600edo
| ← 599edo | 600edo | 601edo → |
600 equal divisions of the octave (abbreviated 600edo or 600ed2), also called 600-tone equal temperament (600tet) or 600 equal temperament (600et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 600 equal parts of exactly 2 ¢ each. Each step represents a frequency ratio of 21/600, or the 600th root of 2.
Theory
600edo has good approximations to harmonics 3, 5, 13, and 23, on top of which we may consider adding 7 or 19. The equal temperament tempers out the tricot comma, [39 -29 3⟩, and the mutt comma, [-44 -3 21⟩ in the 5-limit, 65625/65536, 250047/250000, 5250987/5242880, and 28824005/28697814 in the 7-limit, supporting septimal mutt. The patent val is also a tuning for atomic, whereas the 600e val is a tuning for atomic in the 11-limit. In addition, 600e val is a tuning for 20th-octave temperament soviet ferris wheel as high as the 19-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.045 | -0.314 | -0.826 | +0.682 | -0.528 | -0.955 | +0.487 | -0.274 | +0.423 | +0.964 |
| Relative (%) | +0.0 | +2.2 | -15.7 | -41.3 | +34.1 | -26.4 | -47.8 | +24.3 | -13.7 | +21.1 | +48.2 | |
| Steps (reduced) |
600 (0) |
951 (351) |
1393 (193) |
1684 (484) |
2076 (276) |
2220 (420) |
2452 (52) |
2549 (149) |
2714 (314) |
2915 (515) |
2973 (573) | |
Subsets and supersets
Since 600 factors into 23 × 3 × 52, 600edo has subset edos 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300. Since 600 = 6 × 100, one step of 600edo is named a centitone, being a relative cent of 6edo, otherwise known as the whole tone scale. In addition, because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error using direct approximation.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 283\600 | 566.00 | 81920/59049 | Tricot |
| 3 | 193\600 (7\600) |
386.00 (14.00) |
5/4 (126/125) |
Mutt |
| 12 | 249\600 (1\600) |
498.00 (2.00) |
4/3 (32805/32768) |
Atomic (600e) |
| 20 | 283\600 (13\600) |
566.00 (26.00) |
238/165 (?) |
Soviet ferris wheel (600e) |
| 60 | 249\600 (1\600) |
498.00 (2.00) |
4/3 (32805/32768) |
Minutes (600e) |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct