@@ Line 1: / Line 1: @@
-The '''slendro 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.
+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 ==
 {{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
@@ Line 10: / Line 15: @@
 {{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:
+* [[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 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 949.615
+{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd, 115ddd }}
-{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd }}
+[[Badness]] (Sintel): 0.193
 Scales: [[semaphore5]], [[semaphore9]], [[semaphore14]]
 === 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]]. 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]], splitting 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. 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, mabila 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
-* ''[[Baba]]'' → [[Father family #Baba|Father family]]
+* ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]]
-* ''[[Beep]]'' → [[Bug family #Beep|Bug family]]
+* ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|Very low accuracy temperaments]]
-* ''[[Immunity]]'' → [[Immunity family #Septimal immunity|Immunity family]]
+* [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]]
-* ''[[Decimal]]'' → [[Dicot family #Decimal|Dicot family]]
+* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]
-* ''[[Triforce]]'' → [[Augmented family #Triforce|Augmented family]]
+* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
-* [[Keemun]] → [[Kleismic family #Keemun|Kleismic family]]
+* ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]]
-* ''[[Nautilus]]'' → [[Porcupine family #Nautilus|Porcupine family]]
+* ''[[Triforce]]'' (+128/125) → [[Augmented family #Triforce|Augmented family]]
-* [[Blacksmith]] → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
+* [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic family]]
-* ''[[Spell]]'' → [[Hemimean clan #Spell|Hemimean clan]]
+* ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]]
+* ''[[Hemidim]]'' (+648/625) → [[Diminished family #Hemidim|Diminished family]]
+* ''[[Rhinoceros]]'' (+4375/4374) → [[Unicorn family #Rhinoceros|Unicorn family]]
+* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
+* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]
+* ''[[Semabila]]'' (+28672/28125) → [[Mabila family #Mabila|Mabila family]]
+* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
-Considered below are godzilla, superpelog, negri, nuke, mabila, and hemiripple.
+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 ==
-<span style="display: block; text-align: right;">[[:de:Semiphor, Semaphor, Godzilla|Deutsch]]</span>
 {{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
 [[Comma list]]: 49/48, 81/80
-{{Mapping|legend=1|| 1 0 -4 2 | 0 2 8 1 }}
+{{Mapping|legend=1| 1 0 -4 2 | 0 2 8 1 }}
 : mapping generators: ~2, ~7/4
-{{Multival|legend=1| 2 8 1 8 -4 -20 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1203.8275{{c}}, ~7/4 = 950.3867{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 252.635
+: [[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]]: ~7/6 = [240.000, 257.143] (1\5 to 3\14)
+* 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]]: ~7/6 = [231.174, 266.871]
+* 7- and 9-odd-limit [[diamond tradeoff]]: ~7/4 = [933.129, 968.826]
-* 7- and 9-odd-limit diamond monotone and tradeoff: ~7/6 = [240.000, 257.143]
 {{Optimal ET sequence|legend=1| 5, 14c, 19 }}
-[[Badness]]: 0.026747
+[[Badness]] (Sintel): 0.677
+==== 2.3.5.7.13 subgroup ====
+Subgroup: 2.3.5.7.13
+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
-=== 11-limit ===
+=== Undecimal godzilla ===
 Subgroup: 2.3.5.7.11
@@ Line 76: / Line 145: @@
 Mapping: {{mapping| 1 0 -4 2 -6 | 0 2 8 1 12 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 254.027
+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: ~7/6 = [252.632, 257.143] (4\19 to 3\14)
+* 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)
-* 11-odd-limit diamond tradeoff: ~7/6 = [231.174, 266.871]
+* 11-odd-limit diamond tradeoff: ~7/4 = [933.129, 968.826]
-* 11-odd-limit diamond monotone and tradeoff: ~7/6 = [252.632, 257.143]
-{{Optimal ET sequence|legend=1| 14c, 19, 33cd, 52cd }}
+{{Optimal ET sequence|legend=0| 14c, 19, 33cd }}
-Badness: 0.028947
+Badness (Sintel): 0.957
 ==== 13-limit ====
@@ Line 94: / Line 164: @@
 Mapping: {{mapping| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 253.603
+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: ~7/6 = 252.632 (4\19)
+* 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)
-* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [231.174, 289.210]
+* 13- and 15-odd-limit diamond tradeoff: ~7/4 = [910.890, 968.826]
-* 13- and 15-odd-limit diamond monotone and tradeoff: ~7/6 = 252.632
-{{Optimal ET sequence|legend=1| 14cf, 19, 33cdff, 52cdff }}
+{{Optimal ET sequence|legend=0| 14cf, 19, 33cdff }}
-Badness: 0.022503
+Badness (Sintel): 0.930
 === Semafour ===
@@ Line 112: / Line 183: @@
 Mapping: {{mapping| 1 0 -4 2 5 | 0 2 8 1 -2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 254.042
+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
-{{Optimal ET sequence|legend=1| 14c, 19e, 33cdee }}
+Mapping: {{mapping| 1 0 -4 2 5 -5 | 0 2 8 1 -2 11 }}
-Badness: 0.028510
+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 ===
@@ Line 125: / Line 213: @@
 Mapping: {{mapping| 1 0 -4 2 -10 | 0 2 8 1 17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.079
+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=1| 19e, 24, 43de }}
+{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
-Badness: 0.039647
+Badness (Sintel): 1.31
 ==== 13-limit ====
@@ Line 138: / Line 228: @@
 Mapping: {{mapping| 1 0 -4 2 -10 -5 | 0 2 8 1 17 11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.165
+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=1| 19e, 24, 43de }}
+{{Optimal ET sequence|legend=0| 19e, 24, 43de }}
-Badness: 0.025676
+Badness (Sintel): 1.06
 === Baragon ===
@@ Line 151: / Line 243: @@
 Mapping: {{mapping| 1 0 -4 2 9 | 0 2 8 1 -7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.173
+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=1| 5, 14ce, 19, 24, 43d }}
+{{Optimal ET sequence|legend=0| 19, 24 }}
-Badness: 0.035673
+Badness (Sintel): 1.18
 ==== 13-limit ====
@@ Line 164: / Line 258: @@
 Mapping: {{mapping| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 251.198
+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
-{{Optimal ET sequence|legend=1| 5, 14cef, 19, 24, 43d }}
+Scales: [[Helayo14]], [[Helayo19]], [[Helayo24]]
-Badness: 0.026703
+; 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
@@ Line 177: / Line 301: @@
 {{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]] ([[POTE]]): ~2 = 1\1, ~8/7 = 259.952
+: [[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]]: 0.058216
+[[Badness]] (Sintel): 1.47
 === 11-limit ===
@@ Line 192: / Line 318: @@
 Mapping: {{mapping| 1 0 7 2 5 | 0 2 -6 1 -2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 259.959
+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=1| 9, 14c, 23de, 37bcde }}
+{{Optimal ET sequence|legend=0| 9, 14c, 23de, 37bcde, 60bbccddeee }}
-Badness: 0.028535
+Badness (Sintel): 0.943
 ; Music
-: ''[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae]'' by [http://chrisvaisvil.com/?p=2267 Chris Vaisvil] (in 5\23 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 ==
+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]]: 16/15, 49/45
+{{Mapping|legend=1| 1 0 4 2 | 0 2 -2 1 }}
+[[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 }}
-== Negri ==
+{{Optimal ET sequence|legend=1| 5, 11b, 16bc }}
-{{Main| Negri }}
-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.
+[[Badness]] (Sintel): 1.12
-[[Subgroup]]: 2.3.5
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-[[Comma list]]: 16875/16384
+Comma list: 16/15, 22/21, 49/45
-{{Mapping|legend=1| 1 2 2 | 0 -4 3 }}
+Mapping: {{mapping| 1 0 4 2 1 | 0 2 -2 1 3 }}
-: mapping generators: ~2, ~16/15
+Optimal tunings:
+* WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9298{{c}}
-{{Multival|legend=1| 4 -3 -14 }}
+{{Optimal ET sequence|legend=0| 5, 11b }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 125.7549
+Badness (Sintel): 1.21
-{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
+== Negri ==
+{{Main| Negri }}
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Negri (5-limit)]].''
