840edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
840edo is the 15th [[highly composite edo]], and it is the first one divisible by 7. It does not tune the [[9-odd-limit]] [[consistent]]ly, though a reasonable [[13-limit]] interpretation exists through the [[patent val]]. A [[comma basis]] for the 13-limit is [[729/728]], [[1575/1573]], 67392/67375, 804375/802816, [[250047/250000]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
{{ | {{Harmonics in equal|840}} | ||
Latest revision as of 06:40, 20 February 2025
| ← 839edo | 840edo | 841edo → |
840 equal divisions of the octave (abbreviated 840edo or 840ed2), also called 840-tone equal temperament (840tet) or 840 equal temperament (840et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 840 equal parts of about 1.43 ¢ each. Each step represents a frequency ratio of 21/840, or the 840th root of 2.
840edo is the 15th highly composite edo, and it is the first one divisible by 7. It does not tune the 9-odd-limit consistently, though a reasonable 13-limit interpretation exists through the patent val. A comma basis for the 13-limit 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) | |