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I need a little help understanding what a particular exercise is trying to teach me. For reference, this is in the Phil DeGreg Jazz Keyboard Harmony book, exercise 2-4A. It's labeled 'Diminished / Tri-tone Sub'.

The first line has the guide tone chords listed for CM7, C#dim7, Dm7, D#dim7, Em7, Eb7, Dm7, Db7, CM7.

While I can see that some of these chords are intended to be diminished substitutions, what are they substituting for?

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They are substituting for secondary dominants of the next chord in the progression. The C♯°7 substituting for A7 which is the dominant of D and the D♯°7 substituting for B7 which is the dominant of E. The only diffrence between the diminished 7th chords and the secondary dominants is only one note which is only a half step difference so there is a lot of common ground between the chords being the A and the B♭ in the A7 vs. C♯°7 and the B and the C in the B7 vs. D♯°7.

The tritone subs are also substitutions for the dominants of the next chords in the progressions, however they resolve in an opposite way of typical dominants. So for example the D♭7 to CMaj7 is a substitution for G7 to CMaj7 and the resolutions follow similar patterns like so:

D♭7    CMaj7     G7
D♭ -->   C   <-- D
F  -->   E   <-- F
A♭ -->   G   <-- G  
C♭ -->   B   <-- B  

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