Septischismic clan: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 38:

* ''[[Garistearn]]'' (+118098/117649) → [[94th-octave temperaments #Garistearn|94th-octave temperaments]]

Considered below are cotoneum, newt, gariwizmic, satin, sextile, ~~and~~ world calendar.

==== Subgroup extensions ====

Line 96:

Comma list: 441/440, 10976/10935, 16384/16335

~~Mapping:~~ {{~~mapping~~| 1 0 80 25 -33 | 0 1 -49 -14 23 }}

Optimal tunings:

Line 115:

Comma list: 364/363, 441/440, 3584/3575, 10976/10935

~~Mapping:~~ {{~~mapping~~| 1 0 80 25 -33 -93 | 0 1 -49 -14 23 61 }}

Optimal tunings:

Line 135:

Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262

~~Mapping:~~ {{~~mapping~~| 1 0 80 25 -33 -93 -137 | 0 1 -49 -14 23 61 89 }}

{{Mapping|legend=0| 1 0 80 25 -33 -93 -137 | 0 1 -49 -14 23 61 89 }}

Optimal tunings:

Line 154:

Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728

~~Mapping:~~ {{~~mapping~~| 1 0 80 25 -33 -93 -137 74 | 0 1 -49 -14 23 61 89 -44 }}

{{Mapping|legend=0| 1 0 80 25 -33 -93 -137 74 | 0 1 -49 -14 23 61 89 -44 }}

Optimal tunings:

Line 199:

Comma list: 2401/2400, 3025/3024, 19712/19683

~~Mapping:~~ {{~~mapping~~| 1 1 19 11 -10 | 0 2 -57 -28 46 }}

Optimal tunings:

Line 214:

Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095

~~Mapping:~~ {{~~mapping~~| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}

Optimal tunings:

Line 229:

Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400

~~Mapping:~~ {{~~mapping~~| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}

{{Mapping|legend=0| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}

Optimal tunings:

Line 266:

Comma list: 9801/9800, 19712/19683, 41503/41472

~~Mapping:~~ {{~~mapping~~| 2 0 -119 50 -66 | 0 1 39 -14 23 }}

Optimal tunings:

Line 283:

Comma list: 1716/1715, 2080/2079, 4096/4095, 19712/19683

~~Mapping:~~ {{~~mapping~~| 2 0 -119 50 -66 93 | 0 1 39 -14 23 -27 }}

Optimal tunings:

Line 300:

Comma list: 1216/1215, 1540/1539, 1716/1715, 1729/1728, 2080/2079

~~Mapping:~~ {{~~mapping~~| 2 0 -119 50 -66 93 -131 | 0 1 39 -14 23 -27 44 }}

{{Mapping|legend=0| 2 0 -119 50 -66 93 -131 | 0 1 39 -14 23 -27 44 }}

Optimal tunings:

Line 339:

Comma list: 4000/3993, 19712/19683, 41503/41472

~~Mapping:~~ {{~~mapping~~| 1 2 12 -3 13 | 0 -3 -70 42 -69 }}

Optimal tunings:

Line 354:

Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689

~~Mapping:~~ {{~~mapping~~| 1 2 12 -3 13 -1 | 0 -3 -70 42 -69 34 }}

Optimal tunings:

Line 369:

Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095

~~Mapping:~~ {{~~mapping~~| 1 2 12 -3 13 -1 11 | 0 -3 -70 42 -69 34 -50 }}

{{Mapping|legend=0| 1 2 12 -3 13 -1 11 | 0 -3 -70 42 -69 34 -50 }}

Optimal tunings:

Line 384:

Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573

~~Mapping:~~ {{~~mapping~~| 1 2 12 -3 13 -1 11 16 | 0 -3 -70 42 -69 34 -50 -85 }}

{{Mapping|legend=0| 1 2 12 -3 13 -1 11 16 | 0 -3 -70 42 -69 34 -50 -85 }}

Optimal tunings:

Line 399:

Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155

~~Mapping:~~ {{~~mapping~~| 1 2 12 -3 13 -1 11 16 16 | 0 -3 -70 42 -69 34 -50 -85 -83 }}

