# 600edo

← 599edo | 600edo | 601edo → |

^{3}× 3 × 5^{2}**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 2^{1/600}, 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 2^{3} × 3 × 5^{2}, 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

## Music

*So Thankful For You*(2024) – tricot in 600edo tuning