Superkleismic - Revision history

Squib: subtemperament of portent

2026-03-02T19:43:16Z

subtemperament of portent

← Older revision		Revision as of 19:43, 2 March 2026
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	\| Odd limit 2 = 2.3.5.7.11.19 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26		\| Odd limit 2 = 2.3.5.7.11.19 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26
	}}		}}
	'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression\|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression\|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S\|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S\|19}}) and [[400/399]] ({{S\|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]].		'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression\|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression\|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S\|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well, making it a subtemperament of [[portent]]. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S\|19}}) and [[400/399]] ({{S\|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]].

	The minor-third generator of superkleismic is ~6.3 cents sharp of pure 6/5, even wider than the [[kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11 ([[4L 7s]]), 15 ([[11L 4s]]), or 26 notes ([[15L 11s]]) are available.		The minor-third generator of superkleismic is ~6.3 cents sharp of pure 6/5, even wider than the [[kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11 ([[4L 7s]]), 15 ([[11L 4s]]), or 26 notes ([[15L 11s]]) are available.

	See [[Gamelismic clan #Superkleismic]] for more technical data.		See [[Gamelismic clan #Superkleismic]] for more technical data.

	== Interval chain ==		== Interval chain ==

FloraC: Recategorize (shibboleth family has been dissolved)

2026-02-21T11:13:40Z

Recategorize (shibboleth family has been dissolved)

← Older revision		Revision as of 11:13, 21 February 2026
Line 385:		Line 385:
	[[Category:Superkleismic\| ]] <!-- main article -->		[[Category:Superkleismic\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	~~[[Category:Shibboleth family]]~~
	[[Category:Gamelismic clan]]		[[Category:Gamelismic clan]]
	[[Category:Keemic temperaments]]		[[Category:Keemic temperaments]]
			[[Category:Octagar temperaments]]

FloraC: Cleanup on infobox

2026-02-09T09:46:09Z

Cleanup on infobox

← Older revision		Revision as of 09:46, 9 February 2026
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	{{Infobox regtemp		{{Infobox regtemp
	\| Title = ~~Shibboleth; superkleismic~~		\| Title = Superkleismic
	\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.19		\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.19
	\| Comma basis = [[875/864]], [[1029/1024]] (7-limit); <br> [[100/99]], [[245/242]], [[385/384]] (11-limit); <br> [[100/99]], [[133/132]], [[190/189]], [[385/384]] (L11.19)		\| Comma basis = [[875/864]], [[1029/1024]] (7-limit); <br>[[100/99]], [[245/242]], [[385/384]] (11-limit); <br>[[100/99]], [[133/132]], [[190/189]], [[385/384]] (L11.19)
			\| Mapping = 1; 9 10 -3 2 14
	\| Edo join 1 = 15 \| Edo join 2 = 26		\| Edo join 1 = 15 \| Edo join 2 = 26
	\| ~~Generator~~ = 5/3 \| ~~Generator~~ tuning = 878.2 \| Optimization method = CWE		\| Generators = 5/3 \| Generators tuning = 878.2 \| Optimization method = CWE
	\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], [[11L 4s]], [[15L 11s]]		\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], [[11L 4s]], [[15L 11s]]
	~~\| Mapping = 1; 9 10 -3 2 14~~
	\| Pergen = (P8, ccP4/9)		\| Pergen = (P8, ccP4/9)
	\| Odd limit 1 = 7 \| Mistuning 1 = 6.09 \| Complexity 1 = 15		\| Odd limit 1 = 7 \| Mistuning 1 = 6.09 \| Complexity 1 = 15
	\| Odd limit 2 = (2.3.5.7.11.19) 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26		\| Odd limit 2 = 2.3.5.7.11.19 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26
	}}		}}
	'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression\|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression\|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S\|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S\|19}}) and [[400/399]] ({{S\|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]].		'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression\|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression\|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S\|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S\|19}}) and [[400/399]] ({{S\|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]].

