Coltrane Changes – These are a harmonic progression associated with the great jazz saxophonist John Coltrane. They are also sometimes known as the Coltrane Matrix or Cycle. Trane used this sequence of chords over a traditional II V I chord progression to create more harmonic movement and also to  provide a re-invented platform for improvisation.  

The chord changes feature rather unusual root movement for jazz harmony (by major thirds) and create an augmented triad. The examples below show how the Coltrane changes cycle can be applied over a II V I progression in the key of D major. This is very similar to the approach that Trane used in his composition ‘Countdown’ (based itself on the chord changes of ‘Tune Up’)

The progression presents some challenges for the improviser principally due to the key changes, and I have added some common practice routines that will help you get more comfortable with the sequence. These include arpeggios and also four note melodic groupings that Trane himself favoured when soloing.  

Additional information on Coltrane Changes here: https://en.wikipedia.org/wiki/Coltrane_changes

Here is a MIDI file of the above exercises: