Sensamagic clan: Difference between revisions
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* ''[[Fourfives]]'' (+235298/234375) → [[Fifive family #Fourfives|Fifive family]] | * ''[[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 | Discussed elsewhere are | ||
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* [[Rodan]] (+1029/1024) → [[Gamelismic clan #Rodan|Gamelismic clan]] | * [[Rodan]] (+1029/1024) → [[Gamelismic clan #Rodan|Gamelismic clan]] | ||
* ''[[Shrutar]]'' (+2048/2025) → [[Diaschismic family #Shrutar|Diaschismic family]] | * ''[[Shrutar]]'' (+2048/2025) → [[Diaschismic family #Shrutar|Diaschismic family]] | ||
* ''[[Salsa]]'' (+32805/32768) → [[Schismatic family #Salsa|Schismatic family]] | |||
* ''[[Escaped]]'' (+65625/65536) → [[Escapade family #Escaped|Escapade family]] | * ''[[Escaped]]'' (+65625/65536) → [[Escapade family #Escaped|Escapade family]] | ||
For ''no-twos'' extensions, see [[No-twos subgroup temperaments #BPS]]. | For ''no-twos'' extensions, see [[No-twos subgroup temperaments #BPS]]. | ||
Considered below are bohpier, pycnic | Considered below are bohpier, pycnic, superenneadecal, superthird, magus and leapweek. | ||
== Bohpier == | == Bohpier == | ||
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== Pycnic == | == Pycnic == | ||
: ''For the 5-limit version, see [[ | : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].'' | ||
Pycnic is related to [[triton]], but its mapping differs for the [[ | 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. | 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. | ||
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[[Badness]] (Sintel): 1.87 | [[Badness]] (Sintel): 1.87 | ||
== | == Xenia == | ||
{{ | : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].'' | ||
Xenia is related to [[Starling temperaments #Xenial|xenial]], but its mapping differs for the [[7/1|7th harmonic]]. It may be described as {{nowrap| 19 & 51c }} or {{nowrap| 19 & 70d }}, which tempers out the sensamagic and keega, [[1029/1000]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 245/243, | [[Comma list]]: 245/243, 1029/1000 | ||
{{Mapping|legend=1| 1 | {{Mapping|legend=1| 1 -6 -12 -9 | 0 9 17 14 }} | ||
: mapping generators: ~2, ~ | : mapping generators: ~2, ~9/5 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = | * [[WE]]: ~2 = 1201.0862{{c}}, ~9/5 = 1012.0503{{c}} | ||
: [[error map]]: {{val| +0. | : [[error map]]: {{val| +1.086 -0.020 +5.507 -9.898 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~ | * [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2199{{c}} | ||
: error map: {{val| 0.000 | : error map: {{val| 0.000 -0.976 +4.424 -11.748 }} | ||
= | {{Optimal ET sequence|legend=1| 19, 70d, 89d }} | ||
[[Badness]] (Sintel): 2.25 | |||
Badness (Sintel): | |||
== Magus == | == Magus == | ||
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Badness (Sintel): 1.36 | Badness (Sintel): 1.36 | ||
[[Category:Sensamagic clan| ]] <!-- main article --> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||