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This clan tempers out the slendro diesis, [[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.  


Discussed elsewhere are [[Father family #Baba|baba]], [[Dicot family #Decimal|decimal]], [[Bug family #Beep|beep]], [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Godzilla|godzilla]], [[Kleismic family #Keemun|keemun]], [[Augmented family #Triforce|triforce]], [[Pelogic family #Superpelog|superpelog]], [[Marvel temperaments #Negri|negri]], [[Porcupine family #Nautilus|nautilus]], [[Magic family #Spell|spell]] and [[Immunity family #Immunity|immunity]].  
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 }}


Subgroup: 2.3.7
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


[[Comma list]]: 49/48
[[Comma list]]: 49/48


[[Sval]] [[Mapping]]: [{{val| 1 0 2 }}, {{val| 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 }}


Gencom mapping: [{{val| 1 2 0 3 }}, {{val| 0 -2 0 -1 }}]
: mapping generators: ~2, ~7/4


[[Gencom]]: [2 7/6; 49/48]
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}
: [[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 }}


[[POTE generator]]: ~7/6 = 250.385
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd, 115ddd }}


{{Val list|legend=1| 5, 14, 19, 24, 67dd, 91dd }}
[[Badness]] (Sintel): 0.193


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


== Nuke ==
=== Overview to extensions ===
Subgroup: 2.3.5.7
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.
 
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. 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
* ''[[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]]
* ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|Very low accuracy temperaments]]
* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
* ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]]
* ''[[Triforce]]'' (+128/125) → [[Augmented family #Triforce|Augmented family]]
* [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic family]]
* ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]]
* ''[[Hemidim]]'' (+648/625) → [[Diminished family #Hemidim|Diminished family]]
* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]
* ''[[Semabila]]'' (+28672/28125) → [[Mabila family #Mabila|Mabila family]]
 
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 ==
{{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]]. 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
 
[[Comma list]]: 49/48, 81/80
 
{{Mapping|legend=1| 1 0 -4 2 | 0 2 8 1 }}
 
: mapping generators: ~2, ~7/4
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.8275{{c}}, ~7/4 = 950.3867{{c}}
: [[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]]:
* 7- and 9-odd-limit [[diamond monotone]]: ~7/4 = [942.857, 960.000] (11\14 to 4\5)
* 7- and 9-odd-limit [[diamond tradeoff]]: ~7/4 = [933.129, 968.826]
 
{{Optimal ET sequence|legend=1| 5, 14c, 19 }}
 
[[Badness]] (Sintel): 0.677
 
==== 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
 
Comma list: 45/44, 49/48, 81/80
 
Mapping: {{mapping| 1 0 -4 2 -6 | 0 2 8 1 12 }}
 
Optimal tunings:
* WE: ~2 = 1204.4129{{c}}, ~7/4 = 949.4513{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4361{{c}}
 
Tuning ranges:
* 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)
* 11-odd-limit diamond tradeoff: ~7/4 = [933.129, 968.826]
 
{{Optimal ET sequence|legend=0| 14c, 19, 33cd }}
 
Badness (Sintel): 0.957
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 45/44, 49/48, 78/77, 81/80
 
Mapping: {{mapping| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}
 
Optimal tunings:
* WE: ~2 = 1203.7164{{c}}, ~7/4 = 949.2061{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 946.4131{{c}}
 
Tuning ranges:
* 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)
* 13- and 15-odd-limit diamond tradeoff: ~7/4 = [910.890, 968.826]
 
{{Optimal ET sequence|legend=0| 14cf, 19, 33cdff }}
 
Badness (Sintel): 0.930
 
=== Semafour ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 49/48, 55/54
 
Mapping: {{mapping| 1 0 -4 2 5 | 0 2 8 1 -2 }}
 
Optimal tunings:
* WE: ~2 = 1206.9595{{c}}, ~7/4 = 951.4440{{c}}
* 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=0| 14cf, 19e, 33cdeeff, 52cdeeeff }}
 
Badness (Sintel): 0.975
 
=== Varan ===
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 77/75, 81/80
 
Mapping: {{mapping| 1 0 -4 2 -10 | 0 2 8 1 17 }}
 
Optimal tunings:
* WE: ~2 = 1202.5842{{c}}, ~7/4 = 950.9647{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.1239{{c}}
 
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
 
Badness (Sintel): 1.31
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 66/65, 77/75, 81/80
 
Mapping: {{mapping| 1 0 -4 2 -10 -5 | 0 2 8 1 17 11 }}
 
Optimal tunings:
* WE: ~2 = 1202.4367{{c}}, ~7/4 = 950.7615{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 949.0338{{c}}
 
{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
 
Badness (Sintel): 1.06
 
=== Baragon ===
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 56/55, 81/80
 
Mapping: {{mapping| 1 0 -4 2 9 | 0 2 8 1 -7 }}
 
Optimal tunings:
* WE: ~2 = 1201.1412{{c}}, ~7/4 = 949.7291{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8625{{c}}
 
{{Optimal ET sequence|legend=0| 19, 24 }}
 
Badness (Sintel): 1.18
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 56/55, 81/80, 91/90
 
Mapping: {{mapping| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}
 
Optimal tunings:
* WE: ~2 = 1201.1228{{c}}, ~7/4 = 949.6894{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8468{{c}}
 
{{Optimal ET sequence|legend=0| 19, 24 }}
 
Badness (Sintel): 1.10
 
== Helayo ==
: ''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.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 49/48, 3645/3584
 
{{Mapping|legend=1| 1 0 11 2 | 0 2 -11 1 }}
 
[[Optimal tuning]]s:
* [[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 }}
 
[[Badness]] (Sintel): 2.00
 
Scales: [[Helayo14]], [[Helayo19]], [[Helayo24]]
 
; Music
* ''Helayo EP'' (2023) by [[User:Francium|Francium]] – [https://open.spotify.com/album/2ksz9PrjIygDlmH3SWhnyH Spotify] | [https://francium223.bandcamp.com/album/helayo-ep Bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRadymOhRyLSKj3RydMAKzlJ YouTube] – 3-piece extended play
 
== 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
 
[[Comma list]]: 49/48, 135/128
 
{{Mapping|legend=1| 1 0 7 2 | 0 2 -6 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1208.8222{{c}}, ~7/4 = 946.9590{{c}}
: [[error map]]: {{val| +8.822 -8.037 -6.313 -4.223 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 939.8419{{c}}
: error map: {{val| 0.000 -22.271 -25.365 -28.984 }}
 
{{Optimal ET sequence|legend=1| 9, 14c, 23d, 37bcd, 60bbccdd }}
 
[[Badness]] (Sintel): 1.47
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 45/44, 49/48
 
Mapping: {{mapping| 1 0 7 2 5 | 0 2 -6 1 -2 }}
 
Optimal tunings:
* WE: ~2 = 1208.8663{{c}}, ~7/4 = 946.9861{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 939.7687{{c}}
 
{{Optimal ET sequence|legend=0| 9, 14c, 23de, 37bcde, 60bbccddeee }}
 
Badness (Sintel): 0.943
 
; Music
: ''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 ==
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


[[Comma list]]: 49/48, 3584/3375
[[Comma list]]: 16/15, 49/45


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -6 5 -3 }}]
{{Mapping|legend=1| 1 0 4 2 | 0 2 -2 1 }}


[[POTE generator]]: ~16/15 = 80.9538
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1184.7407{{c}}, ~7/4 = 960.9196{{c}}
: [[error map]]: {{val| -15.259 +19.884 +30.810 -38.425 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.2994{{c}}
: error map: {{val| 0.000 +42.644 +69.088 +3.473 }}


{{Val list|legend=1| 14, 15, 44cd }}
{{Optimal ET sequence|legend=1| 5, 11b, 16bc }}


[[Badness]]: 0.129339
[[Badness]] (Sintel): 1.12


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 77/75, 512/495
Comma list: 16/15, 22/21, 49/45
 
Mapping: {{mapping| 1 0 4 2 1 | 0 2 -2 1 3 }}
 
Optimal tunings:
* WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9298{{c}}
 
{{Optimal ET sequence|legend=0| 5, 11b }}
 
Badness (Sintel): 1.21
 
== 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 and/or 105/104 to the comma list; this will be discussed below under the title of negra.
 
