209edo
Theory
209edo is only consistent to the 5-odd-limit. The equal temperament tempers out 129140163/128000000 (graviton) and 1220703125/1207959552 (ditonma) in the 5-limit. Using the patent val, it tempers out 225/224, 2125764/2100875, and 2500000/2470629 in the 7-limit; 243/242, 3025/3024, 4000/3993, and 16896/16807 in the 11-limit; 351/350, 625/624, 1573/1568, 1625/1617, and 15379/15360 in the 13-limit, so that it provides the optimal patent val for the 13-limit marvo temperament. It also supports the 13-limit spectacle temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.48 | -1.62 | +1.51 | +2.79 | -0.12 | -2.25 | +2.64 | -1.61 | +1.05 | +0.03 | -2.44 |
| Relative (%) | -25.7 | -28.3 | +26.3 | +48.6 | -2.1 | -39.2 | +46.0 | -28.0 | +18.3 | +0.6 | -42.4 | |
| Steps (reduced) |
331 (122) |
485 (67) |
587 (169) |
663 (36) |
723 (96) |
773 (146) |
817 (190) |
854 (18) |
888 (52) |
918 (82) |
945 (109) | |
Subsets and supersets
Since 209 factors into 11 × 19, 209edo contains 11edo and 19edo as its subsets. 627edo, which triples it, gives a good correction to the harmonic 7.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-331 209⟩ | [⟨209 331]] | +0.4658 | 0.4660 | 8.12 |- | 2.3.5 | [-13 17 -6⟩, [-27 -2 13⟩ | [⟨209 331 485]] | +0.5439 | 0.3962 | 6.90 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 71\209
| 407.66
| 15625/12288
| Ditonic
|-
| 1
| 90\209
| 516.75
| 27/20
| Larry / marvo (209) / zarvo (209d)
|-
| 19
| 122\209
(1\209)
| 700.48
(5.74)
| 3/2
(225/224)
| Enneadecal (209d)
Template:Rank-2 end
Template:Orf