Diminished chord interchangeability

[coelacanth]

I am confused about something I just read in Mark Levine's Jazz Theory Book. I sent him an email about it, but I'll post a copy of the email here too in hopes that I can get this issue figured out pronto:

Hi Mark,
I'm a budding jazz guitarist making my way through your Jazz Theory Book, but I've arrived at something on page 88 that's got me puzzled. You notate a voicing containing all eight scale degrees of the E half/whole diminished scale, saying that it's called a "double diminished" voicing because it forms a G° chord in the right hand and a G#° in the left.

Now, it's easy for me to understand where the G#° comes from (E half/whole diminished has the same notes as D whole/half diminished, which produces the chords D°, B°, F°, and G#°), but what about that G° chord?

I even see that the G#° is composed of the 3rd, 5th, 7th, and b9 from E half/whole diminished. This leaves behind #9, #11, 13, and the root, which are enharmonic equivalents of a G°'s chord tones... But if E half/whole diminished is truly symmetrical, and G#° is interchangeable with E7b9, then why isn't G° interchangeable as well? Yet, if it is, it seems this would break down the barriers between the three diminished scales.

E7b9 would be interchangeable with G°, which is interchangeable with F#7b9, which would be interchangeable with A°, which is interchangeable with G#7b9, which would be interchangeable with B°. But G°, A°, and B° come from each of the three diminished scales. Which is totally crazy.

I hope you can resolve my confusion! I love your book, by the way--I can't put it down.
Indran

*I say "enharmonic equivalents" because in the music theory class I took in college, we would've been told that G, Bb, C#, and E a technically not the components of G° (even though they sound like it!), but rather G, Bb, Db, and Fb. Does jazz, as aural as it is, require being less anal about stuff like this?

[JohnW400]

The E symmetrical scale is E F G G# Bb B C# D
The notes of a G dim7 are G Bb Db (C#) Fb (E)
The notes of a G# dim 7 are G# B D F

If I Start this scale on G I get:
G G# Bb B C# D E F = 1 2 3 4 5 6 7 8

The odd notes make up the Gdim7 , the even notes make up the G# dim7.

[coelacanth]

Let me try to rephrase my question.

In melodic minor, diminished, & whole tone harmony, Levine says "everything harmonically contained within [a given] scale is interchangeable: chords, voicings, licks, phrases, patterns, and so on" (because, unlike major scale harmony, there isn't the complication of avoid notes).

This seems to suggest that E7b9 and Gdim7, which are both from the E half/whole diminished scale, are interchangeable chords. However, Gdim7 can also be constructed from the notes in F# half/whole diminished. Why can't I substitute E7b9 for other chords from the F# half/whole diminished scale, such as F#7b9 or A7b9?

(Now that I think about it, it's probably because they're not "harmonically contained within the given scale"!! But I want to hear what you think about it because I still feel confused)

[JohnW400]

I'm not sure what he's trying to say since you mention the melodic minor with the symetrical and the whole tone.

I can see the whole and symetrical as being interchangeable since in the whole tone the chord moves from (say) one augmented chord to the next in whole steps and the symetrical moves (say) from G to G# dim7 to Bb to B dim7. couple this with the inversions of augmented and, diminished, are identical to eachother so perhaps thats what he means by interchangable.

I'm interested to hear his reply to your e-mail. Sorry I mis-read your original post.

[bako]

The scale forms 4 7th chords G7, Bb7, Db7, E7
On Ab, B, D and F it doesn't form a 7th chord
The diminished scale is a more complex symetry that the whole tone.
Only degrees seperated by a minor 3rd are perfect equivalents.

If you take the entire scale as chord tones and tensions on G7 you get:

Ab B D F G Bb Db E
b9 3 5 b7 1 #9 #11 13

This is a nice voicing for our 10 fingered keyboard friends.

The same colors are available for Bb7, Db7 and E7

[coelacanth]

The scale forms 4 7th chords G7, Bb7, Db7, E7
On Ab, B, D and F it doesn't form a 7th chord

So the E half/whole diminished scale produces all of the following chords?:

G7b9, Bb7b9, Db7b9, E7b9
Abdim7, Bdim7, Ddim7, and Fdim7
Gdim7, Bbdim7, Dbdim7, Edim7

That last row is what weirds me out, because G, Bb, Db, and E serve as the root note for BOTH chord types. I suppose this results from there being eight scale degrees rather than seven?

[JohnW400]

That's the way Pat Martino does it. He works back from the diminshed. The symetrical scale also yields four minor seventh and 1/2 dim as well as tons of panditonic chord voicings when you harmonize the scale.

For example if you take G7 (3x343x) it moves to 4x565x or Ab, G, C#, E, with the next chord being Bb7 (same fingering as the G7 but 6x676x) followed by the B, Bb, E, G (7x898x)

Now, I want to know how the melodic minor is interchangable. And if so , why not any of the other 7 note 'synthetic' scales like the Hungarian major or what have you.

[coelacanth]

That's the way Pat Martino does it. He works back from the diminshed [...]
if you take G7 (3x343x) it moves to 4x565x or Ab, G, C#, E, with the next chord being Bb7 (same fingering as the G7 but 6x676x) followed by the B, Bb, E, G (7x898x)

Hmm... Could you explain what you mean by those two parts?

By the way, Levine says on p. 72-73: "The lack of 'avoid' notes means that almost everything in any melodic minor key is interchangeable with everything else in that key. Play a lick, pattern, phrase, chord voicing, motif, and so on, on Cm(Maj7), and it will work as well on Dsusb9, EbMaj7#5, F7#11, Am7b5, and B7alt [...] The only real difference between these chords is the root, and unless you're a bass player, or a pianist playing root position chords, there is no difference between any of the chords."

[JohnW400]

I don't agree. Of the seven possible chords , some work a lot better than others. If your CmiMa run is heavy with C it won''t work quite as well against the G7 or B7 alt as it does against the Ami7b5 or Eb and F's.

All these possiblitie work but on a scale of best choice to not so best .

The major scale also works this way if I use Levines thinking. For Example F lydian works quite well for F, G7, Dmi7 and Bmi7b5 chords as F is in all of those chords. It also could work against the Ami7 but not as well. It really doesn't quite fit the C or Emi. I guess what he means is that since the melodic is not quite as 'stable ' sounding as the major, you can get away with more things with it.

As far as the Pat Martino method, one of his books teaches chords by starting out with the 4 diminished 7th chord inversions and by moving one note at a time you wind up learning all the 7th chords and their inversions. There's more to that book than just this. You should check it out.

As far as the G7 and harmonizing the symetrical scale, every scale can be harmonized by writting out a starting chord and then move each note in the starting chord to it's next note in th escale , and so on.

In C major you get, for example, C Dmi Emi F G Ami B dim and C. You apply the same concept to any scale and you wind up with a harmonized scale. In cases where the notes don't stack up in 3rd's we wind up with 'panditonic' chords. They don't have an exact name but they can be thought as 'possibly' being a standard chord just missing some notes that would define exactly what they are. I'll type up a few examples and post them later

[JohnW400]

The scale is G half-whole symetrical. The notes are G Ab Bb B C# D E F. Using G7 voiced G F B D, write out the modes for each note.

High to Low

D E F G Ab Bb B C# D
B C# D E F G Ab Bb B
F G Ab Bb B C# D E F
G Ab Bb B C# D E F G

This is Example A. Example B is what happens with Gdim7 and example C is what happens with G7#9. I'll let you figure out how I got them.

The chord in parentesis are the possible, implied, harmonies (panditonic)

[John Curran]

For Example F lydian works quite well for F, G7, Dmi7 and Bmi7b5 chords as F is in all of those chords.

It works because all those chords and the F lydian scale are diatonic to the key of C. F is in a Bb major chord too, although I would be reluctant use an F lydian scale against Bb major.

It also could work against the Ami7 but not as well. It really doesn't quite fit the C or Emi.

George Russell would disagree.

In C major you get, for example, C Dmi Emi F G Ami B dim and C.

B dim is correct only if you're referring to triads, which is seldom the case in jazz. Technically the B is a minor 7b5 chord (half diminished) as compared to a diminished one.

Interesting thread...

john

[John Curran]

*I say "enharmonic equivalents" because in the music theory class I took in college, we would've been told that G, Bb, C#, and E a technically not the components of G° (even though they sound like it!), but rather G, Bb, Db, and Fb. Does jazz, as aural as it is, require being less anal about stuff like this?

Wow that's a pretty strict class. Some theory teachers would wince at the C#. But in jazz enharmonic spellings run rampant.

john

[JohnW400]

John,

First, The example shows triads so it's a B diminished triad. Had they been 7th's you would be correct.

Yes I agree with your George Russel comment. You could also cite Bill Evans and Waltz for Debbie. But I mention it only to illustrate the point. The further away you get from the 1-3-5-7-9 etc the more dissnonant the sound.

Regarding Diatonic, So are all the chords mentioned for the C miMa7 . I don't see any chords mentioned that do not belong in that scale. And Cmima7 doesn't quite fit right against a G7 unless you extend the Cmima7 to include the 9th and/or 11th CEbGBD. omitting the C gives you a great G/Eb but then you no longer have cmima7. you have Ebma7#5.

