263edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis end}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 417 -263 }} | | {{monzo| 417 -263 }} | ||
| {{val| 263 417 }} | | {{val| 263 417 }} | ||
| | | −0.2229 | ||
| 0.2229 | | 0.2229 | ||
| 4.89 | | 4.89 | ||
| Line 40: | Line 32: | ||
| 393216/390625, {{monzo| 50 -33 1 }} | | 393216/390625, {{monzo| 50 -33 1 }} | ||
| {{val| 263 417 611 }} | | {{val| 263 417 611 }} | ||
| | | −0.3666 | ||
| 0.2728 | | 0.2728 | ||
| 5.98 | | 5.98 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 65: | Line 51: | ||
| 5/4 | | 5/4 | ||
| [[Würschmidt]] | | [[Würschmidt]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
Revision as of 03:12, 16 November 2024
| ← 262edo | 263edo | 264edo → |
Theory
263et tempers out 393216/390625 (würschmidt comma) and [50 -33 1⟩ in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.
Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit.
Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.
Finally, it is accurate for the 17th harmonic, as the denominator of a convergent to log217, after 80 and before 343.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.71 | +1.52 | -1.53 | +0.77 | -0.98 | -0.01 | -0.94 | +1.38 | +1.60 | +0.21 |
| Relative (%) | +0.0 | +15.5 | +33.3 | -33.4 | +16.9 | -21.6 | -0.3 | -20.5 | +30.3 | +35.1 | +4.6 | |
| Steps (reduced) |
263 (0) |
417 (154) |
611 (85) |
738 (212) |
910 (121) |
973 (184) |
1075 (23) |
1117 (65) |
1190 (138) |
1278 (226) |
1303 (251) | |
Subsets and supersets
263edo is the 56th prime edo.
Notable supersets include 789edo, which triples it to achieve extreme accuracy in the 2.5.7 subgroup, and 1578edo, which sextuples it to be extremely strong in the 11-limit add-17 and in higher limits.
Regular temperament properties
Template:Comma basis end |- | 2.3 | [417 -263⟩ | ⟨263 417] | −0.2229 | 0.2229 | 4.89 |- | 2.3.5 | 393216/390625, [50 -33 1⟩ | ⟨263 417 611] | −0.3666 | 0.2728 | 5.98 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 40\263 | 182.51 | 10/9 | Minortone |- | 1 | 85\263 | 387.83 | 5/4 | Würschmidt Template:Rank-2 end Template:Orf