Extended diminished chords

[theamazingninja]

How do you name extended diminished chords? For instance, i'm trying to harmonize the harmonic minor scale in elevenths, but when I got to the seventh degree, the fully diminished chord, I couldn't figure out what to call it. Please help. Thanks.

[JonR]

How do you name extended diminished chords? For instance, i'm trying to harmonize the harmonic minor scale in elevenths, but when I got to the seventh degree, the fully diminished chord, I couldn't figure out what to call it. Please help. Thanks.Diminished 7th chords are very rarely extended.
In theory they can be - but they would not use the harmonic mnor scale, they would use the WH diminished scale.
Composer/arranger William Russo says that dim7 chords can have 4 extensions, each one a half-step below one of the chord tones (IOW, spelling out the WH dim scale).
Eg, for G#dim7 (vii of A harmonic minor) you could have any of these:

A# = 9
C# = 11
E = b13
G = major 7 ("15", strictly speaking, I guess!? - as the chord already has a 7th - but Russo calls it maj7)

However - although these might occur as melody notes - I've never seen any dim7 chord with any written extensions at all in practice (in 20 years of playing jazz).

If you're sticking strictly to harmonic minor, then the C on G#dim7 would be an "avoid note". Technically a "b11" (diminished 11th), it would not be used as a chord extension, so can be disregarded.
Same applies to A, the b9.

[LaughingSkull]

I fail to see for what purpose (but I was doing the same stuff ...).
For instance in A harm. minor I would call such a chord Bm9b5/G# ( I cant imagine G#dim7b9b11, but who knows perhaps this is better). Jon?

[JonR]

I fail to see for what purpose (but I was doing the same stuff ...).
For instance in A harm. minor I would call such a chord Bm9b5/G# ( I cant imagine G#dim7b9b11, but who knows perhaps this is better). Jon?
"Bm9b5/G#" = G#-B-D-F-A-C#
If you want a C natural on it, it would be "Bm7b5b9/G#" :eek:

But why would you want such a chord (9 or b9) ? It's a harmonic mess - a mix of two different chords (with different functions). It's partly a ii chord (Bm9b5), partly a rootless V chord (E13b9). The G# and the A in particular are fighting each other.
And if you use C natural, then that will fight with the B.

IOW, this is a purely theoretical exercise with no practical purpose. So it's just a game, and the answer/result doesn't matter!

There is no point in harmonising a scale with every possible extension just for the sake of it. No point in going further than the level at which each chord functions correctly, does its harmonic job.
That means, with vii chords (in major or minor keys), you stop at the 7th.
(Same applies to one or two other chords, in major or minor keys, btw.)

[LaughingSkull]

"Bm9b5/G#" = G#-B-D-F-A-C#
If you want a C natural on it, it would be "Bm7b5b9/G#" :eek:

Aargh! I see on the doodle that i had b9 written ... but when composing a post I made simplifications (with error). Sorry.
No point in such a chord, I agree. Ugly.

[leegordo]

"Bm9b5/G#" = G#-B-D-F-A-C#
If you want a C natural on it, it would be "Bm7b5b9/G#" :eek:

But why would you want such a chord (9 or b9) ? It's a harmonic mess - a mix of two different chords (with different functions). It's partly a ii chord (Bm9b5), partly a rootless V chord (E13b9). The G# and the A in particular are fighting each other.
And if you use C natural, then that will fight with the B.

IOW, this is a purely theoretical exercise with no practical purpose. So it's just a game, and the answer/result doesn't matter!

