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.~~

~~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~~.

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.

~~== Approximation of primes ==~~

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{{c}}, 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~~ ==

=== Prime harmonics ===

318 = 2 × 3 × 53, and ~~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.~~

=== Subsets and supersets ===

318 = 2 × 3 × 53, and has subset edos {{EDOs|1, 2, 3, 6, 53, 106, 159}}.

~~== 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|###]]

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[[Category:159edo]]

[[Category:Nexus]]

~~{{todo|improve readability}}~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.
+{{ED intro}}
-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.
+edo 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.
-== Approximation of primes ==
+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)]].
-{{Primes in edo|318|columns=11}}
+At only slightly more than 3.5{{c}}, 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 ==
+=== Prime harmonics ===
+{{harmonics in equal|318}}
-= 2 × 3 × 53, and 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.
+=== Subsets and supersets ===
+= 2 × 3 × 53, and has subset edos {{EDOs|1, 2, 3, 6, 53, 106, 159}}.
-== 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|###]] <!-- 3-digit number -->
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 [[Category:159edo]]
 [[Category:Nexus]]
-{{todo|improve readability}}