Thanks for the input, and my apologies for not being able to clarify until now.

Simon: Yes, you're exactly right: Each channel represents a tuning layer, and it shouldn't be difficult to write the abstraction (I'm at least halfway there now).

Lucas: Here are some helpful details: The layout of the Tonal Plexus (hereafter abbreviated TPX) is optimized for 205-tone equal temperament (a.k.a. 205 Equal Division of the Octave = "205-EDO"). As Simon put it, it's designed to "misuse" the MIDI channels by sending independent pitch-bend data to get each note to the desired pitch ... but for this to work, the patch's pitch bend must match that of the editing software (and, FWIW, limits polyphony to 16 notes).

Simon: Yes, the Pythagorean scale is embedded, but not in any one channel. Instead, each channel comprises one-half of an octave (see attached table). I've highlighted the duplicated notes (i.e., there are duplicate keys, such that within each octave, the highest version of each triple-sharp is enharmonically equivalent to the lowest triple-sharp in the next column of keys), which only mildly complicate calculations (e.g., for the odd-numbered channels, instead of applying one formula to all 106 notes, one must divide into three "zones" with three different constants on which to add (delta * 0.0585) ... so, in Pd, two moses objects to sort notes arriving via the odd-numbered channels, and three to sort on the even-numbered channels.

Lucas: I've chosen MIDI note numbers for simpler arithmetic (and fewer digits to type, and thus mistype).

Again, thanks for chiming in!



​​-- 
Brian Robison
www.brianrobison.org