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Semaphoresmic clan: Difference between revisions

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{{Mapping|legend=2| 1 0 2 | 0 2 1 }}
{{Mapping|legend=2| 1 0 2 | 0 2 1 }}
: sval mapping generators: ~2, ~7/4


{{Mapping|legend=3| 1 0 0 2 | 0 2 0 1 }}
{{Mapping|legend=3| 1 0 0 2 | 0 2 0 1 }}


: [[gencom]]: [2 7/4; 49/48]
: mapping generators: ~2, ~7/4


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 952.295
* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}
: [[error map]]: {{val| 0.000 +2.635 -16.531 }}
: [[error map]]: {{val| +2.832 +1.758 -11.304 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 949.615
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}
: error map: {{val| 0.000 -2.724 -19.211 }}
: error map: {{val| 0.000 -0.577 -18.137 }}


{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd, 115ddd }}
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd, 115ddd }}
Line 44: Line 42:
These all use the same nominal generator as semaphore, though some of them are of very low accuracy.  
These all use the same nominal generator as semaphore, though some of them are of very low accuracy.  


Decimal adds [[25/24]]. Anguirus adds [[2048/2025]]. Those split the octave in two. Negri adds [[225/224]], splitting the hemifourth in two. Triforce adds [[128/125]], splitting the octave in three. Keemun adds [[126/125]], splitting the hemitwelfth in three. Nautilus adds [[250/243]], splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds [[648/625]] with a 1/4-octave period. Blacksmith adds [[28/27]], splitting the octave in five. Spell adds [[3125/3072]], splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Finally, semabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five.  
Decimal adds [[25/24]]. Anguirus adds [[2048/2025]]. Those split the octave in two. Negri adds [[225/224]], splitting the hemifourth in two. Triforce adds [[128/125]], splitting the octave in three. Keemun adds [[126/125]], splitting the hemitwelfth in three. Nautilus adds [[250/243]], splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds [[648/625]] with a 1/4-octave period. Rhinoceros adds [[4375/4374]], splitting the hemifourth in four. Spell adds [[3125/3072]], splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Semabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five. Finally, blackwood adds [[28/27]], reducing intervals of 3 and 7 to the same chain of 1/5-octave periods.  


Discussed elsewhere are  
Discussed elsewhere are  
* ''[[Beep]]'' (+21/20) → [[Bug family #Beep|Bug family]]
* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]
* ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]]
* ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]]
* ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|Very low accuracy temperaments]]
* ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|Very low accuracy temperaments]]
* [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]]
* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]
* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
* ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]]
* ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]]
Line 56: Line 54:
* [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic family]]
* [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic family]]
* ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]]
* ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]]
* ''[[Hemidim]]'' (+648/625) → [[Dimipent family #Hemidim|Dimipent family]]
* ''[[Hemidim]]'' (+648/625) → [[Diminished family #Hemidim|Diminished family]]
* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
* ''[[Rhinoceros]]'' (+4375/4374) → [[Unicorn family #Rhinoceros|Unicorn family]]
* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]
* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]
* ''[[Semabila]]'' (+28672/28125) → [[Mabila family #Mabila|Mabila family]]
* ''[[Semabila]]'' (+28672/28125) → [[Mabila family #Mabila|Mabila family]]
* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]


Considered below are godzilla, helayo, superpelog, baba, negri, and nuke.
Considered below are godzilla, helayo, superpelog, baba, negri, and nuke.
=== Semaerophore ===
Named by [[CompactStar]] in 2023, this extension tempers out [[729/704]]. It is the no-5 [[restriction]] of undecimal godzilla.
Subgroup: 2.3.7.11
Comma list: 49/48, 729/704
Subgroup-val mapping: {{mapping| 1 0 2 -6 | 0 2 1 12 }}
Optimal tunings:
* WE: ~2 = 1204.9027{{c}}, ~7/4 = 948.7772{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 945.4959{{c}}
{{Optimal ET sequence|legend=0| 14, 33d, 47de }}
Badness (Sintel): 1.27
==== 2.3.7.11.19 subgroup ====
Subgroup: 2.3.7.11.19
Comma list: 49/48, 77/76, 729/704
Subgroup-val mapping: {{mapping| 1 0 2 -6 -6 | 0 2 1 12 13 }}
Optimal tunings:
* WE: ~2 = 1204.9645{{c}}, ~7/4 = 948.5749{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 945.2236{{c}}
{{Optimal ET sequence|legend=0| 14, 33d, 47deh }}
Badness (Sintel): 1.08


== Godzilla ==
== Godzilla ==
<span style="display: block; text-align: right;">[[:de:Semiphor, Semaphor, Godzilla|Deutsch]]</span>
{{Main| Semaphore and godzilla }}
{{Main| Semaphore and godzilla }}


Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes.
Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. Like many entries of this clan, godzilla can be extended naturally to the 2.3.5.7.13 subgroup by identifying the hemifourth as ~15/13, tempering out [[91/90]] and [[105/104]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes.


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 79: Line 110:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 948.796
* [[WE]]: ~2 = 1203.8275{{c}}, ~7/4 = 950.3867{{c}}
: [[error map]]: {{val| 0.000 -4.363 +4.054 -20.030 }}
: [[error map]]: {{val| +3.827 -1.182 +1.470 -10.784 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 947.365
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.8216{{c}}
: error map: {{val| 0.000 -7.225 -7.394 -21.461 }}
: error map: {{val| 0.000 -6.312 -3.741 -21.004 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 92: Line 123:
[[Badness]] (Sintel): 0.677
[[Badness]] (Sintel): 0.677


=== 11-limit ===
==== 2.3.5.7.13 subgroup ====
Subgroup: 2.3.5.7.13
 
Comma list: 49/48, 81/80, 91/90
 
Subgroup-val mapping: {{mapping| 1 0 -4 2 -5 | 0 2 8 1 11 }}
 
Optimal tunings:
* WE: ~2 = 1203.7816{{c}}, ~7/4 = 950.5570{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.0037{{c}}
 
{{Optimal ET sequence|legend=0| 5, 14cf, 19 }}
 
Badness (Sintel): 0.591
 
=== Undecimal godzilla ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 99: Line 145:
Mapping: {{mapping| 1 0 -4 2 -6 | 0 2 8 1 12 }}
Mapping: {{mapping| 1 0 -4 2 -6 | 0 2 8 1 12 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 947.456
* WE: ~2 = 1204.4129{{c}}, ~7/4 = 949.4513{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 945.973
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4361{{c}}


Tuning ranges:  
Tuning ranges:  
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Mapping: {{mapping| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}
Mapping: {{mapping| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 947.888
* WE: ~2 = 1203.7164{{c}}, ~7/4 = 949.2061{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 946.397
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4131{{c}}


Tuning ranges:  
Tuning ranges:  
Line 138: Line 184:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 948.209
* WE: ~2 = 1206.9595{{c}}, ~7/4 = 951.4440{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 945.958
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4472{{c}}


{{Optimal ET sequence|legend=0| 14c, 19e, 33cdee, 52cdeee }}
{{Optimal ET sequence|legend=0| 14c, 19e, 33cdee, 52cdeee }}


Badness (Sintel): 0.943
Badness (Sintel): 0.943
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 33/32, 49/48, 55/54, 91/90
Mapping: {{mapping| 1 0 -4 2 5 -5 | 0 2 8 1 -2 11 }}
Optimal tunings:
* WE: ~2 = 1206.9737{{c}}, ~7/4 = 951.7738{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.7732{{c}}
{{Optimal ET sequence|legend=0| 14cf, 19e, 33cdeeff, 52cdeeeff }}
Badness (Sintel): 0.975


=== Varan ===
=== Varan ===
Line 153: Line 214:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 949.616
* WE: ~2 = 1202.5842{{c}}, ~7/4 = 950.9647{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 948.921
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.1239{{c}}


{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
Line 168: Line 229:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 949.525
* WE: ~2 = 1202.4367{{c}}, ~7/4 = 950.7615{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 948.835
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.0338{{c}}


{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
Line 182: Line 243:
Mapping: {{mapping| 1 0 -4 2 9 | 0 2 8 1 -7 }}
Mapping: {{mapping| 1 0 -4 2 9 | 0 2 8 1 -7 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 949.031
* WE: ~2 = 1201.1412{{c}}, ~7/4 = 949.7291{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 948.827
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8625{{c}}


