2 players. Player One solos. Player Two builds an accompaniment out of two notes, i.e. one interval, i.e.
Minor second (m2), e.g. C – Db
Major second (M2), e.g. C – D
Minor third (m3), e.g. C – Eb
Major third (M3), e.g. C – E
Perfect fourth (P4), e.g. C – F
Tritone (TT), e.g. C – F#
Perfect fifth (P5), e.g. C – G
Minor sixth (m6), e.g. C – Ab
Major sixth (M6), e.g. C – A
Minor seventh (m7), e.g. C – Bb
Major seventh (M7), e.g. C – B
The second note may ascend or descend or both in regular or irregular alternation. The rhythmic value of the two notes may be the same or different (first time: start with same note values). They may be long tones (giving more the effect of a drone), or quicker notes, which provide rhythmic drive and spell out a suggested harmony more clearly. You may also experiment with multiple notes on a pitch before switching to the other pitch.
At some point, players switch roles.
Play this game a number of times, each time choosing a new “main” note, e.g. first C, then F, then G, then Bb, and so on. It will be a long time before you have worked your way through all notes and all intervals.
Keep in mind: the fact that only two notes are used makes the harmony somewhat ambiguous, something the soloist can exploit. For example, if the accompaniment is playing C-E, this would work perfectly well with the full chords of C major, C7 or C9, A minor, Am7 or Am9, or even something like Ab augmented (Ab C E). If the switch between notes is fairly slow (a measure or more on each), the soloist could treat note as one note in a triad and have even more possibilities, e.g. C = C, Cm, E, Em, G, Gm, C7, E7, G7, C°, E° (= G°).
Idea 1: Experiment with how long you stay on each pitch, from very briefly to four measures each.
Variation: Make the form ABA, using one set of intervals (e.g. P4) for the first and last sections with a different interval for the middle section (e.g. m2). You might also switch players when you switch intervals, so that, e.g. Player Two uses one interval to play the accompaniment for the A section; Player One takes over the B section with a different interval, and finally Player Two goes back to the first interval for a return of the A section.
Idea 2: Make the B section in a dramatically different key than the A section.