Canou family: Difference between revisions

Line 87:

Badness: 2.197 × 10-3

=== 13-limit ~~===~~

=== Semicanoumint ===

This extension was named ''semicanou'' in the earlier materials. It adds [[352/351]], the minthma, to the comma list. It is a natural extension to the 13-limit.

Subgroup: 2.3.5.7.11.13

~~This adds [[352/351]], the minthma, to the comma list. It is a natural extension to the 13-limit.~~

Comma list: 352/351, 9801/9800, 14641/14580

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Mapping: [{{val| 2 0 0 -2 1 11 }}, {{val| 0 1 2 2 2 -1 }}, {{val| 0 0 4 -3 1 1 }}]

Vals: {{Val list| 80, 94, 118, 174d, 198, 490f }}

Badness: 2.701 × 10-3

=== ~~Gentsemicanou~~ ===

=== Semicanouwolf ===

This extension was named ''gentsemicanou'' in the earlier materials. It adds [[351/350]], the ratwolfsma, as wells as [[364/363]], the gentle comma, to the comma list. Since 351/350 = (81/70)/(15/13), the 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale.

This adds [[351/350]], the ratwolfsma, as wells as [[364/363]], the gentle comma, to the comma list. Since 351/350 = (81/70)/(15/13), the 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale.

Not supported by many patent vals, 80edo easily makes the optimal. Yet 104edo in 104c val and 118edo in 118f val are worth mentioning, and the temperament may be described as 80 & 104c & 118f.

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Mapping: [{{val| 2 0 0 -2 1 0 }}, {{val| 0 1 2 2 2 3 }}, {{val| 0 0 4 -3 1 5 }}]

Vals: {{Val list| 80, 104c, 118f, 198f, 420cff }}

Badness: 3.511 × 10-3

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Badness: 4.523 × 10-3

=== ~~13-limit~~ ===

=== Cantawolf ===

This adds [[351/350]], the ratwolfsma, to the comma list. Since 351/350 = (81/70)/(15/13). The 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale. Again 80edo makes the optimal.

This extension was named ''canta'' in the earlier materials. It adds [[351/350]], the ratwolfsma, to the comma list. Since 351/350 = (81/70)/(15/13). The 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale. Again 80edo makes the optimal.

Subgroup: 2.3.5.7.11

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Mapping: [<1 0 0 -1 6 0|, <0 1 2 2 -2 3|, <0 0 4 -3 -3 5|]

{{Val list~~|legend=1~~| 75ef, 80, 99e, 104c, 179e, 184c, 203ce }}

Vals: {{Val list| 75ef, 80, 99e, 104c, 179e, 184c, 203ce }}

Badness: 3.470 × 10-3

=== ~~Gentcanta~~ ===

=== Cantamint ===

This adds [[352/351]], the minthma, as well as [[364/363]], the gentle comma, to the comma list. It is a natural extension of canta, as 896/891 factors neatly into (352/351)×(364/363). Again 80edo makes the optimal.

This extension was named ''gentcanta'' in the earlier materials. It adds [[352/351]], the minthma, as well as [[364/363]], the gentle comma, to the comma list. It is a natural extension of canta, as 896/891 factors neatly into (352/351)×(364/363). Again 80edo makes the optimal.

Subgroup: 2.3.5.7.11.13

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Mapping: [{{val| 1 0 0 -1 6 11 }}, {{val| 0 1 2 2 -2 -5 }}, {{val| 0 0 4 -3 -3 -3 }}]

Vals: {{Val list| 75e, 80, 99ef, 179ef }}

Badness: 4.781 × 10-3

@@ Line 87: / Line 87: @@
 Badness: 2.197 × 10<sup>-3</sup>
-=== 13-limit ===
+=== Semicanoumint ===
+This extension was named ''semicanou'' in the earlier materials. It adds [[352/351]], the minthma, to the comma list. It is a natural extension to the 13-limit.
 Subgroup: 2.3.5.7.11.13
-This adds [[352/351]], the minthma, to the comma list. It is a natural extension to the 13-limit.
 Comma list: 352/351, 9801/9800, 14641/14580
@@ Line 99: / Line 98: @@
 Mapping: [{{val| 2 0 0 -2 1 11 }}, {{val| 0 1 2 2 2 -1 }}, {{val| 0 0 4 -3 1 1 }}]
-{{Val list|legend=1| 80, 94, 118, 174d, 198, 490f }}
+Vals: {{Val list| 80, 94, 118, 174d, 198, 490f }}
 Badness: 2.701 × 10<sup>-3</sup>
-=== Gentsemicanou ===
+=== Semicanouwolf ===
+This extension was named ''gentsemicanou'' in the earlier materials. It adds [[351/350]], the ratwolfsma, as wells as [[364/363]], the gentle comma, to the comma list. Since 351/350 = (81/70)/(15/13), the 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale.
-This adds [[351/350]], the ratwolfsma, as wells as [[364/363]], the gentle comma, to the comma list. Since 351/350 = (81/70)/(15/13), the 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale.
 Not supported by many patent vals, 80edo easily makes the optimal. Yet 104edo in 104c val and 118edo in 118f val are worth mentioning, and the temperament may be described as 80 & 104c & 118f.
@@ Line 117: / Line 115: @@
 Mapping: [{{val| 2 0 0 -2 1 0 }}, {{val| 0 1 2 2 2 3 }}, {{val| 0 0 4 -3 1 5 }}]
-{{Val list|legend=1| 80, 104c, 118f, 198f, 420cff }}
+Vals: {{Val list| 80, 104c, 118f, 198f, 420cff }}
 Badness: 3.511 × 10<sup>-3</sup>
@@ Line 136: / Line 134: @@
 Badness: 4.523 × 10<sup>-3</sup>
-=== 13-limit ===
+=== Cantawolf ===
-This adds [[351/350]], the ratwolfsma, to the comma list. Since 351/350 = (81/70)/(15/13). The 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale. Again 80edo makes the optimal.
+This extension was named ''canta'' in the earlier materials. It adds [[351/350]], the ratwolfsma, to the comma list. Since 351/350 = (81/70)/(15/13). The 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale. Again 80edo makes the optimal.
 Subgroup: 2.3.5.7.11
@@ Line 147: / Line 145: @@
 Mapping: [<1 0 0 -1 6 0|, <0 1 2 2 -2 3|, <0 0 4 -3 -3 5|]
-{{Val list|legend=1| 75ef, 80, 99e, 104c, 179e, 184c, 203ce }}
+Vals: {{Val list| 75ef, 80, 99e, 104c, 179e, 184c, 203ce }}
 Badness: 3.470 × 10<sup>-3</sup>
-=== Gentcanta ===
+=== Cantamint ===
-This adds [[352/351]], the minthma, as well as [[364/363]], the gentle comma, to the comma list. It is a natural extension of canta, as 896/891 factors neatly into (352/351)×(364/363). Again 80edo makes the optimal.
+This extension was named ''gentcanta'' in the earlier materials. It adds [[352/351]], the minthma, as well as [[364/363]], the gentle comma, to the comma list. It is a natural extension of canta, as 896/891 factors neatly into (352/351)×(364/363). Again 80edo makes the optimal.
 Subgroup: 2.3.5.7.11.13
@@ Line 162: / Line 160: @@
 Mapping: [{{val| 1 0 0 -1 6 11 }}, {{val| 0 1 2 2 -2 -5 }}, {{val| 0 0 4 -3 -3 -3 }}]
-{{Val list|legend=1| 75e, 80, 99ef, 179ef }}
+Vals: {{Val list| 75e, 80, 99ef, 179ef }}
 Badness: 4.781 × 10<sup>-3</sup>