2058/2057: Difference between revisions
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'''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 | |||
== Commatic relations == | == Commatic relations == | ||
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== Temperaments == | == 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]]. | 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 == | == Etymology == | ||
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[[Category:Xenismic]] | [[Category:Xenismic]] | ||
[[Category:Commas with unknown etymology]] | |||