Optimal ET sequence: Difference between revisions

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Revision as of 07:35, 5 May 2023

Many regular temperaments documented on the wiki are accompanied with an optimal GPV sequence. This 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.

No standard beginning cutoff to the list has been specified.

Computation

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

import et_sequence_error as ete
import numpy as np

ete.et_sequence_error(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.