# 600edo

 ← 599edo 600edo 601edo →
Prime factorization 23 × 3 × 52
Step size 2¢
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 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

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 (%) +0.0 +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

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

Francium