Regular temperament - Revision history

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

BudjarnLambeth: /* Lists of temperaments */

2026-03-26T02:24:10Z

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]]: temperaments ~~that people think are~~ 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 (article)
	* [[Survey of efficient temperaments by subgroup]]: ~~recommended useful~~ temperaments ~~based on~~ notes ~~needed~~ per equave and JI subgroup ~~(table)~~		* [[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]]: temperaments by the size of their period and generator ~~(table)~~		* [[Map of rank-2 temperaments]] (table): temperaments (some general, some niche) sorted by the size of their period and generator
	* [[Temperaments for MOS shapes]]: ~~list of~~ temperaments by the scale shape they generate ~~(table, ''work-in-progress'')~~		* [[Temperaments for MOS shapes]] (table): temperaments (some general, some niche) sorted by the scale shape they generate
	* [[Tour of regular temperaments]]: huge gallery of the dozens of families of temperaments that have been described ~~(article,~~ ''very technical - not for the faint of heart'')		* [[Tour of regular temperaments]] (article): huge gallery of the dozens of families of temperaments that have been described; ''very technical - not for the faint of heart''

	=== Other writings on temperaments ===		=== Other writings on temperaments ===

BudjarnLambeth: /* Lists of temperaments */

2026-03-26T02:18:46Z

Lists of temperaments

← Older revision		Revision as of 02:18, 26 March 2026
Line 79:		Line 79:

	More comprehensive lists:		More comprehensive lists:
	* [[Bird's eye view of temperaments by accuracy]]: temperaments that people think are most ~~valuable~~ 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]]: temperaments that people think are most useful for approximating JI, with edo tunings and note counts for the harmonies they target, and explanations of their structure (article)
	* [[Survey of efficient temperaments by subgroup]]: temperaments based on notes needed per equave and JI subgroup (table)		* [[Survey of efficient temperaments by subgroup]]: recommended useful temperaments based on notes needed per equave and JI subgroup (table)
	* [[Map of rank-2 temperaments]]: temperaments by the size of their period and generator (table)		* [[Map of rank-2 temperaments]]: temperaments by the size of their period and generator (table)
	* [[Temperaments for MOS shapes]]: list of temperaments by the scale shape they generate (table, ''work-in-progress'')		* [[Temperaments for MOS shapes]]: list of temperaments by the scale shape they generate (table, ''work-in-progress'')

BudjarnLambeth: /* Lists of temperaments */ wording and list order

2026-03-26T02:17:35Z

Lists of temperaments: wording and list order

← Older revision		Revision as of 02:17, 26 March 2026
Line 79:		Line 79:

	More comprehensive lists:		More comprehensive lists:
	* [[Map of rank-2 temperaments]]: a visual map of temperaments based on the size of their period and generator		* [[Bird's eye view of temperaments by accuracy]]: temperaments that people think are most valuable 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]]: ~~a compilation of rank 2~~ temperaments that people think are most valuable 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]]: temperaments based on notes needed per equave and JI subgroup (table)
	* [[Temperaments for MOS shapes]]: list of temperaments by the scale shape they generate (''~~incomplete~~'')		* [[Map of rank-2 temperaments]]: temperaments by the size of their period and generator (table)
	* [[Survey of efficient temperaments by subgroup]]: a visual map of temperaments based on notes needed per equave and JI subgroup		* [[Temperaments for MOS shapes]]: list of temperaments by the scale shape they generate (table, ''work-in-progress'')
	* [[Tour of regular temperaments]]: a huge gallery of the dozens of families of temperaments that have been described (''very technical - not for the faint of heart'')		* [[Tour of regular temperaments]]: huge gallery of the dozens of families of temperaments that have been described (article, ''very technical - not for the faint of heart'')

