Slendric - Revision history

FloraC: Cleanup on infobox

2026-02-09T09:43:16Z

Cleanup on infobox

← Older revision		Revision as of 09:43, 9 February 2026
Line 1:		Line 1:
	{{Infobox ~~Regtemp~~		{{Interwiki
			\| en = Slendric
			\| de = Slendrisch
			}}
			{{Infobox regtemp
	\| Title = Slendric		\| Title = Slendric
	\| Subgroups = 2.3.7		\| Subgroups = 2.3.7
	\| Comma basis = [[1029/1024]]		\| Comma basis = [[1029/1024]]
	\| Edo join 1 = 5 \| Edo join 2 = 21		\| Edo join 1 = 5 \| Edo join 2 = 21
	~~\| Generator = 8/7 \| Generator tuning = 233.9 \| Optimization method = CTE~~
	~~\| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], [[5L 11s]], ...~~
	\| Mapping = 1; 3 -1		\| Mapping = 1; 3 -1
			\| Generators = 8/7 \| Generators tuning = 233.7 \| Optimization method = CWE
			\| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], [[5L 11s]], …
	\| Pergen = (P8, P5/3)		\| Pergen = (P8, P5/3)
	\| Color name = Latrizoti		\| Color name = Latrizoti
	\| Odd limit 1 = 7 \| Mistuning 1 = 2.11 \| Complexity 1 = 11		\| Odd limit 1 = 7 \| Mistuning 1 = 2.11 \| Complexity 1 = 11
	\| Odd limit 2 = (2.3.7) 27 \| Mistuning 2 = 2.81 \| Complexity 2 = 21		\| Odd limit 2 = 2.3.7 27 \| Mistuning 2 = 2.81 \| Complexity 2 = 21
	}}
	~~{{interwiki~~
	~~\| de = Slendrisch~~
	~~\| en = Slendric~~
	}}		}}
	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

Hstraub: Link to German

2026-01-20T21:33:01Z

Link to German

← Older revision		Revision as of 21:33, 20 January 2026
Line 12:		Line 12:
	\| Odd limit 2 = (2.3.7) 27 \| Mistuning 2 = 2.81 \| Complexity 2 = 21		\| Odd limit 2 = (2.3.7) 27 \| Mistuning 2 = 2.81 \| Complexity 2 = 21
	}}		}}
			{{interwiki
			\| de = Slendrisch
			\| en = Slendric
			}}
	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

Overthink: /* Tunings */ doesn't seem notable enough

2026-01-12T07:12:56Z

Tunings: doesn't seem notable enough

← Older revision		Revision as of 07:12, 12 January 2026
Line 326:		Line 326:

	== Tunings ==		== Tunings ==
	Notable edos that support slendric include {{EDOs\| 31, 36, 41, 46, and 77}}~~. [[Constrained tuning\|Constrained Tenney–Euclidean]] slendric is extremely well-approximated by [[2160edo]]~~.		Notable edos that support slendric include {{EDOs\| 31, 36, 41, 46, and 77}}.

	=== Norm-based tunings ===		=== Norm-based tunings ===

FloraC: Clarify

2025-12-22T09:11:31Z

Clarify

← Older revision		Revision as of 09:11, 22 December 2025
Line 15:		Line 15:
	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

	The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible ~~extensions~~ of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing ~~[[10~~/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing ~~the 5th harmonic~~ 24 generators (8 fifths) down. [[Weak extension]]s such as [[miracle]] and [[valentine]] are somewhat more efficient, but they change the generator chain. From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]])⋅([[441/440]]), and so the logical extension of slendric is to temper out both commas; this places the interval of [[55/32]] at four generators up. ~~Tempering~~ 385/384 and 441/440 ~~without first extending slendric to include the 5th harmonic~~ results in the rank-3 temperament [[portent]], the natural 11-limit [[expansion]] of slendric. Portent is ~~supported~~ by the slendric extensions listed above.		The disadvantage, if you want to think of it that way, is that approximations to the [[5/1\|5th]] [[harmonic]] do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible [[extension]]s of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing 5/1 at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing 5/1 at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing 5/1 at 24 generators (8 fifths) down. [[Weak extension]]s such as [[miracle]] and [[valentine]] are somewhat more efficient, but they change the generator chain.

			From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]])⋅([[441/440]]), and so the logical extension of slendric is to temper out both commas; this places the interval of [[55/32]] at four generators up. Alternatively, giving 5/1 an independent generator and then tempering out 385/384 and 441/440 results in the rank-3 temperament [[portent]], the natural 11-limit [[expansion]] of slendric. Portent is [[support]]ed by the slendric extensions listed above.

	This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.		This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.

