Thank you so much, @PeterthePapercomPoser! Yes. I am planning on improving on it. Today I added the first solo, which I actually like quite a lot! I am trying to learn about different sections for now and, in the future, maybe add the whole band (or even making a new arrangement for it). For now, I will try to complete the solos, development and ending with this ensemble, as adding more instruments might be too big task for now!
You are right, the singers and players (not on piano, of course, but even on piano they play both minor and major thirds almost at the same time to create the effect) make the tones lower on the blue third, so I think your idea is really good! But microtones is still such a unknown world for me. I see you have been composing with them lately! I heard to the invention and really enjoyed it. How does it work? Do you use it for adjusting the thirds according to the tonality of that moment so they are better tuned than with 12TET? I imagine it must be quite complex to decide on which notes to tweak and how much to tweak them.
For passing chords I follow different methods depending on the context. I do not know much so, to be honest, for this time I just tried to keep it simple. I just harmonized in 4-voice close with the doubling of the melody in the bari sax and always leaving at least a minor 3rd between the top two notes. Then, I decided which tones to consider non-harmonic. I think that is the most interesting part, since in Jazz you could harmonize a 2nd in the melody as a passing tone or as an harmonic tone all the same. Then I followed one of four methods for the non-harmonic tones:
Chromatic or step movement to the next harmonic tone in all voices.
Diatonic movement to the next harmonic tone in all voices.
Harmonizing with the dominant (if one note) or a chain of dominants or common progressions such as ii-V-I.
Free counterpoint.
I guess I used some diminished chords but mostly as a way of using the dominant with the b9. I did not use diminished chords as a "free pass" since I composed it mostl for getting used to the different methods.
Finally I just changed the bass here and there but rarely, sometimes doubling other voices and sometimes with free melodies. It is a really "practical" method but, in the end, it actually gave much more freedom than I expected, even if following those simple steps. There are much more complex voicings that I want to get into in the future, but for now I decided to focus on the basics first!
Thank you so much for commenting!