318edo: Difference between revisions
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'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each. | '''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each. | ||
== | == Theory == | ||
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. | |||
== | === Mappings === | ||
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, the [[4096/4095|schismina (4096/4095)]], and the [[cantonisma|cantonisma (10985/10976)]] have been found to be tempered out by this EDO | 318 = 2 × 3 × 53, and 318edo is [[Contorsion|contorted]] in both the 3-limit and the 5-limit, sharing the same mappings with [[53edo]], with inconsistency developing for the 3-limit as a result, albeit only late in the [[circle of fifths]]. 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. | ||
=== Commas === | |||
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, the [[4096/4095|schismina (4096/4095)]], and the [[cantonisma|cantonisma (10985/10976)]] have been found to be tempered out by this EDO. | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 17:08, 7 January 2021
318edo is the 318 equal division of the octave into equal parts of 3.774 cents each.
Theory
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.
Mappings
318 = 2 × 3 × 53, and 318edo is contorted in both the 3-limit and the 5-limit, sharing the same mappings with 53edo, with inconsistency developing for the 3-limit as a result, albeit only late in the circle of fifths. 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.
Commas
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, the schismina (4096/4095), and the cantonisma (10985/10976) have been found to be tempered out by this EDO.