600edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|600}} Because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error. | |||
== 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]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|600}} | {{Harmonics in equal|600}} | ||
=== Subsets and supersets === | |||
Since 600 factors into 2<sup>3</sup> × 3 × 5<sup>2</sup>, it has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}. | |||
[[ | == Regular temperament properties == | ||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 283\600 | |||
| 566.00 | |||
| 81920/59049 | |||
| [[Tricot]] | |||
|- | |||
| 3 | |||
| 193\600<br>(7\600) | |||
| 386.00<br>(14.00) | |||
| 5/4<br>(126/125) | |||
| [[Mutt]] | |||
|- | |||
| 12 | |||
| 249\600<br>(1\600) | |||
| 498.00<br>(2.00) | |||
| 4/3<br>(32805/32768) | |||
| [[Atomic]] (600e) | |||
|} | |||
Revision as of 05:04, 18 April 2023
| ← 599edo | 600edo | 601edo → |
Template:EDO intro Because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error.
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.
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.
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) |