Optimal ET sequence

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 by iterating through all GPVs, finding the error of each and comparing it with the last best error value.

Below is an example using Flora Canou's Temperament Evaluator, using the et_sequence function from te_equal.py. Here is how the optimal ET sequence for Yer temperament was determined, by providing its comma basis and subgroup:

import numpy as np
from lib.te_common import Subgroup
from lib.te_equal import et_sequence

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

Which produces the list: 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh.