Maths vs. Music - Tuning and harmony

[Alex K]

To me the second one does indeed sound like it is played on a detuned bar piano. There appear to be some seriously flat notes in those 7,9 chords.

Yep.  My opinion is that just tuning is great for the main triads, and crap for anything else.  Hence my project idea-- specify exactly what note and system EACH note derives from, to guarantee a properly-tuned dynamic listening experience!

so let's say I'm in the key of C, playing a V-flat9 chord.  Where are the notes, G-B-D-F-Aflat coming from?

I'd guess you'd want GBD built off the G for the purest major sonority, and the F and a-flat from the minor iv, f,  for the best resolution in/to C.  OR would you treat the extended chord as part of B-flat7, and use the A-flat which is subdominant to that?  That might work if you wanted to modulate to c-.

It seems to me the best way to achieve this would be to record the song in equal tempering, and then go through the painstaking process, starting with the tonic, of saying where EVERY SINGLE note is derived.  In fact, I'd even say there's another level of artistry there, since you and I might not choose the same tuning arrangement for this or that chord or section.

Yes, I meant to replay to your idea sooner, I find this super interesting.

I'm a harmony theory noob, so I don't grasp all the implications of this yet.

Always the mathematician, I'm trying to think of examples where this is explicitly impossible, just to get a feel of how far one can go with this technique of dynamically just tuning or how you called it. I suppose enharmonic modulation

https://en.wikipedia.org/wiki/Modulation...modulation

would become awkward simply because during the transition from one key to the other, what is the same pitch in equal tuning appears in two different contexts which would have slightly different pitch in either key in a just tuning -
or one would have to fudge at some point...