Xenharmonic Reference:Tuning system article format - Revision history

Inthar at 23:08, 14 February 2026

2026-02-14T23:08:01Z

← Older revision		Revision as of 23:08, 14 February 2026
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	:''Shortcuts: [[XR:TUN]], [[XR:TS]]''		:''Shortcuts: [[XR:TUN]], [[XR:TS]]''
	''This page is an extension of [[~~XenReference~~:Guidelines]]. It is expected that that page has been read first.''		''This page is an extension of [[Xenharmonic Reference:Guidelines]]. It is expected that that page has been read first.''

	Articles about [[tuning system]]s are some of the most important on this wiki. According to the wiki's mission statement, the ultimate purpose of such an article is to serve as a basic guide to using that tuning system for composition. An individual tuning system must, therefore, be presented as a '''coherent structure with unique rules and particularities''' that govern the flow of composition in that system. Not all tuning systems have independent value for composition, despite whatever value they might have in relation to other structures or in their theoretical properties; ''these should not receive dedicated individual articles.''		Articles about [[tuning system]]s are some of the most important on this wiki. According to the wiki's mission statement, the ultimate purpose of such an article is to serve as a basic guide to using that tuning system for composition. An individual tuning system must, therefore, be presented as a '''coherent structure with unique rules and particularities''' that govern the flow of composition in that system. Not all tuning systems have independent value for composition, despite whatever value they might have in relation to other structures or in their theoretical properties; ''these should not receive dedicated individual articles.''

Inthar: /* Format and content of tables */

2026-01-12T23:46:57Z

Format and content of tables

← Older revision		Revision as of 23:46, 12 January 2026
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	Rank-2 temperament articles should contain two tables, and these constitute the bare minimum of content beyond the introduction. These tables are the '''interval chain''' and the '''tuning spectrum'''.		Rank-2 temperament articles should contain two tables, and these constitute the bare minimum of content beyond the introduction. These tables are the '''interval chain''' and the '''tuning spectrum'''.

	The interval chain includes a list of basic harmonic interpretations of the intervals along the temperament's generator chain, and [[cent]] values for these intervals in some good tuning for the temperament. It may sometimes be convenient to include interval chains for different ([[strong]]) extended mappings within the same table; in some cases, these need separate tunings listed. Interval chains should include most of the harmonic content of the temperament but not be of extreme length; for this reason, it is discouraged to include both positive and negative generators in such a table, but this can be excused if the chain is short enough and for multiperiod/non-octave temperaments where [[complement]]s are not as obvious.		The interval chain includes a list of basic harmonic interpretations of the intervals along the temperament's generator chain, and [[cent]] values for these intervals in some good tuning for the temperament. It may sometimes be convenient to include interval chains for different ([[extension\|strong]]) extended mappings within the same table; in some cases, these need separate tunings listed. Interval chains should include most of the harmonic content of the temperament but not be of extreme length; for this reason, it is discouraged to include both positive and negative generators in such a table, but this can be excused if the chain is short enough and for multiperiod/non-octave temperaments where [[complement]]s are not as obvious.

	The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.		The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.

Inthar at 00:27, 12 January 2026

2026-01-12T00:27:35Z

← Older revision		Revision as of 00:27, 12 January 2026
Line 1:		Line 1:
	:''Shortcuts: [[XB:TUN]], [[XB:TS]]''		:''Shortcuts: [[XR:TUN]], [[XR:TS]]''
	''This page is an extension of [[~~XenBase~~:Guidelines]]. It is expected that that page has been read first.''		''This page is an extension of [[XenReference:Guidelines]]. It is expected that that page has been read first.''

	Articles about [[tuning system]]s are some of the most important on this wiki. According to the wiki's mission statement, the ultimate purpose of such an article is to serve as a basic guide to using that tuning system for composition. An individual tuning system must, therefore, be presented as a '''coherent structure with unique rules and particularities''' that govern the flow of composition in that system. Not all tuning systems have independent value for composition, despite whatever value they might have in relation to other structures or in their theoretical properties; ''these should not receive dedicated individual articles.''		Articles about [[tuning system]]s are some of the most important on this wiki. According to the wiki's mission statement, the ultimate purpose of such an article is to serve as a basic guide to using that tuning system for composition. An individual tuning system must, therefore, be presented as a '''coherent structure with unique rules and particularities''' that govern the flow of composition in that system. Not all tuning systems have independent value for composition, despite whatever value they might have in relation to other structures or in their theoretical properties; ''these should not receive dedicated individual articles.''

Lériendil: changed wording to not refer to "notability" as absolute

2026-01-08T22:38:05Z

changed wording to not refer to "notability" as absolute

← Older revision		Revision as of 22:38, 8 January 2026
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	== Equal tunings ==		== Equal tunings ==
	Multiples of an equal tuning may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Multiples'' section. For example, 50edo ~~should have a separate article~~ from 25edo ~~because it is particularly notable~~, but 100edo should go in the 50edo article.		Multiples of an equal tuning may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Multiples'' section. For example, if enough information on 50edo can be provided separately from 25edo, then 50edo would merit its own article, but if 100edo is mainly being treated as a multiple of 50, it should be discussed in the 50edo article.

	[TBD]		[TBD]

Inthar: /* Equal temperaments */

2025-12-19T21:10:00Z

Equal temperaments

← Older revision		Revision as of 21:10, 19 December 2025
Line 33:		Line 33:
	The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.		The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.

