@jofemodo. Great answer, I can hear Salsa!

My original intent was to present the Melakarta system of 72 distinct scales to Western musicians. But as I continued to study the math involved, I had to go back and learn something about Group Theory. The Intervals are strings of integers, and I have convinced myself that this is probably the most efficient format for storing these (and other even more exotic) scales. This format is independent of the tuning system; although it is based on Equal Temperament, it can be used for any 7 of 12 tone system, Pythagorean, Just, or whatever. You can pick any tonic and build the scale from the string of intervals. Or you can build other systems like 5 of 8, or 13 of 24.

I’m learning Python to implement some of these ideas. I haven’t done any real coding for 15-20 years, QBasic. Yeah, I’m a dinosaur. I wrote code for myself, just to prove that I understood the math. For instance, my trade was printing and I ran scanners when they took up a whole room and had oscilloscope readouts and core memories. So I wrote code to calculate and graph colors, converting from RGB to XYZ to Lab, etc. Started with arc lights and ended up with Photoshop on a G5 Mac.

So, in Python, I have the problem on converting from a string to a series of integers, to a series of floats, doing some calculations, converting back to integers, and then back to strings. Then the strings have to be identified by comparison to the original dictionary of strings. This is easy, although tedious, on paper. Combining 120 scales, 2 at a time is:

20 C 2 = 7140.

That’s a small number for a computer, but a large number to work out by hand. So I’m working on code for this calculation. But once it’s done, it’s done,; it will become a set of data. Of course there are duplications, sometimes 2 scales produce different scales, and other times the same 2 scales. Using the language of Group Theory, I claim that the catalog of the addition of these scales will converge to the kernel of the group.

Two extremes of approaches to Music Theory are represented by:

ARxIV:2010.01728v1

group actions, power mean orbit size, and musical scales

ARxIV:1202.4212v2

harmony explained: progress toward a scientific theory of music

The first paper presents a comprehensive analysis of scale groups, far beyond my naive classifications.

The second presents as the work of a crank, although mine might be also so described. The author’s criticism of John Mehegan’s seminal work seems excessive.

I read Mehegan in my early 20’s, and it was revelatory. 12 keys times 5 chords equals 60 chords. The stellated dodecahedron (5 x 12 = 60), or the stellated icosahedron (3 x 20 = 60).

Don’t bad-rap Mehegan! His books did more for music than any ‘medieval medical textbook’ ever did for medicine. (Paracelsus actually introduced Ayurvedic medicine to Europe).

Sorry, I’m ranting now. Reality check! More later.