601edo
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Prime factorization
601 (prime)
Step size
1.99667¢
Fifth
352\601 (702.829¢)
Semitones (A1:m2)
60:43 (119.8¢ : 85.86¢)
Dual sharp fifth
352\601 (702.829¢)
Dual flat fifth
351\601 (700.832¢)
Dual major 2nd
102\601 (203.661¢)
Consistency limit
3
Distinct consistency limit
3
| ← 600edo | 601edo | 602edo → |
601 equal divisions of the octave (abbreviated 601edo or 601ed2), also called 601-tone equal temperament (601tet) or 601 equal temperament (601et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 601 equal parts of about 2 ¢ each. Each step represents a frequency ratio of 21/601, or the 601st root of 2.
Theory
601edo is inconsistent to the 5-odd-limit and both harmonics 3 and 5 are about halfway between its steps. It can be used in the 2.9.15.7.11.13.19 subgroup, tempering out 41503/41472, 104272/104247, 10648/10647, 388962/388531 and 10097379/10092544.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.874 | -0.956 | -0.440 | -0.249 | -0.236 | +0.071 | -0.082 | +0.868 | -0.009 | +0.434 | +0.677 |
| Relative (%) | +43.8 | -47.9 | -22.0 | -12.5 | -11.8 | +3.6 | -4.1 | +43.5 | -0.4 | +21.7 | +33.9 | |
| Steps (reduced) |
953 (352) |
1395 (193) |
1687 (485) |
1905 (102) |
2079 (276) |
2224 (421) |
2348 (545) |
2457 (53) |
2553 (149) |
2640 (236) |
2719 (315) | |
Subsets and supersets
601edo is the 110th prime edo. 1202edo, which doubles it, gives a good correction to the harmonics 3 and 5.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-1905 601⟩ | [⟨601 1905]] | 0.0393 | 0.0393 | 1.97 |
| 2.9.5 | 32805/32768, [-105 -65 134⟩ | [⟨601 1905 1395]] | 0.1635 | 0.1785 | 8.94 |
| 2.9.5.7 | 32805/32768, 68359375/68024448, [-16 -5 -2 13⟩ | [⟨601 1905 1395 1687]] | 0.1618 | 0.1546 | 7.74 |
| 2.9.5.7.11 | 6250/6237, 41503/41472, 32805/32768, 3294225/3294172 | [⟨601 1905 1395 1687 2079]] | 0.1431 | 0.1432 | 7.17 |
| 2.9.5.7.11.13 | 1575/1573, 6250/6237, 41503/41472, 32805/32768, 2200/2197 | [⟨601 1905 1395 1687 2079 2224]] | 0.1160 | 0.1441 | 7.22 |