When confronted with a dominant chord, a soloist has a host of scale options to choose from. Sometimes enough extensions and alterations are specified to narrow the choices down to a single scale, but there are frequently several options remaining.

As I understand it, a chord is dominant if and only if it has at least 1, 3, and b7. Everything else is an extension or alteration of the dominant sound. This includes b5, 5, #5, b9, 9, #9, 11, #11, b13, and 13.

Below are the scales I would consider over a dominant chord. (I'm sure there are more obscure ones. If it has 1, 3, and b7, it's good to go. Leave a comment if you have more.) I've written them out using scale degrees and chord extensions. Keep in mind that b3 = #9, b5 = #11, and #5 = b13. I use these interchangeably, and I treat chords the same way when it has one or the other alteration.

Mixolydian:
1 2 3 4 5 6 b7 = 1 3 5 b7 9 11 13

Lydian Dominant:
1 2 3 #4 5 6 b7 = 1 3 5 b7 9 #11 13

Altered Dominant:
1 b2 b3 3 b5 b6 b7 = 1 3 b5 #5 b7 b9 #9

Phrygian Major:
1 b2 3 4 5 b6 b7 = 1 3 5 b7 b9 11 b13

Half-Whole Diminished:
1 b2 b3 3 #4 5 6 b7 = 1 3 5 b7 b9 #9 #11 13

Whole Tone:
1 2 3 b5 b6 b7 = 1 3 b5 #5 b7 9

Here are a few rules I've formulated from writing these out.

• I default to Mixolydian or Lydian Dominant if there are no alterations.
• If altered 5 and #9, use Altered Dominant.
• If altered 9 and natural 13, use Half-Whole Diminished.
• If altered 5 and natural 9, use Whole Tone.
• Phrygian Major is nice over V7b9 leading to i, as it's the same notes as Harmonic Minor on i.

I can also just play the arpeggio with leading tones into each note. I wrote about that long ago: Constructing Jazz Scales from Chord Tones.

In the end, I just pick whatever notes make up the sound I'm going for, scales be damned. Dominant chords are frequently used for tension before a release, and that's a perfect time to sprinkle some outside notes around. (I like Whole Tone over a plain 13 chord.) Sometimes I'll just forget the chord and scales completely and play a random chromatic sequence, resolving on the next chord.