600edo: Difference between revisions
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== Theory == | == Theory == | ||
600edo tempers out the [[tricot comma]], {{monzo| 39 -29 3 }}, and the mutt comma, {{monzo| -44 -3 21 }} in the 5-limit, 65625/65536, [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, supporting septimal [[mutt]]. | 600edo tempers out the [[tricot comma]], {{monzo| 39 -29 3 }}, and the mutt comma, {{monzo| -44 -3 21 }} in the 5-limit, 65625/65536, [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, supporting septimal [[mutt]]. | ||
600edo's patent val is a tuning for the [[atomic]] temperament in the 5- and 7-limit and the 600e val is a tuning 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 === | === Prime harmonics === | ||
{{Harmonics in equal|600}} | {{Harmonics in equal|600}} | ||
Revision as of 23:04, 2 May 2023
| ← 599edo | 600edo | 601edo → |
Theory
600edo 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.
600edo's patent val is a tuning for the atomic temperament in the 5- and 7-limit and the 600e val is a tuning 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, it has subset edos 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300. Since 600 = 6 x 100, one step of 600edo is named 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.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
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) |
| 12 | 283\600 (13\600) |
566.00 (26.00) |
238/165 (?) |
Soviet Ferris wheel (600e) |