zlacker

A very nicely written and detailed article, with many details I have not personally learned of, in my own music technology hacking so far .. if anyone else is interested in writing software for musical tuning systems, both Xenharmlib and PyTuning are very extensive libraries for the job .. Xenharmlib for C++ and PyTuning for python.

Xenharmlib has deep support for intervals, chords, scales, non-standard notations, and advanced topics like non-Western harmonics, diatonic set theory, and non-octave-repeating systems and also allows for the mathematical manipulation of ratios and structures (harmonic exploration).

PyTuning allows for generating scales from ratios/cents, EDO, just intonation, and custom temperaments and facilitates calculations such as frequency ratios, comma approximations, and temperament comparisons, aligning with the article's derivations and trade-off discussions at a similar depth.

I hope to see more math of music articles in the future .. its a fascinating subject indeed!