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Semaphoresmic clan: Difference between revisions

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The '''semaphoresmic clan''' (or '''semaphore family''') [[tempering out|tempers out]] the slendro diesis, or semaphoresma, [[49/48]], a triprime comma with factors of 2, 3 and 7.  
{{Technical data page}}
The '''semaphoresmic clan''' (or '''semaphore family''') of [[regular temperament|temperaments]] [[tempering out|tempers out]] the large septimal diesis, or semaphoresma, [[49/48]], a triprime comma with factors of 2, 3 and 7.
 
This article focuses on rank-2 temperaments. See [[Semaphoresmic family]] for the rank-3 temperament resulting from tempering out 49/48 alone in the full 7-limit.  


== Semaphore ==
== Semaphore ==
{{Main| Semaphore and godzilla }}
{{Main| Semaphore and godzilla }}
Semaphore tempers out 49/48, and splits a [[3/1|perfect twelfth]] into two halfs of [[7/4]][[~]][[12/7]], and a [[4/3|perfect fourth]] into two halfs of [[7/6]]~[[8/7]], hence the name ''semaphore'', which sounds like ''semifourth''; its [[ploidacot]] is alpha-dicot. [[19edo]] and [[24edo]] are among the possible edo tunings.


[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7
Line 10: Line 15:
{{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 2 0 3 | 0 -2 0 -1 }}
: mapping generators: ~2, ~7/4
 
: [[gencom]]: [2 7/6; 49/48]


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~7/4 = 952.2948
* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}
* [[POTE]]: ~2 = 1\1, ~7/4 = 949.615
: [[error map]]: {{val| +2.832 +1.758 -11.304 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}
: 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 }}
[[Badness]] (Sintel): 0.193


Scales: [[semaphore5]], [[semaphore9]], [[semaphore14]]
Scales: [[semaphore5]], [[semaphore9]], [[semaphore14]]


=== Overview to extensions ===
=== Overview to extensions ===
The second comma of the comma list defines which 7-limit family member we are looking at.  
The second comma of the comma list defines which 7-limit family member we are looking at:
* Beep adds [[21/20]], for a tuning flat of 9edo;
* Superpelog adds [[135/128]], for a tuning between 9edo and 14c-edo;
* Godzilla adds [[81/80]], for a tuning between 14c-edo and 24edo;
* Helayo adds [[3645/3584]], for a tuning between 14edo and 24c-edo;
* Immunity adds [[2240/2187]], for a tuning sharp of 29edo;
* Baba adds [[16/15]], for a niche exotemperament well tuned around 11b-edo.  


Godzilla adds [[81/80]]. Immunity adds [[2240/2187]]. Helayo adds [[3645/3584]]. Superpelog adds [[135/128]]. Beep adds [[21/20]]. Baba adds [[16/15]]. 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  
* ''[[Beep]]'' (+21/20) → [[Bug family #Beep|Bug family]]
* ''[[Beep]]'' (+21/20) → [[Bug family #Beep|Bug family]]
* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]
* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]
* ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]]
* ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|Very low accuracy temperaments]]
* [[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 39: 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]]
* [[Blacksmith]] (+28/27) → [[Limmic temperaments #Blacksmith|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]]
* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]
* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]
Line 51: Line 66:
{{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 60: Line 76:


: mapping generators: ~2, ~7/4
: mapping generators: ~2, ~7/4
{{Multival|legend=1| 2 8 1 8 -4 -20 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~7/4 = 948.7959
* [[WE]]: ~2 = 1203.8275{{c}}, ~7/4 = 950.3867{{c}}
* [[POTE]]: ~2 = 1\1, ~7/4 = 947.365
: [[error map]]: {{val| +3.827 -1.182 +1.470 -10.784 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.8216{{c}}
: error map: {{val| 0.000 -6.312 -3.741 -21.004 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 73: Line 89:
{{Optimal ET sequence|legend=1| 5, 14c, 19 }}
{{Optimal ET sequence|legend=1| 5, 14c, 19 }}


[[Badness]]: 0.026747
[[Badness]] (Sintel): 0.677
 
==== 2.3.5.7.13 subgroup ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 81/80, 91/90


=== 11-limit ===
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 82: Line 113:
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 = 1\1, ~7/4 = 947.4563
* WE: ~2 = 1204.4129{{c}}, ~7/4 = 949.4513{{c}}
* POTE: ~2 = 1\1, ~7/4 = 945.973
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4361{{c}}


Tuning ranges:  
Tuning ranges:  
Line 90: Line 121:
* 11-odd-limit diamond tradeoff: ~7/4 = [933.129, 968.826]
* 11-odd-limit diamond tradeoff: ~7/4 = [933.129, 968.826]


{{Optimal ET sequence|legend=1| 14c, 19, 33cd }}
{{Optimal ET sequence|legend=0| 14c, 19, 33cd }}


Badness: 0.028947
Badness (Sintel): 0.957


==== 13-limit ====
==== 13-limit ====
Line 101: Line 132:
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 = 1\1, ~7/4 = 947.8877
* WE: ~2 = 1203.7164{{c}}, ~7/4 = 949.2061{{c}}
* POTE: ~2 = 1\1, ~7/4 = 946.397
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4131{{c}}


Tuning ranges:  
Tuning ranges:  
Line 109: Line 140:
* 13- and 15-odd-limit diamond tradeoff: ~7/4 = [910.890, 968.826]
* 13- and 15-odd-limit diamond tradeoff: ~7/4 = [910.890, 968.826]


{{Optimal ET sequence|legend=1| 14cf, 19, 33cdff }}
{{Optimal ET sequence|legend=0| 14cf, 19, 33cdff }}


Badness: 0.022503
Badness (Sintel): 0.930


=== Semafour ===
=== Semafour ===
Line 121: Line 152:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~7/4 = 948.2089
* WE: ~2 = 1206.9595{{c}}, ~7/4 = 951.4440{{c}}
* POTE: ~2 = 1\1, ~7/4 = 945.958
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4472{{c}}
 
{{Optimal ET sequence|legend=0| 14c, 19e, 33cdee, 52cdeee }}
 
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=1| 14c, 19e, 33cdee, 52cdeee }}
{{Optimal ET sequence|legend=0| 14cf, 19e, 33cdeeff, 52cdeeeff }}


Badness: 0.028510
Badness (Sintel): 0.975


=== Varan ===
=== Varan ===
Line 136: Line 182:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~7/4 = 949.6160
* WE: ~2 = 1202.5842{{c}}, ~7/4 = 950.9647{{c}}
* POTE: ~2 = 1\1, ~7/4 = 948.921
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.1239{{c}}


{{Optimal ET sequence|legend=1| 19e, 24, 43de }}
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}


Badness: 0.039647
Badness (Sintel): 1.31


==== 13-limit ====
==== 13-limit ====
Line 151: Line 197:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~7/4 = 949.5255
* WE: ~2 = 1202.4367{{c}}, ~7/4 = 950.7615{{c}}
* POTE: ~2 = 1\1, ~7/4 = 948.835
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.0338{{c}}


{{Optimal ET sequence|legend=1| 19e, 24, 43de }}
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}


Badness: 0.025676
Badness (Sintel): 1.06


=== Baragon ===
=== Baragon ===
Line 165: Line 211:
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 = 1\1, ~7/4 = 949.0311
* WE: ~2 = 1201.1412{{c}}, ~7/4 = 949.7291{{c}}
* POTE: ~2 = 1\1, ~7/4 = 948.827
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8625{{c}}


{{Optimal ET sequence|legend=1| 5, 19, 24 }}
{{Optimal ET sequence|legend=0| 19, 24 }}


Badness: 0.035673
Badness (Sintel): 1.18


==== 13-limit ====
==== 13-limit ====
Line 180: Line 226:
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 = 1\1, ~7/4 = 949.0670
* WE: ~2 = 1201.1228{{c}}, ~7/4 = 949.6894{{c}}
* POTE: ~2 = 1\1, ~7/4 = 948.802
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8468{{c}}


{{Optimal ET sequence|legend=1| 5, 19, 24 }}
{{Optimal ET sequence|legend=0| 19, 24 }}


Badness: 0.026703
Badness (Sintel): 1.10


== Helayo ==
== Helayo ==
: ''For the 5-limit version of this temperament see [[High badness temperaments #Hogzilla]].''
: ''For the 5-limit version of this temperament see [[Miscellaneous 5-limit temperaments #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.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 196: Line 244:


{{Mapping|legend=1| 1 0 11 2 | 0 2 -11 1 }}
{{Mapping|legend=1| 1 0 11 2 | 0 2 -11 1 }}
{{Multival|legend=1| 2 -6 1 -14 -4 19 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~7/4 = 947.0969
* [[WE]]: ~2 = 1204.0199{{c}}, ~7/4 = 950.7917{{c}}
: [[error map]]: {{val| +4.020 -0.372 -0.804 -9.995 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.5047{{c}}
: error map: {{val| 0.000 -6.946 -8.866 -21.321 }}


{{Optimal ET sequence|legend=1| 5c, 14, 19 }}
{{Optimal ET sequence|legend=1| 5c, 14, 19 }}


[[Badness]]: 0.0791
[[Badness]] (Sintel): 2.00


; Music
; Music
Line 210: Line 259:


== Superpelog ==
== Superpelog ==
Superpelog tempers out 135/128 and finds the prime 5 at a stack of three fourths, as does any temperament in the [[mavila family]]. It may be described as {{nowrap| 9 & 14c }}, with [[23edo]] (23d val) giving a tuning close to the optimum.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 216: Line 267:
{{Mapping|legend=1| 1 0 7 2 | 0 2 -6 1 }}
{{Mapping|legend=1| 1 0 7 2 | 0 2 -6 1 }}


{{Multival|legend=1| 2 -6 1 -14 -4 19 }}
[[Optimal tuning]]s:  
 
* [[WE]]: ~2 = 1208.8222{{c}}, ~7/4 = 946.9590{{c}}
[[Optimal tuning]]s:
: [[error map]]: {{val| +8.822 -8.037 -6.313 -4.223 }}
* [[CTE]]: ~2 = 1\1, ~7/4 = 939.0297
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 939.8419{{c}}
* [[POTE]]: ~2 = 1\1, ~7/4 = 940.048
: 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 }}


[[Badness]]: 0.058216
[[Badness]] (Sintel): 1.47


=== 11-limit ===
=== 11-limit ===
Line 234: Line 285:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~7/4 = 938.4673
* WE: ~2 = 1208.8663{{c}}, ~7/4 = 946.9861{{c}}
* POTE: ~2 = 1\1, ~7/4 = 940.041
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 939.7687{{c}}


{{Optimal ET sequence|legend=1| 9, 14c, 23de, 37bcde }}
{{Optimal ET sequence|legend=0| 9, 14c, 23de, 37bcde, 60bbccddeee }}


Badness: 0.028535
Badness (Sintel): 0.943


; Music
; Music
: ''[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae]'' by [[Chris Vaisvil]] ([http://chrisvaisvil.com/?p=2267 blog]) (superpelog[9] in 23edo tuning)
: ''Mindaugas Rex Lithuaniae'' (2012) by [[Chris Vaisvil]] – [https://web.archive.org/web/20201127013438/http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 listen] | [https://www.chrisvaisvil.com/mindaugas-rex-lithuaniae/ blog] – in Superpelog[9], 23edo tuning


== Baba ==
== Baba ==
This low-accuracy extension tempers out 16/15, so the perfect fifth stands in for ~8/5 as in [[father]].
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 252: Line 305:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1\1, ~7/4 = 973.296
* [[WE]]: ~2 = 1184.7407{{c}}, ~7/4 = 960.9196{{c}}
 
: [[error map]]: {{val| -15.259 +19.884 +30.810 -38.425 }}
{{Multival|legend=1| 2 -2 1 -8 -4 8 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.2994{{c}}
: error map: {{val| 0.000 +42.644 +69.088 +3.473 }}


{{Optimal ET sequence|legend=1| 5, 11b, 16bc }}
{{Optimal ET sequence|legend=1| 5, 11b, 16bc }}


[[Badness]]: 0.044321
[[Badness]] (Sintel): 1.12


=== 11-limit ===
=== 11-limit ===
Line 268: Line 322:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1\1, ~7/4 = 978.164
* WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9298{{c}}


{{Optimal ET sequence|legend=1| 5, 11b, 16bc, 27bbcc }}
{{Optimal ET sequence|legend=0| 5, 11b }}


Badness: 0.036538
Badness (Sintel): 1.21


== 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 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
 
{{Multival|legend=1| 4 -3 -14 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~16/15 = 125.396
* [[POTE]]: ~2 = 1\1, ~16/15 = 125.755
 
{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
 
[[Badness]]: 0.086856


=== 7-limit ===
=== 7-limit ===
Line 303: Line 341:


{{Mapping|legend=1| 1 2 2 3 | 0 -4 3 -2 }}
{{Mapping|legend=1| 1 2 2 3 | 0 -4 3 -2 }}
{{Multival|legend=1| 4 -3 2 -14 -8 13 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~15/14 = 124.813
* [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}
* [[POTE]]: ~2 = 1\1, ~15/14 = 125.608
: [[error map]]: {{val| +3.481 +1.118 -1.435 -10.328 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}
: 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 }}


[[Badness]]: 0.026483
[[Badness]] (Sintel): 0.670


==== 2.3.5.7.13 subgroup (negra) ====
==== 2.3.5.7.13 subgroup (negra) ====
Line 319: Line 357:
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:  
* WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}


Optimal tunings:
{{Optimal ET sequence|legend=0| 9, 10, 19, 48df, 67cddf, 86cddff }}
* CTE: ~2 = 1\1, ~14/13 = 124.457
* POTE: ~2 = 1\1, ~14/13 = 125.567


Optimal ET sequence: {{Optimal ET sequence| 9, 10, 19, 48df, 67cddf, 86cddff }}
Badness (Sintel): 0.463


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


Line 337: Line 375:


Mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -5 }}
Mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -5 }}
Wedgie: {{multival| 4 -3 2 5 -14 -8 -6 13 22 7 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~15/14 = 125.780
* WE: ~2 = 1202.1045{{c}}, ~15/14 = 126.6961{{c}}
* POTE: ~2 = 1\1, ~15/14 = 126.474
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.3382{{c}}


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


Badness: 0.026190
Badness (Sintel): 0.866


==== 13-limit ====
==== 13-limit ====
Line 356: Line 392:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/13 = 125.434
* WE: ~2 = 1202.6035{{c}}, ~14/13 = 126.7054{{c}}
* POTE: ~2 = 1\1, ~14/13 = 126.431
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.2534{{c}}


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


Badness: 0.017833
Badness (Sintel): 0.737


=== Negril ===
=== Negril ===
Line 369: Line 405:


Mapping: {{mapping| 1 2 2 3 2 | 0 -4 3 -2 14 }}
Mapping: {{mapping| 1 2 2 3 2 | 0 -4 3 -2 14 }}
Wedgie: {{multival| 4 -3 2 -14 -14 -8 -36 13 -22 -46 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~15/14 = 124.998
* WE: ~2 = 1202.7081{{c}}, ~15/14 = 125.0491{{c}}
* POTE: ~2 = 1\1, ~15/14 = 124.767
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.8066{{c}}


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


Badness: 0.038679
Badness (Sintel): 1.28


==== 13-limit ====
==== 13-limit ====
Line 388: Line 422:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/13 = 124.865
* WE: ~2 = 1202.9319{{c}}, ~14/13 = 125.0204{{c}}
* POTE: ~2 = 1\1, ~14/13 = 124.716
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.7374{{c}}


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


Badness: 0.024383
Badness (Sintel): 1.01


=== Negric ===
=== Negric ===
Line 401: Line 435:


Mapping: {{mapping| 1 2 2 3 3 | 0 -4 3 -2 4 }}
Mapping: {{mapping| 1 2 2 3 3 | 0 -4 3 -2 4 }}
Wedgie: {{multival| 4 -3 2 -4 -14 -8 -20 13 1 -18 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~15/14 = 126.574
* WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{c}}
* POTE: ~2 = 1\1, ~15/14 = 127.039
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.9620{{c}}


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


Badness: 0.030617
Badness (Sintel): 1.01


==== 13-limit ====
==== 13-limit ====
Line 420: Line 452:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~14/13 = 126.153
* WE: ~2 = 1205.7833{{c}}, ~14/13 = 127.6507{{c}}
* POTE: ~2 = 1\1, ~14/13 = 127.039
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.9093{{c}}


