Alphatricot family: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 1: / Line 1: @@
-See [[Hemifamity_temperaments#Tricot|Hemifamity temperaments]].
+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: trimot (53&amp;70) and trillium (53&amp;441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads trimot (supported by 53edo and 70edo), and tempering out [[4375/4374|ragisma]] (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1376 edos).
-[[Category:soft_redirect]]
+See [[Hemifamity_temperaments#Tricot|Hemifamity temperaments]] for more infomation.
+== 5-limit Tricot ==
+Comma: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883
+POTE generator: ~59049/40960 = 634.012
+Map: [&lt;1 0 -13|, &lt;0 3 29|]
+Wedgie: &lt;&lt;3 29 39||
+EDOs: {{EDOs| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
+Badness: 0.0461
+== Trimot (53&amp;70) ==
+Commas: 2430/2401, 5120/5103
+POTE generator: ~81/56 = 634.0259
+Map: [&lt;1 0 -13 -3|, &lt;0 3 29 11|]
+Wedgie: &lt;&lt;3 29 11 39 9 -56||
+EDOs: {{EDOs| 17c, 36c, 53, 70, 229dd, 282dd }}
+Badness: 0.1001
+=== 11-limit ===
+Commas: 99/98, 121/120, 5120/5103
+POTE generator: ~63/44 = 634.0273
+Map: [&lt;1 0 -13 -3 -5|, &lt;0 3 29 11 16|]
+EDOs: {{EDOs| 17c, 53, 70, 123de }}
+Badness: 0.0561
+=== 13-limit ===
+Commas: 99/98, 121/120, 169/168, 352/351
+POTE generator: ~13/9 = 634.0115
+Map: [&lt;1 0 -13 -3 -5 0|, &lt;0 3 29 11 16 7|]
+EDOs: {{EDOs| 17c, 53, 70, 123de }}
+Badness: 0.0321
+== Trillium (53&amp;441) ==
+Commas: 4375/4374, 1099511627776/1098337086315
+POTE generator: ~23625/16384 = 634.0118
+Map: [&lt;1 0 -13 53|, &lt;0 3 29 -95|]
+Wedgie: &lt;&lt;3 29 -95 39 -159 -302||
+EDOs: {{EDOs| 53, 441, 494, 935, 1376, 3193, 4569 }}
+Badness: 0.0309
+=== 11-limit 53&amp;388 ===
+Commas: 4375/4374, 5632/5625, 4108797/4096000
+POTE generator: ~1125/704 = 634.0190
+Map: [&lt;1 0 -13 53 -61|, &lt;0 3 29 -95 122|]
+EDOs: {{EDOs| 53, 323, 388 }}
+Badness: 0.1119
+=== 11-limit 53&amp;494 ===
+Commas: 4375/4374, 131072/130977, 759375/758912
+POTE generator: ~3888/2695 = 634.0094
+Map: [&lt;1 0 -13 53 89|, &lt;0 3 29 -95 175|]
+EDOs: {{EDOs| 53, 441, 494, 935, 1429 }}
+Badness: 0.0468
+[[Category:Temperament]]