=== 7-limit ===
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 49/48, 225/224
 
{{Mapping|legend=1| 1 2 2 3 | 0 -4 3 -2 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}
: [[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 }}
 
[[Badness]] (Sintel): 0.670
 
==== 2.3.5.7.13 subgroup (negra) ====
Subgroup: 2.3.5.7.13
 
Comma list: 49/48, 65/64, 91/90
 
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 }}
 
Optimal tunings:
* WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}
 
{{Optimal ET sequence|legend=0| 9, 10, 19, 48df, 67cddf, 86cddff }}
 
Badness (Sintel): 0.463
 
=== Undecimal negri ===
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 49/48, 56/55
 
Mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -5 }}
 
Optimal tunings:
* WE: ~2 = 1202.1045{{c}}, ~15/14 = 126.6961{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.3382{{c}}
 
{{Optimal ET sequence|legend=0| 9, 10, 19 }}
 
Badness (Sintel): 0.866
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 45/44, 49/48, 56/55, 78/77
 
Mapping: {{mapping| 1 2 2 3 4 4 | 0 -4 3 -2 -5 -3 }}
 
Optimal tunings:
* WE: ~2 = 1202.6035{{c}}, ~14/13 = 126.7054{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.2534{{c}}
 
{{Optimal ET sequence|legend=0| 9, 10, 19 }}
 
Badness (Sintel): 0.737
 
=== Negril ===
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 100/99, 225/224
 
Mapping: {{mapping| 1 2 2 3 2 | 0 -4 3 -2 14 }}
 
Optimal tunings:
* WE: ~2 = 1202.7081{{c}}, ~15/14 = 125.0491{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.8066{{c}}
 
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48d, 77cdd }}
 
Badness (Sintel): 1.28
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 65/64, 91/90, 875/858
 
Mapping: {{mapping| 1 2 2 3 2 4 | 0 -4 3 -2 14 -3 }}
 
Optimal tunings:
* WE: ~2 = 1202.9319{{c}}, ~14/13 = 125.0204{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.7374{{c}}
 
{{Optimal ET sequence|legend=0| 10e, 19, 29, 48df, 77cddf }}
 
Badness (Sintel): 1.01
 
=== Negric ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 49/48, 77/75


Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -6 5 -3 7 }}]
Mapping: {{mapping| 1 2 2 3 3 | 0 -4 3 -2 4 }}


POTE generator: ~16/15 = 80.8171
Optimal tunings:  
* WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.9620{{c}}


Optimal GPV sequence: {{Val list| 14e, 15 }}
{{Optimal ET sequence|legend=0| 9, 19e }}


Badness: 0.069398
Badness (Sintel): 1.01


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 49/48, 66/65, 77/75, 448/429
Comma list: 33/32, 49/48, 65/64, 91/90
 
Mapping: {{mapping| 1 2 2 3 3 4 | 0 -4 3 -2 4 -3 }}
 
Optimal tunings:
* WE: ~2 = 1205.7833{{c}}, ~14/13 = 127.6507{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 126.9093{{c}}
 
{{Optimal ET sequence|legend=0| 9, 19e }}
 
Badness (Sintel): 0.835
 
=== Negroni ===
Subgroup: 2.3.5.7.11


Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -6 5 -3 7 -4 }}]
Comma list: 49/48, 55/54, 225/224


POTE generator: ~16/15 = 81.0243
Mapping: {{mapping| 1 2 2 3 5 | 0 -4 3 -2 -15 }}


Optimal GPV sequence: {{Val list| 14e, 15, 44cdeff }}
Optimal tunings:  
* WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.3642{{c}}


Badness: 0.048553
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddee }}


== Mabila ==
Badness (Sintel): 1.17
{{see also| Mabila family }}


Subgroup: 2.3.5.7
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 49/48, 28672/28125
Comma list: 49/48, 55/54, 65/64, 91/90


[[Mapping]]: [{{val| 1 6 1 5 }}, {{val| 0 -10 3 -5 }}]
Mapping: {{mapping| 1 2 2 3 5 4 | 0 -4 3 -2 -15 -3 }}


{{Multival|legend=1| 10 -3 5 -28 -20 20 }}
Optimal tunings:
* WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.3733{{c}}


[[POTE generator]]: ~75/56 = 529.667
{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddeef }}


{{Val list|legend=1| 9, 25, 34 }}
Badness (Sintel): 0.890


[[Badness]]: 0.133638
=== Wilsec ===
Wilsec splits the fifthward generator of negri in half for 11/8~15/11, tempering out [[121/120]]. Its ploidacot is gamma-octacot.


=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 56/55, 1350/1331
Comma list: 49/48, 121/120, 225/224


Mapping: [{{val| 1 6 1 5 7 }}, {{val| 0 -10 3 -5 -8 }}]
Mapping: {{mapping| 1 -2 5 1 3 | 0 8 -6 4 1 }}


POTE generator: ~15/11 = 529.729
: mapping generators: ~2, ~11/8


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
Optimal tunings:  
* WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2654{{c}}


Badness: 0.061501
{{Optimal ET sequence|legend=0| 9, 20, 29, 38d, 67cdde, 105cdddee }}


=== 13-limit ===
Badness (Sintel): 1.38
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 49/48, 56/55, 91/90, 847/845
Comma list: 49/48, 65/64, 91/90, 121/120


Mapping: [{{val| 1 6 1 5 7 9 }}, {{val| 0 -10 3 -5 -8 -12 }}]
Mapping: {{mapping| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}


POTE generator: ~15/11 = 529.763
Optimal tunings:  
* WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.3053{{c}}


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}


Badness: 0.037270
Badness (Sintel): 1.04


=== 17-limit ===
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 49/48, 56/55, 91/90, 154/153, 375/374
Comma list: 49/48, 65/64, 91/90, 121/120, 154/153


Mapping: [{{val| 1 6 1 5 7 9 1 }}, {{val| 0 -10 3 -5 -8 -12 7 }}]
Mapping: {{mapping| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}


POTE generator: ~15/11 = 529.695
Optimal tunings:  
* WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2633{{c}}


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefg }}


Badness: 0.031888
Badness (Sintel): 1.11


=== 19-limit ===
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187
Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153


Mapping: [{{val| 1 6 1 5 7 9 1 6 }}, {{val| 0 -10 3 -5 -8 -12 7 -4 }}]
Mapping: {{mapping| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}


POTE generator: ~15/11 = 529.736
Optimal tunings:  
* WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2534{{c}}


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefgh }}


Badness: 0.026981
Badness (Sintel): 1.02


== Hemiripple ==
== Nuke ==
{{see also| Ripple family #Hemiripple }}
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


[[Comma list]]: 49/48, 6561/6250
[[Comma list]]: 49/48, 3584/3375


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -10 -16 -5 }}]
{{Mapping|legend=1| 1 2 2 3 | 0 -6 5 -3 }}


{{Multival|legend=1| 10 16 5 2 -20 -33 }}
[[Optimal tuning]]s:
* [[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 }}


[[POTE generator]]: ~36/35 = 50.826
{{Optimal ET sequence|legend=1| 14, 15 }}


{{Val list|legend=1| 23d, 24, 47d, 71bdd }}
[[Badness]] (Sintel): 3.27
 
[[Badness]]: 0.175113


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 49/48, 121/120, 567/550
Comma list: 49/48, 77/75, 512/495


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -10 -16 -5 -13 }}]
Mapping: {{mapping| 1 2 2 3 3 | 0 -6 5 -3 7 }}


POTE generator: ~36/35 = 50.826
Optimal tunings:  
* WE: ~2 = 1196.6821{{c}}, ~16/15 = 80.5936{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 80.8326{{c}}


Optimal GPV sequence: {{Val list| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=0| 14e, 15 }}


Badness: 0.066834
Badness (Sintel): 2.29


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 49/48, 66/65, 121/120, 351/350
Comma list: 49/48, 66/65, 77/75, 448/429


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -10 -16 -5 -13 -7 }}]
Mapping: {{mapping| 1 2 2 3 3 4 | 0 -6 5 -3 7 -4 }}


POTE generator: ~36/35 = 50.635
Optimal tunings:  
* WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 81.0685{{c}}


Optimal GPV sequence: {{Val list| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=0| 14e, 15 }}


Badness: 0.046588
Badness (Sintel): 2.01


[[Category:Regular temperament theory]]
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Slendro]]
[[Category:Semaphoresmic clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Semaphoresmic_clan"