Sensamagic clan - Revision history

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:38:26Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:38, 30 September 2026
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	[[Comma list]]: 245/243		[[Comma list]]: 245/243

	{{Mapping\|legend=2\| 1 1 2 \| 0 2 -1 }}		{{Mapping\|legend=3\| 1 1 2 \| 0 2 -1 }}
	: mapping generators: ~3, ~9/7		: mapping generators: ~3, ~9/7

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:33:44Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:33, 24 September 2026
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	Comma list: 100/99, 245/243, 1344/1331		Comma list: 100/99, 245/243, 1344/1331

	~~Mapping:~~ {{~~mapping~~\| 1 0 0 0 2 \| 0 13 19 23 12 }}		{{Mapping\|legend=0\| 1 0 0 0 2 \| 0 13 19 23 12 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 144/143, 196/195, 275/273		Comma list: 100/99, 144/143, 196/195, 275/273

	~~Mapping:~~ {{~~mapping~~\| 1 0 0 0 2 2 \| 0 13 19 23 12 14 }}		{{Mapping\|legend=0\| 1 0 0 0 2 2 \| 0 13 19 23 12 14 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 245/243, 1331/1323, 3125/3087		Comma list: 245/243, 1331/1323, 3125/3087

	~~Mapping:~~ {{~~mapping~~\| 1 0 0 0 0 \| 0 39 57 69 85 }}		{{Mapping\|legend=0\| 1 0 0 0 0 \| 0 39 57 69 85 }}
	: mapping generators: ~2, ~77/75		: mapping generators: ~2, ~77/75

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	Comma list: 245/243, 275/273, 847/845, 1331/1323		Comma list: 245/243, 275/273, 847/845, 1331/1323

	~~Mapping:~~ {{~~mapping~~\| 1 0 0 0 0 0 \| 0 39 57 69 85 91 }}		{{Mapping\|legend=0\| 1 0 0 0 0 0 \| 0 39 57 69 85 91 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 176/175, 245/243, 1331/1323		Comma list: 176/175, 245/243, 1331/1323

	~~Mapping:~~ {{~~mapping~~\| 1 -2 2 -6 -6 \| 0 11 1 27 29 }}		{{Mapping\|legend=0\| 1 -2 2 -6 -6 \| 0 11 1 27 29 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 91/90, 176/175, 245/243, 1331/1323		Comma list: 91/90, 176/175, 245/243, 1331/1323

	~~Mapping:~~ {{~~mapping~~\| 1 -2 2 -6 -6 5 \| 0 11 1 27 29 -4 }}		{{Mapping\|legend=0\| 1 -2 2 -6 -6 5 \| 0 11 1 27 29 -4 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 245/243, 2560/2541, 3773/3750		Comma list: 245/243, 2560/2541, 3773/3750

	~~Mapping:~~ {{~~mapping~~\| 19 0 14 -7 96 \| 0 1 1 2 -1 }}		{{Mapping\|legend=0\| 19 0 14 -7 96 \| 0 1 1 2 -1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 196/195, 245/243, 832/825, 1001/1000		Comma list: 196/195, 245/243, 832/825, 1001/1000

	~~Mapping:~~ {{~~mapping~~\| 19 0 14 -7 96 10 \| 0 1 1 2 -1 2 }}		{{Mapping\|legend=0\| 19 0 14 -7 96 10 \| 0 1 1 2 -1 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 245/243, 78125/76832		Comma list: 100/99, 245/243, 78125/76832

	~~Mapping:~~ {{~~mapping~~\| 1 -5 -5 -10 2 \| 0 18 20 35 4 }}		{{Mapping\|legend=0\| 1 -5 -5 -10 2 \| 0 18 20 35 4 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 144/143, 196/195, 1375/1352		Comma list: 100/99, 144/143, 196/195, 1375/1352

	~~Mapping:~~ {{~~mapping~~\| 1 -5 -5 -10 2 -8 \| 0 18 20 35 4 32 }}		{{Mapping\|legend=0\| 1 -5 -5 -10 2 -8 \| 0 18 20 35 4 32 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 245/243, 385/384, 1331/1323		Comma list: 245/243, 385/384, 1331/1323

	~~Mapping:~~ {{~~mapping~~\| 1 0 42 -21 -14 \| 0 1 -25 15 11 }}		{{Mapping\|legend=0\| 1 0 42 -21 -14 \| 0 1 -25 15 11 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 169/168, 245/243, 352/351, 364/363		Comma list: 169/168, 245/243, 352/351, 364/363

	~~Mapping:~~ {{~~mapping~~\| 1 0 42 -21 -14 -9 \| 0 1 -25 15 11 8 }}		{{Mapping\|legend=0\| 1 0 42 -21 -14 -9 \| 0 1 -25 15 11 8 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 154/153, 169/168, 245/243, 256/255, 273/272		Comma list: 154/153, 169/168, 245/243, 256/255, 273/272

	~~Mapping:~~ {{~~mapping~~\| 1 0 42 -21 -14 -9 -34 \| 0 1 -25 15 11 8 24 }}		{{Mapping\|legend=0\| 1 0 42 -21 -14 -9 -34 \| 0 1 -25 15 11 8 24 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 136/135, 169/168, 221/220, 245/243, 364/363		Comma list: 136/135, 169/168, 221/220, 245/243, 364/363

	~~Mapping:~~ {{~~mapping~~\| 1 0 42 -21 -14 -9 39 \| 0 1 -25 15 11 8 -22 }}		{{Mapping\|legend=0\| 1 0 42 -21 -14 -9 39 \| 0 1 -25 15 11 8 -22 }}

	Optimal tunings:		Optimal tunings:

FloraC: /* BPS */ update

2026-09-15T09:34:59Z

BPS: update

← Older revision		Revision as of 09:34, 15 September 2026
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	The full 7-limit extensions' relation to BPS is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are sensi, cohemiripple, hedgehog, and fourfives.		The full 7-limit extensions' relation to BPS is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are sensi, cohemiripple, hedgehog, and fourfives.

	These temperaments are distributed into different family pages.		These temperaments are distributed into different family and clan pages.
	* [[Sensi]] (+126/125) → [[Sensipent family #Sensi\|Sensipent family]]		* [[Sensi]] (+126/125) → [[Sensipent family #Sensi\|Sensipent family]]
	* ''[[Hedgehog]]'' (+50/49) → [[~~Porcupine family~~ #Hedgehog\|~~Porcupine family~~]]		* ''[[Hedgehog]]'' (+50/49) → [[Stearnsmic clan #Hedgehog\|Stearnsmic clan]]
	* ''[[Cohemiripple]]'' (+1323/1250) → [[Ripple family #Cohemiripple\|Ripple family]]		* ''[[Cohemiripple]]'' (+1323/1250) → [[Ripple family #Cohemiripple\|Ripple family]]
	* ''[[Fourfives]]'' (+235298/234375) → [[Fifive family #Fourfives\|Fifive family]]		* ''[[Fourfives]]'' (+235298/234375) → [[Fifive family #Fourfives\|Fifive family]]

FloraC: Recategorize

2026-08-15T07:41:50Z

Recategorize

← Older revision		Revision as of 07:41, 15 August 2026
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	Badness (Sintel): 1.36		Badness (Sintel): 1.36

			[[Category:Sensamagic clan\| ]] <!-- main article -->
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:~~Sensamagic clan\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]
	~~[[Category:Listen~~]]

Xenllium at 06:38, 2 May 2026

2026-05-02T06:38:01Z

← Older revision		Revision as of 06:38, 2 May 2026
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1201.0862{{c}}, ~9/5 = 1012.0503{{c}}		* [[WE]]: ~2 = 1201.0862{{c}}, ~9/5 = 1012.0503{{c}}
	: [[error map]]: {{val\| +1.~~0862,~~ -0.~~0196,~~ +5.~~5068,~~ -9.~~8977~~ }}		: [[error map]]: {{val\| +1.086 -0.020 +5.507 -9.898 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2199{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2199{{c}}
	: error map: {{val\| 0.~~0000~~ -0.~~9760,~~ +4.~~4243,~~ -11.~~7475~~ }}		: error map: {{val\| 0.000 -0.976 +4.424 -11.748 }}

	{{Optimal ET sequence\|legend=1\| 19, 70d, 89d }}		{{Optimal ET sequence\|legend=1\| 19, 70d, 89d }}

Xenllium at 06:16, 2 May 2026

2026-05-02T06:16:05Z

@@ Line 162: / Line 162: @@
 : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
-Pycnic is related to [[triton]], but its mapping differs for the [[5/1|5th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[7/1|7th harmonic]].
+Pycnic is related to [[triton]], but its mapping differs for the [[7/1|7th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[5/1|5th harmonic]].
 The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being two cents sharp of it in the CWE tuning for instance. Pycnic has [[mos]] of size 9, 11, 13, 15, 17… which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.
@@ Line 182: / Line 182: @@
 [[Badness]] (Sintel): 1.87
 == Magus ==

FloraC: /* Pycnic */ link

2026-03-16T11:57:03Z

Pycnic: link

← Older revision		Revision as of 11:57, 16 March 2026
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	== Pycnic ==		== Pycnic ==
	: ''For the 5-limit version, see [[~~Miscellaneous 5-limit temperaments~~ #Stump]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''

	Pycnic is related to [[triton]], but its mapping differs for the [[5/1\|5th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[7/1\|7th harmonic]].		Pycnic is related to [[triton]], but its mapping differs for the [[5/1\|5th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[7/1\|7th harmonic]].

FloraC: - salsa (addressed in schismic family)

2025-12-28T07:12:44Z

- salsa (addressed in schismic family)

@@ Line 35: / Line 35: @@
 * ''[[Fourfives]]'' (+235298/234375) → [[Fifive family #Fourfives|Fifive family]]
-The others are weak extensions. Father tempers out [[16/15]], splitting the generator in two. Godzilla tempers out [[49/48]] with a hemitwelfth period. Sidi tempers out [[25/24]], splitting the generator in two with a hemitwelfth period. Clyde tempers out [[3136/3125]] with a 1/6-twelfth period. Superpyth tempers out [[64/63]], splitting the generator in six. Magic tempers out [[225/224]] with a 1/5-twelfth period. Octacot tempers out [[2401/2400]], splitting the generator in five. Hemiaug tempers out [[128/125]]. Pentacloud tempers out [[16807/16384]]. These split the generator in seven. Bamity tempers out [[64827/64000]], splitting the generator in nine. Rodan tempers out [[1029/1024]], splitting the generator in ten. Shrutar tempers out [[2048/2025]], splitting the generator in eleven. Finally, escaped tempers out [[65625/65536]], splitting the generator in sixteen.
+The others are weak extensions. Father tempers out [[16/15]], splitting the generator in two. Godzilla tempers out [[49/48]] with a hemitwelfth period. Sidi tempers out [[25/24]], splitting the generator in two with a hemitwelfth period. Clyde tempers out [[3136/3125]] with a 1/6-twelfth period. Superpyth tempers out [[64/63]], splitting the generator in six. Magic tempers out [[225/224]] with a 1/5-twelfth period. Octacot tempers out [[2401/2400]], splitting the generator in five. Hemiaug tempers out [[128/125]]. Pentacloud tempers out [[16807/16384]]. These split the generator in seven. Bamity tempers out [[64827/64000]], splitting the generator in nine. Rodan tempers out [[1029/1024]], splitting the generator in ten. Shrutar tempers out [[2048/2025]], splitting the generator in eleven. Salsa tempers out [[32805/32768]], splitting the generator in fifteen. Finally, escaped tempers out [[65625/65536]], splitting the generator in sixteen.
 Discussed elsewhere are
@@ Line 50: / Line 50: @@
 * [[Rodan]] (+1029/1024) → [[Gamelismic clan #Rodan|Gamelismic clan]]
 * ''[[Shrutar]]'' (+2048/2025) → [[Diaschismic family #Shrutar|Diaschismic family]]
 * ''[[Escaped]]'' (+65625/65536) → [[Escapade family #Escaped|Escapade family]]
 For ''no-twos'' extensions, see [[No-twos subgroup temperaments #BPS]].
-Considered below are bohpier, pycnic, salsa, superenneadecal, superthird, magus and leapweek.
+Considered below are bohpier, pycnic, superenneadecal, superthird, magus and leapweek.
 == Bohpier ==
@@ Line 181: / Line 182: @@
 [[Badness]] (Sintel): 1.87
 == Magus ==

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

2025-11-27T12:30:30Z

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

← Older revision		Revision as of 12:30, 27 November 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Sensamagic clan\| ]] <!-- main article -->		[[Category:Sensamagic clan\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]
	[[Category:Listen]]		[[Category:Listen]]

FloraC at 10:26, 12 October 2025

2025-10-12T10:26:39Z

← Older revision		Revision as of 10:26, 12 October 2025
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	Pycnic is related to [[triton]], but its mapping differs for the [[5/1\|5th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[7/1\|7th harmonic]].		Pycnic is related to [[triton]], but its mapping differs for the [[5/1\|5th harmonic]]. It is also related to [[liese]], from which its mapping differs for the [[7/1\|7th harmonic]].

	The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being ~~a cent~~ sharp of it in the ~~POTE~~ tuning for instance. Pycnic has [[mos]] of size 9, 11, 13, 15, 17… which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.		The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being two cents sharp of it in the CWE tuning for instance. Pycnic has [[mos]] of size 9, 11, 13, 15, 17… which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Superenneadecal ==		== Superenneadecal ==
	Superenneadecal is a cousin of [[enneadecal]] but sharper fifth is used to temper 245/243.		Superenneadecal is a cousin of [[enneadecal]] but a sharper fifth is used to temper out 245/243.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7