318edo: Difference between revisions

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== Commas ==

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, the [[4096/4095|schismina (4096/4095)]], and the [[cantonisma|cantonisma (10985/10976)]] have 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)]].

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 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, the [[4096/4095|schismina (4096/4095)]], and the [[cantonisma|cantonisma (10985/10976)]] have 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]]

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 == Commas ==
-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, the [[4096/4095|schismina (4096/4095)]], and the [[cantonisma|cantonisma (10985/10976)]] have 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)]].
+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 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, the [[4096/4095|schismina (4096/4095)]], and the [[cantonisma|cantonisma (10985/10976)]] have 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]]