# "Wave" Harmony (for SW or other theory gods)



## fwd0120 (Dec 31, 2013)

So I was reading Mark Levines Jazz Theory book, and on page 87 he is discussing diminished harmony. Now he has gotten to an interesting bit that I 'almost' get, but need explained to me.

The first 4 bars of Jobim's 'Wave' is DMaj7 | Bbdim | Am7 | D7(b9) (sometimes I've seen D9).

So I want to know exactly how that Bbdim fits in there. I want that rule broken down in a way that can penetrate my thick skull.

DMaj7 | Bbdim | Am7 | D7(b9)

Would it be numerically:
I-------?-------?-----? (actually, bar 5 is a GMaj7) So would the D7 be like a secondary dominant to the GMaj7.... Oh well, answer that after this diminished stuff.....

The book says:
"Sometimes a diminished chord is disguised V7b9 of the chord _after_ the next chord."
So would that make the Bbdim the V7b9 of D7? Bb is not a 5th from D, is it? Is it somehow diatonically a 5th away or something? Because it is not a perfect 5th. 

Very confused but on the verge of getting it, so I'd love some help!
If there are any videos explaining, that would be cool, too.

Help a noob!


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## celticelk (Dec 31, 2013)

Bbdim is Bb-Db-Fb, or enharmonically Bb-C#-E. Levine's rule that the diminished acts as the V7b9 of the chord after the next one seems to apply here: two chords down is D7, and the V of D is A. Bbdim contains the b9 (Bb), 3 (C#), and 5 (E) of A7b9. Boom. It also voice-leads nicely into the Am7 which follows: E is a common tone, and the other two tones move down a half-step.


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## fwd0120 (Dec 31, 2013)

Okay, cool. Can I use this like a sub in a ii-V-I? Would that be Em, Bbdim, D?

Also (and most importantly), That movement in 'Wave', the Bbdim to Am7 - does that follow the cycle of 4ths? If the Bbdim is acting like a Vb9 (as in - A7b9), how can it move from a V7 to a minor-7 and the to the I7 (D7).

Wait, I just slightly answered my question (partially). The Am>D7 is a II>V which lets it go to GMaj7 in the 5th bar (which is a key modulation, right?). So he A7b9 to Am7 is mostly voice leading? Is there an actual rule to the flow of that sort of thing?

I think I must be getting a little closer... Thanks for the help!


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## celticelk (Dec 31, 2013)

That 7-to-m7 switch is a common way to modulate in 4ths. Without knowing the melody, I'd read this as starting in D with a I-V sequence, then modulating to G for a ii-V-I.

The diminished triad can stand in for any 7b9 chord with a root a half-step below one of its pitches. We've already seen how it can serve as A7b9; you could also think of those notes Bb-Db-Fb as the b7-b9-3 of C7b9, or the 5-b7-b9 of Eb7b9. If you make that a fully-diminished 7th chord by adding a G to the pitch set, you can also use it in place of Gb7b9; I leave it as an exercise for you to figure out how those notes relate to that 7b9, and the role of the G relative to the three 7b9 chords already mentioned.


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## fwd0120 (Dec 31, 2013)

Wow, that does make a lot more sense. I'll try that out. This is also a good time for me to analyze a few other tunes I know and keep my eye out for this stuff. Thanks a lot!


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## Mr. Big Noodles (Jan 1, 2014)

fwd0120 said:


> So I was reading Mark Levines Jazz Theory book, and on page 87 he is discussing diminished harmony. Now he has gotten to an interesting bit that I 'almost' get, but need explained to me.
> 
> The first 4 bars of Jobim's 'Wave' is DMaj7 | Bbdim | Am7 | D7(b9) (sometimes I've seen D9).
> 
> ...



You should have included the rest of the quote.







Hey, where did you get D&#8710; from? (I figure it's on the leadsheet, but I'm not going to look around for it right now.)



> Not all diminished chords are disguised V7(&#9837;9) chords of the following chord. Sometimes a diminished chord is a disguised V7(&#9837;9) of the chord after the next chord. The second chord in Antonio Carlos Jobim's "Wave" is B&#9837;°. B&#9837;° doesn't appear to be a disguised V7(&#9837;9) of Am7, the following chord. However, Am7 is followed by D7, and Am7 D7 is a ii-V. B&#9837;° is the disguised V (A7(&#9837;9)) of the D7 chord, with Am7 inserted between the two chords to create a ii-V.


I'm tired as hell, so I'll devote more time to this later. Until then, notice a couple of things: a lot of confusion could be cleared up if 1.) the chord was spelled as C#°7/B&#9837; (as it should be), or 2.) if the composer's spellings agreed with what Mark Levine is saying. I should add 3.) if Mr. Levine chose simpler ways to phrase things. "Disguised dominant"? It's a diminished chord, man. It's not disguised at all.

