600edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 28: | Line 22: | ||
|- | |- | ||
| 3 | | 3 | ||
| 193\600<br>(7\600) | | 193\600<br />(7\600) | ||
| 386.00<br>(14.00) | | 386.00<br />(14.00) | ||
| 5/4<br>(126/125) | | 5/4<br />(126/125) | ||
| [[Mutt]] | | [[Mutt]] | ||
|- | |- | ||
| 12 | | 12 | ||
| 249\600<br>(1\600) | | 249\600<br />(1\600) | ||
| 498.00<br>(2.00) | | 498.00<br />(2.00) | ||
| 4/3<br>(32805/32768) | | 4/3<br />(32805/32768) | ||
| [[Atomic]] (600e) | | [[Atomic]] (600e) | ||
|- | |- | ||
| 20 | | 20 | ||
| 283\600<br>(13\600) | | 283\600<br />(13\600) | ||
| 566.00<br>(26.00) | | 566.00<br />(26.00) | ||
| 238/165<br>(?) | | 238/165<br />(?) | ||
| [[Soviet ferris wheel]] (600e) | | [[Soviet ferris wheel]] (600e) | ||
|- | |- | ||
| 60 | | 60 | ||
| 249\600<br>(1\600) | | 249\600<br />(1\600) | ||
| 498.00<br>(2.00) | | 498.00<br />(2.00) | ||
| 4/3<br>(32805/32768) | | 4/3<br />(32805/32768) | ||
| [[Minutes]] (600e) | | [[Minutes]] (600e) | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) | * "So Thankful For You" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/3pKy6BFu0NuQLlkacXFIPg Spotify] | [https://francium223.bandcamp.com/track/so-thankful-for-you Bandcamp] | [https://www.youtube.com/watch?v=cRHgCe_xdGI YouTube] – tricot in 600edo tuning | ||
Revision as of 02:31, 16 November 2024
| ← 599edo | 600edo | 601edo → |
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 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
Template:Rank-2 begin
|-
| 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)
Template:Rank-2 end
Template:Orf