6

As the title says, say I had an E7b9, could this not also be a G#dim7?

If I understand correctly, the notes would be:

E G# B D F = E7b9

- G# B D F = G#dim7

  • Is this correct?

If so:

  • Is this a common substitution?
  • If I see a dim7 chord, should I also think of it as a rootless 7b9 chord to get an expanded harmonic understanding of the tune?
  • Welcome to Music.stackexchange! I think this is a well-phrased question that is clear, gives a nice example. It's relevant and is more than a basic analysis question. Thanks for joining the site and contributing! – jdjazz Nov 27 '17 at 22:27
3

Short answer: I wouldn't describe them as the same but they do have the same function. They are both dissonant chords that desire resolution and both resolve to the same place with very similar voice leading.

We can make this a little more simple to start. E7 is V of A; G#° is vii° of A. Both of these chords want to resolve to A with G# being the leading tone that wants to resolve to the tonic, unless you're playing Jazz, in which case it may be held as the major 7 of an Amaj7 or step down to b7 for an A-7. D is the 7 of E7 or the b5 of G#° and will want to resolve down by step.

Once we add in the b9, the texture changes a little but we have the same functionality. If we utilize the half-whole/whole-half scale, we can then shuffle around our concept of resolution. This scale will create 4 Dominant chords, all a minor third or tritone apart. For E7 we could use the E half-whole scale (E,F,F##,G#,A#,B,C#,D). The 4 Dominant chords that can be derived from the scale are E7b9, F##7b9 (G7b9), A#7b9 (Bb7b9), and C#7b9. The reason this works is because all of the 4 contain the ever important tritone that desires resolution. For E and Bb (Bb is also the standard tritone sub), the tritone falls on the 3 and 7 of the chord; for G7 and C#7, the tritone falls on the 5 and b9. This allows us to have the expected voice leading and resolution for a standard Dominant chord with any of those 4 choices. In the same regard, a fully diminished 7 chord can use the whole-half scale, which will create 4 fully diminished 7 chords (it actually creates 8 fully diminished chords but only the 4 are typically used within the scale). The 4 notes that make up all of these chords are the same as the 3,5,7,b9 of the Dominant chords outlined above. The same way that we are able to state that E7 and G#° have the same function, we can say that these diminished chords have the same function. So you can actually use E7b9, F##7b9 (G7b9), A#7b9 (Bb7b9), C#7b9, G#°7, B°7, D°7, or F°7 to fulfill the same function. This is more commonly known/understood for fully diminished 7 chords, as they are symmetrical (all minor 3rds).

So I wouldn't say that E7b9 and G#°7 are the same chord but they can fulfill the same function, along with the bunch of other chords I mentioned. The thing to keep in mind when thinking of things this way is where this is being applied. If you're composing or arranging a Classical piece, the treatment of these chords will be a little different and whether or not the texture appropriately applies to your piece will probably be very specific to each piece. In Jazz, this sort of approach is very common but it may not be as appropriate in certain subgenres, such as Big Band Swing or Modal Minimalism. You'll probably find that this approach doesn't work so well in Rock or Pop music, largely because of the diatonic nature of these genres but also the standard chord voicings. Like any other musical device, your taste and ear should be used to make the determination as to whether or not this sort of substitution approach should be used.

