< Back to IRCAM Forum

Naive Question on Harmonics and Equal Temperaments

OpenMusic
#1

Hi,

I’d like to know the best algorithmic approach to probe two separate but mutually reinforcing questions.

  • If we parse the frequency material of any given equal-tempered music system, how can we best assess which segments of the harmonic series (up to a given nth harmonic, e.g. the 128th or 256th) it reproduces most faithfully?

  • Given a finite segment of the harmonic series, how can we best estimate the smallest equal-tempered music system that best approximates it (up to a given order of error)?

Any hints or insights on this issue would be much appreciated.

All the best,
António

#2

If you are on Facebook, I would join the group “Microtonal Music and Tuning Theory” and ask these questions, there are theorists there who can answer these questions quite thoroughly (in particular Paul Erlich, who runs the group.)

From their answers, you can probably then design an OM patch to implement the algorithms.

#3

Hi,

Thanks for the suggestion. I’m not on Facebook, do you know if they’re either on Discord or Reddit?

All the best,
António