Stearnsmic clan: Difference between revisions

(9 intermediate revisions by 2 users not shown)

Line 9:

[[Comma list]]: 118098/117649

: mapping generators: ~343/243, ~9/7

Line 27:

The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo (94 & 130) adds [[32805/32768]], supers (58 & 94) adds [[5120/5103]], echidna (22 & 58) adds [[1728/1715]], and hedgehog (14c & 22) adds [[50/49]]. Those are the [[strong extension]]s.

Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Septisuperfourth adds [[6144/6125]] ~~and splits~~ the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five.

Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Bisemidim adds [[126/125]]. Septisuperfourth adds [[6144/6125]]. Those split the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three as well as the generator in two. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five.

All of them extend naturally to the 11-limit via tempering out both [[540/539]] and [[4000/3993]], as well as [[9801/9800]], so that ~[[11/10]] and ~[[9/7]] add up to the semi-octave period. For strong extensions, the generator can be taken to be ~11/10, and three ~11/10's then make a ~4/3 as a result of tempering out 4000/3993, making [[10/9]] and [[12/11]] equidistant from 11/10.

Line 35:

* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth|Escapade family]]

* ''[[Decistearn]]'' (+3136/3125) → [[Trisedodge family #Decistearn|Trisedodge family]]

* ''[[Gamelstearn]]'' (+1029/1024) → [[Compton family #Gamelstearn|Compton family]]

* ''[[Garistearn]]'' (+33554432/33480783) → [[94th-octave temperaments #Garistearn|94th-octave temperaments]]

Line 63:

Line 64:

Comma list: 540/539, 4000/3993, 32805/32768

~~Mapping:~~ {{~~mapping~~| 2 1 22 2 25 | 0 3 -24 5 -25 }}

Optimal tunings:

Line 78:

Line 79:

Comma list: 540/539, 729/728, 1575/1573, 4096/4095

~~Mapping:~~ {{~~mapping~~| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}

Optimal tunings:

Line 112:

Line 113:

Comma list: 540/539, 4000/3993, 5120/5103

~~Mapping:~~ {{~~mapping~~| 2 1 -12 2 -9 | 0 3 23 5 22 }}

Optimal tunings:

Line 127:

Line 128:

Comma list: 352/351, 540/539, 729/728, 1575/1573

~~Mapping:~~ {{~~mapping~~| 2 1 -12 2 -9 -2 | 0 3 23 5 22 13 }}

Optimal tunings:

Line 142:

Line 143:

Comma list: 170/169, 289/288, 352/351, 442/441, 561/560

~~Mapping:~~ {{~~mapping~~| 2 1 -12 2 -9 -2 6 | 0 3 23 5 22 13 3 }}

Optimal tunings:

Line 183:

Line 184:

Comma list: 176/175, 540/539, 896/891

~~Mapping:~~ {{~~mapping~~| 2 1 9 2 12 | 0 3 -6 5 -7 }}

Optimal tunings:

Line 203:

Line 204:

Comma list: 176/175, 351/350, 364/363, 540/539

~~Mapping:~~ {{~~mapping~~| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}

Optimal tunings:

Line 218:

Line 219:

Comma list: 136/135, 176/175, 221/220, 256/255, 540/539

~~Mapping:~~ {{~~mapping~~| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}

Optimal tunings:

Line 231:

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Hedgehog is a relatively low-accuracy temperament which tempers out 50/49 ([[jubilisma]], 245/243 ([[sensamagic comma]]), 250/243 ([[porcupine comma]]), and 2430/2401 ([[nuwell comma]]). It is also a strong extension of [[BPS]].

Hedgehog is a relatively low-accuracy temperament which tempers out 50/49 ([[jubilisma]]), 245/243 ([[sensamagic comma]]), 250/243 ([[porcupine comma]]), and 2430/2401 ([[nuwell comma]]). It is also a strong extension of [[BPS]].

22edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] edo tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note [[mos]] gives scope for harmony while stopping well short of 22. A related temperament is [[#Echidna|echidna]], which offers much more accuracy. They merge on 22edo.

Line 258:

Line 259:

Comma list: 50/49, 55/54, 99/98

~~Mapping:~~ {{~~mapping~~| 2 1 1 2 4 | 0 3 5 5 4 }}

Optimal tunings:

Line 273:

Line 274:

Comma list: 50/49, 55/54, 65/63, 99/98

~~Mapping:~~ {{~~mapping~~| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}

Optimal tunings:

Line 288:

Line 289:

Comma list: 40/39, 50/49, 55/54, 66/65

~~Mapping:~~ {{~~mapping~~| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}

Optimal tunings:

Line 303:

Line 304:

Comma list: 50/49, 245/243, 385/384

~~Mapping:~~ {{~~mapping~~| 2 1 1 2 12 | 0 3 5 5 -7 }}

Optimal tunings:

Line 344:

Line 345:

Comma list: 225/224, 385/384, 4000/3993

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 8 | 0 6 -1 10 -3 }}

Optimal tunings:

Line 359:

Line 360:

Comma list: 225/224, 351/350, 364/363, 385/384

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}

Optimal tunings:

Line 374:

Line 375:

Comma list: 221/220, 273/272, 289/288, 351/350, 375/374

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}

Optimal tunings:

Line 389:

Line 390:

Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}

Optimal tunings:

Line 404:

Line 405:

Comma list: 225/224, 325/324, 385/384, 1573/1568

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}

Optimal tunings:

Line 419:

Line 420:

Comma list: 225/224, 289/288, 325/324, 375/374, 385/384

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}

Optimal tunings:

Line 434:

Line 435:

Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}

Optimal tunings:

Line 449:

Line 450:

Comma list: 99/98, 176/175, 1331/1296

~~Mapping:~~ {{~~mapping~~| 2 1 5 2 4 | 0 6 -1 10 8 }}

Optimal tunings:

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Line 459:

Badness (Sintel): 1.91

== Bisemidim ==

Bisemidim tempers out [[126/125]] and may be described as the {{nowrap| 50 & 58 }} temperament. It splits the ~9/7 generator into three ~[[49/45]]'s, so the [[ploidacot]] for the temperament is diploid alpha-enneacot. [[108edo]] and [[166edo]] in the 166cef val may be recommended as tunings.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 126/125, 118098/117649

: mapping generators: ~343/243, ~49/45

[[Optimal tuning]]s:

* [[WE]]: ~343/243 = 599.8915{{c}}, ~49/45 = 144.5293{{c}}

: [[error map]]: {{val| -0.217 -1.299 +3.292 -1.103 }}

* [[CWE]]: ~343/243 = 600.0000{{c}}, ~49/45 = 144.5351{{c}}

: error map: {{val| 0.000 -1.139 +3.572 -0.799 }}

[[Badness]] (Sintel): 2.47

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 126/125, 540/539, 1344/1331

Optimal tunings:

* WE: ~99/70 = 599.6360{{c}}, ~12/11 = 144.5388{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~12/11 = 144.5623{{c}}

Badness (Sintel): 1.36

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 144/143, 196/195, 364/363

Optimal tunings:

* WE: ~55/39 = 599.5217{{c}}, ~12/11 = 144.5375{{c}}

* CWE: ~55/39 = 600.0000{{c}}, ~12/11 = 144.5698{{c}}

Badness (Sintel): 0.987

== Stearnscape ==

Line 484:

Line 535:

Comma list: 540/539, 4000/3993, 137781/137500

~~Mapping:~~ {{~~mapping~~| 6 3 2 6 11 | 0 6 11 10 9 }}

Optimal tunings:

Line 499:

Line 550:

Comma list: 540/539, 729/728, 1575/1573, 34398/34375

~~Mapping:~~ {{~~mapping~~| 6 3 2 6 11 -6 | 0 6 11 10 9 26 }}

Optimal tunings:

Line 514:

Line 565:

Comma list: 540/539, 729/728, 936/935, 1156/1155, 1575/1573

~~Mapping:~~ {{~~mapping~~| 6 3 2 6 11 -6 5 | 0 6 11 10 9 26 18 }}

Optimal tunings:

Line 525:

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== Octoid ==

: {{Main| Octoid }}

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Octoid]].''

Line 560:

Line 611:

Comma list: 540/539, 1375/1372, 4000/3993

~~Mapping:~~ {{~~mapping~~| 8 1 3 3 16 | 0 3 4 5 3 }}

Optimal tunings:

Line 579:

Line 630:

Comma list: 540/539, 625/624, 729/728, 1375/1372

~~Mapping:~~ {{~~mapping~~| 8 1 3 3 16 -21 | 0 3 4 5 3 13 }}

Optimal tunings:

Line 594:

Line 645:

Comma list: 375/374, 540/539, 625/624, 715/714, 729/728

~~Mapping:~~ {{~~mapping~~| 8 1 3 3 16 -21 -14 | 0 3 4 5 3 13 12 }}

Optimal tunings:

Line 609:

Line 660:

Comma list: 324/323, 375/374, 400/399, 495/494, 540/539, 715/714

~~Mapping:~~ {{~~mapping~~| 8 1 3 3 16 -21 -14 34 | 0 3 4 5 3 13 12 0 }}

Optimal tunings:

Line 626:

Line 677:

Comma list: 169/168, 325/324, 364/363, 540/539

~~Mapping:~~ {{~~mapping~~| 8 1 3 3 16 14 | 0 3 4 5 3 4 }}

Optimal tunings:

Line 641:

Line 692:

Comma list: 169/168, 221/220, 289/288, 325/324, 540/539

~~Mapping:~~ {{~~mapping~~| 8 1 3 3 16 14 21 | 0 3 4 5 3 4 3 }}

Optimal tunings:

Line 656:

Line 707:

Comma list: 169/168, 221/220, 286/285, 289/288, 325/324, 400/399

~~Mapping:~~ {{~~mapping~~| 8 1 3 3 16 14 21 34 | 0 3 4 5 3 4 3 0 }}

Optimal tunings:

Line 675:

Line 726:

Comma list: 540/539, 1375/1372, 4000/3993, 4225/4224

~~Mapping:~~ {{~~mapping~~| 16 2 6 6 32 67 | 0 3 4 5 3 -1 }}

: mapping generators: ~448/429, ~7/5

Line 691:

Line 742:

Comma list: 540/539, 715/714, 936/935, 4000/3993, 4225/4224

~~Mapping:~~ {{~~mapping~~| 16 2 6 6 32 67 81 | 0 3 4 5 3 -1 -2 }}

Optimal tunings:

Line 706:

Line 757:

Comma list: 400/399, 540/539, 715/714, 936/935, 1331/1330, 1445/1444

~~Mapping:~~ {{~~mapping~~| 16 2 6 6 32 67 81 68 | 0 3 4 5 3 -1 -2 0 }}

Optimal tunings:

