The jazz musician's interest in harmony took a sharp turn with 'be-bop'. Early development of this music is poorly-understood because it occurred during a lengthy musician's strike, so documentation (recording) is sparse. But listening to early '40s recordings, with Monk in particular, helps us appreciate the changes not only to rhythm and structures, but to harmony.
Chords got extended (9ths, 11ths, flatted-13ths, &c.), incorporating notes that appear to the traditional ear as dissonances. Voicings and inversions exacerbated the 'clashing' nature of these intervals (eg: reducing a 9th one octave makes it a 2nd). The 'natural' overtones (octaves and fifths) were inconsistent in the new forms, and - with the asymetric rhythms and staccato style - made every note stand out.
By the early 1950s, the harmonies of bop had become integrated with more widely-played musics ('cool-jazz', pop, R&B). Herman Blount, who had come up as an R&B musician (with Wynonie Harris, &c.) got a job as arranger/director with the Fletcher Henderson Orchestra; his job was to 'modernize' the sound. Naturally, he went with bop harmonies. He also did a sideline combo, which added John Gilmore on sax in 1953. Gilmore remained with Blount (Sun Ra), eventually leading the Solar Arkestra when illness forced Blount to retire in the late 80s.
So context for the Gilmore quote includes the historical context (a significant development in jazz/popular harmony) and his close ties with the person.
Sun Ra's dramatic but well-contructed political and philosphic world-view often confuses the casual observer/listener. Again - look at context! Contemporaries include Elijah Muhammed, L.Ron Hubbard, Harry Partch, and John Cage - and Blount was aware of ALL their work.
Finally - absent the mystical works of Pythagoras - harmony is a cultural artifact. Listen to Javanese or Karnatic or Shona traditional music (listen to Charley Patton or Elmore James!) and you hear a different set of intervals in use. Nobody uses just intonation, just like nobody agrees whether A is 442 or 440. Charles Ives says "My God - what has sound to do with music?"
Music is something done by a person or persons which results in an aural-based image in the mind of another person or persons. One listens and deduces the rules...