{{Mapping|legend=0| 1 2 12 -3 13 -1 11 16 16 | 0 -3 -70 42 -69 34 -50 -85 -83 }}

Optimal tunings:

Line 436:

Comma list: 5632/5625, 9801/9800, 151263/151250

~~Mapping:~~ {{~~mapping~~| 6 0 71 150 230 | 0 1 -6 -14 -22 }}

Optimal tunings:

Line 451:

Comma list: 1716/1715, 2080/2079, 5632/5625, 10648/10647

~~Mapping:~~ {{~~mapping~~| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }}

Optimal tunings:

Line 466:

Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625

~~Mapping:~~ {{~~mapping~~| 6 0 71 150 230 279 35 | 0 1 -6 -14 -22 -27 -1 }}

{{Mapping|legend=0| 6 0 71 150 230 279 35 | 0 1 -6 -14 -22 -27 -1 }}

Optimal tunings:

Line 477:

== World calendar ==

World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap| 12 & 364 }} temperament. The name derives from a {{w|World Calendar|certain calendar layout}} by the same name ― because a possible scale is 31 30 30 31 30 30 31 30 30 31 30 30 in 364edo, which is the proposed layout for month lengths in the namesake calendar from January to December.

World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap| 12 & 364 }} temperament. The name derives from a {{w|World Calendar|certain calendar layout}} by the same name ― because a possible scale is [31 30 30 31 30 30 31 30 30 31 30 30] in 364edo, which is the proposed layout for month lengths in the namesake calendar from January to December.

[[Subgroup]]: 2.3.5.7

Line 555:

Comma list: 19712/19683, 41503/41472, 703125/702464

~~Mapping:~~ {{~~mapping~~| 1 1 6 11 -10 | 0 7 -44 -98 161 }}

: mapping generators: ~2, ~1323/1250

Line 571:

Comma list: 2080/2079, 4096/4095, 19712/19683, 31250/31213

~~Mapping:~~ {{~~mapping~~| 1 1 6 11 -10 -7 | 0 7 -44 -98 161 128 }}

: mapping generators: ~2, ~1323/1250

Line 587:

Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 31250/31213

~~Mapping:~~ {{~~mapping~~| 1 1 6 11 -10 -7 5 | 0 7 -44 -98 161 128 -9 }}

{{Mapping|legend=0| 1 1 6 11 -10 -7 5 | 0 7 -44 -98 161 128 -9 }}

: mapping generators: ~2, ~1323/1250

Line 627:

Comma list: 19712/19683, 41503/41472, 1953125/1948617

~~Mapping:~~ {{~~mapping~~| 1 -3 -15 67 -102 | 0 9 34 -126 207 }}

Optimal tunings:

Line 642:

Comma list: 2080/2079, 4096/4095, 19712/19683, 78125/78078

~~Mapping:~~ {{~~mapping~~| 1 -3 -15 67 -102 -34 | 0 9 34 -126 207 74 }}

Optimal tunings:

Line 657:

Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 59375/59319

~~Mapping:~~ {{~~mapping~~| 1 -3 -15 67 -102 -34 -36 | 0 9 34 -126 207 74 79 }}

{{Mapping|legend=0| 1 -3 -15 67 -102 -34 -36 | 0 9 34 -126 207 74 79 }}

Optimal tunings:

