318edo: Difference between revisions

(23 intermediate revisions by 10 users not shown)

Line 1:

~~'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.~~

~~== Mappings ==~~

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.

~~318 = 2 × 3 × 53~~, ~~and 318edo is~~ [[~~Contorsion~~|~~contorted~~]] in the ~~5-limit~~, ~~sharing~~ the ~~same mapping 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 [[540/539]], [[4000/3993]], [[9801/9800]] and [[1771561/1769472]]. In the 13-limit, [[1575/1573]], [[2080/2079]], [[4096/4095]], and [[10985/10976]].

~~== Commas ==~~

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.

~~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). 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~~, ~~[[4096/4095]]~~, and the [[cantonisma|cantonisma (10985/10976)]] has been found to be tempered out by this EDO. It is of note that 318edo divides the [[4/3]] perfect fourth into two even halves through means other than tempering out the [[676/675|island comma (676/675)]], and that this EDO likewise divides the [[2187/2048|apotome (2187/2048)]] in half by means other than tempering out the [[243/242|rastma (243/242)]].

=== Prime harmonics ===

=== Subsets and supersets ===

{{nowrap| 318 = 2 × 3 × 53 }}, so 318edo has subset edos {{EDOs| 2, 3, 6, 53, 106, 159 }}.

~~[[Category:Equal divisions of the octave]]~~

[[Category:53edo]]

[[Category:159edo]]

[[Category:Nexus]]

@@ Line 1: / Line 1: @@
-'''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.
+{{Infobox ET}}
+{{ED intro}}
-== Mappings ==
+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.
-= 2 × 3 × 53, and 318edo is [[Contorsion|contorted]] in the 5-limit, sharing the same mapping 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 [[540/539]], [[4000/3993]], [[9801/9800]] and [[1771561/1769472]]. In the 13-limit, [[1575/1573]], [[2080/2079]], [[4096/4095]], and [[10985/10976]].
-== Commas ==
+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.
-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). 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, [[4096/4095]], and the [[cantonisma|cantonisma (10985/10976)]] has been found to be tempered out by this EDO.  It is of note that 318edo divides the [[4/3]] perfect fourth into two even halves through means other than tempering out the [[676/675|island comma (676/675)]], and that this EDO likewise divides the [[2187/2048|apotome (2187/2048)]] in half by means other than tempering out the [[243/242|rastma (243/242)]].
+=== Prime harmonics ===
+{{Harmonics in equal|318}}
+=== Subsets and supersets ===
+{{nowrap| 318 = 2 × 3 × 53 }}, so 318edo has subset edos {{EDOs| 2, 3, 6, 53, 106, 159 }}.
-[[Category:Equal divisions of the octave]]
 [[Category:53edo]]
+[[Category:159edo]]
 [[Category:Nexus]]