Semaphoresmic clan: Difference between revisions

(7 intermediate revisions by the same user not shown)

Line 14:

~~: sval mapping generators: ~2, ~7/4~~

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

: mapping generators: ~2, ~7/4

[[Optimal tuning]]s:

Line 26:

Line 24:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}

: 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 }}

Line 49:

Line 42:

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

Line 61:

Line 54:

* [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic 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]]

* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]

Line 73:

Line 66:

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

Line 88:

Line 82:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.8216{{c}}

: 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]]:

* 7- and 9-odd-limit [[diamond monotone]]: ~7/4 = [942.857, 960.000] (11\14 to 4\5)

Line 102:

Line 91:

[[Badness]] (Sintel): 0.677

=== 11-~~limit~~ ===

==== 2.3.5.7.13 subgroup ====

Subgroup: 2.3.5.7.11.13

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}}

Badness (Sintel): 0.591

=== Undecimal godzilla ===

Subgroup: 2.3.5.7.11

Line 112:

Line 116:

* WE: ~2 = 1204.4129{{c}}, ~7/4 = 949.4513{{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:

* 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)

Line 134:

Line 135:

* WE: ~2 = 1203.7164{{c}}, ~7/4 = 949.2061{{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:

* 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)

Line 156:

Line 154:

* WE: ~2 = 1206.9595{{c}}, ~7/4 = 951.4440{{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}}

~~-->~~

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 ===

Line 174:

Line 184:

* WE: ~2 = 1202.5842{{c}}, ~7/4 = 950.9647{{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}}

~~-->~~

Line 192:

Line 199:

* WE: ~2 = 1202.4367{{c}}, ~7/4 = 950.7615{{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}}

~~-->~~

Line 210:

Line 214:

* WE: ~2 = 1201.1412{{c}}, ~7/4 = 949.7291{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8625{{c}}

~~<!--~~

* CTE: ~2 = 1200.000{{c}}, ~7/4 = 949.031{{c}}

* POTE: ~2 = 1200.000{{c}}, ~7/4 = 948.827{{c}}

~~-->~~

Badness (Sintel): 1.18

Line 228:

Line 229:

* WE: ~2 = 1201.1228{{c}}, ~7/4 = 949.6894{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 948.8468{{c}}

~~<!--~~

* CTE: ~2 = 1200.000{{c}}, ~7/4 = 949.067{{c}}

* POTE: ~2 = 1200.000{{c}}, ~7/4 = 948.802{{c}}

~~-->~~

Badness (Sintel): 1.10

Line 252:

Line 250:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.5047{{c}}

: 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 }}~~

~~-->~~

Line 277:

Line 272:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 939.8419{{c}}

: 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 }}~~

~~-->~~

Line 297:

Line 287:

* WE: ~2 = 1208.8663{{c}}, ~7/4 = 946.9861{{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 }}

Line 322:

Line 309:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.2994{{c}}

: 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 }}~~

~~-->~~

Line 342:

Line 324:

* WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{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}}

~~-->~~

Line 352:

Line 331:

== 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 ===

Line 390:

Line 347:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}

: 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 }}~~

~~-->~~

Line 405:

Line 357:

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}}

~~<!--~~

* 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 }}

Badness (Sintel): 0.463

=== ~~11-limit~~ ===

=== Undecimal negri ===

Subgroup: 2.3.5.7.11

Line 432:

Line 379:

* WE: ~2 = 1202.1045{{c}}, ~15/14 = 126.6961{{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}}

~~-->~~

Line 450:

Line 394:

* WE: ~2 = 1202.6035{{c}}, ~14/13 = 126.7054{{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}}

~~-->~~

Line 468:

Line 409:

* WE: ~2 = 1202.7081{{c}}, ~15/14 = 125.0491{{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}}

~~-->~~

Line 486:

Line 424:

* WE: ~2 = 1202.9319{{c}}, ~14/13 = 125.0204{{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}}

~~-->~~

Line 504:

Line 439:

* WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{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}}

~~-->~~

Line 522:

Line 454:

* WE: ~2 = 1205.7833{{c}}, ~14/13 = 127.6507{{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}}

~~-->~~

Line 540:

Line 469:

* WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{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}}

~~-->~~

Line 558:

Line 484:

* WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{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}}

~~-->~~

Line 567:

Line 490:

=== 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, ~16/11

: mapping generators: ~2, ~11/8

Optimal tunings:

* WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{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 }}

Line 591:

Line 513:

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:

* WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{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 }}

Line 609:

Line 528:

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:

* WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{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}}

~~-->~~

Line 627:

Line 543:

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:

* WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{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}}

~~-->~~

Line 654:

Line 567:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 81.0408{{c}}

: 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 }}~~

~~-->~~

Line 674:

Line 582:

* WE: ~2 = 1196.6821{{c}}, ~16/15 = 80.5936{{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}}

~~-->~~

Line 692:

Line 597:

* WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{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}}