Overthink: L notation is discouraged

2025-12-25T13:28:12Z

L notation is discouraged

← Older revision		Revision as of 13:28, 25 December 2025
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	\| Pergen = (P8, ccP4/9)		\| Pergen = (P8, ccP4/9)
	\| Odd limit 1 = 7 \| Mistuning 1 = 6.09 \| Complexity 1 = 15		\| Odd limit 1 = 7 \| Mistuning 1 = 6.09 \| Complexity 1 = 15
	\| Odd limit 2 = (~~L11~~.19) 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26		\| Odd limit 2 = (2.3.5.7.11.19) 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26
	}}		}}
	'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression\|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression\|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S\|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S\|19}}) and [[400/399]] ({{S\|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]].		'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression\|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression\|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S\|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S\|19}}) and [[400/399]] ({{S\|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]].

FloraC: /* Tunings */ + basic norm-based tunings

2025-11-16T13:03:51Z

Tunings: + basic norm-based tunings

@@ Line 166: / Line 166: @@
 == Tunings ==
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"
 |-
-! Edo<br>Generators
+! Edo<br>generators
 ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
 ! Generator (¢)

FloraC: /* Interval chain */ cleanup

2025-11-16T13:00:46Z

Interval chain: cleanup

← Older revision		Revision as of 13:00, 16 November 2025
Line 21:		Line 21:

	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	! #		! rowspan="2" \| #
	! Cents*		! rowspan="2" \| Cents*
	! Approximate 11-limit add-19 ~~ratios~~		! colspan="2" \| Approximate ratios
			\|-
			! 11-limit add-19
	! Full 19-limit extension		! Full 19-limit extension
	\|-		\|-
Line 161:		Line 163:
	\| 128/65		\| 128/65
	\|}		\|}
	<nowiki>*</nowiki> ~~in L11.~~19 [[CWE]] tuning		<nowiki>*</nowiki> In 11-limit add-19 [[CWE]] tuning, octave reduced

	== Tunings ==		== Tunings ==

FloraC: Cleanup

2025-11-16T12:58:53Z

Cleanup

← Older revision		Revision as of 12:58, 16 November 2025
Line 11:		Line 11:
	\| Odd limit 2 = (L11.19) 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26		\| Odd limit 2 = (L11.19) 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26
	}}		}}
			'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out [[875/864]] ([[S-expression\|S5/S6]]), the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out [[1029/1024]] ([[S-expression\|S7/S8]]), the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out [[100/99]] ({{S\|10}}) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. This implies [[385/384]] and [[441/440]] are tempered out as well. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = ([[19/18]])⋅([[20/19]]), we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S\|19}}) and [[400/399]] ({{S\|20}}). Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]], in addition to [[120/119]] and [[170/169]].
	'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out ~~{{S\|5/S6}} =~~ [[875/864]], the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out ~~S7/S8 =~~ [[1029/1024]], the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out ~~S10 =~~ [[100/99]] (~~as well as [[385/384]] and [[441/440]]~~) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = [[20/19]] × [[19~~/18~~]], we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out ~~S19 =~~ [[361/360]] and ~~S20 =~~ [[400/399]]. Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]] (in addition to [[120/119]] and [[170/169]]).

	The minor-third generator of superkleismic is ~6.3 cents sharp of pure 6/5, even wider than the [[kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11 ([[4L 7s]]), 15 ([[11L 4s]]), or 26 notes ([[15L 11s]]) are available.		The minor-third generator of superkleismic is ~6.3 cents sharp of pure 6/5, even wider than the [[kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11 ([[4L 7s]]), 15 ([[11L 4s]]), or 26 notes ([[15L 11s]]) are available.

