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Semaphoresmic clan: Difference between revisions

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Line 14: Line 14:


{{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:  
Line 26: Line 24:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}
: error map: {{val| 0.000 -0.577 -18.137 }}
: error map: {{val| 0.000 -0.577 -18.137 }}
<!--
 
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/4 = 952.295{{c}}
: [[error map]]: {{val| 0.000 +2.635 -16.531 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/4 = 949.615{{c}}
: error map: {{val| 0.000 -2.724 -19.211 }}
-->
{{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 49: 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. Blackwood adds [[28/27]], with a 1/5-octave period. 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.  


Discussed elsewhere are  
Discussed elsewhere are  
Line 61: 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]]
* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
Line 68: Line 61:


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 88: Line 113:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.8216{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.8216{{c}}
: error map: {{val| 0.000 -6.312 -3.741 -21.004 }}
: error map: {{val| 0.000 -6.312 -3.741 -21.004 }}
<!--
 
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/4 = 948.796{{c}}
: [[error map]]: {{val| 0.000 -4.363 +4.054 -20.030 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/4 = 947.365{{c}}
: error map: {{val| 0.000 -7.225 -7.394 -21.461 }}
-->
[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 7- and 9-odd-limit [[diamond monotone]]: ~7/4 = [942.857, 960.000] (11\14 to 4\5)
* 7- and 9-odd-limit [[diamond monotone]]: ~7/4 = [942.857, 960.000] (11\14 to 4\5)
Line 102: Line 122:
[[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 112: Line 147:
* WE: ~2 = 1204.4129{{c}}, ~7/4 = 949.4513{{c}}
* WE: ~2 = 1204.4129{{c}}, ~7/4 = 949.4513{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4361{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4361{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 947.456{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 945.973{{c}}
-->
Tuning ranges:  
Tuning ranges:  
* 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)
* 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)
Line 134: Line 166:
* WE: ~2 = 1203.7164{{c}}, ~7/4 = 949.2061{{c}}
* WE: ~2 = 1203.7164{{c}}, ~7/4 = 949.2061{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4131{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4131{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 947.888{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 946.397{{c}}
-->
Tuning ranges:  
Tuning ranges:  
* 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)
* 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)
Line 156: Line 185:
* WE: ~2 = 1206.9595{{c}}, ~7/4 = 951.4440{{c}}
* WE: ~2 = 1206.9595{{c}}, ~7/4 = 951.4440{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4472{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4472{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 948.209{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 945.958{{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 174: Line 215:
* WE: ~2 = 1202.5842{{c}}, ~7/4 = 950.9647{{c}}
* WE: ~2 = 1202.5842{{c}}, ~7/4 = 950.9647{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.1239{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.1239{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 949.616{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 948.921{{c}}
-->
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}


Line 192: Line 230:
* WE: ~2 = 1202.4367{{c}}, ~7/4 = 950.7615{{c}}
* WE: ~2 = 1202.4367{{c}}, ~7/4 = 950.7615{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.0338{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.0338{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 949.525{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 948.835{{c}}
-->
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}


Line 210: Line 245:
* WE: ~2 = 1201.1412{{c}}, ~7/4 = 949.7291{{c}}
* WE: ~2 = 1201.1412{{c}}, ~7/4 = 949.7291{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8625{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8625{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 949.031{{c}}
{{Optimal ET sequence|legend=0| 19, 24 }}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 948.827{{c}}
-->
{{Optimal ET sequence|legend=0| 5, 19, 24 }}


Badness (Sintel): 1.18
Badness (Sintel): 1.18
Line 228: Line 260:
* WE: ~2 = 1201.1228{{c}}, ~7/4 = 949.6894{{c}}
* WE: ~2 = 1201.1228{{c}}, ~7/4 = 949.6894{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8468{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8468{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 949.067{{c}}
{{Optimal ET sequence|legend=0| 19, 24 }}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 948.802{{c}}
-->
{{Optimal ET sequence|legend=0| 5, 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 252: Line 281:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.5047{{c}}
* [[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 }}
<!--
 
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/4 = 947.097{{c}}
: [[error map]]: {{val| 0.000 -7.761 -4.380 -21.729 }}
-->
{{Optimal ET sequence|legend=1| 5c, 14, 19 }}
{{Optimal ET sequence|legend=1| 5c, 14, 19 }}


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


; Music
; Music
Line 277: Line 305:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 939.8419{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 939.8419{{c}}
: error map: {{val| 0.000 -22.271 -25.365 -28.984 }}
: error map: {{val| 0.000 -22.271 -25.365 -28.984 }}
<!--
 
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/4 = 939.030{{c}}
: [[error map]]: {{val| 0.000 -23.896 -20.492 -29.796 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/4 = 940.048{{c}}
: error map: {{val| 0.000 -21.859 -26.602 -28.778 }}
-->
{{Optimal ET sequence|legend=1| 9, 14c, 23d, 37bcd, 60bbccdd }}
{{Optimal ET sequence|legend=1| 9, 14c, 23d, 37bcd, 60bbccdd }}


Line 297: Line 320:
* WE: ~2 = 1208.8663{{c}}, ~7/4 = 946.9861{{c}}
* WE: ~2 = 1208.8663{{c}}, ~7/4 = 946.9861{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 939.7687{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 939.7687{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 938.467{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 940.041{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 14c, 23de, 37bcde, 60bbccddeee }}
{{Optimal ET sequence|legend=0| 9, 14c, 23de, 37bcde, 60bbccddeee }}


Line 322: Line 342:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.2994{{c}}
* [[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 }}
<!--
 
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/4 = 968.739{{c}}
: [[error map]]: {{val| 0.000 +35.523 +76.208 -0.087 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/4 = 973.296{{c}}
: error map: {{val| 0.000 +44.637 +67.094 +4.470 }}
-->
{{Optimal ET sequence|legend=1| 5, 11b, 16bc }}
{{Optimal ET sequence|legend=1| 5, 11b, 16bc }}


Line 342: Line 357:
* WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{c}}
* WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9298{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9298{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~7/4 = 972.258{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/4 = 978.164{{c}}
-->
{{Optimal ET sequence|legend=0| 5, 11b }}
{{Optimal ET sequence|legend=0| 5, 11b }}


Line 352: Line 364:
== 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:
* [[WE]]: ~2 = 1202.3403{{c}}, ~16/15 = 126.0002{{c}}
: [[error map]]: {{val| +2.340 -1.275 -3.633 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 125.6610{{c}}
: error map: {{val| 0.000 -4.599 -9.331 }}
<!--
* [[CTE]]: ~2 = 1200.000{{c}}, ~16/15 = 125.396{{c}}
: [[error map]]: {{val| 0.000 -3.539 -10.126 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~16/15 = 125.755{{c}}
: 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 390: Line 380:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}
: error map: {{val| 0.000 -3.694 -10.009 -19.695 }}
: error map: {{val| 0.000 -3.694 -10.009 -19.695 }}
<!--
 
* [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 124.813{{c}}
: [[error map]]: {{val| 0.000 -1.209 -11.874 -18.453 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~15/14 = 125.608{{c}}
: error map: {{val| 0.000 -4.387 -9.490 -20.042 }}
-->
{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}


Line 405: Line 390:
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:  
* WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}
* WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~14/13 = 124.457{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/13 = 125.567{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 10, 19, 48df, 67cddf, 86cddff }}
{{Optimal ET sequence|legend=0| 9, 10, 19, 48df, 67cddf, 86cddff }}


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 432: Line 412:
* WE: ~2 = 1202.1045{{c}}, ~15/14 = 126.6961{{c}}
* WE: ~2 = 1202.1045{{c}}, ~15/14 = 126.6961{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.3382{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.3382{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~15/14 = 125.780{{c}}
* POTE: ~2 = 1200.000{{c}}, ~15/14 = 126.474{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 9, 10, 19 }}


Line 450: Line 427:
* WE: ~2 = 1202.6035{{c}}, ~14/13 = 126.7054{{c}}
* WE: ~2 = 1202.6035{{c}}, ~14/13 = 126.7054{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.2534{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.2534{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~14/13 = 125.434{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/13 = 126.431{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 9, 10, 19 }}


Line 468: Line 442:
* WE: ~2 = 1202.7081{{c}}, ~15/14 = 125.0491{{c}}
* WE: ~2 = 1202.7081{{c}}, ~15/14 = 125.0491{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.8066{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.8066{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~15/14 = 124.998{{c}}
* POTE: ~2 = 1200.000{{c}}, ~15/14 = 124.767{{c}}
-->
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48d, 77cdd }}
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48d, 77cdd }}