{{Optimal ET sequence|legend=0| 5, 19, 24 }}
{{Optimal ET sequence|legend=0| 19, 24 }}


Badness (Sintel): 1.18
Badness (Sintel): 1.18
Line 197: Line 258:
Mapping: {{mapping| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}
Mapping: {{mapping| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 949.067
* WE: ~2 = 1201.1228{{c}}, ~7/4 = 949.6894{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 948.802
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8468{{c}}


{{Optimal ET sequence|legend=0| 5, 19, 24 }}
{{Optimal ET sequence|legend=0| 19, 24 }}


Badness (Sintel): 1.10
Badness (Sintel): 1.10


== Helayo ==
== Helayo ==
: ''For the 5-limit version of this temperament see [[Miscellaneous 5-limit temperaments #Hogzilla]].''
: ''For the 5-limit version of this temperament see [[Syntonic–kleismic equivalence continuum #Hogzilla]].''


Helayo tempers out 3645/3584 and may be thought of as the opposite of godzilla with respect to 19edo. Like godzilla, 19edo's generator is close to the optimum.  
Helayo tempers out 3645/3584 and may be thought of as the opposite of godzilla with respect to 19edo. Like godzilla, 19edo's generator is close to the optimum.  
Line 216: Line 277:
{{Mapping|legend=1| 1 0 11 2 | 0 2 -11 1 }}
{{Mapping|legend=1| 1 0 11 2 | 0 2 -11 1 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 947.097
* [[WE]]: ~2 = 1204.0199{{c}}, ~7/4 = 950.7917{{c}}
: [[error map]]: {{val| 0.000 -7.761 -4.380 -21.729 }}
: [[error map]]: {{val| +4.020 -0.372 -0.804 -9.995 }}
* [[CWE]]: ~2 = 1200.000, ~7/4 = 947.505
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.5047{{c}}
: error map: {{val| 0.000 -6.946 -8.866 -21.321 }}
: error map: {{val| 0.000 -6.946 -8.866 -21.321 }}


Line 225: Line 286:


[[Badness]] (Sintel): 2.00
[[Badness]] (Sintel): 2.00
Scales: [[Helayo14]], [[Helayo19]], [[Helayo24]]


; Music
; Music
Line 238: Line 301:
{{Mapping|legend=1| 1 0 7 2 | 0 2 -6 1 }}
{{Mapping|legend=1| 1 0 7 2 | 0 2 -6 1 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 939.030
* [[WE]]: ~2 = 1208.8222{{c}}, ~7/4 = 946.9590{{c}}
: [[error map]]: {{val| 0.000 -23.896 -20.492 -29.796 }}
: [[error map]]: {{val| +8.822 -8.037 -6.313 -4.223 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 940.048
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 939.8419{{c}}
: error map: {{val| 0.000 -21.859 -26.602 -28.778 }}
: error map: {{val| 0.000 -22.271 -25.365 -28.984 }}


{{Optimal ET sequence|legend=1| 9, 14c, 23d, 37bcd, 60bbccdd }}
{{Optimal ET sequence|legend=1| 9, 14c, 23d, 37bcd, 60bbccdd }}
Line 256: Line 319:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 938.467
* WE: ~2 = 1208.8663{{c}}, ~7/4 = 946.9861{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 940.041
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 939.7687{{c}}


{{Optimal ET sequence|legend=0| 9, 14c, 23de, 37bcde, 60bbccddeee }}
{{Optimal ET sequence|legend=0| 9, 14c, 23de, 37bcde, 60bbccddeee }}
Line 276: Line 339:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 968.739
* [[WE]]: ~2 = 1184.7407{{c}}, ~7/4 = 960.9196{{c}}
: [[error map]]: {{val| 0.000 +35.523 +76.208 -0.087 }}
: [[error map]]: {{val| -15.259 +19.884 +30.810 -38.425 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 973.296
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.2994{{c}}
: error map: {{val| 0.000 +42.644 +69.088 +3.473 }}
: error map: {{val| 0.000 +42.644 +69.088 +3.473 }}


Line 293: Line 356:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 972.258
* WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{c}}
* POTE: ~2 = 1200.000, ~7/4 = 978.164
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9298{{c}}


{{Optimal ET sequence|legend=0| 5, 11b }}
{{Optimal ET sequence|legend=0| 5, 11b }}
Line 302: Line 365:
== Negri ==
== Negri ==
{{Main| Negri }}
{{Main| Negri }}
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Negri (5-limit)]].''


Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.  
Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 and/or 105/104 to the comma list; this will be discussed below under the title of negra.  
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 16875/16384
 
{{Mapping|legend=1| 1 2 2 | 0 -4 3 }}
 
: mapping generators: ~2, ~16/15
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~16/15 = 125.396
: [[error map]]: {{val| 0.000 -3.539 -10.126 }}
* [[POTE]]: ~2 = 1200.000, ~16/15 = 125.755
: error map: {{val| 0.000 -4.975 -9.049 }}
 
{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
 
[[Badness]] (Sintel): 2.04


=== 7-limit ===
=== 7-limit ===
Line 331: Line 377:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~15/14 = 124.813
* [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}
: [[error map]]: {{val| 0.000 -1.209 -11.874 -18.453 }}
: [[error map]]: {{val| +3.481 +1.118 -1.435 -10.328 }}
* [[POTE]]: ~2 = 1200.000, ~15/14 = 125.608
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}
: error map: {{val| 0.000 -4.387 -9.490 -20.042 }}
: error map: {{val| 0.000 -3.694 -10.009 -19.695 }}


{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
Line 345: Line 391:
Comma list: 49/48, 65/64, 91/90
Comma list: 49/48, 65/64, 91/90


Sval mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -3 }}
Subgroup-val mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -3 }}


Gencom mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 }}
Gencom mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 }}
: gencom: [2 14/13; 49/48 65/64 91/90]


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~14/13 = 124.457
* WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}
* POTE: ~2 = 1200.000, ~14/13 = 125.567
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}


{{Optimal ET sequence|legend=0| 9, 10, 19, 48df, 67cddf, 86cddff }}
{{Optimal ET sequence|legend=0| 9, 10, 19, 48df, 67cddf, 86cddff }}
Line 359: Line 403:
Badness (Sintel): 0.463
Badness (Sintel): 0.463


=== 11-limit ===
=== Undecimal negri ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 367: Line 411:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~15/14 = 125.780
* WE: ~2 = 1202.1045{{c}}, ~15/14 = 126.6961{{c}}
* POTE: ~2 = 1200.000, ~15/14 = 126.474
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.3382{{c}}


{{Optimal ET sequence|legend=0| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 9, 10, 19 }}
Line 382: Line 426:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~14/13 = 125.434
* WE: ~2 = 1202.6035{{c}}, ~14/13 = 126.7054{{c}}
* POTE: ~2 = 1200.000, ~14/13 = 126.431
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.2534{{c}}


{{Optimal ET sequence|legend=0| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 9, 10, 19 }}
Line 397: Line 441:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~15/14 = 124.998
* WE: ~2 = 1202.7081{{c}}, ~15/14 = 125.0491{{c}}
* POTE: ~2 = 1200.000, ~15/14 = 124.767
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.8066{{c}}


{{Optimal ET sequence|legend=0| 10e, 19, 29, 48d, 77cdd }}
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48d, 77cdd }}
Line 412: Line 456:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~14/13 = 124.865
* WE: ~2 = 1202.9319{{c}}, ~14/13 = 125.0204{{c}}
* POTE: ~2 = 1200.000, ~14/13 = 124.716
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.7374{{c}}


{{Optimal ET sequence|legend=0| 10e, 19, 29, 48df, 77cddf }}
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48df, 77cddf }}
Line 427: Line 471:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~15/14 = 126.574
* WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{c}}
* POTE: ~2 = 1200.000, ~15/14 = 127.039
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.9620{{c}}


{{Optimal ET sequence|legend=0| 9, 19e }}
{{Optimal ET sequence|legend=0| 9, 19e }}
Line 442: Line 486:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~14/13 = 126.153
* WE: ~2 = 1205.7833{{c}}, ~14/13 = 127.6507{{c}}
* POTE: ~2 = 1200.000, ~14/13 = 127.039
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.9093{{c}}


{{Optimal ET sequence|legend=0| 9, 19e }}
{{Optimal ET sequence|legend=0| 9, 19e }}
Line 457: Line 501:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~15/14 = 123.735
* WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{c}}
* POTE: ~2 = 1200.000, ~15/14 = 124.539
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.3642{{c}}


{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddee }}
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddee }}
Line 472: Line 516:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~15/14 = 123.644
* WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{c}}
* POTE: ~2 = 1200.000, ~14/13 = 124.545
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.3733{{c}}


{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddeef }}
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddeef }}
Line 480: Line 524:


=== Wilsec ===
=== Wilsec ===
Wilsec splits the fifthward generator of negri in half for 11/8~15/11, tempering out [[121/120]]. Its ploidacot is gamma-octacot.
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 121/120, 225/224
Comma list: 49/48, 121/120, 225/224


Mapping: {{mapping| 1 6 -1 5 4 | 0 -8 6 -4 -1 }}
Mapping: {{mapping| 1 -2 5 1 3 | 0 8 -6 4 1 }}


: mapping generators: ~2, ~16/11
: mapping generators: ~2, ~11/8


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/8 = 537.627
* WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{c}}
* POTE: ~2 = 1200.000, ~11/8 = 537.186
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2654{{c}}


{{Optimal ET sequence|legend=0| 9, 20, 29, 38d, 67cdde, 105cdddee }}
{{Optimal ET sequence|legend=0| 9, 20, 29, 38d, 67cdde, 105cdddee }}
Line 501: Line 547:
Comma list: 49/48, 65/64, 91/90, 121/120
Comma list: 49/48, 65/64, 91/90, 121/120


Mapping: {{mapping| 1 6 -1 5 4 7 | 0 -8 6 -4 -1 -6 }}
Mapping: {{mapping| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/8 = 537.802
* WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{c}}
* POTE: ~2 = 1200.000, ~11/8 = 537.208
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.3053{{c}}


{{Optimal ET sequence|legend=0| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}
{{Optimal ET sequence|legend=0| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}
Line 516: Line 562:
Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
Comma list: 49/48, 65/64, 91/90, 121/120, 154/153


Mapping: {{mapping| 1 6 -1 5 4 7 -2 | 0 -8 6 -4 -1 -6 11 }}
Mapping: {{mapping| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/8 = 537.492
* WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{c}}
* POTE: ~2 = 1200.000, ~11/8 = 537.230
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2633{{c}}


{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefg }}
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefg }}
Line 531: Line 577:
Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153


Mapping: {{mapping| 1 6 -1 5 4 7 -2 7 | 0 -8 6 -4 -1 -6 11 -5 }}
Mapping: {{mapping| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~11/8 = 537.553
* WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{c}}
* POTE: ~2 = 1200.000, ~11/8 = 537.214
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2534{{c}}


{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefgh }}
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefgh }}
Line 551: Line 597:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~16/15 = 81.345
* [[WE]]: ~2 = 1197.0059{{c}}, ~16/15 = 80.7519{{c}}
: [[error map]]: {{val| 0.000 +9.975 +20.411 -12.861 }}
: [[error map]]: {{val| -2.994 +7.546 +11.457 -20.064 }}
* [[POTE]]: ~2 = 1200.000, ~16/15 = 80.954
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 81.0408{{c}}
: error map: {{val| 0.000 +12.322 +18.456 -11.688 }}
: error map: {{val| 0.000 +11.800 +18.890 -11.948 }}


{{Optimal ET sequence|legend=1| 14, 15 }}
{{Optimal ET sequence|legend=1| 14, 15 }}
Line 568: Line 614:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~16/15 = 80.908
* WE: ~2 = 1196.6821{{c}}, ~16/15 = 80.5936{{c}}
* POTE: ~2 = 1200.000, ~16/15 = 80.817
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 80.8326{{c}}


{{Optimal ET sequence|legend=0| 14e, 15 }}
{{Optimal ET sequence|legend=0| 14e, 15 }}
Line 583: Line 629:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~16/15 = 81.320
* WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{c}}
* POTE: ~2 = 1200.000, ~16/15 = 81.024
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 81.0685{{c}}


{{Optimal ET sequence|legend=0| 14e, 15 }}
{{Optimal ET sequence|legend=0| 14e, 15 }}
Line 590: Line 636:
Badness (Sintel): 2.01
Badness (Sintel): 2.01


[[Category:Semaphoresmic clan| ]] <!-- main article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Semaphoresmic clan| ]] <!-- main article -->
[[Category:Rank 2]]
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