Sensamagic clan - Revision history

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

FloraC: Sort by badness

2025-10-12T10:25:50Z

Sort by badness

Show changes

FloraC: + intro to certain entries

2025-10-12T10:21:04Z

+ intro to certain entries

← Older revision		Revision as of 10:21, 12 October 2025
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Bohpier]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Bohpier]].''

	Bohpier is named after its interesting [[relationship between Bohlen–Pierce and octave-ful temperaments\|relationship with the non-octave Bohlen–Pierce equal temperament]].		Bohpier tempers out 3125/3087 and may be described as the {{nowrap\| 41 & 49 }} temperament. It is named after its interesting [[relationship between Bohlen–Pierce and octave-ful temperaments\|relationship with the non-octave Bohlen–Pierce equal temperament]].

			[[41edo]] itself makes for an excellent tuning, though [[90edo]] and [[131edo]] are interesting alternatives. Another notable tuning is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 146.4741{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[WE]] and/or [[CWE]] (shown below) is largely unnoticeable.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Pycnic ==		== Pycnic ==
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Stump]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #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]].

	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 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.
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Magus]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Magus]].''

	Magus temperament tempers out [[50331648/48828125]] ~~(salegu)~~ in the 5-limit. This temperament can be described as {{nowrap\| 46 & 49 }} temperament, which tempers out the sensamagic and 28672/28125 ~~(sazoquingu)~~. The alternative extension [[starling temperaments #Amigo\|amigo]] ({{nowrap\|43 & 46}}) tempers out the same 5-limit comma as the magus, but with the [[126/125\|starling comma]] (126/125) rather than the sensamagic tempered out.		Magus temperament tempers out [[50331648/48828125]] in the 5-limit. This temperament can be described as {{nowrap\| 46 & 49 }} temperament, which tempers out the sensamagic and [[28672/28125]]. The alternative extension [[starling temperaments #Amigo\|amigo]] ({{nowrap\| 43 & 46 }}) tempers out the same 5-limit comma as the magus, but with the [[126/125\|starling comma]] (126/125) rather than the sensamagic tempered out.

	Magus has a generator of a sharp ~5/4 ~~(so that~~ ~[[25/16]] is twice as sharp so that it makes sense to equate with [[11/7]] by tempering [[176/175]]), so that three reaches [[128/125]] short of the octave (where 128/125 is tuned narrow); this is significant because magus reaches [[3/2]] as ([[25/16]])/([[128/125]])<sup>3</sup>, that is, {{nowrap\|2 + 3 × 3 {{=}} 11}} generators. Therefore, it implies that [[25/24]] is split into three [[128/125]]'s. Therefore, in the 5-limit, magus can be thought of as a higher-complexity and sharper analogue of [[würschmidt]] (which reaches [[3/2]] as (25/16)/(128/125)<sup>2</sup> implying 25/24 is split into two 128/125's thus having a guaranteed neutral third), which itself is a higher-complexity and sharper analogue of [[magic]] (which equates 25/24 with 128/125 by flattening 5). For more details on these connections see [[Würschmidt comma]].		Magus has a generator of a sharp ~5/4, and ~[[25/16]] is twice as sharp so that it makes sense to equate with [[11/7]] by tempering out [[176/175]]), so that three reaches [[128/125]] short of the octave, where 128/125 is tuned narrow; this is significant because magus reaches [[3/2]] as ([[25/16]])/([[128/125]])<sup>3</sup>, that is, {{nowrap\| 2 + 3 × 3 {{=}} 11 }} generators. Therefore, it implies that [[25/24]] is split into three [[128/125]]'s. Therefore, in the 5-limit, magus can be thought of as a higher-complexity and sharper analogue of [[würschmidt]] (which reaches [[3/2]] as (25/16)/(128/125)<sup>2</sup> implying 25/24 is split into two 128/125's thus having a guaranteed neutral third), which itself is a higher-complexity and sharper analogue of [[magic]] (which equates 25/24 with 128/125 by flattening 5). For more details on these connections see [[Würschmidt comma]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Leapweek ==		== Leapweek ==
	: ''Not to be confused with scales produced by leap week calendars such as [[Symmetry454]].''		: ''Not to be confused with scales produced by leap week calendars such as [[Symmetry454]].''

			Leapweek may be described as the {{nowrap\| 46 & 63 }} temperament, generated by a perfect fifth and being a strong extension of [[leapfrog]]. [[109edo]] makes for an excellent tuning.

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

FloraC: - POTE tunings

2025-10-12T10:05:34Z

- POTE tunings

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus

2025-10-12T09:52:49Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

Show changes