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Dizzying Dominant Sevenths
The most common chord progression in traditional jazz is the ii-V7-I progression, and its minor version, iim7(b5), V7 (b9), i. These progressions are also sometimes extended into iii-vi-ii-V-I progressions, with some chords occasionally undergoing tritone substitutions or mode changes.
A player benefits greatly from recognizing these progressions when they occur (both visually and aurally) and being prepared to comp and improvise over them with assuredness.