@@ Line 9: / Line 9: @@
 [[Comma list]]: 118098/117649
-{{Mapping|legend=2| 2 1 2 | 0 3 5 }}
+{{Mapping|legend=3| 2 1 2 | 0 3 5 }}
-{{Mapping|legend=3| 2 1 0 2 | 0 3 0 5 }}
+{{Mapping|legend=5| 2 1 0 2 | 0 3 0 5 }}
 : mapping generators: ~343/243, ~9/7
@@ Line 27: / Line 27: @@
 The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo (94 & 130) adds [[32805/32768]], supers (58 & 94) adds [[5120/5103]], echidna (22 & 58) adds [[1728/1715]], and hedgehog (14c & 22) adds [[50/49]]. Those are the [[strong extension]]s.
-Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Septisuperfourth adds [[6144/6125]] and splits the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five.
+Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Bisemidim adds [[126/125]]. Septisuperfourth adds [[6144/6125]]. Those split the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three as well as the generator in two. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five.
 All of them extend naturally to the 11-limit via tempering out both [[540/539]] and [[4000/3993]], as well as [[9801/9800]], so that ~[[11/10]] and ~[[9/7]] add up to the semi-octave period. For strong extensions, the generator can be taken to be ~11/10, and three ~11/10's then make a ~4/3 as a result of tempering out 4000/3993, making [[10/9]] and [[12/11]] equidistant from 11/10.
@@ Line 35: / Line 35: @@
 * ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth|Escapade family]]
 * ''[[Decistearn]]'' (+3136/3125) → [[Trisedodge family #Decistearn|Trisedodge family]]
+* ''[[Gamelstearn]]'' (+1029/1024) → [[Compton family #Gamelstearn|Compton family]]
 * ''[[Garistearn]]'' (+33554432/33480783) → [[94th-octave temperaments #Garistearn|94th-octave temperaments]]
@@ Line 63: / Line 64: @@
 Comma list: 540/539, 4000/3993, 32805/32768
-Mapping: {{mapping| 2 1 22 2 25 | 0 3 -24 5 -25 }}
+{{Mapping|legend=0| 2 1 22 2 25 | 0 3 -24 5 -25 }}
 Optimal tunings:
@@ Line 78: / Line 79: @@
 Comma list: 540/539, 729/728, 1575/1573, 4096/4095
-Mapping: {{mapping| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}
+{{Mapping|legend=0| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}
 Optimal tunings:
@@ Line 112: / Line 113: @@
 Comma list: 540/539, 4000/3993, 5120/5103
-Mapping: {{mapping| 2 1 -12 2 -9 | 0 3 23 5 22 }}
+{{Mapping|legend=0| 2 1 -12 2 -9 | 0 3 23 5 22 }}
 Optimal tunings:
@@ Line 127: / Line 128: @@
 Comma list: 352/351, 540/539, 729/728, 1575/1573
-Mapping: {{mapping| 2 1 -12 2 -9 -2 | 0 3 23 5 22 13 }}
+{{Mapping|legend=0| 2 1 -12 2 -9 -2 | 0 3 23 5 22 13 }}
 Optimal tunings:
@@ Line 142: / Line 143: @@
 Comma list: 170/169, 289/288, 352/351, 442/441, 561/560
-Mapping: {{mapping| 2 1 -12 2 -9 -2 6 | 0 3 23 5 22 13 3 }}
+{{Mapping|legend=0| 2 1 -12 2 -9 -2 6 | 0 3 23 5 22 13 3 }}
 Optimal tunings:
@@ Line 183: / Line 184: @@
 Comma list: 176/175, 540/539, 896/891
-Mapping: {{mapping| 2 1 9 2 12 | 0 3 -6 5 -7 }}
+{{Mapping|legend=0| 2 1 9 2 12 | 0 3 -6 5 -7 }}
 Optimal tunings:
@@ Line 203: / Line 204: @@
 Comma list: 176/175, 351/350, 364/363, 540/539
-Mapping: {{mapping| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}
+{{Mapping|legend=0| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}
 Optimal tunings:
@@ Line 218: / Line 219: @@
 Comma list: 136/135, 176/175, 221/220, 256/255, 540/539
-Mapping: {{mapping| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}
+{{Mapping|legend=0| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}
 Optimal tunings:
@@ Line 231: / Line 232: @@
 {{See also| Sensamagic clan }}
-Hedgehog is a relatively low-accuracy temperament which tempers out 50/49 ([[jubilisma]], 245/243 ([[sensamagic comma]]), 250/243 ([[porcupine comma]]), and 2430/2401 ([[nuwell comma]]). It is also a strong extension of [[BPS]].
