137edo: Difference between revisions
Cleanup and set straight the rank-2 temps it supports |
+one-linear overview and note more 5-limit commas |
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== Theory == | == Theory == | ||
137edo | 137edo is a fairly accurate 5-limit temperament and also a strong no-7 19-limit temperament. The equal temperament [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]), {{monzo| -13 17 -6 }} ([[graviton]]), {{monzo| 8 14 -13 }} ([[parakleisma]]), and {{monzo| -29 -11 20 }} (gammic comma) in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[1728/1715]], 2430/2401 in the 7-limit; [[243/242]] in the 11-limit; [[351/350]] in the 13-limit; [[375/374]] and [[442/441]] in the 17-limit; and [[324/323]] and [[495/494]] in the 19-limit. It provides the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament [[tempering out]] [[2430/2401]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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| 271.53 | | 271.53 | ||
| 75/64 | | 75/64 | ||
| [[Orwell]] ( | | [[Orwell]] (137e) / [[sabric]] (137d) | ||
|- | |- | ||
| 1 | | 1 | ||