Optimal ET sequence: Difference between revisions

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m Cmloegcmluin moved page ET sequence to Optimal GPV sequence: per discussion on Facebook here: https://www.facebook.com/groups/xenwiki/permalink/2980917012174283/
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val list / ET sequence → Optimal GPV sequence
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Many [[regular temperaments]] documented on the wiki are accompanied with a sequence of [[generalized patent val]]s for [[ET]]s which support the temperament, where each subsequent [[val]] included improves upon the [[TE error]] of the previous val.  
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.  


No standard beginning or ending cutoff to the list has been specified.
No standard beginning or ending cutoff to the list has been specified.
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== How to compute ==
== How to compute ==


Val lists 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 val list for [[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>
<pre>

Revision as of 17:21, 7 December 2021

Many regular temperaments documented on the wiki are accompanied with an Optimal GPV sequence. This gives generalized patent vals (GPVs) for ETs 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.

How to compute

Optimal GPV sequences can be computed using Flora Canou's Tuning Optimizer & TE Temperament Measures Calculator, using the et_sequence_error function. For example, here's 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])</nowiki>

Which produces the list: 13, 24, 33, 37, 46, 57, 70, 127.