Guidelines for Dominants in Jazz

I’ve listed some guidelines to dominant chords that beginners and musicians coming from other types of music often need to have explained to them, from the mild to the spicy.  They are not ‘rules’ but ‘guidelines’ that will help open up an understanding of what jazz players have been doing with dominants for well over half a century.

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For the sake of argument, we'll talk about the key of D (two sharps), in which A7 is the V chord.

1. The essential tones of a dominant are the Major 3 and flat 7 -- C# and G for an A7. Those are the only tones an accompanist really 'needs' to play to express the V chord. Also, these are the strongest notes to target in a dominant phrase to explicitly state the V chord in the harmony.
2. A 'functioning' dominant is one that is going to its I or i chord. A non-functioning dominant would be like the Bb7 in a Bb blues, because is not the V of any chord (until it goes to the IV chord).  Another example is a II7 that eventually changes to a ii-7 before moving to the V and back to the I.
3. The dominant in a ii-V is a functioning dominant. In fast tune, you are likely to just think of the V chord instead of the ii and then the V for the cadence, especially since the ii and V are diatonic. If you target the b7 and the root of the V early in your ii-V line, you have already expressed the 'ii' via 'essential tones' (essential tones are 3rds and 7ths).
4. Any functioning Dom.7 chord can be altered with almost any type of 'extension.' The only taboo note is the Major 7 -- you wouldn't want to play an Ab in an A7 unless it was a chromatic movement (see 'bebop' scale). Traditionally, the 11 is somewhat 'weak' also. Adding a b9, 9, #9, b5, #5, 13 are all cool to add in your A7, however if you have one player thinking A9 and one player thinking A7b9, you might get some bad 'rub' if they aren't listening to each other.  The ‘outside’ notes can help ‘lead’ the listener chromatically back to the I, which where a functioning dominant goes.
5. While A Mixolydian is the 'diatonic' way to play over our A7, you can also play a BbminMaj7 scale, or a DminMaj7 scale. These are referred to as the 'altered' scale, they are just different modes of the Harmonic or Melodic Minor when you start on the A. They bring out various altered tones as listed in guideline #4.
6. You can also play a Bbdim arpeggio/chord or any inversion of it (Gdim, C#/Dbdim, Edim). This is like an A7b9 substitution.
7. You can substitute the tritone Dominant of a functioning V instead of the V7. Instead of A7, you can substitute Eb7. A tritone sub voicing is also a V7#11 voicing.
8. You can substitute the dominant rooted at any note of the V's tritone diminished arpeggio on a functioning V chord. The tritone sub in D is Eb7 (Eb is the tritone of the V, which is A). The Ebdim arpeggio is Eb, A, C, Gb. For the A7 five chord, you can sub Eb7, C7, Gb7. As stated in guideline #7, Eb is a A7#11 voicing. The C7 is A7(b9,#9). The Gb7 is A7(b9,13).
9. Because of #6 and #8, you can play the A Half-Whole diminished scale for a A7 (A, A#, C, C#, D#, E, F#, G). If it is easier, you can think of this scale as E Whole-Half scale (E being the ii chord).
10. Pretty much any diatonic chord can be re-harmonized as a dominant. The vi chord can be played as a VI7 (A Train). The ii chord can be played as a II7 (There is No Greater Love). The iii chord can be played as III7 (All of Me). I can't think of a vii chord going dominant, but the bVII7 dominant is the 'back-door' dominant that can resolve to the I (G-7 / C7 / Dmaj7). Remember C7 is one of the 4 dominants out of the tritone diminished in guideline #8.
11. You can play the whole tone scale on Dom7#11 or Dom7#5 chords (A whole-tone on A7). It can sound pretty 'out' if the rest of the band isn't hip and seems to work better in some scenarios.
12. The melodic minor has 2 diatonic dominants. The MM IV is Dom7#11, the MM V is Dom7(b13). For playing Bb melodic minor over A7, you can try Eb7#11 or F7b13. If you were thinking E Harmonic minor, you could try A7#11 or B7b13.
13. The Barry Harris 'Six to Diminished' concept re-harmonizes the diatonic chords to either be a 'Sixth' chord or Dom7b9. The 'V' chords are played using ‘diminished’ voicings with the V's b9 as in guideline #6.  The diminished voicing of the V always leads to the neighboring inversion of the I6 voicing.  There is an extra chord inserted to account for the #5 of the 'Barry Harris' scale explained later. For D major, the chords are all the B-6 inversions (which serve as the I, III, V, VI chords), plus all the C#dim inversions (which serve as the II, IV, bVI and VII chords). So in D Major: I = D6, II = Edim (A7b9), III = F#-6 or F#maj6 (don't voice 3rd – and inverted I6), IV = Gdim (A7b9), V= A9/11/13 (inverted I6), bVI = A#dim or Bbdim (A7b9), VI = B-7 (inverted I6), VII = C#dim (A7b9). This creates a chord scale that is constantly descending from V (A7b9) to I (inversion of D6). It diatonically relates to the 3rd mode of the Harmonic Minor Scale (minus the 5). So, the 'Barry Harris' Maj#5 scale is the VI as Harmonic Minor. For D, the Maj#5 Barry Harris scale is essentially B Harmonic Minor (plus the A note). This scale has all the B-6 and C#dim inversions listed above.