There is no point in harmonising a scale with every possible extension just for the sake of it. No point in going further than the level at which each chord functions correctly, does its harmonic job.
That means, with vii chords (in major or minor keys), you stop at the 7th.
(Same applies to one or two other chords, in major or minor keys, btw.)
'ow about this? it is not necessary to extend 'Dim' chords If you do you are merely inverting them for no useful reason ,,,.....If you do invert a 'Dim' chord ,and, you would like to emphasize it for any reason, such as maybe sound Key based then you could take the note in the 'Dim' chord which best suits the BASS , and sound that note in the BASS of the music if there IS BASS music in the piece. If not, then , i'ts a useless piece of figuring!
leegordo

[JonR]

'ow about this? it is not necessary to extend 'Dim' chords If you do you are merely inverting them for no useful reasonExtending a dim chord is not the same as inverting it. You can add other notes to the 4 notes of the chord - from the other 4 notes of the WH dim scale, as I mentioned above. (And I consider William Russo a reasonable authority - check him out.)

Otherwise I agree. Inverting it makes no sense - because it's a symmetrical chord, it doesn't really matter which note is the bass (other than reasons of providing voice-leading in the bass).

And extensions are not a lot of practical use either. (I assume you'd agree with me there...)

[theamazingninja]

well here is what i'm trying to do:

harmonizing the har. min. scale in triads is easy:

Cm
Ddim
Eb
Fm
G
Ab
Bdim

Harmonizing in sevenths is easy:

Cm(maj7)
Dm7b5
Ebmaj7#5
Fm7
G7
Abmaj7
Bdim7

When I get to harmonizing the scale in ninths, I came up with:

Cm9(maj7)
Dm7(b5,b9)
Ebmaj9(#5)
Fm9
G7(b9)
Abmaj7(#9)
and here is where I'm not sure: Bdim7(b9)

And you can see where I totally get confused with elevenths and thirteenths.

I am just wondering because the other chords are possible to harmonize using extended harmony. But whenever I get to the diminished chord on the seventh degree, I get confused at the way to name it.

P.S. Thank you everyone for your help and comments. I really would like to understand this.

[theamazingninja]

BTW, I am merely doing this to understand why the other chords are possible to have extensions, but not the diminished chord.

[dublshot]

The Bdim7 does not have any 5 note extension with the root B, or any other note of the chord, each of which may be used as the root. All 5 note extensions of Bdim7 are the 7b9 type with each root being the note added: G 7b9, A# 7b9,
C# 7b9, E 7b9. This is because of the symetrical property of the Bdim7.
The G7b9 is used for the C harmonic minor.



Chordware.com

[Jed]

BTW, I am merely doing this to understand why the other chords are possible to have extensions, but not the diminished chord.


Any chord can be extended, . . . but not every extension is usable or musical. As Jon (I think) mentioned, the legit extensions for a diminished chord come from the whole-half diminished scale (so natural 9th, 11th, b13 & b15). It might be easier to think of these diminished chord extensions as chord tones of another diminished chord up a major 2nd.

The larger issue is how we think about extensions in general. Although you can extend any chord, only those extensions that are a whole step above a chord tone (when viewed as a scale) seem to have much use, with the one notable exception being dominant chords.

In the diatonic progression of the major scale, each chord has a specific set of allowable (read musical / useable) extensions. Theory of course lets us name anything but having a name doesn't make something sound any better.

cheers,

Cmin (maj7) - 9 11
Dmin7b5 - 11 b13
Ebaug maj7 - 9 13
Fmin7 - 9 #11 13 (I'm not sure what to think about the #11)
G7 b9 b13
Abmaj7 - #9 #11 13 (I'm not sure what to think about the #9)
Bdim7 - b13 b15

The problem with looking at things from a purely theoretical pov is that we quickly move beyond the purpose of music theory. Music theory seeks to explain what people have done and why it sounded good, not what is mathematically possible.

[JonR]

The problem with looking at things from a purely theoretical pov is that we quickly move beyond the purpose of music theory. Music theory seeks to explain what people have done and why it sounded good, not what is mathematically possible.Exactly. This more or less what I meant when I said:
"There is no point in harmonising a scale with every possible extension just for the sake of it. No point in going further than the level at which each chord functions correctly, does its harmonic job."

[JonR]

BTW, I am merely doing this to understand why the other chords are possible to have extensions, but not the diminished chord.Simple answer - because it doesn't sound right.
There are also practical limitations on other chords, not only the diminished.

