497edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 36: | Line 27: | ||
| 0.1961 | | 0.1961 | ||
| 8.12 | | 8.12 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 53: | Line 37: | ||
| 262144/234375 | | 262144/234375 | ||
| [[Luna]] | | [[Luna]] | ||
{{rank-2 end}} | |||
{{orf}} | {{orf}} | ||
Revision as of 01:37, 16 November 2024
| ← 496edo | 497edo | 498edo → |
Theory
497et only is consistent to the 5-odd-limit. Using the patent val, the equal temperament tempers out 2100875/2097152, 48828125/48771072, 67108864/66976875, and 200120949/200000000 in the 7-limit; 5632/5625, 42875/42768, 43923/43904, 131072/130977, 151263/151250, 160083/160000, and 391314/390625 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.66 | +0.00 | -0.62 | -1.09 | -0.81 | -0.29 | +0.66 | -1.13 | -0.53 | +0.04 | -0.51 |
| Relative (%) | +27.4 | +0.2 | -25.5 | -45.3 | -33.8 | -11.9 | +27.5 | -46.9 | -22.0 | +1.8 | -21.0 | |
| Steps (reduced) |
788 (291) |
1154 (160) |
1395 (401) |
1575 (84) |
1719 (228) |
1839 (348) |
1942 (451) |
2031 (43) |
2111 (123) |
2183 (195) |
2248 (260) | |
Subsets and supersets
497 factors into 7 × 41, with 7edo and 41edo as its subset edos. 1491edo, which triples it, gives a good correction to harmonics 3 and 7.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [788 -497⟩ | [⟨497 788]] | -0.2084 | 0.2084 | 8.63 |- | 2.3.5 | [38 -2 -15⟩, [12 -31 16⟩ | [⟨497 788 1154]] | -0.1396 | 0.1961 | 8.12 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 80\497 | 193.16 | 262144/234375 | Luna Template:Rank-2 end Template:Orf