Optimal ET sequence: Difference between revisions
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Cmloegcmluin (talk | contribs) val list / ET sequence → Optimal GPV sequence |
m Update links and misc cleanup |
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Many [[regular temperaments]] documented on the wiki are accompanied with an ''' | Many [[regular temperaments]] documented on the wiki are accompanied with an '''optimal GPV sequence'''. This 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. | ||
No standard beginning | No standard beginning cutoff to the list has been specified. | ||
== | == 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/ | |||
<pre> | <pre> | ||
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import numpy as np | 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]) | ete.et_sequence_error(np.array([[7,-4],[-1,1],[-1,-1],[-1,0],[1,1]]), subgroup=[2,11,13,17,19]) | ||
</pre> | </pre> | ||
Revision as of 19:13, 18 August 2022
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.