Hemimage temperaments: Difference between revisions

Line 213:

The ''cotoneum'' temperament (41&217, named after the Latin for "[[Wikipedia:quince|quince]]") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41]], [[176edo|176]], [[217edo|217]], and [[258edo~~|258~~]] ~~EDOs~~, and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.

The ''cotoneum'' temperament (41&217, named after the Latin for "[[Wikipedia:quince|quince]]") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41-]], [[176edo|176-]], [[217edo|217-]], and [[258edo]], and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 10976/10935, 823543/819200

[[Mapping]]: [{{val|1 ~~2 -18 -3~~}}, {{val|0 -1 49 14}}]

[[Mapping]]: [{{val| 1 0 80 25 }}, {{val| 0 1 -49 -14 }}]

Mapping generators: ~2, ~3

[[POTE ~~generator~~]]: ~3/2 = 702.317

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.317

Line 234:

Line 236:

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

Mapping: [{{val|1 2 -~~18 -3 13~~}}, {{val|0 -1 49 14 -23}}]

Mapping: [{{val| 1 0 80 25 -33 }}, {{val| 0 1 -49 -14 23 }}]

POTE ~~generator~~: ~3/2 = 702.303

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.303

Optimal GPV sequence: {{Val list| 41, 135c, 176, 217 }}

Line 247:

Line 249:

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

Mapping: [{{val|1 2 -18 -~~3 13 29~~}}, {{val|0 -1 49 14 -23 -61}}]

Mapping: [{{val| 1 0 80 25 -33 -93 }}, {{val| 0 1 -49 -14 23 61 }}]

POTE ~~generator~~: ~3/2 = 702.306

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.306

Optimal GPV sequence: {{Val list| 41, 176, 217 }}

Line 260:

Line 262:

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

Mapping: [{{val|1 2 -18 -~~3 13 29 41~~}}, {{val|0 -1 49 14 -23 -61 -89}}]

Mapping: [{{val| 1 0 80 25 -33 -93 -137 }}, {{val| 0 1 -49 -14 23 61 89 }}]

POTE ~~generator~~: ~3/2 = 702.307

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.307

Optimal GPV sequence: {{Val list| 41, 176, 217 }}

Line 273:

Line 275:

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

Mapping: [{{val|1 2 -18 -~~3 13 29 41~~ -14}}, {{val|0 -1 49 14 -23 -61 -89 44}}]

Mapping: [{{val| 1 0 80 25 -33 -93 -137 74 }}, {{val| 0 1 -49 -14 23 61 89 -44 }}]

POTE ~~generator~~: ~3/2 = 702.308

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.308

Optimal GPV sequence: {{Val list| 41, 176, 217 }}

@@ Line 213: / Line 213: @@
 {{Main| Cotoneum }}
-The ''cotoneum'' temperament (41&amp;217, named after the Latin for "[[Wikipedia:quince|quince]]") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41]], [[176edo|176]], [[217edo|217]], and [[258edo|258]] EDOs, and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.
+The ''cotoneum'' temperament (41&amp;217, named after the Latin for "[[Wikipedia:quince|quince]]") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41-]], [[176edo|176-]], [[217edo|217-]], and [[258edo]], and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 10976/10935, 823543/819200
-[[Mapping]]: [{{val|1 2 -18 -3}}, {{val|0 -1 49 14}}]
+[[Mapping]]: [{{val| 1 0 80 25 }}, {{val| 0 1 -49 -14 }}]
+Mapping generators: ~2, ~3
 {{Multival|legend=1| 1 -49 -14 -80 -25 105 }}
-[[POTE generator]]: ~3/2 = 702.317
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.317
 {{Val list|legend=1| 41, 135c, 176, 217, 258, 475 }}
@@ Line 234: / Line 236: @@
 Comma list: 441/440, 10976/10935, 16384/16335
-Mapping: [{{val|1 2 -18 -3 13}}, {{val|0 -1 49 14 -23}}]
+Mapping: [{{val| 1 0 80 25 -33 }}, {{val| 0 1 -49 -14 23 }}]
-POTE generator: ~3/2 = 702.303
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.303
 Optimal GPV sequence: {{Val list| 41, 135c, 176, 217 }}
@@ Line 247: / Line 249: @@
 Comma list: 364/363, 441/440, 3584/3575, 10976/10935
-Mapping: [{{val|1 2 -18 -3 13 29}}, {{val|0 -1 49 14 -23 -61}}]
+Mapping: [{{val| 1 0 80 25 -33 -93 }}, {{val| 0 1 -49 -14 23 61 }}]
-POTE generator: ~3/2 = 702.306
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.306
 Optimal GPV sequence: {{Val list| 41, 176, 217 }}
@@ Line 260: / Line 262: @@
 Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262
-Mapping: [{{val|1 2 -18 -3 13 29 41}}, {{val|0 -1 49 14 -23 -61 -89}}]
+Mapping: [{{val| 1 0 80 25 -33 -93 -137 }}, {{val| 0 1 -49 -14 23 61 89 }}]
-POTE generator: ~3/2 = 702.307
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.307
 Optimal GPV sequence: {{Val list| 41, 176, 217 }}
@@ Line 273: / Line 275: @@
 Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728
-Mapping: [{{val|1 2 -18 -3 13 29 41 -14}}, {{val|0 -1 49 14 -23 -61 -89 44}}]
+Mapping: [{{val| 1 0 80 25 -33 -93 -137 74 }}, {{val| 0 1 -49 -14 23 61 89 -44 }}]
-POTE generator: ~3/2 = 702.308
+Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.308
 Optimal GPV sequence: {{Val list| 41, 176, 217 }}