This is a blues which sounds a bit off-key, but where I stay within the harmonies. It has been performed for several times. Here you can listen to a recording I made at home with a guitarist and a bass trombone player. I played the soprano saxophone. Bass and drums came from Band in a Box, i.e. from the computer.
Where does the name come from? The tritone is a dissonant interval consisting of three whole steps. For improvisation you should play the third and the seventh. However, between the major third and the minor seventh, there is the tritone. Take, as an example, the chord C7. The third is E and the seventh Bb. There are mainly dominant seventh chords in the blues. Thus I could compose a blues with many tritones.
You can find the lead sheets here:
TritoneBlues_C TritoneBlues_Bb TritoneBlues_Eb