  • Wow. I'll have to re-read this a few times to full absorb the knowledge bomb. Thank you very much. – Cephlin Aug 17 '16 at 10:09
  • @Cephlin Glad to provide that for you. Feel free to ask any follow up questions too and I can modify the answer to include it. Again, this approach definitely works better in some situations than others, Jazz being the place you'll find the full list of substitutions most frequently. I definitely encourage you to try it elsewhere, as it can work, but don't let cool/interesting theory be the deciding factor; use your ear. – Basstickler Aug 17 '16 at 14:29
  • @Cephlin, I see the points made here, but I disagree somewhat. There are many cases where a diminished chord has no dom7 equivalent. A good example is "Wave" by Jobim. See measure 2 here. As another example, in a ii-V-I progression, the Imaj chord is often delayed with a Idim chord. The Idim chord cannot be thought of as a dom7 chord. To your Q about whether it opens up new harmonic possibilities, I think the answer is "only in certain scenarios, & you must be careful." – jdjazz Nov 27 '17 at 21:48
  • @Cephlin, for instance, the chords E7b9, G7b9, Bb7b9, or Db7b9 can all be voiced as a G#dim7 chord. So when you see a G#dim7 chord, 2 things are true: (1) there's no automatic guarantee that the G#dim7 will be functionally equivalent to any of the four dom7(b9) chords and (2) if there is a functional equivalent, then G#dim7 chord will probably only be equivalent to one of the four dom7(b9) chords. Figuring out which dom7(b9) is the equivalent takes a little work. If you do that work, then you can proceed with the substitution knowing that you haven't changed the harmonic function. – jdjazz Nov 27 '17 at 21:54
  • @jdjazz - I think the distinction to be made here is that diminished chords don't always have a dominant function. I'd say that when a diminished chord does have a dominant function, it will have a dominant chord as an available sub for it. Depending on your tastes, you can have 4 different dominant b9 chords available. I might agree that there are some more obvious choices or choices that are more closely related to the key but in an extreme reharm, you could sub any of the 4 and they would all have the same function. – Basstickler Nov 27 '17 at 22:59
5

As you've correctly pointed out, a G#dim7 is an upper structure of an E7b9 chord. Obviously, they are not identical because a G#dim7 doesn't have the note E. However, both can have the same function: they can be used to lead into a (minor or major) chord with root A.

That these chords are closely related is also reflected by the fact that they share at least one chord scale: the diminished (half-whole / whole-half) scale. One appropriate scale over an E7b9 is the half-whole scale starting on E, and the chord scale for G#dim7 is the whole-half scale starting on G#. Clearly, they are both the same scale:

E F G G# A# B C# D

Note that many 4-part chords can be interpreted as an upper structure of a 5-part chord. Some examples:

E9    - G#m7(b5)
Em9   - Gmaj7
Emaj9 - G#m7
4

Summary

I disagree somewhat with some of the other answers. Your question

if I see a [G#dim7] chord, should I also think of it as a rootless [E7(♭9)] chord to get an expanded harmonic understanding of the tune?

is a really good one, and you've made an important connection that can serve as a shortcut in many cases. However, the true answer to your question is "only in certain circumstances, and you must be careful. A little analysis is needed to make this substitution."

There Will Always Be Four 7(♭9) Choices

If we look a little further, we see that four chords can be voiced as a G♯ diminished chord:

  • rootless E7(♭9): G♯-B-D-F
  • rootless G7(♭9): B-D-F-G♯
  • rootless B♭7(♭9): D-F-G♯-B
  • rootless D♭7(♭9): F-G♯-B-D
  • G♯dim7: G♯-B-D-F

    (My chord spellings contain enharmonic errors, but these help illustrate the point.)

So when we see a G♯dim7 chord, there's no way to automatically know which of the four 7(♭9) chords would be functionally equivalent. For that, we must do more analysis and look at, e.g., the neighboring chords.

Not All Diminished Chords Have 7(♭9) Equivalent

There are many cases where a diminished chord has no dominant 7th equivalent. One simple example is the following progression:

| Dmin7 | G7 | Co7 | CMaj7 |

In a ii-V-I progression, the Imaj chord is often delayed with a Idim chord as this example shows. The C diminished chord could be a rootless voicing for D7(♭9), F7(♭9), A♭7(♭9), or B7(♭9), but none of those would have the same function as the Cdim7 in bar 3. Moreover, using an F altered scale would probably sound quite odd in measure 3.

The Value

Given all this, it might seem bleak. But that's not entirely the case. All this means is that we can't jump to conclusions without a little additional analysis. If we see G♯dim7, there could be a 7(♭9) chord that serves the same harmonic function. However, we must look to the neighboring chords to figure out (a) whether there is or isn't a 7(♭9) chord that is functionally equivalent and (b) which of the four 7(♭9) chords is the correct choice.

