318edo: Difference between revisions
Removed novelty tag for now. We can add it back later, but I think we should start with the biggest edos: 6000000, 4191814, 2901533… and work our way down. We should add the tag to bigger ones first. |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|318}} | |||
318edo is [[contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]]. Besides, it shares its representations of the 11th and 17th [[Overtone series|harmonics]] with [[159edo]]. However, compared to 159edo, the [[patent val]]s differ on the mappings for 7, 13, and 19. | |||
In the 5-limit, it tempers out the same commas as 53edo, including the [[32805/32768|schisma (32805/32768)]], the [[15625/15552|kleisma (15625/15552)]], the [[amity comma|amity comma (1600000/1594323)]], the [[semicomma|semicomma (2109375/2097152)]], the [[vulture comma|vulture comma (10485760000/10460353203)]], etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the [[4000/3993|wizardharry (4000/3993)]], the [[9801/9800|kalisma (9801/9800)]] and the [[nexuma|nexus comma (1771561/1769472)]]. In the 13-limit, 1575/1573, 2080/2079, it tempers out the [[4096/4095|schismina (4096/4095)]], and the [[cantonisma|cantonisma (10985/10976)]]. | |||
At only slightly more than 3.5 cents, the step size of 318edo is really close to being [[unnoticeable comma|unnoticeable]] as is the case with other mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another. | |||
=== Prime harmonics === | |||
{{harmonics in equal|318}} | |||
== | |||
=== Subsets and supersets === | |||
318 = 2 × 3 × 53, and has subset edos {{EDOs|1, 2, 3, 6, 53, 106, 159}}. | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 22:38, 19 July 2023
| ← 317edo | 318edo | 319edo → |
318edo is contorted in both the 3-limit and the 5-limit, sharing the same mappings with 53edo. Besides, it shares its representations of the 11th and 17th harmonics with 159edo. However, compared to 159edo, the patent vals differ on the mappings for 7, 13, and 19.
In the 5-limit, it tempers out the same commas as 53edo, including the schisma (32805/32768), the kleisma (15625/15552), the amity comma (1600000/1594323), the semicomma (2109375/2097152), the vulture comma (10485760000/10460353203), etc. In the 7-limit it tempers out the stearnsma (118098/117649) and 589824/588245. In the 11-limit it tempers out the swetisma (540/539), the wizardharry (4000/3993), the kalisma (9801/9800) and the nexus comma (1771561/1769472). In the 13-limit, 1575/1573, 2080/2079, it tempers out the schismina (4096/4095), and the cantonisma (10985/10976).
At only slightly more than 3.5 cents, the step size of 318edo is really close to being unnoticeable as is the case with other mega-EDOs in this vicinity, so the steps themselves run a pretty high risk of blending completely into one another.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.07 | -1.41 | +0.99 | -0.37 | +0.98 | +0.70 | +0.60 | -1.86 | +0.61 | -1.64 |
| Relative (%) | +0.0 | -1.8 | -37.3 | +26.1 | -9.9 | +26.0 | +18.7 | +15.9 | -49.3 | +16.2 | -43.4 | |
| Steps (reduced) |
318 (0) |
504 (186) |
738 (102) |
893 (257) |
1100 (146) |
1177 (223) |
1300 (28) |
1351 (79) |
1438 (166) |
1545 (273) |
1575 (303) | |
Subsets and supersets
318 = 2 × 3 × 53, and has subset edos 1, 2, 3, 6, 53, 106, 159.