+Hedgehog is a relatively low-accuracy temperament which tempers out 50/49 ([[jubilisma]]), 245/243 ([[sensamagic comma]]), 250/243 ([[porcupine comma]]), and 2430/2401 ([[nuwell comma]]). It is also a strong extension of [[BPS]].
 edo provides an obvious tuning, which happens to be the only [[patent val|patent-val]] edo tuning, but if you are looking for an alternative you could try the {{val| 146 232 338 411 }} (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note [[mos]] gives scope for harmony while stopping well short of 22. A related temperament is [[#Echidna|echidna]], which offers much more accuracy. They merge on 22edo.
@@ Line 258: / Line 259: @@
 Comma list: 50/49, 55/54, 99/98
-Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }}
+{{Mapping|legend=0| 2 1 1 2 4 | 0 3 5 5 4 }}
 Optimal tunings:
@@ Line 273: / Line 274: @@
 Comma list: 50/49, 55/54, 65/63, 99/98
-Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}
+{{Mapping|legend=0| 2 1 1 2 4 3 | 0 3 5 5 4 6 }}
 Optimal tunings:
@@ Line 288: / Line 289: @@
 Comma list: 40/39, 50/49, 55/54, 66/65
-Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}
+{{Mapping|legend=0| 2 1 1 2 4 6 | 0 3 5 5 4 2 }}
 Optimal tunings:
@@ Line 303: / Line 304: @@
 Comma list: 50/49, 245/243, 385/384
-Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }}
+{{Mapping|legend=0| 2 1 1 2 12 | 0 3 5 5 -7 }}
 Optimal tunings:
@@ Line 344: / Line 345: @@
 Comma list: 225/224, 385/384, 4000/3993
-Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}
+{{Mapping|legend=0| 2 1 5 2 8 | 0 6 -1 10 -3 }}
 Optimal tunings:
@@ Line 359: / Line 360: @@
 Comma list: 225/224, 351/350, 364/363, 385/384
-Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
+{{Mapping|legend=0| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
 Optimal tunings:
@@ Line 374: / Line 375: @@
 Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
-Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}
+{{Mapping|legend=0| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}
 Optimal tunings:
@@ Line 389: / Line 390: @@
 Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
-Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}
+{{Mapping|legend=0| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}
 Optimal tunings:
@@ Line 404: / Line 405: @@
 Comma list: 225/224, 325/324, 385/384, 1573/1568
-Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
+{{Mapping|legend=0| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
 Optimal tunings:
@@ Line 419: / Line 420: @@
 Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
-Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}
+{{Mapping|legend=0| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}
 Optimal tunings:
@@ Line 434: / Line 435: @@
 Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594
-Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}
+{{Mapping|legend=0| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}
 Optimal tunings:
@@ Line 449: / Line 450: @@
 Comma list: 99/98, 176/175, 1331/1296
-Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}
+{{Mapping|legend=0| 2 1 5 2 4 | 0 6 -1 10 8 }}
 Optimal tunings:
@@ Line 458: / Line 459: @@
 Badness (Sintel): 1.91
+== Bisemidim ==
+Bisemidim tempers out [[126/125]] and may be described as the {{nowrap| 50 & 58 }} temperament. It splits the ~9/7 generator into three ~[[49/45]]'s, so the [[ploidacot]] for the temperament is diploid alpha-enneacot. [[108edo]] and [[166edo]] in the 166cef val may be recommended as tunings.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 126/125, 118098/117649
+{{Mapping|legend=1| 2 1 2 2 | 0 9 11 15 }}
+: mapping generators: ~343/243, ~49/45
+[[Optimal tuning]]s:
+* [[WE]]: ~343/243 = 599.8915{{c}}, ~49/45 = 144.5293{{c}}
+: [[error map]]: {{val| -0.217 -1.299 +3.292 -1.103 }}
+* [[CWE]]: ~343/243 = 600.0000{{c}}, ~49/45 = 144.5351{{c}}
+: error map: {{val| 0.000 -1.139 +3.572 -0.799 }}
