Badness - Revision history

FloraC: Address the term efficiency

2026-03-20T08:15:44Z

Address the term *efficiency*

← Older revision		Revision as of 08:15, 20 March 2026
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	'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. in terms of both [[complexity]] and [[error]], two measures that usually vary in opposite directions.		'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. in terms of both [[complexity]] and [[error]], two measures that usually vary in opposite directions.

	Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.		Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error. A temperament is said to be '''efficient''' if it achieves low badness.

	Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]]. Some also have several normalizing coefficients.		Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]]. Some also have several normalizing coefficients.

FloraC: Update

2025-12-03T18:27:34Z

Update

← Older revision		Revision as of 18:27, 3 December 2025
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	Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.		Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.

	Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]].		Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]]. Some also have several normalizing coefficients.

	~~:'''~~Note~~:'''~~ [[~~Gene Ward Smith\|Smith~~]] [[TE logflat badness]] is the badness ~~appearing on temperament~~ pages~~, unless stated otherwise~~.''		{{Note\| [[Sintel]]'s [[TE logflat badness]] is generally the badness metric used throughout this wiki. Many old pages still use [[Gene Ward Smith\|Smith]]'s; those are being phased out. }}

	== External links ==		== External links ==

FloraC: Move some essential info from the complexity article

2025-11-13T10:06:35Z

Move some essential info from the complexity article

← Older revision		Revision as of 10:06, 13 November 2025
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	'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. ~~It generally describes the trade-off between~~ [[complexity]] and [[error]], two measures that usually vary in opposite directions.		'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. in terms of both [[complexity]] and [[error]], two measures that usually vary in opposite directions.

			Complexity and error are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s) typically do not have low complexity. Badness is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.

	Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]].		Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]].

FloraC: Clarify; +an external link

2024-10-23T11:06:06Z

Clarify; +an external link

← Older revision		Revision as of 11:06, 23 October 2024
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	Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]].		Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]].

	'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''		:'''Note:''' [[Gene Ward Smith\|Smith]] [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''

			== External links ==
			* [http://tonalsoft.com/enc/b/badness.aspx Tonalsoft Encyclopedia \| ''Badness'']

	[[Category:Badness\| ]] <!-- Main article -->		[[Category:Badness\| ]] <!-- Main article -->

ArrowHead294 at 15:17, 29 May 2024

2024-05-29T15:17:57Z

← Older revision		Revision as of 15:17, 29 May 2024
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	'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. It generally describes the trade-off between [[complexity]] and [[error]], two measures that usually vary in opposite directions.		'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. It generally describes the trade-off between [[complexity]] and [[error]], two measures that usually vary in opposite directions.

	Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]] and [[TE logflat badness]].		Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]], and [[TE logflat badness]].

	'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''		'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''

	[[Category:Badness\| ]] <!-- ~~main~~ article -->		[[Category:Badness\| ]] <!-- Main article -->

Fredg999: Improve lead section

2023-02-26T06:02:44Z

Improve lead section

← Older revision		Revision as of 06:02, 26 February 2023
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	'''Badness''' is ~~concept~~ that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness [[measures]] are in use, including [[Cangwu badness]], [[TE simple badness]] and [[TE logflat badness]].		'''Badness''' is a measure that allows the comparative evaluation of tunings, temperaments, interval approximations, etc. It generally describes the trade-off between [[complexity]] and [[error]], two measures that usually vary in opposite directions.

			Several different badness measures are in use, including [[Cangwu badness]], [[TE simple badness]] and [[TE logflat badness]].

	'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''		'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''

	[[Category:Badness\| ]] <!-- main article -->		[[Category:Badness\| ]] <!-- main article -->

Fredg999 category edits: Categories, sort key

2023-02-26T05:49:24Z

Categories, sort key

← Older revision		Revision as of 05:49, 26 February 2023
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	'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''		'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''

	[[Category:~~badness]]~~		[[Category:Badness\| ]] <!-- main article -->
	~~[[Category:measure~~]]

Xenwolf: thanks to the (correct!) redirect pages we can link even better :)

2020-07-24T11:46:54Z

thanks to the (correct!) redirect pages we can link even better :)

← Older revision		Revision as of 11:46, 24 July 2020
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	'''Badness''' is concept that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness [[~~measure\|~~measures]] are in use, including [[~~Cangwu_badness\|~~Cangwu badness]], [[~~Tenney-Euclidean_temperament_measures#TE simple badness\|~~TE simple badness]] and [[~~Tenney-Euclidean_metrics#Logflat~~ TE badness\|TE logflat badness]].		'''Badness''' is concept that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness [[measures]] are in use, including [[Cangwu badness]], [[TE simple badness]] and [[TE logflat badness]].

			'''''Note:''' [[TE logflat badness]] is the badness appearing on temperament pages, unless stated otherwise.''

	~~Note: TE logflat badness is the badness appearing on temperament pages, unless stated otherwise.~~
	[[Category:badness]]		[[Category:badness]]
	[[Category:measure]]		[[Category:measure]]

FloraC: Important clarification

2020-07-24T10:53:48Z

Important clarification

← Older revision		Revision as of 10:53, 24 July 2020
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	'''Badness''' is concept that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness [[measure\|measures]] are in use, including [[Cangwu_badness\|Cangwu badness]], [[Tenney-Euclidean_temperament_measures#TE simple badness\|TE simple badness]] and [[Tenney-Euclidean_metrics#Logflat TE badness\| TE logflat badness]].		'''Badness''' is concept that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness [[measure\|measures]] are in use, including [[Cangwu_badness\|Cangwu badness]], [[Tenney-Euclidean_temperament_measures#TE simple badness\|TE simple badness]] and [[Tenney-Euclidean_metrics#Logflat TE badness\|TE logflat badness]].

			Note: TE logflat badness is the badness appearing on temperament pages, unless stated otherwise.
	[[Category:badness]]		[[Category:badness]]
	[[Category:measure]]		[[Category:measure]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		'''Badness''' is concept that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness [[measure\|measures]] are in use, including [[Cangwu_badness\|Cangwu badness]], [[Tenney-Euclidean_temperament_measures#TE simple badness\|TE simple badness]] and [[Tenney-Euclidean_metrics#Logflat TE badness\| TE logflat badness]].
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~		[[Category:badness]]
	~~: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2014-04-07 18:55:21 UTC</tt>.<br>~~		[[Category:measure]]
	~~: The original revision id was <tt>501150490</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Badness is concept that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness [[measure\|measures]] are in use, including [[Cangwu badness]], [[Tenney-~~Euclidean temperament measures~~#TE simple badness\|TE simple badness]] and [[Tenney-~~Euclidean metrics~~#Logflat TE badness\| TE logflat badness]].~~</pre></div>~~
	~~<h4>Original HTML content~~:~~</h4>~~
	~~<div style="width:100%; max-height:400pt; overflow~~:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Badness</title></head><body><strong>Badness</strong> is concept that allows comparative evaluation of tunings, temperaments, interval approximations etc. Several different badness <a class="wiki_link" href="/measure">measures</a> are in use, including <a class="wiki_link" href="/Cangwu%20badness">Cangwu badness</a>, <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">TE simple badness</a> and <a class="wiki_link" href="/Tenney-Euclidean%20metrics#Logflat TE badness"> TE logflat badness</a>.</body></html></pre></div>