‘Fuchsia Swing Song’ is the title track from Sam Rivers debut album as leader. The whole album is a fine example of the “Advanced Form” Jazz evolving at this time.
As with many of these “Advanced Form” tunes (Link), it’s a good idea to begin with the melody. This is particularly true for songs written by horn players, for obvious reasons. This head is 16 bars long. The melody is squarely in Bb minor (natural and briefly harmonic). Basic blues harmony with a chromatic section in the middle fits the melody well (Example 1).
While the implied key and basic harmonic framework is pretty conventional the minor key and the fourth and second intervals give the melody a unique sound.
The actual chordal accompaniment (see above) that Jaki Byard plays moves further away from typical Destionational Harmony (the B Major 7 and E7b5) but the blues based reference points remain mostly in place.
Example 2 is the first 16 bars of Jaki Byard’s solo. Notice how he works the little three note motif that holds it all together.