Squib: described relationship between slendric's 11-limit extensions and portent. i plan to make similar changes to other pages

2025-12-21T16:56:42Z

described relationship between slendric's 11-limit extensions and portent. i plan to make similar changes to other pages

← Older revision		Revision as of 16:56, 21 December 2025
Line 15:		Line 15:
	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

	The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. [[Weak extension]]s such as [[miracle]] and [[valentine]] are somewhat more efficient, but they change the generator chain. From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]])⋅([[441/440]]), and so the logical extension of slendric is to temper out both commas ~~(as in [[portent]])~~; this places the interval of [[55/32]] at four generators up.		The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. [[Weak extension]]s such as [[miracle]] and [[valentine]] are somewhat more efficient, but they change the generator chain. From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]])⋅([[441/440]]), and so the logical extension of slendric is to temper out both commas; this places the interval of [[55/32]] at four generators up. Tempering 385/384 and 441/440 without first extending slendric to include the 5th harmonic results in the rank-3 temperament [[portent]], the natural 11-limit [[expansion]] of slendric. Portent is supported by the slendric extensions listed above.

	This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.		This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.

FloraC: Rewrite about weak extensions to mention more examples

2025-12-14T07:51:37Z

Rewrite about weak extensions to mention more examples

← Older revision		Revision as of 07:51, 14 December 2025
Line 15:		Line 15:
	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

	The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. ([[~~Miracle~~]] ~~tempers out~~ [[~~225/224~~]], ~~splitting~~ the generator ~~in half and placing 5/1 at 7 generators down, but it is generally considered its own temperament rather than an extension of slendric~~.) From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]]) × ([[441/440]]), and so the logical extension of slendric is to temper out both commas (as in [[portent]]); this places the interval of [[55/32]] at four generators up.		The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. [[Weak extension]]s such as [[miracle]] and [[valentine]] are somewhat more efficient, but they change the generator chain. From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]])⋅([[441/440]]), and so the logical extension of slendric is to temper out both commas (as in [[portent]]); this places the interval of [[55/32]] at four generators up.

	This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.		This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.

Squib at 05:03, 14 December 2025

2025-12-14T05:03:39Z

← Older revision		Revision as of 05:03, 14 December 2025
Line 15:		Line 15:
	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

	The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. ([[Miracle]] ~~splits~~ the generator in half and ~~places~~ 5/1 at 7 generators down, but it is generally considered its own temperament rather than an extension of slendric.) From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]]) × ([[441/440]]), and so the logical extension of slendric is to temper out both commas (as in [[portent]]); this places the interval of [[55/32]] at four generators up.		The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. ([[Miracle]] tempers out [[225/224]], splitting the generator in half and placing 5/1 at 7 generators down, but it is generally considered its own temperament rather than an extension of slendric.) From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]]) × ([[441/440]]), and so the logical extension of slendric is to temper out both commas (as in [[portent]]); this places the interval of [[55/32]] at four generators up.

	This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.		This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.

Squib at 01:00, 14 December 2025

2025-12-14T01:00:30Z

← Older revision		Revision as of 01:00, 14 December 2025
Line 15:		Line 15:
	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

	The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]]) × ([[441/440]]), and so the logical extension of slendric is to temper out both commas (as in [[portent]]); this places the interval of [[55/32]] at four generators up.		The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. ([[Miracle]] splits the generator in half and places 5/1 at 7 generators down, but it is generally considered its own temperament rather than an extension of slendric.) From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]]) × ([[441/440]]), and so the logical extension of slendric is to temper out both commas (as in [[portent]]); this places the interval of [[55/32]] at four generators up.

	This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.		This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.

Squib at 00:25, 14 December 2025

2025-12-14T00:25:58Z

← Older revision		Revision as of 00:25, 14 December 2025
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	'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group \| ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group \| ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

	The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]]) × ([[441/440]]), and so the logical extension of slendric is to temper out both commas; this places the interval of [[55/32]] at four generators up.		The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible extensions of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing [[5/1]] at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down. From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]]) × ([[441/440]]), and so the logical extension of slendric is to temper out both commas (as in [[portent]]); this places the interval of [[55/32]] at four generators up.

	This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.		This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.

FloraC: /* Tunings */ correct subgroup

2025-11-16T12:27:44Z

Tunings: correct subgroup

← Older revision		Revision as of 12:27, 16 November 2025
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	=== Norm-based tunings ===		=== Norm-based tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-~~limit~~ norm-based tunings (tempered-octave)		\|+ style="font-size: 105%; white-space: nowrap;" \| 2.3.7-subgroup norm-based tunings (tempered-octave)
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
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	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-~~limit~~ norm-based tunings (pure-octave)		\|+ style="font-size: 105%; white-space: nowrap;" \| 2.3.7-subgroup norm-based tunings (pure-octave)
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|