Sensamagic clan: Difference between revisions

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* ''[[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:

* [[Rodan]] (+1029/1024) → [[Gamelismic clan #Rodan|Gamelismic clan]]

* ''[[Shrutar]]'' (+2048/2025) → [[Diaschismic family #Shrutar|Diaschismic family]]

* ''[[Salsa]]'' (+32805/32768) → [[Schismatic family #Salsa|Schismatic 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 ==

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[[Badness]] (Sintel): 1.87

~~== Salsa ==~~

~~{{See also| Schismatic family }}~~

~~[[Subgroup]]: 2.3.5.7~~

~~[[Comma list]]: 245/243, 32805/32768~~

~~{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}~~

~~: mapping generators: ~2, ~128/105~~

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1200.7707{{c}}, ~128/105 = 351.2748{{c}}

~~: [[error map]]: {{val| +0.771 +1.365 -1.315 -3.024 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 351.0471{{c}}

~~: error map: {{val| 0.000 +0.139 -3.068 -5.213 }}~~

~~{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd }}~~

~~[[Badness]] (Sintel): 2.03~~

~~=== 11-limit ===~~

~~Subgroup: 2.3.5.7.11~~

~~Comma list: 243/242, 245/242, 385/384~~

~~Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1200.3891{{c}}, ~11/9 = 351.1275{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0141{{c}}

~~{{Optimal ET sequence|legend=0| 17, 24, 41, 106d }}~~

~~Badness (Sintel): 1.30~~

~~=== 13-limit ===~~

~~Subgroup: 2.3.5.7.11.13~~

~~Comma list: 105/104, 144/143, 243/242, 245/242~~

~~Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.9362{c}}, ~11/9 = 351.0061{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0247{{c}}

~~{{Optimal ET sequence|legend=0| 17, 24, 41 }}~~

~~Badness (Sintel): 1.27~~

== Magus ==

@@ 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]]
+* ''[[Salsa]]'' (+32805/32768) → [[Schismatic family #Salsa|Schismatic 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
-== Salsa ==
-{{See also| Schismatic family }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 245/243, 32805/32768
-{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}
-: mapping generators: ~2, ~128/105
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.7707{{c}}, ~128/105 = 351.2748{{c}}
-: [[error map]]: {{val| +0.771 +1.365 -1.315 -3.024 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 351.0471{{c}}
-: error map: {{val| 0.000 +0.139 -3.068 -5.213 }}
-{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd }}
-[[Badness]] (Sintel): 2.03
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 243/242, 245/242, 385/384
-Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}
-Optimal tunings:
-* WE: ~2 = 1200.3891{{c}}, ~11/9 = 351.1275{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0141{{c}}
-{{Optimal ET sequence|legend=0| 17, 24, 41, 106d }}
-Badness (Sintel): 1.30
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 105/104, 144/143, 243/242, 245/242
-Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}
-Optimal tunings:
-* WE: ~2 = 1199.9362{c}}, ~11/9 = 351.0061{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0247{{c}}
-{{Optimal ET sequence|legend=0| 17, 24, 41 }}
-Badness (Sintel): 1.27
 == Magus ==