118edo: Difference between revisions

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'''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.

'''118edo''' is the [[EDO|equal division of the octave]] into 118 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.

Revision as of 11:54, 15 February 2019 view source Xenllium (talk \| contribs) autopatrolled 4,516 edits No edit summary Tags: Mobile edit Mobile web edit ← Older edit		Revision as of 00:04, 22 May 2020 view source Winspear (talk \| contribs) 18 edits Fixed EDo error Tag: Visual edit Newer edit →
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	'''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.		'''118edo''' is the [[EDO\|equal division of the octave]] into 118 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 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.