Optimal ET sequence: Difference between revisions
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Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per recent discussion to subsume GP/uniform property into "optimal" (along with support property and error-decreasing property); as well as sequence being of ETs, not vals/maps |
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== Computation == | == Computation == | ||
Optimal | Optimal ET sequences can be computed using [[Flora Canou]]'s [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator], using the <code>et_sequence</code> function. For example, here is how the optimal ET sequence for [[No-threes subgroup temperaments #Yer_.28rank_3.29|Yer temperament]] was determined, by providing its comma basis and subgroup: | ||
<syntaxhighlight lang="python"> | <syntaxhighlight lang="python"> | ||
Revision as of 15:08, 7 May 2023
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.