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Just add b9th, but what about b13th?

Let's step back. Here is the summary of the steps, which you need to process in a split second on the stage when sight reading:

  1. Identify the chord tones of the diminished 7th chord
  2. Produce four dominant chords which share the tritones with the diminished 7th chord
  3. Pick one of them you like, hopefully, the one closest to the context, as explained
  4. Add b9th then blow

Since we are accustomed to adding the b13th when we blow such phrase, would it work in this situation? It works most of the time, as I did on the D7 to A dim7 example. On the other hand, b13th of Ab7 is F-flat, and it will take away from the context. In any case, improvising live does not need to be theoretically correct, while it is still important to know what you are doing.

End of this subject.