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.

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 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 that are tempered out by this EDO have been found~~, ~~while only one 13-limit comma~~, [[cantonisma|~~the~~ 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 [[676/675|~~the~~ island comma (676/675)]], and that this EDO likewise divides [[2187/2048|~~the~~ apotome (2187/2048)]] in half by means other than tempering out [[243/242|~~the~~ rastma (243/242)]].

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 vals 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). 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)]].

[[Category:Equal divisions of the octave]]

[[Category:53edo]]

[[Category:Nexus]]

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 '''318edo''' is the '''318 equal division of the octave''' into equal parts of 3.774 cents each.
-= 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 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 that are tempered out by this EDO have been found, while only one 13-limit comma, [[cantonisma|the 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 [[676/675|the island comma (676/675)]], and that this EDO likewise divides [[2187/2048|the apotome (2187/2048)]] in half by means other than tempering out [[243/242|the rastma (243/242)]].
+= 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 vals 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). 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)]].
 [[Category:Equal divisions of the octave]]
 [[Category:53edo]]
 [[Category:Nexus]]