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 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.

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: 0.074002

=== 13-limit ===

==== 13-limit ====

Subgroup: 2.3.5.7.11.13

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Badness: 0.035641

=== 17-limit ===

==== 17-limit ====

Subgroup: 2.3.5.7.11.13.17

Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619

Mapping: [{{~~val~~| 3 6 19 30 22 36 16 ~~}}, {{val~~| 0 -3 -29 -52 -28 -60 -9 }}]

Mapping: {{mapping| 3 6 19 30 22 36 16 | 0 -3 -29 -52 -28 -60 -9 }}

Optimal tuning (POTE): ~34/27 = 1\3, ~11/10 = 165.9805

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Badness: 0.025972

=== Noletaland ===

Noletaland is described as 282 & 1323, and it combines the smallest consistent edo in the 29-odd-limit with the smallest uniquely consistent. It reaches 4/3 in nine generators ([[noleta]]-…) and tempers out the landscape comma (…-land). Noletaland reaches [[13/11]] in 2 generators, and [[29/19]] in 5. Then there's [[44/25]] in 4, and [[152/115]] in also 4.

Subgroup: 2.3.5.7.11.13.17

Comma list: 2058/2057, 12376/12375, 14875/14872, 43904/43875, 250047/250000

Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}

Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.329

==== 19-limit ====

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 2926/2925, 3136/3135, 5985/5984, 12376/12375, 14875/14872, 256000/255879

Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}

Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.329

==== 23-limit ====

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 2926/2925, 3136/3135, 5985/5984, 10626/10625, 12376/12375, 21736/21735, 256000/255879

Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 | 0 -9 -87 -156 -178 -180 -121 -38 -126 }}

Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.330

==== 29-limit ====

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 2926/2925, 3136/3135, 5104/5103, 5985/5984, 12376/12375, 21736/21735, 10626/10625, 256000/255879

Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 19 | 0 -9 -87 -156 -178 -180 -121 -38 -126 -32 }}

Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.330

{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323, 2082de }}

[[Category:Temperament families]]

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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&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.
+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 195: / Line 195: @@
 Badness: 0.074002
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
@@ Line 208: / Line 208: @@
 Badness: 0.035641
-=== 17-limit ===
+==== 17-limit ====
 Subgroup: 2.3.5.7.11.13.17
 Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619
-Mapping: [{{val| 3 6 19 30 22 36 16 }}, {{val| 0 -3 -29 -52 -28 -60 -9 }}]
+Mapping: {{mapping| 3 6 19 30 22 36 16 | 0 -3 -29 -52 -28 -60 -9 }}
 Optimal tuning (POTE): ~34/27 = 1\3, ~11/10 = 165.9805
@@ Line 220: / Line 220: @@
 Badness: 0.025972
+=== Noletaland ===
+Noletaland is described as 282 & 1323, and it combines the smallest consistent edo in the 29-odd-limit with the smallest uniquely consistent. It reaches 4/3 in nine generators ([[noleta]]-…) and tempers out the landscape comma (…-land). Noletaland reaches [[13/11]] in 2 generators, and [[29/19]] in 5. Then there's [[44/25]] in 4, and [[152/115]] in also 4.
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 2058/2057, 12376/12375, 14875/14872, 43904/43875, 250047/250000
+Mapping: {{mapping| 3 6 19 30 35 36 29 | 0 -9 -87 -156 -178 -180 -121 }}
+Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.329
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 2926/2925, 3136/3135, 5985/5984, 12376/12375, 14875/14872, 256000/255879
+Mapping: {{mapping| 3 6 19 30 35 36 29 18 | 0 -9 -87 -156 -178 -180 -121 -38 }}
+Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.329
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 2926/2925, 3136/3135, 5985/5984, 10626/10625, 12376/12375, 21736/21735, 256000/255879
+Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 | 0 -9 -87 -156 -178 -180 -121 -38 -126 }}
+Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.330
+==== 29-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 2926/2925, 3136/3135, 5104/5103, 5985/5984, 12376/12375, 21736/21735, 10626/10625, 256000/255879
+Mapping: {{mapping| 3 6 19 30 35 36 29 18 31 19 | 0 -9 -87 -156 -178 -180 -121 -38 -126 -32 }}
+Optimal tuning (CTE): ~63/50 = 1\3, ~351/340 = 55.330
+{{Optimal ET sequence|legend=1| 282, 759def, 1041, 1323, 2082de }}
 [[Category:Temperament families]]