Optimal ET sequence: Difference between revisions

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Many [[regular temperaments]] documented on the wiki are accompanied with an '''~~Optimal~~ GPV sequence'''. This gives [[generalized patent val]]s (GPVs) for [[ET]]s which support the temperament, where each subsequent GPV included improves upon the [[TE error]] of the previous GPV.

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 ~~or ending~~ cutoff to the list has been specified.

No standard beginning cutoff to the list has been specified.

== ~~How to compute~~ ==

== 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/~~te_temperament_measures Tuning Optimizer & TE~~ Temperament ~~Measures Calculator~~], using the <code>~~et_sequence_error~~</code> function. For example, here's how the optimal GPV sequence for [[~~Subgroup_temperaments~~#Yer_.28rank_3.29|Yer temperament]] was determined, by providing its comma basis and subgroup:

<pre>

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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])~~</nowiki>~~

ete.et_sequence_error(np.array([[7,-4],[-1,1],[-1,-1],[-1,0],[1,1]]), subgroup=[2,11,13,17,19])

</pre>

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-Many [[regular temperaments]] documented on the wiki are accompanied with an '''Optimal GPV sequence'''. This gives [[generalized patent val]]s (GPVs) for [[ET]]s which support the temperament, where each subsequent GPV included improves upon the [[TE error]] of the previous GPV.
+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 or ending cutoff to the list has been specified.
+No standard beginning cutoff to the list has been specified.
-== How to compute ==
+== 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/te_temperament_measures Tuning Optimizer & TE Temperament Measures Calculator], using the <code>et_sequence_error</code> function. For example, here's how the optimal GPV sequence for [[Subgroup_temperaments#Yer_.28rank_3.29|Yer temperament]] was determined, by providing its comma basis and subgroup:
 <pre>
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 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])</nowiki>
+ete.et_sequence_error(np.array([[7,-4],[-1,1],[-1,-1],[-1,0],[1,1]]), subgroup=[2,11,13,17,19])
 </pre>