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- particularly, it is of note that | '''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 318edo EDO ''does not'' temper out [[676/675|the island comma (676/675)]] despite the ability of this EDO to divide the [[4/3]] perfect fourth into two even halves. | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Nexus]] | [[Category:Nexus]] | ||
Revision as of 04:34, 7 January 2021
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 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 the schisma (32805/32768), the kleisma (15625/15552), the amity comma (1600000/1594323), the semicomma (2109375/2097152), and the vulture comma (10485760000/10460353203). In the 11-limit it tempers out the swetisma (540/539), the wizardharry comma (4000/3993), the kalisma (9801/9800) and 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, the cantonisma (10985/10976) has been found to be tempered out by this EDO- particularly, it is of note that 318edo EDO does not temper out the island comma (676/675) despite the ability of this EDO to divide the 4/3 perfect fourth into two even halves.