Optimal ET sequence - Revision history

FloraC: Update to reflect how you're supposed to use this script since v1.14.0

2025-10-10T09:01:22Z

Update to reflect how you're supposed to use this script since v1.14.0

← Older revision		Revision as of 09:01, 10 October 2025
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	<syntaxhighlight lang="python">		<syntaxhighlight lang="python">
	~~import te_common as te~~
	~~from te_equal import et_sequence~~
	import numpy as np		import numpy as np
			from lib.te_common import Subgroup
			from lib.te_equal import et_sequence

	et_sequence(np.column_stack([[7, -1, -1, -1, 1], [-4, 1, -1, 0, 1]]), subgroup=~~te.~~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]))
	</syntaxhighlight>		</syntaxhighlight>

FloraC: Oops

2023-12-05T15:07:06Z

Oops

← Older revision		Revision as of 15:07, 5 December 2023
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	</syntaxhighlight>		</syntaxhighlight>

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

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]

FloraC: Code was outdated

2023-12-05T15:03:43Z

Code was outdated

← Older revision		Revision as of 15:03, 5 December 2023
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	== Computation ==		== Computation ==
	Optimal ET 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 ET sequence for [[No-threes subgroup temperaments #Yer_.28rank_3.29\|Yer temperament]] was determined, by providing its comma basis and subgroup:		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.

			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:

	<syntaxhighlight lang="python">		<syntaxhighlight lang="python">
	import et_sequence ~~as ete~~		import te_common as te
			from te_equal import et_sequence
	import numpy as np		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])		et_sequence(np.column_stack([[7, -1, -1, -1, 1], [-4, 1, -1, 0, 1]]), subgroup=te.Subgroup ([2, 11, 13, 17, 19]))
	</syntaxhighlight>		</syntaxhighlight>

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

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per recent discussion to subsume GP/uniform property into "optimal" (along with support property and error-decreasing property); as well as sequence being of ETs, not vals/maps

2023-05-07T15:08:11Z

"optimal GPV sequence" → "optimal ET sequence", per recent discussion to subsume GP/uniform property into "optimal" (along with support property and error-decreasing property); as well as sequence being of ETs, not vals/maps

← Older revision		Revision as of 15:08, 7 May 2023
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	== 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 ET 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 ET sequence for [[No-threes subgroup temperaments #Yer_.28rank_3.29\|Yer temperament]] was determined, by providing its comma basis and subgroup:

	<syntaxhighlight lang="python">		<syntaxhighlight lang="python">

FloraC: Upgrade

2023-05-05T08:06:16Z

Upgrade

← Older revision		Revision as of 08:06, 5 May 2023
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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 ==		== 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:

	<~~pre~~>		<syntaxhighlight lang="python">
	import ~~et_sequence_error~~ as ete		import et_sequence as ete
	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(np.array([[7, -4], [-1, 1], [-1, -1], [-1, 0], [1, 1]]), subgroup=[2, 11, 13, 17, 19])
	</~~pre~~>		</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]]

FloraC: FloraC moved page Optimal GPV sequence to Optimal ET sequence: Community decision. See talk

2023-05-05T07:35:15Z

FloraC moved page Optimal GPV sequence to Optimal ET sequence: Community decision. See talk

← Older revision	Revision as of 07:35, 5 May 2023
(No difference)

FloraC: Update links and misc cleanup

2022-08-18T19:13:11Z

Update links and misc cleanup

← Older revision		Revision as of 19:13, 18 August 2022
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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>		<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])~~</nowiki>~~		ete.et_sequence_error(np.array([[7,-4],[-1,1],[-1,-1],[-1,0],[1,1]]), subgroup=[2,11,13,17,19])
	</pre>		</pre>

Cmloegcmluin: val list / ET sequence → Optimal GPV sequence

2021-12-07T17:21:42Z

val list / ET sequence → Optimal GPV sequence

← Older revision		Revision as of 17:21, 7 December 2021
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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>

Cmloegcmluin: Cmloegcmluin moved page ET sequence to Optimal GPV sequence: per discussion on Facebook here: https://www.facebook.com/groups/xenwiki/permalink/2980917012174283/

2021-12-07T17:18:52Z

Cmloegcmluin moved page ET sequence to Optimal GPV sequence: per discussion on Facebook here: https://www.facebook.com/groups/xenwiki/permalink/2980917012174283/

← Older revision	Revision as of 17:18, 7 December 2021
(No difference)

Cmloegcmluin: fix broken github link, and add example result list, per Kite's suggestions (thanks Kite!)

2021-12-05T18:32:59Z

fix broken github link, and add example result list, per Kite's suggestions (thanks Kite!)

← Older revision		Revision as of 18:32, 5 December 2021
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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:		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:

	<pre>		<pre>
Line 13:		Line 13:
	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])</nowiki>
	</pre>		</pre>

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

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]