FloraC at 15:44, 22 October 2025

2025-10-22T15:44:59Z

← Older revision		Revision as of 15:44, 22 October 2025
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	\| Title = Shibboleth; superkleismic		\| Title = Shibboleth; superkleismic
	\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.19		\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.19
	\| Comma basis = [[875/864]], [[1029/1024]] (7-limit); <br> [[100/99]], [[~~385~~/~~384~~]], [[~~441~~/~~440~~]] (11-limit); <br> [[100/99]], [[133/132]], [[190/189]], [[385/384]] (L11.19)		\| Comma basis = [[875/864]], [[1029/1024]] (7-limit); <br> [[100/99]], [[245/242]], [[385/384]] (11-limit); <br> [[100/99]], [[133/132]], [[190/189]], [[385/384]] (L11.19)
	\| Edo join 1 = 15 \| Edo join 2 = 26		\| Edo join 1 = 15 \| Edo join 2 = 26
	\| Generator = 5/3 \| Generator tuning = 878.2 \| Optimization method = ~~CTE~~		\| Generator = 5/3 \| Generator tuning = 878.2 \| Optimization method = CWE
	\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], [[11L 4s]], [[15L 11s]]		\| MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], [[11L 4s]], [[15L 11s]]
	\| Mapping = 1; 9 10 -3 2 14		\| Mapping = 1; 9 10 -3 2 14

Overthink: Made target scale size based on harmonics rather than the whole diamond

2025-10-19T04:50:40Z

Made target scale size based on harmonics rather than the whole diamond

← Older revision		Revision as of 04:50, 19 October 2025
Line 8:		Line 8:
	\| Mapping = 1; 9 10 -3 2 14		\| Mapping = 1; 9 10 -3 2 14
	\| Pergen = (P8, ccP4/9)		\| Pergen = (P8, ccP4/9)
	\| Odd limit 1 = 7 \| Mistuning 1 = 6.09 \| Complexity 1 = 41		\| Odd limit 1 = 7 \| Mistuning 1 = 6.09 \| Complexity 1 = 15
	\| Odd limit 2 = (L11.19) 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 56		\| Odd limit 2 = (L11.19) 21 \| Mistuning 2 = 8.85 \| Complexity 2 = 26
	}}		}}

Lériendil at 06:03, 6 August 2025

2025-08-06T06:03:17Z

← Older revision		Revision as of 06:03, 6 August 2025
Line 12:		Line 12:
	}}		}}

	'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out {{S\|5/S6}} = [[875/864]], the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out S7/S8 = [[1029/1024]], the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out S10 = [[100/99]] (as well as [[385/384]] and [[441/440]]) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. ~~Since~~ in superkleismic, the interval [[21/20]] stands for half [[10/9]] = [[20/19]] × [[19/18]], we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out S19 = [[361/360]] and S20 = [[400/399]]. Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]] (in addition to [[120/119]] and [[170/169]]).		'''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit]] such that three [[6/5]] generators reach [[7/4]] (tempering out {{S\|5/S6}} = [[875/864]], the keema) and such that three [[8/7]] intervals reach [[3/2]] (tempering out S7/S8 = [[1029/1024]], the gamelisma), making it a member of the [[gamelismic clan]] and a [[keemic temperaments\|keemic temperament]]; its [[5-limit]] comma is [[1953125/1889568]], the shibboleth comma. It [[extension\|extends]] extremely easily to the [[11-limit]] as well, by tempering out S10 = [[100/99]] (as well as [[385/384]] and [[441/440]]) so that two generators reach [[16/11]], which also serves to extend the structure of [[orgone]] in the 2.7.11 subgroup. Furthermore, since in superkleismic, the interval [[21/20]] stands for half [[10/9]] = [[20/19]] × [[19/18]], we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out S19 = [[361/360]] and S20 = [[400/399]]. Superkleismic can also be defined in the [[13-limit]], where two generators are identified with [[13/9]] alongside 16/11, tempering out [[144/143]] and [[325/324]], and extended to 17 to reach the full [[19-limit]], based on the equivalence (8/7)<sup>2</sup> ~ [[17/13]] (natural in slendric) and tempering out [[273/272]] and [[833/832]] (in addition to [[120/119]] and [[170/169]]).

	The minor-third generator of superkleismic is ~6.3 cents sharp of pure 6/5, even wider than the [[kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11 ([[4L 7s]]), 15 ([[11L 4s]]), or 26 notes ([[15L 11s]]) are available.		The minor-third generator of superkleismic is ~6.3 cents sharp of pure 6/5, even wider than the [[kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you orgone. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11 ([[4L 7s]]), 15 ([[11L 4s]]), or 26 notes ([[15L 11s]]) are available.