~~-->~~

@@ Line 14: / Line 14: @@
 {{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]]: [2 7/4; 49/48]
+: mapping generators: ~2, ~7/4
 [[Optimal tuning]]s:
@@ Line 26: / Line 24: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}
 : 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 }}
@@ Line 49: / Line 42: @@
 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
@@ Line 61: / Line 54: @@
 * [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic 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]]
 * ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
@@ Line 73: / Line 66: @@
 {{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
@@ Line 88: / Line 82: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.8216{{c}}
 : 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]]:
 * 7- and 9-odd-limit [[diamond monotone]]: ~7/4 = [942.857, 960.000] (11\14 to 4\5)
@@ Line 102: / Line 91: @@
 [[Badness]] (Sintel): 0.677
-=== 11-limit ===
+==== 2.3.5.7.13 subgroup ====
+Subgroup: 2.3.5.7.11.13
+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
@@ Line 112: / Line 116: @@
 * WE: ~2 = 1204.4129{{c}}, ~7/4 = 949.4513{{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:
 * 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)
@@ Line 134: / Line 135: @@
 * WE: ~2 = 1203.7164{{c}}, ~7/4 = 949.2061{{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:
 * 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)
@@ Line 156: / Line 154: @@
 * WE: ~2 = 1206.9595{{c}}, ~7/4 = 951.4440{{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 }}
 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 ===
@@ Line 174: / Line 184: @@
 * WE: ~2 = 1202.5842{{c}}, ~7/4 = 950.9647{{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 }}
@@ Line 192: / Line 199: @@
 * WE: ~2 = 1202.4367{{c}}, ~7/4 = 950.7615{{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 }}
@@ Line 210: / Line 214: @@
 * WE: ~2 = 1201.1412{{c}}, ~7/4 = 949.7291{{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
@@ Line 228: / Line 229: @@
 * WE: ~2 = 1201.1228{{c}}, ~7/4 = 949.6894{{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
@@ Line 252: / Line 250: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 947.5047{{c}}
 : 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 }}
@@ Line 277: / Line 272: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 939.8419{{c}}
 : 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 }}
@@ Line 297: / Line 287: @@
 * WE: ~2 = 1208.8663{{c}}, ~7/4 = 946.9861{{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 }}
@@ Line 322: / Line 309: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 972.2994{{c}}
 : 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 }}
@@ Line 342: / Line 324: @@
 * WE: ~2 = 1187.4876{{c}}, ~7/4 = 967.9643{{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 }}
@@ Line 352: / Line 331: @@
 == 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 ===
@@ Line 390: / Line 347: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}
 : 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 }}
@@ Line 405: / Line 357: @@
 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}}
-<!--
-* 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 }}
 Badness (Sintel): 0.463
-=== 11-limit ===
+=== Undecimal negri ===
 Subgroup: 2.3.5.7.11
@@ Line 432: / Line 379: @@
 * WE: ~2 = 1202.1045{{c}}, ~15/14 = 126.6961{{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 }}
@@ Line 450: / Line 394: @@
 * WE: ~2 = 1202.6035{{c}}, ~14/13 = 126.7054{{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 }}
@@ Line 468: / Line 409: @@
 * WE: ~2 = 1202.7081{{c}}, ~15/14 = 125.0491{{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 }}
@@ Line 486: / Line 424: @@
 * WE: ~2 = 1202.9319{{c}}, ~14/13 = 125.0204{{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 }}
@@ Line 504: / Line 439: @@
 * WE: ~2 = 1205.7810{{c}}, ~15/14 = 127.6513{{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 }}
@@ Line 522: / Line 454: @@
 * WE: ~2 = 1205.7833{{c}}, ~14/13 = 127.6507{{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 }}
@@ Line 540: / Line 469: @@
 * WE: ~2 = 1203.4738{{c}}, ~15/14 = 124.8992{{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 }}
@@ Line 558: / Line 484: @@
 * WE: ~2 = 1203.5354{{c}}, ~14/13 = 124.9118{{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 }}
@@ Line 567: / Line 490: @@
 === 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, ~16/11
+: mapping generators: ~2, ~11/8
 Optimal tunings:
 * WE: ~2 = 1203.6080{{c}}, ~11/8 = 538.8007{{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 }}
@@ Line 591: / Line 513: @@
 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:
 * WE: ~2 = 1203.7672{{c}}, ~11/8 = 538.8948{{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 }}
@@ Line 609: / Line 528: @@
 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:
 * WE: ~2 = 1203.7154{{c}}, ~11/8 = 538.8932{{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 }}
@@ Line 627: / Line 543: @@
 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:
 * WE: ~2 = 1203.5906{{c}}, ~11/8 = 538.8216{{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 }}
@@ Line 654: / Line 567: @@
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 81.0408{{c}}
 : 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 }}
@@ Line 674: / Line 582: @@
 * WE: ~2 = 1196.6821{{c}}, ~16/15 = 80.5936{{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 }}
@@ Line 692: / Line 597: @@
 * WE: ~2 = 1195.6248{{c}}, ~16/15 = 80.7288{{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 }}