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.

'''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- particularly, it is of note that this EDO ''does not'' temper out [[676/675|the island comma (676/675)]] despite the number of steps needed to reach the [[4/3]] perfect fourth being divisible by two.

[[Category:Equal divisions of the octave]]

[[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.
+'''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- particularly, it is of note that this EDO ''does not'' temper out [[676/675|the island comma (676/675)]] despite the number of steps needed to reach the [[4/3]] perfect fourth being divisible by two.
 [[Category:Equal divisions of the octave]]
 [[Category:Nexus]]