2058/2057: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = xenisma
+| Color name = 17u1uuz<sup>3</sup>2, sululutrizo 2nd
 | Comma = Yes
 }}
+'''2058/2057''', the '''xenisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.7.11.17 [[subgroup]]) [[comma]] measuring about 0.84 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s exceed [[34/21]].
-'''2058/2057''', the '''xenisma''', is a [[17-limit]] (also 2.3.7.11.17 [[subgroup]]) [[comma]] measuring about 0.84 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s exceed [[34/21]].
 == Commatic relations ==
@@ Line 24: / Line 24: @@
 == Temperaments ==
 Tempering out this comma in the 17-limit results in the rank-6 '''xenismic temperament''', or in the 2.3.7.11.17 subgroup, the rank-4 '''xenic temperament'''. In either case it enables [[xenismic chords]].
+=== Xenic ===
+[[Subgroup]]: 2.3.7.11.17
+[[Comma list]]: 2058/2057
+{{Mapping|legend=2| 1 0 0 0 1 | 0 1 0 0 1 | 0 0 1 0 3 | 0 0 0 1 -2 }}
+: sval mapping generators: ~2, ~3, ~7, ~11
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~3/2 = 701.9397, ~7/4 = 968.6818, ~11/8 = 551.4639
+* [[CWE]]: ~2 = 1\1, ~3/2 = 701.9446, ~7/4 = 968.6908, ~11/8 = 551.4738
+{{Optimal ET sequence|legend=1| 46, 58, 63, 72, 89, 118, 135, 207, 342, 400, 535, 742, 1395, 1930, 2672 }}
+=== Xenismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Comma list]]: 2058/2057
+[[Mapping]]:<br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 3 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || -2 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~3/2 = 701.9397, ~5/4 = 386.3137, ~7/4 = 968.6818, ~11/8 = 551.4639, ~13/8 = 840.5277
+* [[CWE]]: ~2 = 1\1, ~3/2 = 701.9445, ~5/4 = 386.3208, ~7/4 = 968.6908, ~11/8 = 551.4738, ~13/8 = 840.5389
+{{Optimal ET sequence|legend=1| 43, 46, 58, 72, 103, 121, 149, 161, 190g, 224, 270, 311, 354, 400, 460, 581, 742, 814, 935, 1084, 1323, 1395, 2137, 3072e, 3342eg, 4156eg }}*
+<nowiki>*</nowiki> [[optimal patent val]]: [[3756edo|3756]]
 == Etymology ==
@@ Line 31: / Line 76: @@
 [[Category:Xenismic]]
+[[Category:Commas with unknown etymology]]