	=== Other writings on temperaments ===		=== Other writings on temperaments ===

BudjarnLambeth: /* Lists of temperaments */ add 1 item

2026-03-26T02:13:12Z

Lists of temperaments: add 1 item

← Older revision		Revision as of 02:13, 26 March 2026
Line 81:		Line 81:
	* [[Map of rank-2 temperaments]]: a visual map of temperaments based on the size of their period and generator		* [[Map of rank-2 temperaments]]: a visual map of temperaments based on the size of their period and generator
	* [[Bird's eye view of temperaments by accuracy]]: a compilation of rank 2 temperaments that people think are most valuable 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]]: a compilation of rank 2 temperaments that people think are most valuable for approximating JI, with edo tunings and note counts for the harmonies they target and explanations of their structure
			* [[Temperaments for MOS shapes]]: list of temperaments by the scale shape they generate (''incomplete'')
	* [[Survey of efficient temperaments by subgroup]]: a visual map of temperaments based on notes needed per equave and JI subgroup		* [[Survey of efficient temperaments by subgroup]]: a visual map of temperaments based on notes needed per equave and JI subgroup
	* [[Tour of regular temperaments]]: a huge gallery of the dozens of families of temperaments that have been described; not for the faint of heart		* [[Tour of regular temperaments]]: a huge gallery of the dozens of families of temperaments that have been described (''very technical - not for the faint of heart'')

	=== Other writings on temperaments ===		=== Other writings on temperaments ===

Overthink: mention single-pitch tuning

2026-01-12T06:53:16Z

mention single-pitch tuning

← Older revision		Revision as of 06:53, 12 January 2026
Line 12:		Line 12:
	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 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.

	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. 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 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'']].

	== History ==		== History ==

Overthink: elaborate on commas

2026-01-12T06:50:01Z

elaborate on commas

← Older revision		Revision as of 06:50, 12 January 2026
Line 10:		Line 10:
	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 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''.

	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.		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.

	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. 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 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. 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'']].

Overthink: briefly mention generators and commas in intro paragraphs

2026-01-12T06:46:03Z

briefly mention generators and commas in intro paragraphs

← Older revision		Revision as of 06:46, 12 January 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. 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 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''.

	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.		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.

	One particularly simple kind of regular temperaments is ~~the~~ 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 ~~[[comma]]s~~ are tempered out, but all are preserved as small pitch differences. 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 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. 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'']].

	== History ==		== History ==

FloraC: Style

2025-12-22T09:00:29Z

Style

← Older revision		Revision as of 09:00, 22 December 2025
Line 12:		Line 12:
	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.		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.

	One particularly simple kind of regular temperaments is the 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 [[comma]]s are tempered out, but all are preserved as small pitch differences. 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 the 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 [[comma]]s are tempered out, but all are preserved as small pitch differences. 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'']].

	== History ==		== History ==

FloraC: /* Further reading */ simplify certain links

2025-12-03T18:11:07Z

← Older revision		Revision as of 06:50, 12 January 2026
Line 10:		Line 10:
	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 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''.

	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.		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.

	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. 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 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. 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'']].

← Older revision		Revision as of 18:11, 3 December 2025
Line 58:		Line 58:
	* ''[[A Middle Path]]'': this is [[Paul Erlich]]'s guide to RTT (regular temperament theory)		* ''[[A Middle Path]]'': this is [[Paul Erlich]]'s guide to RTT (regular temperament theory)
	* [[Dave Keenan & Douglas Blumeyer's guide to RTT]]		* [[Dave Keenan & Douglas Blumeyer's guide to RTT]]
	* [[~~Keenan's explanation of vals\|~~Keenan Pepper's explanation of vals]]		* [[Keenan Pepper's explanation of vals]]

	=== Key regular temperament concepts ===		=== Key regular temperament concepts ===
Line 74:		Line 74:
	Temperaments that approximate important harmonies relatively well with a small number of notes:		Temperaments that approximate important harmonies relatively well with a small number of notes:
	* [[Low harmonic entropy linear temperaments]]		* [[Low harmonic entropy linear temperaments]]
	* [[Middle Path table of ~~five~~-limit rank ~~two~~ temperaments]]		* [[Middle Path table of 5-limit rank-2 temperaments]]
	* [[Middle Path table of ~~seven~~-limit rank ~~two~~ temperaments]]		* [[Middle Path table of 7-limit rank-2 temperaments]]
	* [[Middle Path table of ~~eleven~~-limit rank ~~two~~ temperaments]]		* [[Middle Path table of 11-limit rank-2 temperaments]]

	More comprehensive lists:		More comprehensive lists:
Line 85:		Line 85:

	=== 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]]

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