Theory & Impro Relationship between Diminished & Dominant Chords

[JSL]

For some time, I was a bit confused over how & why patterns based on the “half/whole” diminished scale could be used over a dominant chord. I’ve since discovered the relationships between them. Here’s an analysis that hopefully sheds some light on this, with a mention of some practical applications (I'll try to be concise). I’ll use a G7 chord and its associated G half/whole diminished scale as an example.

G7 with extensions: G B D F A C E (1 3 5 b7 9 11 13).

G half/whole dim scale: G Ab Bb B C# D E F.

So how does that scale relate to G7? The first thing to notice is that this diminished scale can be viewed as two diminished chords, a half step apart:

G Bb C# E and Ab B D F (for purposes below, I’ll use the inversion: B D F Ab)

Now we can analyze the chord tones in those two diminished chords in terms for G7.

G Bb C# E in G7 is the root, followed by three extensions: 1 #9 #11 13. Technically the #11 is A#; I’m using the enharmonic, Bb, because it is also the b3 (explained below).

B D F Ab in G7 is 3 5 b7 b9.

So, what we have is a G7 chord with four extensions: b9 #9 #11 13. Note that the #9 is also the b3 (hence Bb) and the #11 is the b5. But since the major 3 and 5 are also present in the chord those altered tones are extensions, built in the ‘higher reaches’ of the chord.

That’s it, in a nutshell. So what? You may be asking. There is a practical application to all of this. First off, it really helps to use a keyboard to see how it all fits together and most importantly how it sounds. If you play either of those two diminished chords over a G7 chord on the keyboard, you’ll hear how they fit in very nicely, with some beautiful tension. The tension wants to be released and you can resolve any of those chords (G7 or either of the two diminished chords) to a C major chord. Try that on the piano; play each of those diminished chords followed by Cmaj7. It works well over the ii-V7 part of the ii-V7-I progression, resolving to the I chord, or on any V7-I cadence.

Playing them on the sax, you can use arpeggios, single note lines, diminished patterns, etc. based on any or all those chords or the related diminished scale.

Speaking of the ii-V7 progression, the ii & V7 chords are interchangeable because they share the same chord tones (the ii chord, D F A C is 5 7 9 11 in G7). So, you can also play those diminished chords over both the ii & V7 chords. Try it on the keyboard and see.

There's quite a bit more to say on the diminished chord, but I'll stop here for now.

 

[progger]

Quite a bit more indeed! But that's some good stuff, and in any event, we can hear the cozy relationship between diminished and dominant harmonies as far back as Bach and Vivaldi, or maybe even earlier.

A concept I find useful, and that I work on with my composition students from time to time, is that chords in much of western music seem to find themselves in three fundamental "jobs," or maybe "teams." (I'm sure "function" would be more academic.) (And For brevity I'll keep it to major tonality, but these things can apply just as well to minor, or modal interchange.) On "Team Tonic" we have our I chord along with its common substitutes, III and vi; on "Team Subdominant" we have our IV chord, of course, and its close cousin, the ii chord; and finally, we have the source of all the drama, "Team Dominant." That's V... and vii... the diminished champion. (We don't get a fully diminished seventh chord without a bit of non-diatonic chromaticism, except in harmonic minor modality, but that's probably one of the most common uses of chromaticism we see in western music, I'd imagine.)

 

[Dr G]

Quite a bit more indeed! But that's some good stuff, and in any event, we can hear the cozy relationship between diminished and dominant harmonies as far back as Bach and Vivaldi, or maybe even earlier.

A concept I find useful, and that I work on with my composition students from time to time, is that chords in much of western music seem to find themselves in three fundamental "jobs," or maybe "teams." (I'm sure "function" would be more academic.) (And For brevity I'll keep it to major tonality, but these things can apply just as well to minor, or modal interchange.) On "Team Tonic" we have our I chord along with its common substitutes, III and vi; on "Team Subdominant" we have our IV chord, of course, and its close cousin, the ii chord; and finally, we have the source of all the drama, "Team Dominant." That's V... and vii... the diminished champion. (We don't get a fully diminished seventh chord without a bit of non-diatonic chromaticism, except in harmonic minor modality, but that's probably one of the most common uses of chromaticism we see in western music, I'd imagine.)

Am I missing something or is that a typo regarding "III" on Team Tonic? The diatonic chord on the third is iii. No?

 

[progger]

Sorry, just a typo – yes, iii minor! (Although using upper-case vs lower-case roman numerals based on the quality of the third isn't standardized... but it's what I normally do, so I should at least stay consistent within my own nomenclature, I suppose.)

 

[skeller047]

I have analyzed the tonic / subdominant / dominant harmony nomenclature thusly:

If the chord doesn’t contain the 4th degree of the scale, it’s tonic
If the chord contains the root AND the fourth, it’s subdominant
If the chord contains the fourth and NOT the root, it’s dominant

This allows one to analyze odd chords, or ambiguous chords, by function. It’s useful sometimes 🙂

 

[JSL]

I have analyzed the tonic / subdominant / dominant harmony nomenclature thusly:

If the chord doesn’t contain the 4th degree of the scale, it’s tonic
If the chord contains the root AND the fourth, it’s subdominant
If the chord contains the fourth and NOT the root, it’s dominant

This allows one to analyze odd chords, or ambiguous chords, by function. It’s useful sometimes 🙂

Seems like a handy guide, Steve. Am I correct in assuming those would be chords without extensions? I mean, for example, in the key of C, on the G7 dominant chord with extensions the 11th would be C (the 'root'of the C scale). Or am I missing something?

I do find it pretty easy to remember the 'teams' that progger mentioned. I, iii, vi chords as tonic, IV as subdominant, and V, vii as dominant V. Very handy to understand this.

There are also dominant & diminished chord 'families' (as I think Barry Harris called them). I'll post that when I have more time.

 

[skeller047]

Seems like a handy guide, Steve. Am I correct in assuming those would be chords without extensions? I mean, for example, in the key of C, on the G7 dominant chord with extensions the 11th would be C (the 'root'of the C scale). Or am I missing something?

G11 in the key of C is kind of ambiguous. I would say it’s subdominant, because it sounds most like G7sus4, or Dm7/G, with the added color tone of the 3rd (the B).

But this gets us into modal harmony territory because sus chords are so common in modal tunes, and one of its attractions (to me anyway!) is that harmonic motion is more ambiguous in a modal context. The flavor of the tune is determined by the mode of the moment, and not by the tension-resolution model of diatonic harmony.

@progger (such a smart fella) mentioned modal interchange, and in fact a lot of tunes in modern jazz substitute changes in mode for harmonic motion and chord changes in diatonic sense. Or mix the two approaches - Recorda Me being a prime example of this.

My approach comes from looking at tunes that have non-diatonic chords interspersed with more-or-less diatonic changes. Like a backdoor ii-V, for example ( Fm7- Bb7 in C) - this remains subdominant-dominant, even though the root (C) COULD be played over the bVII7 (Bb7). Often people play a diminished or altered scale on that chord, both of which omit the root.

Bottom line, the whole tonic-subdominant-dominant approach is just another tool, perhaps “lens” is a better word, for understanding how harmony works.

 

[JSL]

G11 in the key of C is kind of ambiguous. I would say it’s subdominant, because it sounds most like G7sus4, or Dm7/G, with the added color tone of the 3rd (the B).

But this gets us into modal harmony territory because sus chords are so common in modal tunes, and one of its attractions (to me anyway!) is that harmonic motion is more ambiguous in a modal context. The flavor of the tune is determined by the mode of the moment, and not by the tension-resolution model of diatonic harmony.

Thanks for explanation. I'll admit it gets a bit 'over my head', but it does make sense. Interesting.

 

[progger]

To build on my "teams" bit, I thought it might be... fun... to wade into the perilous and murky waters of a minor tonal center. There are a couple reasons why functional harmony in a minor key gives people trouble, particularly since we draw our default chord options from both harmonic and natural minor before we even bring anything else in like parallel major interchange or secondary dominant action.

