Optimal ET sequence

From Xenharmonic Wiki
Jump to navigation Jump to search

Many regular temperaments documented on the wiki are accompanied with an optimal ET sequence, which suggests some useful equal tunings to tune the temperament as well as mos scales available. Technically, it gives generalized patent vals (GPVs) for equal temperaments which support the temperament, where each subsequent GPV included improves upon the TE error of the previous GPV, though no standard beginning cutoff to the list has been specified.

Computation

Optimal ET sequences can be computed using Flora Canou's Temperament Evaluator, using the et_sequence function. For example, here is how the optimal ET sequence for Yer temperament was determined, by providing its comma basis and subgroup:

import et_sequence as ete
import numpy as np

ete.et_sequence(np.array([[7, -4], [-1, 1], [-1, -1], [-1, 0], [1, 1]]), subgroup=[2, 11, 13, 17, 19])

Which produces the list: 13, 24, 33, 37, 46, 57, 70, 127.