On point number 1, the expectation of C#°7 is to resolve to D (or D7, in this case). In the given progression, the resolution is slightly delayed by the presence of another pre-dominant function. C#°7 is vii°/V, in terms of function. You can think of the progression as "[D:] I [G:] vii°/V ii V", by that logic. Mark Levine thinks of diminished chords as being rootless dominant chords, so C#°7 (C# E G B&#9837 is really A7(&#9837;9) (A C# E G B&#9837. Thus, his view of this progression is A7 Am7 D7, or V/V ii V.

On point number 2, a lot of jazz composers don't think of their harmonic choices in this way. You might run into some people who consider B&#9837;° to be a dominant substitute to lead in to Am7. It goes like this: V of Am is E7. Do a tritone substitution, and you get B&#9837;7 (&#9837;II7 of Am). That gives you a B&#9837; root. When put like that, you're looking at the chromatic motion from B&#9837; to A. Then, any diminished or dominant chord can act like a dominant substitute to lead into the resolving chord. In this case, the composer is considering the approach to ii rather than a delayed approach to V.


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## fwd0120 (Jan 1, 2014)

Okay, that actually makes sense (it wouldn't have a few days ago)! Thanks.

Yes, the first 4 bars in Wave are DMaj7 | Bbdim | Am7 | D7(b9), but ML's figure is just bar 1-3.

I'll keep on analyzing some tunes for these so until I am fully acclimated to the concept, but I do believe it makes sense now. Now I just need to get practical with it. Off to the woodshed!


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## Mr. Big Noodles (Jan 1, 2014)

fwd0120 said:


> Yes, the first 4 bars in Wave are DMaj7 | Bbdim | Am7 | D7(b9), but ML's figure is just bar 1-3.





Is there a bar 0? Perhaps -1? I think you mean that Levine shows bars 2-4. At any rate, the focus of the passage is the ii V portion.



> I'll keep on analyzing some tunes for these so until I am fully acclimated to the concept, but I do believe it makes sense now. Now I just need to get practical with it. Off to the woodshed!


It might help to do a bit more research. The chords that matter in nearly all progressions are the leading tone functions. This means dominant seventh chords and diminished chords. You might have a progression like this: Em Am D7 G (vi ii V7 I)









D7 tells us we're in the key of G. After we hit D7, there's no turning back: the tonic is imminent. That's fine, because it feels good. Sometimes, a composer will want to emphasize the V7 in order to build anticipation for the resolution. In Common Practice Period (CPP) music (classical music from 1600-1900, give or take a few decades), there are a few ways to do this. The diatonic solution is to precede the V7 by what is known as a "cadential 6/4". Here is the same progression, with the cadential 6/4 added:

Em Am G/D D7 G
vi ii I6/4 V7 I






Notice that the bass note of I6/4 is the same as V. This is essential to the sonority. That I6/4 is not functioning as a tonic chord, but more as an anticipation of the V7 chord. You can read more about it here:

Chords in Inversion



> The Cadential 6/4 chord:
> 
> This is a specific and most common use of second inversion triads, found frequently at the end of phrases. It consists of a second inversion tonic triad, followed by a root position dominant chord, which then usually resolves according to form a cadence. Notice how the bass note is doubled and remains on the same pitch class in a cadential 6/4, and the other voices resolve smoothly downward. For this reason, these two chords (I 6/4 and V) are almost always grouped together as a pair, and as such, form a cadential 6/4 cadence.


The highlighted part is important. I6/4 will not sound like a tonic chord in this case, because it is heard as an integral part of the dominant. It is essentially a prolongation of the dominant harmony. I will also add that the cadential 6/4 helps to add a bit more motion to the dominant harmony, so things don't sound as static.



Because the I6/4 V group is such a strong figure, it is often inserted at cadence points even after a strong predominant chord is sounded. For example, the secondary dominant V/V should go straight to V. The first bar here is a representation of that voice leading:









(The seventh of the V chord is optional. Since we're doing a I6/4 between them, the octave D is more important.)



Notice the resolution of the secondary leading tone to D, along with the bass motion to the D an octave lower. When we get to the progression, the same notes exist in the same place in the I6/4, so we can slip it in there seamlessly. And, because the I6/4 is heard as part of the dominant, this is really nothing too out there.



There are some instances when the cadential 6/4 is used to solve problems in voice leading. The classic case is with the German augmented sixth chord. Augmented sixth chords are nice, because you get this chromatic contrary motion leading to the dominant octave: E&#9837; going down to D, and C# going up to D. However, when there is a perfect fifth in the chord, you get an unappealing parallel fifth.








(Edit: I just realized that I left a parallel fifth from the vi going to Ger+6. Er, ignore that.)

Lo, stick a I6/4 in there, and you can easily avoid that parallelism.


===================


In jazz harmony, the equivalent of I6/4 V is ii V. So, you can think of ii V as the standard cadential grouping, and it can disrupt the normal resolution of a predominant chord with no ill effects.


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## fwd0120 (Jan 1, 2014)

Such a great wealth of info! 
That is sure to keep me busy for a while. Thanks!!!!

And yes, my typo, I meant measures 2-4. Here is the leadsheet.

http://www.realbooksite.com/jazz-sheet-music-images/Jazz-Sheet-Music-Page-452.jpg

Thanks again, I will definitely work on these and continue to research!


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