Optimal ET sequence: Difference between revisions
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Many [[regular temperaments]] documented on the wiki are accompanied with an '''optimal | Many [[regular temperaments]] documented on the wiki are accompanied with an '''optimal ET sequence''', which suggests some useful [[equal tuning]]s to tune the temperament as well as [[mos scale]]s available. Technically, it gives [[generalized patent val]]s (GPVs) for [[equal temperament]]s 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 == | == Computation == | ||
Optimal GPV 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 GPV sequence for [[No-threes subgroup temperaments #Yer_.28rank_3.29|Yer temperament]] was determined, by providing its comma basis and subgroup: | Optimal GPV 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 GPV sequence for [[No-threes subgroup temperaments #Yer_.28rank_3.29|Yer temperament]] was determined, by providing its comma basis and subgroup: | ||
< | <syntaxhighlight lang="python"> | ||
import | import et_sequence as ete | ||
import numpy as np | import numpy as np | ||
ete. | ete.et_sequence(np.array([[7, -4], [-1, 1], [-1, -1], [-1, 0], [1, 1]]), subgroup=[2, 11, 13, 17, 19]) | ||
</ | </syntaxhighlight> | ||
Which produces the list: 13, 24, 33, 37, 46, 57, 70, 127. | Which produces the list: 13, 24, 33, 37, 46, 57, 70, 127. | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 08:06, 5 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 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 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.