Alphatricot family: Difference between revisions

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The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&70, also ~~known~~ as ''trimot''), trident (53&229) and trillium (53&441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to septimal tricot, [[6144/6125|porwell comma]] (6144/6125) leads to trident, and [[4375/4374|ragisma]] (4375/4374) leads to trillium.

The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&70, also called as "trimot"), trident (53&229) and trillium (53&441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to septimal tricot, [[6144/6125|porwell comma]] (6144/6125) leads to trident, and [[4375/4374|ragisma]] (4375/4374) leads to trillium.

== Tricot ==

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[[Badness]]: 0.046093

== Septimal tricot ~~(aka trimot)~~ ==

== Septimal tricot ==

Subgroup: 2.3.5.7

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POTE generator: ~63/44 = 634.0273

~~Vals~~: {{Val list| 17c, 36ce, 53, 70, 123de }}

Optimal GPV sequence: {{Val list| 17c, 36ce, 53, 70, 123de }}

Badness: 0.056134

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POTE generator: ~13/9 = 634.0115

~~Vals~~: {{Val list| 17c, 36ce, 53, 70, 123de }}

Optimal GPV sequence: {{Val list| 17c, 36ce, 53, 70, 123de }}

Badness: 0.032102

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POTE generator: ~231/160 = 634.0669

~~Vals~~: {{Val list| 53, 176, 229 }}

Optimal GPV sequence: {{Val list| 53, 176, 229 }}

Badness: 0.074272

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POTE generator: ~13/9 = 634.0652

~~Vals~~: {{Val list| 53, 176, 229 }}

Optimal GPV sequence: {{Val list| 53, 176, 229 }}

Badness: 0.046593

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POTE generator: ~3888/2695 = 634.0094

~~Vals~~: {{Val list| 53, 441, 494, 935, 1429 }}

Optimal GPV sequence: {{Val list| 53, 441, 494, 935, 1429 }}

Badness: 0.046758

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POTE generator: ~75/52 = 634.0095

~~Vals~~: {{Val list| 53, 441, 494, 935, 1429 }}

Optimal GPV sequence: {{Val list| 53, 441, 494, 935, 1429 }}

Badness: 0.019393

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POTE generator: ~231/160 = 634.0190

~~Vals~~: {{Val list| 53, 335, 388 }}

Optimal GPV sequence: {{Val list| 53, 335, 388 }}

Badness: 0.111931

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POTE generator: ~75/52 = 634.0181

~~Vals~~: {{Val list| 53, 335, 388 }}

Optimal GPV sequence: {{Val list| 53, 335, 388 }}

Badness: 0.054837

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POTE generator: ~11/10 = 165.9835

~~Vals~~: {{Val list| 159, 282, 441 }}

Optimal GPV sequence: {{Val list| 159, 282, 441 }}

Badness: 0.074002

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POTE generator: ~11/10 = 165.9842

~~Vals~~: {{Val list| 159, 282, 441 }}

Optimal GPV sequence: {{Val list| 159, 282, 441 }}

Badness: 0.035641

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POTE generator: ~11/10 = 165.9805

~~Vals~~: {{Val list| 159, 282, 441 }}

Optimal GPV sequence: {{Val list| 159, 282, 441 }}

Badness: 0.025972

@@ Line 1: / Line 1: @@
-The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&amp;70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&amp;70, also known as ''trimot''), trident (53&amp;229) and trillium (53&amp;441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to septimal tricot, [[6144/6125|porwell comma]] (6144/6125) leads to trident, and [[4375/4374|ragisma]] (4375/4374) leads to trillium.
+The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&amp;70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&amp;70, also called as "trimot"), trident (53&amp;229) and trillium (53&amp;441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to septimal tricot, [[6144/6125|porwell comma]] (6144/6125) leads to trident, and [[4375/4374|ragisma]] (4375/4374) leads to trillium.
 == Tricot ==
@@ Line 18: / Line 18: @@
 [[Badness]]: 0.046093
-== Septimal tricot (aka trimot) ==
+== Septimal tricot ==
-{{see also| Hemifamity temperaments #Tricot (aka trimot) }}
+{{see also| Hemifamity temperaments #Tricot }}
 Subgroup: 2.3.5.7
@@ Line 44: / Line 44: @@
 POTE generator: ~63/44 = 634.0273
-Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
+Optimal GPV sequence: {{Val list| 17c, 36ce, 53, 70, 123de }}
 Badness: 0.056134
@@ Line 57: / Line 57: @@
 POTE generator: ~13/9 = 634.0115
-Vals: {{Val list| 17c, 36ce, 53, 70, 123de }}
+Optimal GPV sequence: {{Val list| 17c, 36ce, 53, 70, 123de }}
 Badness: 0.032102
@@ Line 85: / Line 85: @@
 POTE generator: ~231/160 = 634.0669
-Vals: {{Val list| 53, 176, 229 }}
+Optimal GPV sequence: {{Val list| 53, 176, 229 }}
 Badness: 0.074272
@@ Line 98: / Line 98: @@
 POTE generator: ~13/9 = 634.0652
-Vals: {{Val list| 53, 176, 229 }}
+Optimal GPV sequence: {{Val list| 53, 176, 229 }}
 Badness: 0.046593
@@ Line 126: / Line 126: @@
 POTE generator: ~3888/2695 = 634.0094
-Vals: {{Val list| 53, 441, 494, 935, 1429 }}
+Optimal GPV sequence: {{Val list| 53, 441, 494, 935, 1429 }}
 Badness: 0.046758
@@ Line 139: / Line 139: @@
 POTE generator: ~75/52 = 634.0095
-Vals: {{Val list| 53, 441, 494, 935, 1429 }}
+Optimal GPV sequence: {{Val list| 53, 441, 494, 935, 1429 }}
 Badness: 0.019393
@@ Line 152: / Line 152: @@
 POTE generator: ~231/160 = 634.0190
-Vals: {{Val list| 53, 335, 388 }}
+Optimal GPV sequence: {{Val list| 53, 335, 388 }}
 Badness: 0.111931
@@ Line 165: / Line 165: @@
 POTE generator: ~75/52 = 634.0181
-Vals: {{Val list| 53, 335, 388 }}
+Optimal GPV sequence: {{Val list| 53, 335, 388 }}
 Badness: 0.054837
@@ Line 193: / Line 193: @@
 POTE generator: ~11/10 = 165.9835
-Vals: {{Val list| 159, 282, 441 }}
+Optimal GPV sequence: {{Val list| 159, 282, 441 }}
 Badness: 0.074002
@@ Line 206: / Line 206: @@
 POTE generator: ~11/10 = 165.9842
-Vals: {{Val list| 159, 282, 441 }}
+Optimal GPV sequence: {{Val list| 159, 282, 441 }}
 Badness: 0.035641
@@ Line 219: / Line 219: @@
 POTE generator: ~11/10 = 165.9805
-Vals: {{Val list| 159, 282, 441 }}
+Optimal GPV sequence: {{Val list| 159, 282, 441 }}
 Badness: 0.025972