840edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|840}} ==Theory== 840edo is the 15th highly melodic EDO, and it is the first one divisible by 7. === Harmonics === {{harmonics in equal|840}} ..." |
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==Theory== | ==Theory== | ||
840edo is the 15th [[highly melodic EDO]], and it is the first one divisible by 7. | 840edo is the 15th [[highly melodic EDO]], and it is the first one divisible by 7. | ||
=== | |||
It tunes the [[13-limit|13-prime-limit]] consistently, being the first highly melodic EDO past [[60edo]] to do so, however it does not tune the 9-odd-limit consistently. A comma basis for the 2.3.5.7.11.13 subgroup is [[729/728]], [[1575/1573]], 67392/67375, 804375/802816, [[250047/250000]]. | |||
=== Odd harmonics === | |||
{{harmonics in equal|840}} | {{harmonics in equal|840}} | ||
[[Category:Highly melodic]] | [[Category:Highly melodic]] | ||
Revision as of 00:34, 8 October 2022
| ← 839edo | 840edo | 841edo → |
Theory
840edo is the 15th highly melodic EDO, and it is the first one divisible by 7.
It tunes the 13-prime-limit consistently, being the first highly melodic EDO past 60edo to do so, however it does not tune the 9-odd-limit consistently. A comma basis for the 2.3.5.7.11.13 subgroup is 729/728, 1575/1573, 67392/67375, 804375/802816, 250047/250000.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.526 | -0.599 | -0.254 | +0.376 | +0.111 | -0.528 | +0.303 | -0.670 | -0.370 | +0.648 | +0.297 |
| Relative (%) | -36.9 | -42.0 | -17.8 | +26.3 | +7.7 | -36.9 | +21.2 | -46.9 | -25.9 | +45.3 | +20.8 | |
| Steps (reduced) |
1331 (491) |
1950 (270) |
2358 (678) |
2663 (143) |
2906 (386) |
3108 (588) |
3282 (762) |
3433 (73) |
3568 (208) |
3690 (330) |
3800 (440) | |