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 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 ~~EDO~~ divides the [[4/3]] perfect fourth into two even halves through means other than tempering out [[676/675|the island comma (676/675)]].

'''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 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)]].

[[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 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 EDO divides the [[4/3]] perfect fourth into two even halves through means other than tempering out [[676/675|the island comma (676/675)]].
+'''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 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)]].
 [[Category:Equal divisions of the octave]]
 [[Category:Nexus]]