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 [[equal temperament]]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 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.

~~No standard beginning cutoff to~~ the ~~list has been specified~~.

== Computation ==

Optimal ET sequences can be computed by iterating through all GPVs, finding the error of each and comparing it with the last best error value.

~~== Computation ==~~

Below is an example using [[Flora Canou]]'s [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator], using the <code>et_sequence</code> function from <code>te_equal.py</code>. 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:

~~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:

<~~pre~~>

~~import et_sequence_error as ete~~

import numpy as np

from lib.te_common import Subgroup

from lib.te_equal import et_sequence

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

et_sequence(np.column_stack([[7, -1, -1, -1, 1], [-4, 1, -1, 0, 1]]), subgroup=Subgroup ([2, 11, 13, 17, 19]))

</~~pre~~>

</syntaxhighlight>

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

Which produces the list: 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh.

[[Category:Regular temperament theory]]

@@ Line 1: / Line 1: @@
-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.
+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.
-No standard beginning cutoff to the list has been specified.
+== Computation ==
+Optimal ET sequences can be computed by iterating through all GPVs, finding the error of each and comparing it with the last best error value.
-== Computation ==
+Below is an example using [[Flora Canou]]'s [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator], using the <code>et_sequence</code> function from <code>te_equal.py</code>. 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:
-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:
-<pre>
+<syntaxhighlight lang="python">
-import et_sequence_error as ete
 import numpy as np
+from lib.te_common import Subgroup
+from lib.te_equal import et_sequence
-ete.et_sequence_error(np.array([[7,-4],[-1,1],[-1,-1],[-1,0],[1,1]]), subgroup=[2,11,13,17,19])
+et_sequence(np.column_stack([[7, -1, -1, -1, 1], [-4, 1, -1, 0, 1]]), subgroup=Subgroup ([2, 11, 13, 17, 19]))
-</pre>
+</syntaxhighlight>
-Which produces the list: 13, 24, 33, 37, 46, 57, 70, 127.
+Which produces the list: 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh.
 [[Category:Regular temperament theory]]