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. This EDO shares its representations of the 3rd, 5th, 11th and 17th [[Overtone series|harmonics]] with [[159edo]]. However, compared to 159ededo, the patent vals differ on the mappings for 7, 13, and 19. In the 5-limit, it tempers out [[32805/32768|the schisma (32805/32768)]], [[15625/15552|the kleisma (15625/15552)]], [[amity comma|the amity comma (1600000/1594323)]], [[semicomma|the semicomma (2109375/2097152)]], and [[vulture comma|the vulture comma (10485760000/10460353203)]]. In the 11-limit it tempers out the swetisma (540/539), [[4000/3993|the wizardharry comma (4000/3993)]], [[9801/9800|the kalisma (9801/9800)]] and [[nexuma|the nexus comma (1771561/1769472)]]. So far, none of the 7-limit commas this EDO tempers out have been found, while only one 13-limit comma, [[cantonisma|the cantonisma (10985/10976)]] has been found to be tempered out by this EDO.

[[Category:Equal divisions of the octave]]

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{{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.

=== Prime harmonics ===

=== 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|###]]

[[Category:53edo]]

[[Category:159edo]]

[[Category:Nexus]]

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-'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.  This EDO shares its representations of the 3rd, 5th, 11th and 17th [[Overtone series|harmonics]] with [[159edo]].  However, compared to 159ededo, the patent vals differ on the mappings for 7, 13, and 19.  In the 5-limit, it tempers out [[32805/32768|the schisma (32805/32768)]], [[15625/15552|the kleisma (15625/15552)]], [[amity comma|the amity comma (1600000/1594323)]], [[semicomma|the semicomma (2109375/2097152)]], and [[vulture comma|the vulture comma (10485760000/10460353203)]].  In the 11-limit it tempers out the swetisma (540/539), [[4000/3993|the wizardharry comma (4000/3993)]], [[9801/9800|the kalisma (9801/9800)]] and [[nexuma|the nexus comma (1771561/1769472)]].  So far, none of the 7-limit commas this EDO tempers out have been found, while only one 13-limit comma, [[cantonisma|the cantonisma (10985/10976)]] has been found to be tempered out by this EDO.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+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.
+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.
+=== Prime harmonics ===
+{{harmonics in equal|318}}
+=== Subsets and supersets ===
+= 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:53edo]]
+[[Category:159edo]]
 [[Category:Nexus]]