Eg, in a major key, the following are practical - and therefore used more or less widely (at least in jazz):

I: maj7, 9, 6/13
ii: 7, 9, 11
iii: 7, 11
IV: maj7, 9, #11, 6/13
V: 7, 9, 6/13
vi: 7, 9, 11
vii: 7.

The extensions that are typically avoided are those that make a b9 interval with a lower chord tone (a really nasty sound): 11ths on I and V, b9s on iii and vii, b13 on iii and vi.
The 13 is possible on the ii chord, but very rarely used.
11ths can be used on I and V if the 3rd is omitted, making sus4 chords. (Because the b9 between 3 and 11 is removed.) However, an 11th would still not be used alongside a maj7 on I - it makes a confusing dissonance:
Csus4 = C-F-G = OK
Cmaj7sus4 = C-F-G-B = not OK (Try it and see... ;) doesn't sound too bad, perhaps, but works as a partial Fmaj7#11, not a C-root chord. Or maybe it's G7/C? In short, it's a confusing harmonic sound.)
Now try:
Cmaj11 = C-E-G-B-(D)-F = not OK (Isolate the E and F together if you don't quite hear the bad interval... Again, it's like a confusing mixture of a C chord with its functional opposite, G7. The 9th, D, is optional, btw.)


The chords in a minor key - at least in jazz - are harmonised from a combination of natural minor (ii, III, vi, VI), harmonic minor (V, vii) and melodic minor (i).
So you get the following extensions:

i: 6, maj7, 9
ii: 7 *
III: maj7, 9, 6/13
iv: 7, 9, 11
V: 7, b9 *
VI: maj7, 9, #11, 6/13
vii: dim7

* The ii chord can take an 11th (it's very common as a melody note), but you never see it indicated on a chord symbol.
The ii chord occasionally (not often) has a major 9th, suggesting the "locrian natural 2 scale", which is a mode of melodic minor - but not the melodic minor of the key.
Likewise, the V chord - more often - has other alterations such as #9. b5 and #5, suggesting the "superlocrian" or "altered" scale - a mode of yet another melodic minor scale.
(Yes, the V chord can have a b9, despite what I said above... go figure. I'm sure there's a good theoretical explanation, but we don't need to care. It sounds OK in that context, but not in others.)

Eg, in key of A minor:
ii = Bm9b5. Scale = B-C#-D-E-F-G-A = D melodic minor
V = E7alt (#5#9, b5b9, etc). Scale = E-F-G-Ab(G#)-Bb-C-D = F melodic minor
(As I said, that ii chord would be rare, but that V is very common.)

This might seem a bit of a mess theoretically - ! :rolleyes: - but that's because - as Jed says - it's all based on what musicians actually do, in their experiments to find the notes and chords that work best musically, giving them the sounds they want. (Eg, C# sounds better on Bm7b5 than C does - even tho it's outside the key.)

[Jed]

Exactly. This more or less what I meant when I said:
"There is no point in harmonising a scale with every possible extension just for the sake of it. No point in going further than the level at which each chord functions correctly, does its harmonic job."

As you well know, . . .

All of this is just a variation on the "mathematics and music theory don't mix" discussion. Many have tried, but music theory defies any simple mathematical approach. We all must be careful to avoid confusing the numbers we use to describe music concepts with anything resembling mathematics.

. . . so many are tempted, . . but it's a dead and unmusical end.

cheers,

[JonR]

All of this is just a variation on the "mathematics and music theory don't mix" discussion. Many have tried, but music theory defies any simple mathematical approach. We all must be careful to avoid confusing the numbers we use to describe music concepts with anything resembling mathematics.

. . . so many are tempted, . . but it's a dead and unmusical end.

cheers,+1!
We're on the same page here... :)

[theamazingninja]

Thank you everyone for helping me understand this better. It makes total sense to me now that just cause it's possible doesn't mean it's usable, and that music and mathmatics are two seperate things.