+{{Optimal ET sequence|legend=1| 50, 58, 108, 166c, 408ccc }}
+[[Badness]] (Sintel): 2.47
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 126/125, 540/539, 1344/1331
+{{Mapping|legend=0| 2 1 2 2 5 | 0 9 11 15 8 }}
+Optimal tunings:
+* WE: ~99/70 = 599.6360{{c}}, ~12/11 = 144.5388{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~12/11 = 144.5623{{c}}
+{{Optimal ET sequence|legend=0| 50, 58, 108, 166ce, 224cee }}
+Badness (Sintel): 1.36
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 126/125, 144/143, 196/195, 364/363
+{{Mapping|legend=0| 2 1 2 2 5 5 | 0 9 11 15 8 10 }}
+Optimal tunings:
+* WE: ~55/39 = 599.5217{{c}}, ~12/11 = 144.5375{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~12/11 = 144.5698{{c}}
+{{Optimal ET sequence|legend=0| 50, 58, 166cef, 224ceeff }}
+Badness (Sintel): 0.987
 == Stearnscape ==
@@ Line 484: / Line 535: @@
 Comma list: 540/539, 4000/3993, 137781/137500
-Mapping: {{mapping| 6 3 2 6 11 | 0 6 11 10 9 }}
+{{Mapping|legend=0| 6 3 2 6 11 | 0 6 11 10 9 }}
 Optimal tunings:
@@ Line 499: / Line 550: @@
 Comma list: 540/539, 729/728, 1575/1573, 34398/34375
-Mapping: {{mapping| 6 3 2 6 11 -6 | 0 6 11 10 9 26 }}
+{{Mapping|legend=0| 6 3 2 6 11 -6 | 0 6 11 10 9 26 }}
 Optimal tunings:
@@ Line 514: / Line 565: @@
 Comma list: 540/539, 729/728, 936/935, 1156/1155, 1575/1573
-Mapping: {{mapping| 6 3 2 6 11 -6 5 | 0 6 11 10 9 26 18 }}
+{{Mapping|legend=0| 6 3 2 6 11 -6 5 | 0 6 11 10 9 26 18 }}
 Optimal tunings:
@@ Line 525: / Line 576: @@
 == Octoid ==
-: {{Main| Octoid }}
+{{Main| Octoid }}
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Octoid]].''
@@ Line 560: / Line 611: @@
 Comma list: 540/539, 1375/1372, 4000/3993
-Mapping: {{mapping| 8 1 3 3 16 | 0 3 4 5 3 }}
+{{Mapping|legend=0| 8 1 3 3 16 | 0 3 4 5 3 }}
 Optimal tunings:
@@ Line 579: / Line 630: @@
 Comma list: 540/539, 625/624, 729/728, 1375/1372
-Mapping: {{mapping| 8 1 3 3 16 -21 | 0 3 4 5 3 13 }}
+{{Mapping|legend=0| 8 1 3 3 16 -21 | 0 3 4 5 3 13 }}
 Optimal tunings:
@@ Line 594: / Line 645: @@
 Comma list: 375/374, 540/539, 625/624, 715/714, 729/728
-Mapping: {{mapping| 8 1 3 3 16 -21 -14 | 0 3 4 5 3 13 12 }}
+{{Mapping|legend=0| 8 1 3 3 16 -21 -14 | 0 3 4 5 3 13 12 }}
 Optimal tunings:
@@ Line 609: / Line 660: @@
 Comma list: 324/323, 375/374, 400/399, 495/494, 540/539, 715/714
-Mapping: {{mapping| 8 1 3 3 16 -21 -14 34 | 0 3 4 5 3 13 12 0 }}
+{{Mapping|legend=0| 8 1 3 3 16 -21 -14 34 | 0 3 4 5 3 13 12 0 }}
 Optimal tunings:
@@ Line 626: / Line 677: @@
 Comma list: 169/168, 325/324, 364/363, 540/539
-Mapping: {{mapping| 8 1 3 3 16 14 | 0 3 4 5 3 4 }}
+{{Mapping|legend=0| 8 1 3 3 16 14 | 0 3 4 5 3 4 }}
 Optimal tunings:
@@ Line 641: / Line 692: @@
 Comma list: 169/168, 221/220, 289/288, 325/324, 540/539
-Mapping: {{mapping| 8 1 3 3 16 14 21 | 0 3 4 5 3 4 3 }}
+{{Mapping|legend=0| 8 1 3 3 16 14 21 | 0 3 4 5 3 4 3 }}
 Optimal tunings:
@@ Line 656: / Line 707: @@
 Comma list: 169/168, 221/220, 286/285, 289/288, 325/324, 400/399
-Mapping: {{mapping| 8 1 3 3 16 14 21 34 | 0 3 4 5 3 4 3 0 }}
+{{Mapping|legend=0| 8 1 3 3 16 14 21 34 | 0 3 4 5 3 4 3 0 }}
 Optimal tunings:
@@ Line 675: / Line 726: @@
 Comma list: 540/539, 1375/1372, 4000/3993, 4225/4224
-Mapping: {{mapping| 16 2 6 6 32 67 | 0 3 4 5 3 -1 }}
+{{Mapping|legend=0| 16 2 6 6 32 67 | 0 3 4 5 3 -1 }}
 : mapping generators: ~448/429, ~7/5
@@ Line 691: / Line 742: @@
 Comma list: 540/539, 715/714, 936/935, 4000/3993, 4225/4224
-Mapping: {{mapping| 16 2 6 6 32 67 81 | 0 3 4 5 3 -1 -2 }}
+{{Mapping|legend=0| 16 2 6 6 32 67 81 | 0 3 4 5 3 -1 -2 }}
 Optimal tunings:
@@ Line 706: / Line 757: @@
 Comma list: 400/399, 540/539, 715/714, 936/935, 1331/1330, 1445/1444
-Mapping: {{mapping| 16 2 6 6 32 67 81 68 | 0 3 4 5 3 -1 -2 0 }}
+{{Mapping|legend=0| 16 2 6 6 32 67 81 68 | 0 3 4 5 3 -1 -2 0 }}
 Optimal tunings:

Stearnsmic clan: Difference between revisions

FloraC (talk | contribs)