Regular temperament - Revision history

Naren: Add link to RTT notes

2026-08-24T17:57:45Z

Add link to RTT notes

← Older revision		Revision as of 17:57, 24 August 2026
Line 95:		Line 95:
	* [https://youtu.be/ZoAuVgndmbU ''Tuning Theory 2: Temperament ("Microtonal" Theory)''], a video lecture by [[John Moriarty]]		* [https://youtu.be/ZoAuVgndmbU ''Tuning Theory 2: Temperament ("Microtonal" Theory)''], a video lecture by [[John Moriarty]]
	* [https://hkm2685.github.io/temperament-map/rank2/viewer/ Rank-2 temperament maps]: An interactive map of all temperaments with octave, half-octave, third-octave, or tritave period logged on the wiki, sorted by size of generator		* [https://hkm2685.github.io/temperament-map/rank2/viewer/ Rank-2 temperament maps]: An interactive map of all temperaments with octave, half-octave, third-octave, or tritave period logged on the wiki, sorted by size of generator
			* [https://narenratan.com/writing/regular-temperament-theory/ ''Regular temperament theory notes''] - Notes presenting RTT as an extension of Erv Wilson's keyboard mapping theory

	[[Category:Regular temperament theory\| ]] <!-- Main article -->		[[Category:Regular temperament theory\| ]] <!-- Main article -->

Fredg999: Interwiki

2026-07-19T06:43:06Z

Interwiki

← Older revision		Revision as of 06:43, 19 July 2026
Line 1:		Line 1:
	{{Interwiki		{{Interwiki
			\| de = Reguläre_Temperatur
	\| en = Regular temperament		\| en = Regular temperament
	~~\| de = Reguläre_Temperatur~~		\| es = Temperamento regular
	\| es =
	\| ja = レギュラーテンペラメント		\| ja = レギュラーテンペラメント
	}}		}}

FloraC: Text replacement - "octave" to "octave"

2026-07-14T14:15:39Z

Text replacement - "octave" to "octave"

← Older revision		Revision as of 14:15, 14 July 2026
Line 8:		Line 8:
	{{Wikipedia}}		{{Wikipedia}}

	A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. A regular temperament is [[generate]]d by a set of generating intervals, usually one of which is considered the [[period]], and any note which is part of the regular temperament can be reached by stacking whole numbers of these generating intervals above a defined root note. For example, [[meantone]] temperament is generated by the [[~~2/1\|~~octave]] and a tempered (detuned) version of the [[3/2\|perfect fifth]], with the octave usually being considered the period, and every interval in meantone can be expressed as an integer number of octaves plus an integer number of fifths. In meantone, a {{W\|major second}} is equal to two perfect fifths minus an octave, and a {{W\|major third}} is four perfect fifths minus two octaves. Regular temperaments theoretically have an infinite number of notes, and besides [[equal temperament]]s, regular temperaments usually<ref group="note">This is true if there exist two generators such that size in [[cent]]s of one generator divided by that of the other is an {{W\|irrational number}}. This is not true for tunings where every generator is a whole number of steps of some [[edo]] or other [[equal-step tuning]].</ref> have an infinite number of notes in between ''any two other notes''.		A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. A regular temperament is [[generate]]d by a set of generating intervals, usually one of which is considered the [[period]], and any note which is part of the regular temperament can be reached by stacking whole numbers of these generating intervals above a defined root note. For example, [[meantone]] temperament is generated by the [[octave]] and a tempered (detuned) version of the [[3/2\|perfect fifth]], with the octave usually being considered the period, and every interval in meantone can be expressed as an integer number of octaves plus an integer number of fifths. In meantone, a {{W\|major second}} is equal to two perfect fifths minus an octave, and a {{W\|major third}} is four perfect fifths minus two octaves. Regular temperaments theoretically have an infinite number of notes, and besides [[equal temperament]]s, regular temperaments usually<ref group="note">This is true if there exist two generators such that size in [[cent]]s of one generator divided by that of the other is an {{W\|irrational number}}. This is not true for tunings where every generator is a whole number of steps of some [[edo]] or other [[equal-step tuning]].</ref> have an infinite number of notes in between ''any two other notes''.

	In addition to unlimited modulation, regular temperaments are by definition thought of as being approximations of some system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). For example, the octave in meantone represents the just ratio [[2/1]], the perfect fifth [[3/2]], and the major third [[5/4]]. Certain intervals are tempered to the [[1/1\|unison]], or [[tempering out\|tempered out]]; in a regular temperament, these intervals are known as [[comma]]s. In meantone, since stacking up four perfect fifths, down two octaves, and down a major third reaches the unison, we get that {{nowrap\|(3/2)<sup>4</sup> / (2/1)<sup>2</sup> / (5/4) {{=}} [[81/80]]}} is tempered out, and thus 81/80 is a comma of meantone. Any two just intervals separated by a comma of a temperament, for example [[9/8]] and [[10/9]] in meantone, are mapped to the same tempered interval in the temperament, in this case a major second. A temperament only qualifies as a regular temperament if this interpretation works in a perfectly consistent way: The product of two tempered intervals must always be the tempered version of the product of the JI intervals; for example, if the ratios 3/2 and 5/4 are in the target interval set, then ~3/2 × ~5/4 = ~[[15/8]] must always be true. ("~" denotes tempered.) In any temperament, each target interval is mapped to a unique tempered interval, though a tempered interval can represent multiple target intervals.		In addition to unlimited modulation, regular temperaments are by definition thought of as being approximations of some system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). For example, the octave in meantone represents the just ratio [[2/1]], the perfect fifth [[3/2]], and the major third [[5/4]]. Certain intervals are tempered to the [[1/1\|unison]], or [[tempering out\|tempered out]]; in a regular temperament, these intervals are known as [[comma]]s. In meantone, since stacking up four perfect fifths, down two octaves, and down a major third reaches the unison, we get that {{nowrap\|(3/2)<sup>4</sup> / (2/1)<sup>2</sup> / (5/4) {{=}} [[81/80]]}} is tempered out, and thus 81/80 is a comma of meantone. Any two just intervals separated by a comma of a temperament, for example [[9/8]] and [[10/9]] in meantone, are mapped to the same tempered interval in the temperament, in this case a major second. A temperament only qualifies as a regular temperament if this interpretation works in a perfectly consistent way: The product of two tempered intervals must always be the tempered version of the product of the JI intervals; for example, if the ratios 3/2 and 5/4 are in the target interval set, then ~3/2 × ~5/4 = ~[[15/8]] must always be true. ("~" denotes tempered.) In any temperament, each target interval is mapped to a unique tempered interval, though a tempered interval can represent multiple target intervals.

FloraC: /* History */ improve linking

2026-06-16T10:31:22Z

History: improve linking

← Older revision		Revision as of 10:31, 16 June 2026
Line 24:		Line 24:
	* [[Adriaan Fokker]] (1887–1972): [[Fokker block\|periodicity blocks]]		* [[Adriaan Fokker]] (1887–1972): [[Fokker block\|periodicity blocks]]
	* [[Harry Partch]] (1901–1974): [[JI\|extended JI]]		* [[Harry Partch]] (1901–1974): [[JI\|extended JI]]
	* [[Erv Wilson]] (1928–2016): extended tonespace (and projections), [[mos]], scale tree, [[~~Harmonic~~ template~~\|harmonic templates~~]]		* [[Erv Wilson]] (1928–2016): extended tonespace (and projections), [[mos]], [[scale tree]], [[harmonic template]]s
	* [[Easley Blackwood]] (1933–2023): Blackwood[10], syntonic comma vanishing relation as equation		* [[Easley Blackwood]] (1933–2023): Blackwood[10], syntonic comma vanishing relation as equation
	* [[George Secor]] (1943–2020): miracle temperament		* [[George Secor]] (1943–2020): miracle temperament

Naren: Add harmonic templates to Erv Wilson bullet point

2026-06-15T19:14:05Z

Add harmonic templates to Erv Wilson bullet point

← Older revision		Revision as of 19:14, 15 June 2026
Line 24:		Line 24:
	* [[Adriaan Fokker]] (1887–1972): [[Fokker block\|periodicity blocks]]		* [[Adriaan Fokker]] (1887–1972): [[Fokker block\|periodicity blocks]]
	* [[Harry Partch]] (1901–1974): [[JI\|extended JI]]		* [[Harry Partch]] (1901–1974): [[JI\|extended JI]]
	* [[Erv Wilson]] (1928–2016): extended tonespace (and projections), [[mos]], scale tree		* [[Erv Wilson]] (1928–2016): extended tonespace (and projections), [[mos]], scale tree, [[Harmonic template\|harmonic templates]]
	* [[Easley Blackwood]] (1933–2023): Blackwood[10], syntonic comma vanishing relation as equation		* [[Easley Blackwood]] (1933–2023): Blackwood[10], syntonic comma vanishing relation as equation
	* [[George Secor]] (1943–2020): miracle temperament		* [[George Secor]] (1943–2020): miracle temperament

FloraC: Move external links to external links section

2026-06-12T19:57:49Z

Move external links to external links section

← Older revision		Revision as of 19:57, 12 June 2026
Line 1:		Line 1:
	{{~~interwiki~~		{{Interwiki
			\| en = Regular temperament
	\| de = Reguläre_Temperatur		\| de = Reguläre_Temperatur
	~~\| en = Regular temperament~~
	\| es =		\| es =
	\| ja = レギュラーテンペラメント		\| ja = レギュラーテンペラメント
Line 79:		Line 79:

	More comprehensive lists:		More comprehensive lists:
	* [https://hkm2685.github.io/temperament-map/rank2/viewer/ Rank-2 temperament maps] (website): An interactive map of all temperaments with octave, half-octave, third-octave, or tritave period logged on the wiki, sorted by size of generator
	* [[Bird's eye view of temperaments by accuracy]] (article): temperaments the Xen Wiki contributors find most useful for approximating JI - with edo tunings and note counts for the harmonies they target, and explanations of their structure		* [[Bird's eye view of temperaments by accuracy]] (article): temperaments the Xen Wiki contributors find most useful for approximating JI - with edo tunings and note counts for the harmonies they target, and explanations of their structure
	* [[Survey of efficient temperaments by subgroup]] (table): good general-purpose temperaments, sorted by size (notes per equave) and by JI subgroup		* [[Survey of efficient temperaments by subgroup]] (table): good general-purpose temperaments, sorted by size (notes per equave) and by JI subgroup
Line 93:		Line 92:

	== External links ==		== External links ==
	* [http://x31eq.com/paradigm.html ~~Graham Breed~~'~~s "~~The Regular Mapping Paradigm"]		* [http://x31eq.com/paradigm.html ''The Regular Mapping Paradigm''] by [[Graham Breed]]
	* [https://youtu.be/ZoAuVgndmbU ~~John Moriarty –~~ Tuning Theory 2: Temperament ("Microtonal" Theory)], a video lecture		* [https://youtu.be/ZoAuVgndmbU ''Tuning Theory 2: Temperament ("Microtonal" Theory)''], a video lecture by [[John Moriarty]]
			* [https://hkm2685.github.io/temperament-map/rank2/viewer/ Rank-2 temperament maps]: An interactive map of all temperaments with octave, half-octave, third-octave, or tritave period logged on the wiki, sorted by size of generator

	[[Category:Regular temperament theory\| ]] <!-- Main article -->		[[Category:Regular temperament theory\| ]] <!-- Main article -->

Hkm: /* Lists of temperaments */

2026-06-12T06:07:24Z

Lists of temperaments

← Older revision		Revision as of 06:07, 12 June 2026
Line 79:		Line 79:

	More comprehensive lists:		More comprehensive lists:
			* [https://hkm2685.github.io/temperament-map/rank2/viewer/ Rank-2 temperament maps] (website): An interactive map of all temperaments with octave, half-octave, third-octave, or tritave period logged on the wiki, sorted by size of generator
	* [[Bird's eye view of temperaments by accuracy]] (article): temperaments the Xen Wiki contributors find most useful for approximating JI - with edo tunings and note counts for the harmonies they target, and explanations of their structure		* [[Bird's eye view of temperaments by accuracy]] (article): temperaments the Xen Wiki contributors find most useful for approximating JI - with edo tunings and note counts for the harmonies they target, and explanations of their structure
	* [[Survey of efficient temperaments by subgroup]] (table): good general-purpose temperaments, sorted by size (notes per equave) and by JI subgroup		* [[Survey of efficient temperaments by subgroup]] (table): good general-purpose temperaments, sorted by size (notes per equave) and by JI subgroup

Overthink: remove unneeded link

2026-06-08T19:45:10Z

remove unneeded link

← Older revision		Revision as of 19:45, 8 June 2026
Line 8:		Line 8:
	{{Wikipedia}}		{{Wikipedia}}

	A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. A regular temperament is [[generate]]d by a set of ~~[[generator\|~~generating intervals]], usually one of which is considered the [[period]], and any note which is part of the regular temperament can be reached by stacking whole numbers of these generating intervals above a defined root note. For example, [[meantone]] temperament is generated by the [[2/1\|octave]] and a tempered (detuned) version of the [[3/2\|perfect fifth]], with the octave usually being considered the period, and every interval in meantone can be expressed as an integer number of octaves plus an integer number of fifths. In meantone, a {{W\|major second}} is equal to two perfect fifths minus an octave, and a {{W\|major third}} is four perfect fifths minus two octaves. Regular temperaments theoretically have an infinite number of notes, and besides [[equal temperament]]s, regular temperaments usually<ref group="note">This is true if there exist two generators such that size in [[cent]]s of one generator divided by that of the other is an {{W\|irrational number}}. This is not true for tunings where every generator is a whole number of steps of some [[edo]] or other [[equal-step tuning]].</ref> have an infinite number of notes in between ''any two other notes''.		A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. A regular temperament is [[generate]]d by a set of generating intervals, usually one of which is considered the [[period]], and any note which is part of the regular temperament can be reached by stacking whole numbers of these generating intervals above a defined root note. For example, [[meantone]] temperament is generated by the [[2/1\|octave]] and a tempered (detuned) version of the [[3/2\|perfect fifth]], with the octave usually being considered the period, and every interval in meantone can be expressed as an integer number of octaves plus an integer number of fifths. In meantone, a {{W\|major second}} is equal to two perfect fifths minus an octave, and a {{W\|major third}} is four perfect fifths minus two octaves. Regular temperaments theoretically have an infinite number of notes, and besides [[equal temperament]]s, regular temperaments usually<ref group="note">This is true if there exist two generators such that size in [[cent]]s of one generator divided by that of the other is an {{W\|irrational number}}. This is not true for tunings where every generator is a whole number of steps of some [[edo]] or other [[equal-step tuning]].</ref> have an infinite number of notes in between ''any two other notes''.

	In addition to unlimited modulation, regular temperaments are by definition thought of as being approximations of some system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). For example, the octave in meantone represents the just ratio [[2/1]], the perfect fifth [[3/2]], and the major third [[5/4]]. Certain intervals are tempered to the [[1/1\|unison]], or [[tempering out\|tempered out]]; in a regular temperament, these intervals are known as [[comma]]s. In meantone, since stacking up four perfect fifths, down two octaves, and down a major third reaches the unison, we get that {{nowrap\|(3/2)<sup>4</sup> / (2/1)<sup>2</sup> / (5/4) {{=}} [[81/80]]}} is tempered out, and thus 81/80 is a comma of meantone. Any two just intervals separated by a comma of a temperament, for example [[9/8]] and [[10/9]] in meantone, are mapped to the same tempered interval in the temperament, in this case a major second. A temperament only qualifies as a regular temperament if this interpretation works in a perfectly consistent way: The product of two tempered intervals must always be the tempered version of the product of the JI intervals; for example, if the ratios 3/2 and 5/4 are in the target interval set, then ~3/2 × ~5/4 = ~[[15/8]] must always be true. ("~" denotes tempered.) In any temperament, each target interval is mapped to a unique tempered interval, though a tempered interval can represent multiple target intervals.		In addition to unlimited modulation, regular temperaments are by definition thought of as being approximations of some system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). For example, the octave in meantone represents the just ratio [[2/1]], the perfect fifth [[3/2]], and the major third [[5/4]]. Certain intervals are tempered to the [[1/1\|unison]], or [[tempering out\|tempered out]]; in a regular temperament, these intervals are known as [[comma]]s. In meantone, since stacking up four perfect fifths, down two octaves, and down a major third reaches the unison, we get that {{nowrap\|(3/2)<sup>4</sup> / (2/1)<sup>2</sup> / (5/4) {{=}} [[81/80]]}} is tempered out, and thus 81/80 is a comma of meantone. Any two just intervals separated by a comma of a temperament, for example [[9/8]] and [[10/9]] in meantone, are mapped to the same tempered interval in the temperament, in this case a major second. A temperament only qualifies as a regular temperament if this interpretation works in a perfectly consistent way: The product of two tempered intervals must always be the tempered version of the product of the JI intervals; for example, if the ratios 3/2 and 5/4 are in the target interval set, then ~3/2 × ~5/4 = ~[[15/8]] must always be true. ("~" denotes tempered.) In any temperament, each target interval is mapped to a unique tempered interval, though a tempered interval can represent multiple target intervals.

Overthink: explain a bunch of stuff better

2026-06-08T01:45:17Z

explain a bunch of stuff better

← Older revision		Revision as of 01:45, 8 June 2026
Line 8:		Line 8:
	{{Wikipedia}}		{{Wikipedia}}

	A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. A regular temperament is [[generate]]d by a set of [[generator\|generating intervals]] (usually one of which is considered the [[period]]), and any note ~~that~~ can be reached by stacking ~~any number~~ of these generating intervals is considered to be ~~part~~ of ~~the regular temperament~~. Regular temperaments ~~generally~~ have an infinite number of notes; and ~~other than~~ [[equal temperament]]s, every ~~regular temperament actually has~~ an infinite number of notes in between ''any two other notes''.		A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. A regular temperament is [[generate]]d by a set of [[generator\|generating intervals]], usually one of which is considered the [[period]], and any note which is part of the regular temperament can be reached by stacking whole numbers of these generating intervals above a defined root note. For example, [[meantone]] temperament is generated by the [[2/1\|octave]] and a tempered (detuned) version of the [[3/2\|perfect fifth]], with the octave usually being considered the period, and every interval in meantone can be expressed as an integer number of octaves plus an integer number of fifths. In meantone, a {{W\|major second}} is equal to two perfect fifths minus an octave, and a {{W\|major third}} is four perfect fifths minus two octaves. Regular temperaments theoretically have an infinite number of notes, and besides [[equal temperament]]s, regular temperaments usually<ref group="note">This is true if there exist two generators such that size in [[cent]]s of one generator divided by that of the other is an {{W\|irrational number}}. This is not true for tunings where every generator is a whole number of steps of some [[edo]] or other [[equal-step tuning]].</ref> have an infinite number of notes in between ''any two other notes''.

	In addition to unlimited modulation, regular temperaments by definition ~~are~~ thought of as being approximations of some ~~more complicated~~ system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). ~~A temperament only qualifies as a regular temperament if this interpretation works~~ in ~~a perfectly consistent way:~~ the ~~sum of two tempered intervals must always be~~ the ~~tempered version of~~ the sum of the JI intervals. Multiple pure intervals may be represented by the same tempered interval (so they are tempered together), but a single pure interval must never be represented by different tempered intervals. Certain intervals are tempered to the [[1/1\|unison]]; in a regular temperament, these intervals are known as [[comma]]s. Any two just intervals ~~seperated~~ by a comma of a temperament are mapped to the same tempered interval in ~~that~~ temperament. ~~For~~ example, ~~[[meantone]] temperament,~~ the ~~[[5-limit]] temperament tempering out [[81~~/~~80]], maps [[81/64]]~~ and [[5/4~~]] to~~ the ~~same~~ interval, ~~as 81~~/~~64 and~~ 5/4 ~~differ by 81~~/~~80 in JI~~.		In addition to unlimited modulation, regular temperaments are by definition thought of as being approximations of some system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). For example, the octave in meantone represents the just ratio [[2/1]], the perfect fifth [[3/2]], and the major third [[5/4]]. Certain intervals are tempered to the [[1/1\|unison]], or [[tempering out\|tempered out]]; in a regular temperament, these intervals are known as [[comma]]s. In meantone, since stacking up four perfect fifths, down two octaves, and down a major third reaches the unison, we get that {{nowrap\|(3/2)<sup>4</sup> / (2/1)<sup>2</sup> / (5/4) {{=}} [[81/80]]}} is tempered out, and thus 81/80 is a comma of meantone. Any two just intervals separated by a comma of a temperament, for example [[9/8]] and [[10/9]] in meantone, are mapped to the same tempered interval in the temperament, in this case a major second. A temperament only qualifies as a regular temperament if this interpretation works in a perfectly consistent way: The product of two tempered intervals must always be the tempered version of the product of the JI intervals; for example, if the ratios 3/2 and 5/4 are in the target interval set, then ~3/2 × ~5/4 = ~[[15/8]] must always be true. ("~" denotes tempered.) In any temperament, each target interval is mapped to a unique tempered interval, though a tempered interval can represent multiple target intervals.

	One particularly simple kind of regular temperaments is equal temperaments, which represent all intervals by multiples of a single ~~smallest~~ step. ~~At the other extreme,~~ JI itself can be considered a [[trivial temperament]] where no tempering is happening: no commas are tempered out, ~~but~~ all are preserved as small pitch differences. Another example of a trivial temperament is [[single-pitch tuning]], where there are ''no'' generating intervals, and ~~there is~~ only a single pitch. In between lies the cornucopia of temperaments discussed in [[Paul Erlich]]'s seminal work, [[:File:MiddlePath2015.pdf\|''A Middle Path Between Just Intonation and the Equal Temperaments'']].		One particularly simple kind of regular temperaments is equal temperaments, which represent all intervals by multiples of a single step size. JI itself can be considered a [[trivial temperament]] where no tempering is happening: No commas are tempered out, and all of them are preserved as small pitch differences. Another example of a trivial temperament is [[single-pitch tuning]], where there are ''no'' generating intervals, and only a single pitch is available. In between JI and equal temperaments lies the cornucopia of temperaments discussed in [[Paul Erlich]]'s seminal work, [[:File:MiddlePath2015.pdf\|''A Middle Path Between Just Intonation and the Equal Temperaments'']].

	== History ==		== History ==
Line 87:		Line 87:
	=== Other writings on temperaments ===		=== Other writings on temperaments ===
	* [[Mike's lectures on regular temperament theory\|Mike Battaglia's lectures on RTT]]		* [[Mike's lectures on regular temperament theory\|Mike Battaglia's lectures on RTT]]

			== Notes ==
			<references group="note"/>

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

BudjarnLambeth: /* Lists of temperaments */

2026-03-26T02:24:27Z

Lists of temperaments

← Older revision		Revision as of 02:24, 26 March 2026
Line 79:		Line 79:

	More comprehensive lists:		More comprehensive lists:
	* [[Bird's eye view of temperaments by accuracy]] (article): temperaments the Xen Wiki contributors find most useful for approximating JI - with edo tunings and note counts for the harmonies they target, and explanations of their structure ~~(article)~~		* [[Bird's eye view of temperaments by accuracy]] (article): temperaments the Xen Wiki contributors find most useful for approximating JI - with edo tunings and note counts for the harmonies they target, and explanations of their structure
	* [[Survey of efficient temperaments by subgroup]] (table): good general-purpose temperaments, sorted by size (notes per equave) and by JI subgroup		* [[Survey of efficient temperaments by subgroup]] (table): good general-purpose temperaments, sorted by size (notes per equave) and by JI subgroup
	* [[Map of rank-2 temperaments]] (table): temperaments (some general, some niche) sorted by the size of their period and generator		* [[Map of rank-2 temperaments]] (table): temperaments (some general, some niche) sorted by the size of their period and generator