-[[Badness]]: 0.086856
+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 ===
@@ Line 229: / Line 376: @@
 {{Mapping|legend=1| 1 2 2 3 | 0 -4 3 -2 }}
-{{Multival|legend=1| 4 -3 2 -14 -8 13 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}
-[[Optimal tuning]] ([[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 }}
-[[Badness]]: 0.026483
+[[Badness]] (Sintel): 0.670
 ==== 2.3.5.7.13 subgroup (negra) ====
@@ Line 242: / Line 391: @@
 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: [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 tuning (POTE): ~2 = 1\1, ~14/13 = 125.567
+{{Optimal ET sequence|legend=0| 9, 10, 19, 48df, 67cddf, 86cddff }}
-{{Optimal ET sequence|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
+Badness (Sintel): 0.463
-=== 11-limit ===
+=== Undecimal negri ===
 Subgroup: 2.3.5.7.11
@@ Line 259: / Line 410: @@
 Mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -5 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 126.474
+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=1| 9, 10, 19 }}
+{{Optimal ET sequence|legend=0| 9, 10, 19 }}
-Badness: 0.026190
+Badness (Sintel): 0.866
 ==== 13-limit ====
@@ Line 272: / Line 425: @@
 Mapping: {{mapping| 1 2 2 3 4 4 | 0 -4 3 -2 -5 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.431
+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=1| 9, 10, 19 }}
+{{Optimal ET sequence|legend=0| 9, 10, 19 }}
-Badness: 0.017833
+Badness (Sintel): 0.737
 === Negril ===
@@ Line 285: / Line 440: @@
 Mapping: {{mapping| 1 2 2 3 2 | 0 -4 3 -2 14 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.767
+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=1| 19, 29, 48d, 77cdd }}
+{{Optimal ET sequence|legend=0| 10e, 19, 29, 48d, 77cdd }}
-Badness: 0.038679
+Badness (Sintel): 1.28
 ==== 13-limit ====
@@ Line 298: / Line 455: @@
 Mapping: {{mapping| 1 2 2 3 2 4 | 0 -4 3 -2 14 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.716
+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=1| 19, 29, 48df, 77cddf }}
+{{Optimal ET sequence|legend=0| 10e, 19, 29, 48df, 77cddf }}
-Badness: 0.024383
+Badness (Sintel): 1.01
 === Negric ===
@@ Line 311: / Line 470: @@
 Mapping: {{mapping| 1 2 2 3 3 | 0 -4 3 -2 4 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 127.039
+Optimal tunings:
+* WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 126.9620{{c}}
-{{Optimal ET sequence|legend=1| 9, 19e }}
+{{Optimal ET sequence|legend=0| 9, 19e }}
-Badness: 0.030617
+Badness (Sintel): 1.01
 ==== 13-limit ====
@@ Line 324: / Line 485: @@
 Mapping: {{mapping| 1 2 2 3 3 4 | 0 -4 3 -2 4 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 127.039
+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=1| 9, 19e }}
+{{Optimal ET sequence|legend=0| 9, 19e }}
-Badness: 0.020205
+Badness (Sintel): 0.835
 === Negroni ===
@@ Line 337: / Line 500: @@
 Mapping: {{mapping| 1 2 2 3 5 | 0 -4 3 -2 -15 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.539
+Optimal tunings:
+* WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 124.3642{{c}}
-{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddee }}
+{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddee }}
-Badness: 0.035296
+Badness (Sintel): 1.17
 ==== 13-limit ====
@@ Line 350: / Line 515: @@
 Mapping: {{mapping| 1 2 2 3 5 4 | 0 -4 3 -2 -15 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.545
+Optimal tunings:
+* WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 124.3733{{c}}
-{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddeef }}
+{{Optimal ET sequence|legend=0| 10, 19e, 29, 77cddeef }}
-Badness: 0.021559
+Badness (Sintel): 0.890
 === 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
 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, ~11/8
-Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.186
+Optimal tunings:
+* WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2654{{c}}
-{{Optimal ET sequence|legend=1| 9, 20, 29, 38d, 67cdde }}
+{{Optimal ET sequence|legend=0| 9, 20, 29, 38d, 67cdde, 105cdddee }}
-Badness: 0.041886
+Badness (Sintel): 1.38
 ==== 13-limit ====
@@ Line 374: / Line 547: @@
 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 tuning (POTE): ~2 = 1\1, ~11/8 = 537.208
+Optimal tunings:
+* WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.3053{{c}}
-{{Optimal ET sequence|legend=1| 9, 20, 29, 38df, 67cddef }}
