118edo: Difference between revisions
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''118edo'' | '''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 [[ | 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. | 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: | |||
[[Category: | 118edo is the 17th [[The Riemann Zeta Function and Tuning|zeta peak edo]]. | ||
[[Category:Edo]] | |||
[[Category:gamelismic]] | |||
[[Category:guiron]] | [[Category:guiron]] | ||
[[Category:parakleismic]] | [[Category:parakleismic]] | ||
[[Category:portent]] | [[Category:portent]] | ||
[[Category:schismic]] | [[Category:schismic]] | ||
Revision as of 11:54, 15 February 2019
118edo is the 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 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.
118edo is the 17th zeta peak edo.