600edo

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← 599edo600edo601edo →
Prime factorization 23 × 3 × 52
Step size
Fifth 351\600 (702¢) (→117\200)
Semitones (A1:m2) 57:45 (114¢ : 90¢)
Consistency limit 9
Distinct consistency limit 9

600 equal divisions of the octave (abbreviated 600edo), or 600-tone equal temperament (600tet), 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 of 600edo 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

Approximation of prime harmonics in 600edo
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 +2 -16 -41 +34 -26 -48 +24 -14 +21 +48
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

Table of rank-2 temperaments by generator
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