Line 486: Line 457:
* WE: ~2 = 1202.9319{{c}}, ~14/13 = 125.0204{{c}}
* WE: ~2 = 1202.9319{{c}}, ~14/13 = 125.0204{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.7374{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.7374{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~14/13 = 124.865{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/13 = 124.716{{c}}
-->
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48df, 77cddf }}
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48df, 77cddf }}


Line 504: Line 472:
* WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{c}}
* WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.9620{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.9620{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~15/14 = 126.574{{c}}
* POTE: ~2 = 1200.000{{c}}, ~15/14 = 127.039{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 19e }}
{{Optimal ET sequence|legend=0| 9, 19e }}


Line 522: Line 487:
* WE: ~2 = 1205.7833{{c}}, ~14/13 = 127.6507{{c}}
* WE: ~2 = 1205.7833{{c}}, ~14/13 = 127.6507{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.9093{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.9093{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~14/13 = 126.153{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/13 = 127.039{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 19e }}
{{Optimal ET sequence|legend=0| 9, 19e }}


Line 540: Line 502:
* WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{c}}
* WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.3642{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.3642{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~15/14 = 123.735{{c}}
* POTE: ~2 = 1200.000{{c}}, ~15/14 = 124.539{{c}}
-->
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddee }}
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddee }}


Line 558: Line 517:
* WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{c}}
* WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.3733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.3733{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~15/14 = 123.644{{c}}
* POTE: ~2 = 1200.000{{c}}, ~14/13 = 124.545{{c}}
-->
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddeef }}
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddeef }}


Line 567: Line 523:


=== 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:  
* WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{c}}
* WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2654{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2654{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~11/8 = 537.627{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 537.186{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 20, 29, 38d, 67cdde, 105cdddee }}
{{Optimal ET sequence|legend=0| 9, 20, 29, 38d, 67cdde, 105cdddee }}


Line 591: Line 546:
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:  
* WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{c}}
* WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.3053{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.3053{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~11/8 = 537.802{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 537.208{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}
{{Optimal ET sequence|legend=0| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}


Line 609: Line 561:
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:  
* WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{c}}
* WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2633{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2633{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~11/8 = 537.492{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 537.230{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefg }}
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefg }}


Line 627: Line 576:
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:  
* WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{c}}
* WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2534{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2534{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~11/8 = 537.553{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/8 = 537.214{{c}}
-->
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefgh }}
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefgh }}


Line 654: Line 600:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 81.0408{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 81.0408{{c}}
: error map: {{val| 0.000 +11.800 +18.890 -11.948 }}
: error map: {{val| 0.000 +11.800 +18.890 -11.948 }}
<!--
 
* [[CTE]]: ~2 = 1200.000{{c}}, ~16/15 = 81.345{{c}}
: [[error map]]: {{val| 0.000 +9.975 +20.411 -12.861 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~16/15 = 80.954{{c}}
: error map: {{val| 0.000 +12.322 +18.456 -11.688 }}
-->
{{Optimal ET sequence|legend=1| 14, 15 }}
{{Optimal ET sequence|legend=1| 14, 15 }}


Line 674: Line 615:
* WE: ~2 = 1196.6821{{c}}, ~16/15 = 80.5936{{c}}
* WE: ~2 = 1196.6821{{c}}, ~16/15 = 80.5936{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 80.8326{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 80.8326{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~16/15 = 80.908{{c}}
* POTE: ~2 = 1200.000{{c}}, ~16/15 = 80.817{{c}}
-->
{{Optimal ET sequence|legend=0| 14e, 15 }}
{{Optimal ET sequence|legend=0| 14e, 15 }}


Line 692: Line 630:
* WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{c}}
* WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 81.0685{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 81.0685{{c}}
<!--
 
* CTE: ~2 = 1200.000{{c}}, ~16/15 = 81.320{{c}}
* POTE: ~2 = 1200.000{{c}}, ~16/15 = 81.024{{c}}
-->
{{Optimal ET sequence|legend=0| 14e, 15 }}
{{Optimal ET sequence|legend=0| 14e, 15 }}


Line 701: Line 636:


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Semaphoresmic clan| ]] <!-- main article -->
[[Category:Semaphoresmic clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Semaphoresmic_clan"