  • 1
    'Diminished' is a description of what a chord IS. 'Dominant' is a description of what a chord DOES. That's why I flinch when hearing a C7 chord describes as a 'Dominant 7th'. It often ISN'T being a dominant 7th. It might not even be being a secondary dominant. – Laurence Payne Nov 29 '17 at 15:37
  • @LaurencePayne, how else would we describe chords with a flat 7th? – jdjazz Nov 29 '17 at 20:03
  • When naming a chord specifically, just 'C7', 'Ab7' or whatever. Generically, I admit we have a problem. 'Dominant 7th shape' is unwieldy, though more accurate than just 'Dominant 7th' when the chord ISN'T a dominant. It's like calling every major triad a 'tonic'. – Laurence Payne Nov 29 '17 at 22:17
3

They are similar, but they are not the same. Most chords have some relation to smaller chords. For example, a dominant 7th will have a diminished triad made from the third, the fifth, and the seventh. These relationships exist because of how the is constructed and while it exits the chords themselves are independent of each other.

If you were and just play G#dim7 alone and no context, no one would mistake it for an E7b9. However when you add in progressions that would imply E as the root and when you are playing with others that will play an E in there part you can get away with just playing the G#dim7 as a rootless vocing of E7b9.

2

Add a note a major third below any of the four notes of a dim7 chord and you'll have a dom7(b9). Or, to put it another way, treat any inversion of a dim7 chord as a rootless dom7(b9). To put it yet ANOTHER way, there are four seperate tritone intervals in a dim7 chord, each one can act as the bare bones of a dom7 chord.

This is why dim7 chords are so useful for modulation. They can go four ways!

  • I wanted to place a similar question here, but it turns out this thread is close to what I was going to ask. In one of piano arrangements I have seen a dom7b9 chord is clearly defined with additional symbol Diminished. Does it make sense in theory, if applied only for piano? The problem is though this additional symbol in that piece may be given for bayan (button accordion) where a single button can be used to play a Dim (i guess). I was thinking whether it's appropriate to mark 7b9 as Dim for piano? – alexsms Aug 1 '18 at 13:52
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I am in the process of self-teaching jazz guitar, and most of the gurus who offer training online suggest that, to simplify the approach to chords, one can think of ALL chords as either major, minor or seventh. Joe Pass himself even suggests this approach, calling all the variations on these chords (such as a major 6 +9 for the major category, minor 11th flat 5 in the minor category, and sharp 9th in the seventh category) "color tones". So in that regard, mentally speaking at least, there are no diminished chords. I tend to favor this approach, so to me it's easier to consider a diminished chord as a dominant seventh flat 9, or just another "color" of the dominant chord. It does make sense because to me it's easier to fit another variation of the dominant chord into the scheme of things, rather than to consider a whole new chord "type", if you will. I believe Jimmy Bruno agrees with this approach as well, being himself a proponent of "simplification" when it comes to the approach to jazz guitar.

  • Thanks for the post and for joining the site! This is an awesome approach and Joe Pass is an outstanding resource to cite. A small fix is needed: the fundamental chords would include dim chords. They occupy yet another space from maj, min, and dom7th chords. Color tones can account for the variations in major chords (Cmaj7, Cmaj6, Cmaj9, etc.), in minor chords (Cmin7, Cmin9, etc.), and in dom7th chords (C7, C9, C7#11, etc.). But the diminished chord is an altogether different chord with oftentimes distinct harmonic functions. It's the 4th "type" of chord, onto which we can add color tones. – jdjazz Nov 27 '17 at 21:43
  • 1
    In other words, you can't always find an equivalent dom7 chord to use as a mental replacement for the diminished chord. A great example is the Bb dim chord in Wave by Jobim. – jdjazz Nov 27 '17 at 21:45

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