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


Badness: 0.020205
Badness (Sintel): 0.835


=== Negroni ===
=== Negroni ===
Line 435: Line 467:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~15/14 = 123.735
* WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{c}}
* POTE: ~2 = 1\1, ~15/14 = 124.539
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.3642{{c}}


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


Badness: 0.035296
Badness (Sintel): 1.17


==== 13-limit ====
==== 13-limit ====
Line 450: Line 482:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~15/14 = 123.644
* WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{c}}
* POTE: ~2 = 1\1, ~14/13 = 124.545
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.3733{{c}}


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


Badness: 0.021559
Badness (Sintel): 0.890


=== 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 = 1\1, ~11/8 = 537.627
* WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{c}}
* POTE: ~2 = 1\1, ~11/8 = 537.186
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2654{{c}}


Optimal ET sequence: {{Optimal ET sequence| 9, 20, 29, 38d, 67cdde, 105cdddee }}
{{Optimal ET sequence|legend=0| 9, 20, 29, 38d, 67cdde, 105cdddee }}


Badness: 0.041886
Badness (Sintel): 1.38


==== 13-limit ====
==== 13-limit ====
Line 479: Line 513:
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 = 1\1, ~11/8 = 537.802
* WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{c}}
* POTE: ~2 = 1\1, ~11/8 = 537.208
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.3053{{c}}


Optimal ET sequence: {{Optimal ET sequence| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}
{{Optimal ET sequence|legend=0| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}


Badness: 0.025192
Badness (Sintel): 1.04


==== 17-limit ====
==== 17-limit ====
Line 494: Line 528:
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 = 1\1, ~11/8 = 537.492
* WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{c}}
* POTE: ~2 = 1\1, ~11/8 = 537.230
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2633{{c}}


Optimal ET sequence: {{Optimal ET sequence| 9, 20g, 29g, 38df, 67cddefg }}
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefg }}


Badness: 0.021778
Badness (Sintel): 1.11


==== 19-limit ====
==== 19-limit ====
Line 509: Line 543:
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 = 1\1, ~11/8 = 537.553
* WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{c}}
* POTE: ~2 = 1\1, ~11/8 = 537.214
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2534{{c}}


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


Badness: 0.016828
Badness (Sintel): 1.02


== Nuke ==
== Nuke ==
Nuke tempers out 3584/3375 and is the {{nowrap| 14 & 15 }} temperament. It splits the hemifourth into three generators of ~16/15. Its ploidacot is omega-hexacot. [[15edo]] is about as accurate as it can be tuned.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 527: Line 563:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2 = 1\1, ~16/15 = 80.9538
* [[WE]]: ~2 = 1197.0059{{c}}, ~16/15 = 80.7519{{c}}
: [[error map]]: {{val| -2.994 +7.546 +11.457 -20.064 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 81.0408{{c}}
: error map: {{val| 0.000 +11.800 +18.890 -11.948 }}


{{Optimal ET sequence|legend=1| 14, 15, 44cd }}
{{Optimal ET sequence|legend=1| 14, 15 }}


[[Badness]]: 0.129339
[[Badness]] (Sintel): 3.27


=== 11-limit ===
=== 11-limit ===
Line 541: Line 580:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1\1, ~16/15 = 80.8171
* WE: ~2 = 1196.6821{{c}}, ~16/15 = 80.5936{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 80.8326{{c}}


{{Optimal ET sequence|legend=1| 14e, 15 }}
{{Optimal ET sequence|legend=0| 14e, 15 }}


Badness: 0.069398
Badness (Sintel): 2.29


=== 13-limit ===
=== 13-limit ===
Line 555: Line 595:


Optimal tunings:  
Optimal tunings:  
* POTE: ~2 = 1\1, ~16/15 = 81.0243
* WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 81.0685{{c}}


{{Optimal ET sequence|legend=1| 14e, 15, 44cdeff }}
{{Optimal ET sequence|legend=0| 14e, 15 }}


Badness: 0.048553
Badness (Sintel): 2.01


[[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"