+{{Optimal ET sequence|legend=0| 9, 20, 29, 38df, 67cddef, 105cdddeefff }}
-Badness: 0.025192
+Badness (Sintel): 1.04
 ==== 17-limit ====
@@ Line 387: / Line 562: @@
 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 tuning (POTE): ~2 = 1\1, ~11/8 = 537.230
+Optimal tunings:
+* WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2633{{c}}
-{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
+{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefg }}
-Badness: 0.021778
+Badness (Sintel): 1.11
 ==== 19-limit ====
@@ Line 400: / Line 577: @@
 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 tuning (POTE): ~2 = 1\1, ~11/8 = 537.214
+Optimal tunings:
+* WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 537.2534{{c}}
-{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
+{{Optimal ET sequence|legend=0| 9, 20g, 29g, 38df, 67cddefgh }}
-Badness: 0.016828
+Badness (Sintel): 1.02
 == 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
@@ Line 415: / Line 596: @@
 {{Mapping|legend=1| 1 2 2 3 | 0 -6 5 -3 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 80.9538
+[[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 }}
-{{Optimal ET sequence|legend=1| 14, 15, 44cd }}
+{{Optimal ET sequence|legend=1| 14, 15 }}
-[[Badness]]: 0.129339
+[[Badness]] (Sintel): 3.27
 === 11-limit ===
@@ Line 428: / Line 613: @@
 Mapping: {{mapping| 1 2 2 3 3 | 0 -6 5 -3 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 80.8171
+Optimal tunings:
+* 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 ===
@@ Line 441: / Line 628: @@
 Mapping: {{mapping| 1 2 2 3 3 4 | 0 -6 5 -3 7 -4 }}
-Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 81.0243
+Optimal tunings:
+* WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{c}}
-{{Optimal ET sequence|legend=1| 14e, 15, 44cdeff }}
+* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 81.0685{{c}}
-Badness: 0.048553
-== Mabila ==
-{{See also| Mabila family }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 49/48, 28672/28125
-[[Mapping]]: {{mapping| 1 6 1 5 | 0 -10 3 -5 }}
-{{Multival|legend=1| 10 -3 5 -28 -20 20 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/56 = 529.667
-{{Optimal ET sequence|legend=1| 9, 25, 34 }}
-[[Badness]]: 0.133638
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 49/48, 56/55, 1350/1331
-Mapping: {{mapping| 1 6 1 5 7 | 0 -10 3 -5 -8 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.729
-{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
-Badness: 0.061501
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 56/55, 91/90, 847/845
-Mapping: {{mapping| 1 6 1 5 7 9 | 0 -10 3 -5 -8 -12 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.763
-{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
-Badness: 0.037270
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 49/48, 56/55, 91/90, 154/153, 375/374
-Mapping: {{mapping| 1 6 1 5 7 9 1 | 0 -10 3 -5 -8 -12 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.695
-{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
-Badness: 0.031888
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187
-Mapping: {{mapping| 1 6 1 5 7 9 1 6 | 0 -10 3 -5 -8 -12 7 -4 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.736
-{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
-Badness: 0.026981
-== Hemiripple ==
-{{See also| Ripple family #Hemiripple }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 49/48, 6561/6250
-{{Mapping|legend=1| 1 2 3 3 | 0 -10 -16 -5 }}
-{{Multival|legend=1| 10 16 5 2 -20 -33 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 50.826
-{{Optimal ET sequence|legend=1| 23d, 24, 47d, 71bdd }}
-[[Badness]]: 0.175113
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 49/48, 121/120, 567/550
-Mapping: {{mapping| 1 2 3 3 4 | 0 -10 -16 -5 -13 }}
-Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.826
-{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
-Badness: 0.066834
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 66/65, 121/120, 351/350
-Mapping: {{mapping| 1 2 3 3 4 4 | 0 -10 -16 -5 -13 -7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.635
-{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
+{{Optimal ET sequence|legend=0| 14e, 15 }}
-Badness: 0.046588
+Badness (Sintel): 2.01
+[[Category:Semaphoresmic clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Slendro clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Semaphoresmic clan: Difference between revisions