Which brings me back to my original question. How is everything in a melodic minor harmonically interchangable with every other chord in that scale? yet no other 7 note scale?

1-3-5-7-9-11-13 contain all the notes in the scale stacked in thirds. This gives you C, Emi, G, Bdim, Dm, F , Ami.

Put any of these triad over a C pedal. The further away you get from C the more dissonant it sounds (forwards and back)

Cmi, Eb+ , G, B dim , Dmi, F, A dim. Same thing. put each triad over the C pedal and the further away you go the more dissonant the sound.

Playing Bmi7b5 arpeggio ver a Cmima7 is the 7 9 11 713. I just don;'t see the difference if the scale is major. There are still 'avoid' notes in both

[JohnW400]

Well after thinking it over (during diner with a nice bottle of white wine) the only thing I can think of is that it has to do with the augmented triad in the Ebma7#5.

It throws the whole scale into a dominant, unresolved sound. Other than that .....

[John Curran]

John,
Regarding the B dim, as the OP expressed confusion over diminished chords I though it appropriate to keep diminished and half diminished relationships separated. Technically you are correct, the triad is diminished but this is misleading as the function of the chord in the example quoted is a locrian or half diminished one, not a true diminished. I point this out for the benefit of the novice theorists out there.

The major scale also works this way if I use Levines thinking. For Example F lydian works quite well for F, G7, Dmi7 and Bmi7b5 chords as F is in all of those chords. It also could work against the Ami7 but not as well. It really doesn't quite fit the C or Emi.

I have some problems with the theoretical logic of the above statement. It implies for example that it would be inappropriate to play an E phrygian over the above mentioned G7 chord as there is no E in a G7 chord. But Wes did this all the time. Also by logical extension your statement implies that one could play an F lydian over any chord that has an F in it. I've tried to point out that this may not be so, again for the benefit of beginning theory students.

I still maintain that F lydian works over the above mentioned chords because they share the same key center, not because all those chords have an F in them.

The foregoing examples were given as examples in the key of C major, I'm still digesting your issues re: CmiMaj7.

john

[mr. beaumont]

I have some problems with the theoretical logic of the above statement. It implies for example that it would inappropriate to play an E phrygian over the above mentioned G7 chord as there is no E in a G7 chord. But Wes did this all the time.

john

john, i agree, but since we're trying NOT to confuse people...

E Phrygian= G mixolydian, which is G major with a flat seventh, or a C major scale.

so of course it would work over a G7. but why would you view it as phrygian? even if you play it E to E it's not going to have that "phrygian sound" over a G7. it's going to sound like you're going after a G13 sound, if you ask me...

there's a lot of use to the modes, but this seems to be just an example of how they can overcomplicate things...or am i missing something?

[John Curran]

but why would you view it as phrygian? even if you play it E to E it's not going to have that "phrygian sound" over a G7. it's going to sound like you're going after a G13 sound, if you ask me...

Hey Mr B. I agree, the diatonic modes at least are all relative and interchangeable. One might analyze an E to E scale (as you mentioned) as an E phrygian scale or a myxolidian idea starting on E. They are equivalent. Different ways of expressing the same thing. I've transcribed two different Wes solos where he uses ostensibly phrygian 16th note scales as pick ups to an idea, although never playing a strict root to root scale. E.g. against Bb7: G Ab Bb C D Eb F G Ab Bb. Is this G phrygian or Bb mixolydian, or both?

Having just reviewed George Russell's lydian chromatic system I've been approaching dom 7th chords by playing a lydian scale one step lower. e.g. over G7 playing F lydian. Am I playing F lydian or G myxolydian? Both. They are the same thing.

there's a lot of use to the modes, but this seems to be just an example of how they can overcomplicate things...or am i missing something?

Again, agreed. Although my comments were aimed at examples given in C major, the original post involved diminished and melodic minor key centers which are a little more complex.

But I totally agree about over-complicating modes.

john

[JohnW400]

To clarify

Yes you can use any mode in C against any chord in the C scale. F lydian works against Emi7 but if you play the mode F to F it's not going to fit quite as well as say E phrigian E to E.

I used triad to illustrate how to harminize a scale. I wasn't sure what level the OP is at theory wise so I used something simple to show how to harmonize any scale.

You mention the diatonic modes being interchangable. Hence back to my original reply where I want to know why the melodic minor is interchangeable but not any other 7 note scale.

The whole tone and 1/2-whole (or whole-1/2 if you prefer) are definately interchangable. but the rest? I'm still not convinced that say one thing in that scale works for everything else in that scale. There are going to be avoid tones somewhere.

[memyselfandus]

Casa Valdez Studios: Symmetrical Scales-Diminished, Wholetone & Symetrical Major