Canousmic temperaments - Revision history

FloraC: - data for extensions beyond 31. Re-phrasing description

2026-05-17T15:54:05Z

- data for extensions beyond 31. Re-phrasing description

← Older revision		Revision as of 15:54, 17 May 2026
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	Superlimmal is essentially an 80-form, and may be described as the {{nowrap\| 80 & 311 }} temperament. It uses an ever slightly sharpened [[27/25\|large limma]] as the generator, nine exceed the octave by [[126/125]]. Note that in the data that follow, the generator is its [[octave complement]], [[~]][[50/27]], so that 57 of them [[octave reduction\|octave reduced]] make the [[3/2\|perfect fifth]].		Superlimmal is essentially an 80-form, and may be described as the {{nowrap\| 80 & 311 }} temperament. It uses an ever slightly sharpened [[27/25\|large limma]] as the generator, nine exceed the octave by [[126/125]]. Note that in the data that follow, the generator is its [[octave complement]], [[~]][[50/27]], so that 57 of them [[octave reduction\|octave reduced]] make the [[3/2\|perfect fifth]].

	Superlimmal gets all the primes up to [[29/1\|29]] reasonably covered, but is acceptable just as a 13-limit microtemperament, given a relatively simple [[comma basis]]. It can also be extended to include prime [[37/1\|37]] by tempering out ([[27/25]])/([[40/37]]) = [[1000/999]]~~, where~~ 40/37 is ~~notably~~ the mediant of [[27/25]] and [[13/12]], ~~which could be interpreted as an explanation of~~ the sharpened limma.		Superlimmal gets all the primes up to [[29/1\|29]] reasonably covered, but is acceptable just as a 13-limit microtemperament, given a relatively simple [[comma basis]]. It can also be extended to include prime [[37/1\|37]] by mapping it to 87 generator steps, tempering out ([[27/25]])/([[40/37]]) = [[1000/999]]. Since 40/37 is the mediant of [[27/25]] and [[13/12]], this extension further consolidates the sharpened limma.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Badness (Sintel): 1.09		Badness (Sintel): 1.09

	~~=== No-31's 37-limit ===~~
	~~Subgroup: 2.3.5.7.11.13.17.19.23.29.37~~

	~~Comma list: 595/594, 760/759, 784/783, 925/924, 969/968, 1000/999, 1045/1044, 1105/1104, 1275/1274~~

	~~Mapping: {{mapping\| 1 -49 -74 -117 -56 25 -11 -49 -15 -83 -72 \| 0 57 86 135 67 -24 17 60 22 99 87 }}~~

	~~Optimal tuning:~~
	* WE: ~2 = 1199.9549{{c}}, ~37/20 = 1064.9140{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~37/20 = 1064.9538{{c}}

	~~{{Optimal ET sequence\|legend=0\| 80, 231, 311 }}~~

	~~Badness (Sintel): 1.06~~

	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:Canousmic temperaments\| ]] <!-- main article -->		[[Category:Canousmic temperaments\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: + link to satin

2026-05-16T08:49:29Z

+ link to satin

← Older revision		Revision as of 08:49, 16 May 2026
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	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* [[Godzilla]] (+49/48 or 81/80) → [[Semaphoresmic clan #Godzilla\|Semaphoresmic clan]]		* [[Godzilla]] (+49/48 or 81/80) → [[Semaphoresmic clan #Godzilla\|Semaphoresmic clan]]
			* ''[[Satin]]'' (+2100875/2097152) → [[Garischismic clan #Satin\|Garischismic clan]]
	* ''[[Kleischismic]]'' (+32805/32768) → [[Schismatic family #Kleischismic\|Schismatic family]]		* ''[[Kleischismic]]'' (+32805/32768) → [[Schismatic family #Kleischismic\|Schismatic family]]
	* ''[[Pentaorwell]]'' (+1728/1715) → [[Orwellismic temperaments #Pentaorwell\|Orwellismic temperaments]]		* ''[[Pentaorwell]]'' (+1728/1715) → [[Orwellismic temperaments #Pentaorwell\|Orwellismic temperaments]]

FloraC: - satin (more properly addressed in garischismic clan). Sort links by ploidacot

2026-05-16T08:48:06Z

- satin (more properly addressed in garischismic clan). Sort links by ploidacot

@@ Line 3: / Line 3: @@
 Temperaments discussed elsewhere are:
-* [[Godzilla]] (+49/48 or 81/80) → [[Slendro clan #Godzilla|Slendro clan]]
+* [[Godzilla]] (+49/48 or 81/80) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]]
 * ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic|Sycamore family]]
 * [[Parakleismic]] (+3136/3125 or 4375/4374) → [[Ragismic microtemperaments #Parakleismic|Ragismic microtemperaments]]
-* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
+* ''[[Turkey (temperament)|Turkey]]'' (+5250987/5242880) → [[Vulture family #Turkey|Vulture family]]
 * ''[[Marthirds]]'' (+15625/15552) → [[Kleismic family #Marthirds|Kleismic family]]
-* ''[[Kleischismic]]'' (+32805/32768) → [[Schismatic family #Kleischismic|Schismatic family]]
+* ''[[Semiluna]]'' (+95703125/95551488) → [[Luna family #Semiluna|Luna family]]
 * ''[[Quartiquart]]'' (+390625/388962) → [[Quartonic family #Quartiquart|Quartonic family]]
-Badness (Sintel): 0.871
+Considered below is superlimmal.
 == Superlimmal ==

FloraC: Switch to Sintel's badness, WE & CWE tunings. - redundant category

2026-05-16T08:41:27Z

Switch to Sintel's badness, WE & CWE tunings. - redundant category

Show changes

FloraC: Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

2025-11-27T12:24:14Z

Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

← Older revision		Revision as of 12:24, 27 November 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Canousmic temperaments\| ]] <!-- main article -->		[[Category:Canousmic temperaments\| ]] <!-- main article -->
	[[Category:Canou\| ]] <!-- key article -->		[[Category:Canou\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Oops

2025-10-21T12:33:12Z

Oops

← Older revision		Revision as of 12:33, 21 October 2025
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	* [[Godzilla]] (+49/48 or 81/80) → [[Slendro clan #Godzilla\|Slendro clan]]		* [[Godzilla]] (+49/48 or 81/80) → [[Slendro clan #Godzilla\|Slendro clan]]
	* ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic\|Sycamore family]]		* ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic\|Sycamore family]]
	* ''[[Pentaorwell]]'' (+1728/1715) → [[Orwellismic temperaments #~~Pentorwell~~\|Orwellismic temperaments]]		* ''[[Pentaorwell]]'' (+1728/1715) → [[Orwellismic temperaments #Pentaorwell\|Orwellismic temperaments]]
	* ''[[Amicable]]'' (+2401/2400) → [[Breedsmic temperaments #Amicable\|Breedsmic temperaments]]		* ''[[Amicable]]'' (+2401/2400) → [[Breedsmic temperaments #Amicable\|Breedsmic temperaments]]
	* [[Parakleismic]] (+3136/3125 or 4375/4374) → [[Ragismic microtemperaments #Parakleismic\|Ragismic microtemperaments]]		* [[Parakleismic]] (+3136/3125 or 4375/4374) → [[Ragismic microtemperaments #Parakleismic\|Ragismic microtemperaments]]

FloraC at 12:31, 21 October 2025

2025-10-21T12:31:06Z

← Older revision		Revision as of 12:31, 21 October 2025
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	* [[Godzilla]] (+49/48 or 81/80) → [[Slendro clan #Godzilla\|Slendro clan]]		* [[Godzilla]] (+49/48 or 81/80) → [[Slendro clan #Godzilla\|Slendro clan]]
	* ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic\|Sycamore family]]		* ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic\|Sycamore family]]
	* ''[[~~Pentorwell~~]]'' (+1728/1715) → [[Orwellismic temperaments #Pentorwell\|Orwellismic temperaments]]		* ''[[Pentaorwell]]'' (+1728/1715) → [[Orwellismic temperaments #Pentorwell\|Orwellismic temperaments]]
	* ''[[Amicable]]'' (+2401/2400) → [[Breedsmic temperaments #Amicable\|Breedsmic temperaments]]		* ''[[Amicable]]'' (+2401/2400) → [[Breedsmic temperaments #Amicable\|Breedsmic temperaments]]
	* [[Parakleismic]] (+3136/3125 or 4375/4374) → [[Ragismic microtemperaments #Parakleismic\|Ragismic microtemperaments]]		* [[Parakleismic]] (+3136/3125 or 4375/4374) → [[Ragismic microtemperaments #Parakleismic\|Ragismic microtemperaments]]

Lériendil: Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content"

2025-06-24T00:32:46Z

Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:32, 24 June 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Canousmic temperaments\| ]] <!-- main article -->		[[Category:Canousmic temperaments\| ]] <!-- main article -->
	[[Category:Canou\| ]] <!-- key article -->		[[Category:Canou\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:03, 12 June 2025

2025-06-12T05:03:29Z

← Older revision		Revision as of 05:03, 12 June 2025
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	{{Mapping\|legend=1\| 1 8 12 18 \| 0 -57 -86 -135 }}		{{Mapping\|legend=1\| 1 8 12 18 \| 0 -57 -86 -135 }}

	~~{{Multival\|legend=1\| 57 86 135 3 53 72 }}~~

	[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/25 = 135.0464		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/25 = 135.0464

Lériendil: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:47:48Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:47, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	This is a collection of rank-2 temperaments that temper out the [[canousma]], 4802000/4782969 = {{monzo\| 4 -14 3 4 }}. For the rank-3 temperament, see [[Canou family]].		This is a collection of rank-2 temperaments that temper out the [[canousma]], 4802000/4782969 = {{monzo\| 4 -14 3 4 }}. For the rank-3 temperament, see [[Canou family]].