277edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| -439 277 }} | | {{monzo| -439 277 }} | ||
| {{mapping| 277 439 }} | | {{mapping| 277 439 }} | ||
| 0.0473 | | +0.0473 | ||
| 0.0473 | | 0.0473 | ||
| 1.09 | | 1.09 | ||
| Line 36: | Line 28: | ||
| 32805/32768, {{monzo| -11 -37 30 }} | | 32805/32768, {{monzo| -11 -37 30 }} | ||
| {{mapping| 277 439 643 }} | | {{mapping| 277 439 643 }} | ||
| 0.1398 | | +0.1398 | ||
| 0.1364 | | 0.1364 | ||
| 3.15 | | 3.15 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 55: | Line 41: | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
Revision as of 02:06, 16 November 2024
| ← 276edo | 277edo | 278edo → |
Theory
277edo is a good 5-limit tuning; however, it is inconsistent in the 7-odd-limit. The equal temperament tempers out 32805/32768 (schisma) and [-11 -37 30⟩ in the 5-limit.
The patent val ⟨277 439 643 778] tempers out 4375/4374, 65625/65536, and 829440/823543 in the 7-limit; 540/539, 6250/6237, 15488/15435, and 35937/35840 in the 11-limit; 625/624, 729/728, 1573/1568, 2080/2079, and 2200/2197 in the 13-limit. It supports pontiac.
The 277d val ⟨277 439 643 777] tempers out 1029/1024, 10976/10935, and 48828125/48771072 in the 7-limit; 385/384, 441/440, 19712/19683, and 234375/234256 in the 11-limit; 625/624, 847/845, 1001/1000, and 1575/1573 in the 13-limit. It supports guiron and widefourth.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.15 | -0.75 | +1.57 | -1.14 | -0.09 | -0.98 | +1.40 | -0.12 | +1.47 | -1.35 |
| Relative (%) | +0.0 | -3.5 | -17.4 | +36.3 | -26.3 | -2.2 | -22.7 | +32.4 | -2.7 | +33.9 | -31.2 | |
| Steps (reduced) |
277 (0) |
439 (162) |
643 (89) |
778 (224) |
958 (127) |
1025 (194) |
1132 (24) |
1177 (69) |
1253 (145) |
1346 (238) |
1372 (264) | |
Subsets and supersets
277edo is the 59th prime edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-439 277⟩ | [⟨277 439]] | +0.0473 | 0.0473 | 1.09 |- | 2.3.5 | 32805/32768, [-11 -37 30⟩ | [⟨277 439 643]] | +0.1398 | 0.1364 | 3.15 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 115\277 | 498.19 | 4/3 | Helmholtz Template:Rank-2 end Template:Orf