b5, #5, b9, #9
They may be in any combination. It is more common to have one of each, for example an altered 5th and an altered 9th rather than both being altered 5ths (or altered 9ths).
The altered chords create more tension[?] and dissonance and in jazz harmony they are preferable to a generic dominant chord with either diatonic tensions (9 and 13) or no tensions whatsoever.
However, in more recent times, even such altered harmony has become commonplace, and more dissonant chromatic harmony is being explored by jazz players such as David Liebman and Randy Sandke.
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