	== Equal ~~temperaments~~ ==		== Equal tunings ==
	Multiples of an ~~edo~~ may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Multiples'' section. For example, 50edo should have a separate article from 25edo because it is particularly notable, but 100edo should go in the 50edo article.		Multiples of an equal tuning may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Multiples'' section. For example, 50edo should have a separate article from 25edo because it is particularly notable, but 100edo should go in the 50edo article.

	[TBD]		[TBD]

Inthar: /* Equal temperaments */

2025-12-19T21:08:00Z

Equal temperaments

← Older revision		Revision as of 21:08, 19 December 2025
Line 34:		Line 34:

	== Equal temperaments ==		== Equal temperaments ==
	Multiples of an edo may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''~~Contortion~~'' section. For example, 50edo should have a separate article from 25edo because it is particularly notable, but 100edo should go in the 50edo article.		Multiples of an edo may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Multiples'' section. For example, 50edo should have a separate article from 25edo because it is particularly notable, but 100edo should go in the 50edo article.

	[TBD]		[TBD]

Ground at 20:15, 19 December 2025

2025-12-19T20:15:16Z

← Older revision		Revision as of 20:15, 19 December 2025
Line 33:		Line 33:
	The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.		The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.

	=== Equal temperaments ===		== Equal temperaments ==
	Multiples of an edo may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Contortion'' section. For example, 50edo should have a separate article from 25edo because it is particularly notable, but 100edo should go in the 50edo article.		Multiples of an edo may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Contortion'' section. For example, 50edo should have a separate article from 25edo because it is particularly notable, but 100edo should go in the 50edo article.

	[TBD]		[TBD]

Ground at 20:14, 19 December 2025

2025-12-19T20:14:47Z

← Older revision		Revision as of 20:14, 19 December 2025
Line 32:		Line 32:

	The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.		The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.

			=== Equal temperaments ===
			Multiples of an edo may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the ''Contortion'' section. For example, 50edo should have a separate article from 25edo because it is particularly notable, but 100edo should go in the 50edo article.

			[TBD]

Lériendil: /* Outline of the article */

2025-12-13T16:28:39Z

Outline of the article

← Older revision		Revision as of 16:28, 13 December 2025
Line 17:		Line 17:
	Following an introduction, an article follows roughly this fixed structure, following [https://en.xen.wiki/w/Xenharmonic_Wiki:Temperament_page_style_guide#Other_sections_not_discussed_here that of xen.wiki]:		Following an introduction, an article follows roughly this fixed structure, following [https://en.xen.wiki/w/Xenharmonic_Wiki:Temperament_page_style_guide#Other_sections_not_discussed_here that of xen.wiki]:
	* Structural theory		* Structural theory
	* General theory (incl. notation systems and basic harmonies)		** General theory (incl. notation systems and basic harmonies)
	* Interval chains		** Interval chains
	* Extensions and related objects		** Extensions and related objects
	* Scales and compositional theory		* Scales and compositional theory
	* Tunings		* Tunings
	* Tuning considerations (incl. optimal tunings)		** Tuning considerations (incl. optimal tunings)
	* Tuning spectrum		** Tuning spectrum
	* Other sections (instruments/existing music, history, etc.)		* Other sections (instruments/existing music, history, etc.)

Lériendil: /* Regular temperaments */

2025-12-13T16:28:26Z

Regular temperaments

← Older revision		Revision as of 16:28, 13 December 2025
Line 12:		Line 12:

	== Regular temperaments ==		== Regular temperaments ==
			As mentioned, temperament articles must begin with an introduction section. As far as a temperament's structure is explained, it should generally be phrased in terms of what ''equivalences it makes between stacks of intervals'' (e.g. "Slendric is the basic harmonic interpretation of the structure where the perfect fifth (~[[3/2]]) is split into three equal parts, each representing the interval [[8/7]].") Proceeding along the [[generator chain]] is also a good way to make sense of [[rank-2 temperament]] structures in particular, and many useful [[rank-3 temperament]]s also consist of rank-2 spines with an additional offset interval. Referencing [[EDO]]s which the temperament covers is also helpful for intuitizing the temperament as an object. Introductions should also include an infobox, which includes more compact information (such as the [[comma basis]] and [[mapping]]).

	[~~TBD~~]		=== Outline of the article ===
			Following an introduction, an article follows roughly this fixed structure, following [https://en.xen.wiki/w/Xenharmonic_Wiki:Temperament_page_style_guide#Other_sections_not_discussed_here that of xen.wiki]:
			* Structural theory
			* General theory (incl. notation systems and basic harmonies)
			* Interval chains
			* Extensions and related objects
			* Scales and compositional theory
			* Tunings
			* Tuning considerations (incl. optimal tunings)
			* Tuning spectrum
			* Other sections (instruments/existing music, history, etc.)

			=== Format and content of tables ===
			Rank-2 temperament articles should contain two tables, and these constitute the bare minimum of content beyond the introduction. These tables are the '''interval chain''' and the '''tuning spectrum'''.

			The interval chain includes a list of basic harmonic interpretations of the intervals along the temperament's generator chain, and [[cent]] values for these intervals in some good tuning for the temperament. It may sometimes be convenient to include interval chains for different ([[strong]]) extended mappings within the same table; in some cases, these need separate tunings listed. Interval chains should include most of the harmonic content of the temperament but not be of extreme length; for this reason, it is discouraged to include both positive and negative generators in such a table, but this can be excused if the chain is short enough and for multiperiod/non-octave temperaments where [[complement]]s are not as obvious.

			The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an [[unchanged interval]] along the positive chain of generators. [[Odd-limit monotonicity]] bounds should be included as properties of EDO tunings. Keep in mind the spectrum is ''a chance to make detailed comments about specific tunings'', not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.