118edo: Difference between revisions
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== Theory == | == Theory == | ||
118edo represents the intersection of the [[5-limit]] [[schismatic]] and [[parakleismic]] temperaments, [[tempering out]] both the [[schisma]], {{monzo| -15 8 1 }} and the [[parakleisma]], {{monzo| 8 14 -13 }}, as well as the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, and the [[kwazy]], {{monzo| -53 10 16 }}. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent. | 118edo represents the intersection of the [[5-limit]] [[schismatic]] and [[parakleismic]] temperaments, [[tempering out]] both the [[schisma]], {{monzo| -15 8 1 }} and the [[parakleisma]], {{monzo| 8 14 -13 }}, as well as the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, and the [[kwazy]], {{monzo| -53 10 16 }}. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent. In addition, 118edo excellently represents the 22 Shruti scale. | ||
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 family|gamelan]] 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 family|gamelan]] 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. | ||
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|9 | |9 | ||
|limma | |limma, dayavati | ||
|fluorine | |fluorine | ||
|[[256/243]] | |[[256/243]] | ||
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|- | |- | ||
|11 | |11 | ||
|apotome | |apotome, ranjani | ||
|sodium | |sodium | ||
|[[2187/2048]] | |[[16/15]], [[2187/2048]] | ||
|- | |- | ||
|18 | |18 | ||
|diminished tone | |diminished tone, ratika | ||
|argon | |argon | ||
|[[10/9]] | |[[10/9]] | ||
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|- | |- | ||
|20 | |20 | ||
|major tone | |major tone, raudri | ||
|calcium | |calcium | ||
|[[9/8]] | |[[9/8]] | ||
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|- | |- | ||
|29 | |29 | ||
|Pythagorean minor 3rd | |Pythagorean minor 3rd, krodha | ||
|copper | |copper | ||
|[[32/27]] | |[[32/27]] | ||
|- | |- | ||
|31 | |31 | ||
|Classical minor 3rd | |Classical minor 3rd, vajrika | ||
|gallium | |gallium | ||
|[[6/5]] | |[[6/5]] | ||
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|- | |- | ||
|38 | |38 | ||
|Classical major 3rd | |Classical major 3rd, prasarini | ||
|strontium | |strontium | ||
|[[5/4]] | |[[5/4]] | ||
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|indium | |indium | ||
|[[4/3]] | |[[4/3]] | ||
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|51 | |||
|Kshiti | |||
|antimony | |||
|[[27/20]] | |||
|- | |||
|58 | |||
|Rakta | |||
|cerium | |||
|[[45/32]] | |||
|- | |- | ||
|59 | |59 | ||
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|praseodymium | |praseodymium | ||
|[[99/70]], [[140/99]] | |[[99/70]], [[140/99]] | ||
|- | |||
|60 | |||
|Literal tritone, sandipani | |||
|neodymium | |||
|[[729/512]] | |||
|- | |- | ||
|69 | |69 | ||
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|actinium | |actinium | ||
|[[27/16]] | |[[27/16]] | ||
|- | |||
|100 | |||
|Tivra | |||
|fermium | |||
|[[9/5]] | |||
|- | |- | ||
|109 | |109 | ||