etc.) clear.

---

Just to satisfy my own curiosity I tried some sequential harmony with these chords leading them as secondary dominants to diatonic seventh chords. I figured why not post them here?

Diminished major sevenths:

Inverted, "altered" diminished sevenths:

I hope I got all the spellings right, it's pretty tough spelling!

Answer 2

Why this chord works

Here's how to think about the theory, holistically: you can move any note of a diminished 7th chord up a whole step and retain its diminished functions. In so doing, you create a chord built off the whole-half diminished scale (and hence you rule out use of the half-whole diminished scale). No matter which chord tone you move up, the end result contains the notes of a major triad with a ♭9.

If we cycle through each tone in the diminished 7th chord, and move it up a whole step, we end up spelling out the entire whole-half diminished scale. For example, if we apply this trick to Cdim7 (C-E♭-G♭-B♭♭), then we end up with the entire C whole-half diminished scale: C-D-E♭-F-G♭-A♭-A-B.

Functions

If you see a C diminished 7th chord and you notice that the C whole-half diminished scale is an appropriate* fit for the chord, you can use C-E♭-G♭-B (which I'll call CdimΔ7) in place of C-E♭-G♭-B♭♭ (Cdim7). Here are some examples of where this dimΔ7 chord is used:

• The dimΔ7 chord is often used to delay resolution to a major I chord, as Michael Curtis says. For example, | Dmin | G7 | CMaj | turns into | Dmin | G7 | CdimΔ7 CMaj |. The BMaj triad resolves nicely up to a CMaj triad in the last measure.
• The dimΔ7 chord can also function as an altered dominant 7th chord, as you suggest. Specifically, you can voice B7alt using any of these: CdimΔ7, E♭dimΔ7, G♭dimΔ7, or AdimΔ7. However, doing so implies certain alterations to your B7 chord. But you will hear instances where all four dimΔ7 chords appear in sequence over a single altered dominant chord. For example, on m. 20-21 of Autumn Leaves are often voiced this way. Measure 20 usually has the chord A^ø7, but we're essentially extending D⁷alt backwards one measure:
• The dimΔ7 chord can work really well over a ♭VI chord. A classic example is m. 2 of the A section of Wave by Jobim. This results in the B♭ whole-half diminished scale, which contains all of the melody notes in measure 2.
• The dimΔ7 voicing can sound great over a ♯iidim chord. In fact, measure 12 of Night and Day implies this sort of voicing. The chord is written as E♭dim7, but the melody note for all of beat 1 is D--a full step above the last chord tone in E♭dim7.

These are just some examples. Instead of providing an exhaustive list, simply use the principle above: wherever you see a diminished 7th chord, try raising any one of the chord tones by a whole step and check to see if the resulting dimΔ7 chord sounds good. Much of the time, it will!

Voicing this chord

Raising the chord tone by a full step won't always produce an immediately cool chord voicing... C-E♭-G♭-B sounds a lot better than D-E♭-G♭-A. (Pardon my enharmonic spellings.) In jazz, other tricks are often employed at the same time, in order to open up the dimΔ7 voicing and make it sound good. This could entail inverting the resulting chord, applying a drop-2 technique to the resulting chord, etc.

^{*By "appropriate fit," I mean it works considering the preceding/following chords, it doesn't clash with the melody that occurs over the Cdim7 chord, etc.}

Answer 3

I guess you mean diminished 7th chord, not just a diminished triad?

Well, for a start, it's no longer a nice symmetrical choice of four dom7b9 chords, depending on which 'virtual root' you choose. Cdim7/D is D7b9. Cdim(maj7)/D is D13b9. That's OK, because we're shifting the 5th, the least important note on a dom7 shape chord. But rooted on B it just displaces the 7th of B7b9 to double the tonic, resulting in a rather weak chord. Rooted on F it's pleasantly Lydian, but I'd still rather have an A in the chord somewhere. And rooted on Ab we're getting into Hendrix territory!

But those are just SOME of the functions it might take. Out of context, we can name a chord but we can't really say what it DOES, what its function is, until we see it doing it! What's the function of a C major triad? Tonic in C? bIII in A major? major? Whats C7? Dom7 in F? Tonic in a C major blues? Something Lydian in Bb?