@@ Line 38: / Line 38: @@
 * ''[[Garistearn]]'' (+118098/117649) → [[94th-octave temperaments #Garistearn|94th-octave temperaments]]
-Considered below are cotoneum, newt, gariwizmic, satin, sextile, and world calendar.
+Considered below are [[#Cotoneum|cotoneum]], [[#Newt|newt]], [[#Gariwizmic|gariwizmic]], [[#Satin|satin]], [[#Sextile|sextile]], [[#World calendar|world calendar]], [[#Heptacot|heptacot]], and [[#Garitritonic|garitritonic]].
 ==== Subgroup extensions ====
@@ Line 96: / Line 96: @@
 Comma list: 441/440, 10976/10935, 16384/16335
-Mapping: {{mapping| 1 0 80 25 -33 | 0 1 -49 -14 23 }}
+{{Mapping|legend=0| 1 0 80 25 -33 | 0 1 -49 -14 23 }}
 Optimal tunings:
@@ Line 115: / Line 115: @@
 Comma list: 364/363, 441/440, 3584/3575, 10976/10935
-Mapping: {{mapping| 1 0 80 25 -33 -93 | 0 1 -49 -14 23 61 }}
+{{Mapping|legend=0| 1 0 80 25 -33 -93 | 0 1 -49 -14 23 61 }}
 Optimal tunings:
@@ Line 135: / Line 135: @@
 Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262
-Mapping: {{mapping| 1 0 80 25 -33 -93 -137 | 0 1 -49 -14 23 61 89 }}
+{{Mapping|legend=0| 1 0 80 25 -33 -93 -137 | 0 1 -49 -14 23 61 89 }}
 Optimal tunings:
@@ Line 154: / Line 154: @@
 Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728
-Mapping: {{mapping| 1 0 80 25 -33 -93 -137 74 | 0 1 -49 -14 23 61 89 -44 }}
+{{Mapping|legend=0| 1 0 80 25 -33 -93 -137 74 | 0 1 -49 -14 23 61 89 -44 }}
 Optimal tunings:
@@ Line 199: / Line 199: @@
 Comma list: 2401/2400, 3025/3024, 19712/19683
-Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}
+{{Mapping|legend=0| 1 1 19 11 -10 | 0 2 -57 -28 46 }}
 Optimal tunings:
@@ Line 214: / Line 214: @@
 Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095
-Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
+{{Mapping|legend=0| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
 Optimal tunings:
@@ Line 229: / Line 229: @@
 Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400
-Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
+{{Mapping|legend=0| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
 Optimal tunings:
@@ Line 266: / Line 266: @@
 Comma list: 9801/9800, 19712/19683, 41503/41472
-Mapping: {{mapping| 2 0 -119 50 -66 | 0 1 39 -14 23 }}
+{{Mapping|legend=0| 2 0 -119 50 -66 | 0 1 39 -14 23 }}
 Optimal tunings:
@@ Line 283: / Line 283: @@
 Comma list: 1716/1715, 2080/2079, 4096/4095, 19712/19683
-Mapping: {{mapping| 2 0 -119 50 -66 93 | 0 1 39 -14 23 -27 }}
+{{Mapping|legend=0| 2 0 -119 50 -66 93 | 0 1 39 -14 23 -27 }}
 Optimal tunings:
@@ Line 300: / Line 300: @@
 Comma list: 1216/1215, 1540/1539, 1716/1715, 1729/1728, 2080/2079
-Mapping: {{mapping| 2 0 -119 50 -66 93 -131 | 0 1 39 -14 23 -27 44 }}
+{{Mapping|legend=0| 2 0 -119 50 -66 93 -131 | 0 1 39 -14 23 -27 44 }}
 Optimal tunings:
@@ Line 339: / Line 339: @@
 Comma list: 4000/3993, 19712/19683, 41503/41472
-Mapping: {{mapping| 1 2 12 -3 13 | 0 -3 -70 42 -69 }}
+{{Mapping|legend=0| 1 2 12 -3 13 | 0 -3 -70 42 -69 }}
 Optimal tunings:
@@ Line 354: / Line 354: @@
 Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689
-Mapping: {{mapping| 1 2 12 -3 13 -1 | 0 -3 -70 42 -69 34 }}
+{{Mapping|legend=0| 1 2 12 -3 13 -1 | 0 -3 -70 42 -69 34 }}
 Optimal tunings:
@@ Line 369: / Line 369: @@
 Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095
-Mapping: {{mapping| 1 2 12 -3 13 -1 11 | 0 -3 -70 42 -69 34 -50 }}
+{{Mapping|legend=0| 1 2 12 -3 13 -1 11 | 0 -3 -70 42 -69 34 -50 }}
 Optimal tunings:
@@ Line 384: / Line 384: @@
 Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573
-Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 | 0 -3 -70 42 -69 34 -50 -85 }}
+{{Mapping|legend=0| 1 2 12 -3 13 -1 11 16 | 0 -3 -70 42 -69 34 -50 -85 }}
 Optimal tunings:
@@ Line 399: / Line 399: @@
 Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155
-Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 16 | 0 -3 -70 42 -69 34 -50 -85 -83 }}
+{{Mapping|legend=0| 1 2 12 -3 13 -1 11 16 16 | 0 -3 -70 42 -69 34 -50 -85 -83 }}
 Optimal tunings:
@@ Line 436: / Line 436: @@
 Comma list: 5632/5625, 9801/9800, 151263/151250
-Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }}
+{{Mapping|legend=0| 6 0 71 150 230 | 0 1 -6 -14 -22 }}
 Optimal tunings:
@@ Line 451: / Line 451: @@
 Comma list: 1716/1715, 2080/2079, 5632/5625, 10648/10647
-Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }}
+{{Mapping|legend=0| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }}
 Optimal tunings:
@@ Line 466: / Line 466: @@
 Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625
-Mapping: {{mapping| 6 0 71 150 230 279 35 | 0 1 -6 -14 -22 -27 -1 }}
+{{Mapping|legend=0| 6 0 71 150 230 279 35 | 0 1 -6 -14 -22 -27 -1 }}
 Optimal tunings:
@@ Line 477: / Line 477: @@
 == World calendar ==
-World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap| 12 & 364 }} temperament. The name derives from a {{w|World Calendar|certain calendar layout}} by the same name ― because a possible scale is 31 30 30 31 30 30 31 30 30 31 30 30 in 364edo, which is the proposed layout for month lengths in the namesake calendar from January to December.
+World calendar tempers out the [[dimcomp comma]] and the septischisma, and can be described as the {{nowrap| 12 & 364 }} temperament. The name derives from a {{w|World Calendar|certain calendar layout}} by the same name ― because a possible scale is [31 30 30 31 30 30 31 30 30 31 30 30] in 364edo, which is the proposed layout for month lengths in the namesake calendar from January to December.
 [[Subgroup]]: 2.3.5.7
@@ Line 555: / Line 555: @@
 Comma list: 19712/19683, 41503/41472, 703125/702464
-Mapping: {{mapping| 1 1 6 11 -10 | 0 7 -44 -98 161 }}
+{{Mapping|legend=0| 1 1 6 11 -10 | 0 7 -44 -98 161 }}
 : mapping generators: ~2, ~1323/1250
@@ Line 571: / Line 571: @@
 Comma list: 2080/2079, 4096/4095, 19712/19683, 31250/31213
-Mapping: {{mapping| 1 1 6 11 -10 -7 | 0 7 -44 -98 161 128 }}
+{{Mapping|legend=0| 1 1 6 11 -10 -7 | 0 7 -44 -98 161 128 }}
 : mapping generators: ~2, ~1323/1250
@@ Line 587: / Line 587: @@
 Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 31250/31213
-Mapping: {{mapping| 1 1 6 11 -10 -7 5 | 0 7 -44 -98 161 128 -9 }}
+{{Mapping|legend=0| 1 1 6 11 -10 -7 5 | 0 7 -44 -98 161 128 -9 }}
 : mapping generators: ~2, ~1323/1250
@@ Line 627: / Line 627: @@
 Comma list: 19712/19683, 41503/41472, 1953125/1948617
-Mapping: {{mapping| 1 -3 -15 67 -102 | 0 9 34 -126 207 }}
+{{Mapping|legend=0| 1 -3 -15 67 -102 | 0 9 34 -126 207 }}
 Optimal tunings:
@@ Line 642: / Line 642: @@
 Comma list: 2080/2079, 4096/4095, 19712/19683, 78125/78078
-Mapping: {{mapping| 1 -3 -15 67 -102 -34 | 0 9 34 -126 207 74 }}
+{{Mapping|legend=0| 1 -3 -15 67 -102 -34 | 0 9 34 -126 207 74 }}
 Optimal tunings:
@@ Line 657: / Line 657: @@
 Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 59375/59319
-Mapping: {{mapping| 1 -3 -15 67 -102 -34 -36 | 0 9 34 -126 207 74 79 }}
+{{Mapping|legend=0| 1 -3 -15 67 -102 -34 -36 | 0 9 34 -126 207 74 79 }}
 Optimal tunings: