622edo: Difference between revisions
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== | 622edo is [[enfactoring|enfactored]] in the 41-limit, having the same tuning as the highly notable [[311edo]]. In that regard, 622edo is a [[Compound scale|compound]] of two 311edos that don't intersect, and provides barely anything new apart from most characteristics of what it doubles. | ||
{{Harmonics in equal|622|columns= | |||
622edo has potential as an add-43 system, correcting 311edo's mapping for [[43/32|43]], which is the first harmonic not represented consistently by 311edo. Some 43-limit commas it tempers out are 1849/1848, 1850/1849, 50000/49923, 59168/59049, 300125/299538, 6837602/6834375, 1048576/1048383. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|622|columns=13}} | |||
{{Harmonics in equal|622|start=14|columns=13|collapsed=1|title=Approximation of prime harmonics in 622edo (continued)}} | |||
Latest revision as of 15:26, 10 March 2026
| ← 621edo | 622edo | 623edo → |
622 equal divisions of the octave (abbreviated 622edo or 622ed2), also called 622-tone equal temperament (622tet) or 622 equal temperament (622et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 622 equal parts of about 1.93 ¢ each. Each step represents a frequency ratio of 21/622, or the 622nd root of 2.
622edo is enfactored in the 41-limit, having the same tuning as the highly notable 311edo. In that regard, 622edo is a compound of two 311edos that don't intersect, and provides barely anything new apart from most characteristics of what it doubles.
622edo has potential as an add-43 system, correcting 311edo's mapping for 43, which is the first harmonic not represented consistently by 311edo. Some 43-limit commas it tempers out are 1849/1848, 1850/1849, 50000/49923, 59168/59049, 300125/299538, 6837602/6834375, 1048576/1048383.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.296 | -0.462 | -0.337 | +0.451 | +0.630 | -0.775 | -0.407 | +0.665 | +0.648 | +0.945 | -0.540 | -0.767 |
| Relative (%) | +0.0 | +15.3 | -23.9 | -17.5 | +23.4 | +32.6 | -40.2 | -21.1 | +34.4 | +33.6 | +49.0 | -28.0 | -39.7 | |
| Steps (reduced) |
622 (0) |
986 (364) |
1444 (200) |
1746 (502) |
2152 (286) |
2302 (436) |
2542 (54) |
2642 (154) |
2814 (326) |
3022 (534) |
3082 (594) |
3240 (130) |
3332 (222) | |
| Harmonic | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.264 | +0.088 | +0.450 | -0.008 | +0.157 | -0.207 | -0.275 | -0.137 | +0.093 | -0.530 | +0.181 | -0.281 | -0.786 |
| Relative (%) | -13.7 | +4.6 | +23.3 | -0.4 | +8.1 | -10.7 | -14.3 | -7.1 | +4.8 | -27.5 | +9.4 | -14.6 | -40.8 | |
| Steps (reduced) |
3375 (265) |
3455 (345) |
3563 (453) |
3659 (549) |
3689 (579) |
3773 (41) |
3825 (93) |
3850 (118) |
3921 (189) |
3965 (233) |
4028 (296) |
4105 (373) |
4141 (409) | |