118edo: Difference between revisions

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''118edo'' ~~divides~~ the octave into ~~118 equal~~ parts~~, each~~ of 10.17 cents. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1> and the parakleisma, |8 14 -13>, as well as the vishnuzma, |23 6 -14>, the hemithirds comma, |38 -2 -15> and the kwazy, |-53 10 16>. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.

'''118edo''' is the [[EDO|equal division of the octave]] into 400 parts of 10.1695 cents each. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1> and the parakleisma, |8 14 -13>, as well as the vishnuzma, |23 6 -14>, the hemithirds comma, |38 -2 -15> and the kwazy, |-53 10 16>. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.

In the 7-limit it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[~~99edo|~~99edo]] does better with that.

In the 7-limit, it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[99edo]] does better with that.

In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.

[[Category:~~edo~~]]

[[Category:~~gamelisma~~]]

118edo is the 17th [[The Riemann Zeta Function and Tuning|zeta peak edo]].

[[Category:Edo]]

[[Category:gamelismic]]

[[Category:guiron]]

[[Category:parakleismic]]

[[Category:portent]]

[[Category:schismic]]

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-''118edo'' divides the octave into 118 equal parts, each of 10.17 cents. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1&gt; and the parakleisma, |8 14 -13&gt;, as well as the vishnuzma, |23 6 -14&gt;, the hemithirds comma, |38 -2 -15&gt; and the kwazy, |-53 10 16&gt;. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.
+'''118edo''' is the [[EDO|equal division of the octave]] into 400 parts of 10.1695 cents each. It represents the intersection of the 5-limit schismatic and parakleismic temperaments, tempering out both the schisma, |-15 8 1&gt; and the parakleisma, |8 14 -13&gt;, as well as the vishnuzma, |23 6 -14&gt;, the hemithirds comma, |38 -2 -15&gt; and the kwazy, |-53 10 16&gt;. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent.
-In the 7-limit it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[99edo|99edo]] does better with that.
+In the 7-limit, it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but [[99edo]] does better with that.
 In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.
-[[Category:edo]]
-[[Category:gamelisma]]
+edo is the 17th [[The Riemann Zeta Function and Tuning|zeta peak edo]].
+[[Category:Edo]]
+[[Category:gamelismic]]
 [[Category:guiron]]
 [[Category:parakleismic]]
 [[Category:portent]]
 [[Category:schismic]]