The thing that seems to cause needless complication, though, is the ii chord in a minor key, which is, by default, a diminished triad... or a half-diminished 7th if we extend it. Even though there's a diminished triad in there, though, it really belongs on team subdominant, and an easy way to conceptualize/navigate... say... Dmin7b5... is to just pretend it's Fmin. With a natural six in the bass.

Harmonic minor is, of course, where we get our "natural" diminished seventh chord, and as far as I can tell it's the only place it really happens without additional chromaticism. As everyone from Bach to Bird knew well, that vii(dim7) is the perfect companion to a V7(b9) chord, and it's so useful that it works just as well if we fly it over to a parallel major world.

The multi-headed nature of a minor tonality makes the "teams" a little more complicated, but not all that much. III and VI are both capable stand-ins for i on "Team Tonic," ii and iv are still "Team Subdominant," V and vii are very much "Team Dominant," although in natural minor our v chord can be quite minor, which really makes it more of a "Team Tonic" sub for our parallel major. Ooph. It's a polite enough sound, though, and usually doesn't cause too much aural confusion... most of the time... I think...

Ultimately, if we're writing/arranging/improvising in any tonal center, we can eventually get to the point where we understand all the potential "default" chords at our creative disposal to include anything from our parallel major or minor keys (including harmonic minor, natural minor, and melodic minor). I find that to be liberating and empowering, even if it seems overwhelming at first!

 

[Pete Thomas]

A concept I find useful, and that I work on with my composition students from time to time, is that chords in much of western music seem to find themselves in three fundamental "jobs," or maybe "teams."

I really like the teams idea. It kind of fits with my concept of:

Tonic = at home
Subdominant = off somewhere else
Dominant = homesick so off back home ASAP

The fly in the ointment though is the IIm7 V7

Although I very much agree that IIm7 is in the subdominant team, it can also be treated as part of team dominant (it's basically a dominant with a sus 4 or 11)

I've seen transcriptions of Charlie Parker solos where he does a dominant lick over a IIm7 V7, ie treats it as team dominant.

 

[Pete Effamy]

Much as I love the study of functional harmony, I think you have to be careful not to bolt everything down too much. Some harmony is not following function all the time.

Some harmony can be like a few moves on a Rubic’s cube, making a coloured face come into focus a few moves later.

Claus Ogerman’s harmony is interesting in this way.

 

[progger]

Although I very much agree that IIm7 is in the subdominant team, it can also be treated as part of team dominant (it's basically a dominant with a sus 4 or 11)

That's absolutely true, and one of the countless ways in which any kind of musical categorization gets very squishy very fast. Play a V over a ii, play a ii over a V, it'll work fine, it'll just maybe switch what "flavor" of dominant action is happening (suspended-ish, normal-ish, altered-ish?). They can all be kind of layered on top of each other, and inevitably will.

Honestly, any of "team subdominant" can be immediately promoted to "team dominant (suspended faction)" instantly, the bass just has to move to V!

Furthermore, with my favorite composers (Wayne, Herbie, Joe Henderson, Ravel, Prokofiev, Khachaturian...), these concepts can all be stretched and abstracted so far that they're basically just a reference to a reference to a reference.

I seem to remember there being a Debussy quote that's something along the lines of "any chord can follow any chord." That is, ultimately, of course, correct!

 

[JSL]

As everyone from Bach to Bird knew well, that vii(dim7) is the perfect companion to a V7(b9) chord, and it's so useful that it works just as well if we fly it over to a parallel major world.

+1. While I don't usually visualize it as vii, I often play a diminished 7 arpeggio rooted on the '3' of the V7(b9) chord. I see it as 3 5 b7 b9 of the V. But of course, that's also vii(dim7). Thanks for the insight.

III and VI are both capable stand-ins for i on "Team Tonic,"

Yeah, one place I use that iii7(b5) chord is over a iii-VI7 in bar 8 (or 7 & 8) of a blues, leading into the ii-V in bars 9, 10.

I've seen transcriptions of Charlie Parker solos where he does a dominant lick over a IIm7 V7, ie treats it as team dominant.

I remember watching a video of Barry Harris where he stated, "there's no such thing as the ii chord". It confused me a bit at the time, but I came to realize he was simply saying that in a IIm-V progression, you can play the V7 chord over the IIm7 chord and in fact, they are interchangeable. You could play the IIm chord over the thing as well. They share a lot of chord tones:
Dmin7 (with 9,11,13) = D F A C E G B
G7 (with 9,11, I3) = G B D F A C E (of course some, or all of those extensions could be altered)

Hey Pete, I hope you don't mind we've been using lower case (ii) for minor chords and upper case for major & dominant. I know you prefer upper case with "m" or "min" for minor chords. I could go either way, but just to stay consistent have stuck with lower case.

 

[Pete Thomas]

Hey Pete, I hope you don't mind we've been using lower case (ii) for minor chords and upper case for major & dominant. I know you prefer upper case with "m" or "min" for minor chords

I don’t mind. There’s no Cafe rules. I just prefer to make it clear by using min7 or m7.

The lower case uppercase comes from classical but as we/I use chord symbols like Cm7 etc I just kept it consistent if it’s numbers rather than letters. Ie we don’t use lower case C or D so I just keep the numerals consistent to avoid confusion and always add the m or min so it seems redundant to change the case.

 

[JSL]

The lower case uppercase comes from classical but as we/I use chord symbols like Cm7 etc I just kept it consistent if it’s numbers rather than letters. Ie we don’t use lower case C or D so I just keep the numerals consistent to avoid confusion and always add the m or min so it seems redundant to change the case.

That's a great explanation, Pete. I'll admit I hadn't thought of it that way. But it definitely makes sense. I'm going to adopt that system, not to obey and 'rules', but because it is so logical.

One thing that some would say is that it should be Cmin7, rather than Cm7, because the 'm' could be mistaken for major. But I don't really buy that because I've always read 'm' as minor and "M" as major. There's no way I can see Cm7 as anything but minor7.

 

[JSL]

Ok, here goes:
Here are a few more observations on the dominant & related diminished chord. Looking first at the diminished 7 chord, because it is a symmetrical chord all 4 chord tones can function as the root. Meaning the G diminished chord (G Bb C# E) discussed in the OP of this thread, is also Bbdim7, C#dim7, and Edim7. All the same chord. So, what does this mean in relation to the dom7 chord?

It means that G7(b9), Bb7(b9), C#7(b9), and E7(b9) are all in the same ‘family’ (as Barry Harris would say) and they can all substitute for each other. Also note that G7 & C#7 are tritones, and Bb7 & E7 are tritones. So those chords fit the well-known tritone substitution. To analyze why all four chords are in the same family (team?) I’ll again use the G7 chord example.

Take G7 with altered extensions b9, #9, #11, and (unaltered) 13:

G B D F Ab C# Bb E

Next, look at the other three dominant chords in the family, with their extensions (please excuse the enharmonic notes; I kept them all the same for a reason):

Bb D F Ab B C# E G

C# F Ab B D E G Bb

E Ab B D F G Bb C#

Note all the same notes occur in all four chords. The chord tones are in different positions because of the different roots. Also, I realize that some of the enharmonic notes are not technically correct. For example, in E7, the Ab should be G#, but it’s still the same note. C#7b9 should probably be Dd7b9, etc. But the comparison between chords is more apparent keeping the same enharmonic names.

The chord tones, when rearranged into a scale all spell the same ‘half/whole’ diminished scale. So, any patterns built on that particular scale can be used over each of those chords. The same is true for the two diminished chords found in that scale. For example:

Take the diminished 7 chord found in 3 5 b7 b9 for each of those chords:

G7b9: B D F Ab

Bb7b9: D F Ab B

C#7b9: F Ab B D

E7b9: Ab B D F

It’s obviously the same dim7 chord in different inversions. In the same family or team. This same analysis will apply to the other two diminished chords & associated dominant 7 chords. Four in each ‘family’, adding up to all 12 dominant chords. I’ll admit I don’t use a lot of chord substitutions, but I think it’s interesting how this all fits together.