167edo: Difference between revisions

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== Theory ==

167et [[tempering out|tempers out]] the [[würschmidt comma]], 393216/390625, and the leapday comma, {{monzo| 31 -21 1 }}, in the [[5-limit]]; [[2401/2400]], [[3136/3125]], and 179200/177147 in the [[7-limit]]; [[896/891]], 2200/2187, ~~and~~ 3388/3375 in the [[11-limit]]; [[325/324]], [[352/351]], [[364/363]], [[1001/1000]], and [[1716/1715]] in the [[13-limit]], providing the [[optimal patent val]] for 11- and 13-limit [[polypyth]] temperament; [[256/255]], [[442/441]], [[595/594]], [[715/714]], and [[936/935]] in the [[17-limit]]. It also [[support]]s the 11-limit [[unthirds]] temperament.

167et [[tempering out|tempers out]] the [[würschmidt comma]], 393216/390625, and the leapday comma, {{monzo| 31 -21 1 }}, in the [[5-limit]]; [[2401/2400]], [[3136/3125]], [[6144/6125]], and 179200/177147 in the [[7-limit]]; [[896/891]], [[2200/2187]], [[3025/3024]], [[3388/3375]], and [[4000/3993]] in the [[11-limit]]; [[325/324]], [[352/351]], [[364/363]], [[1001/1000]], and [[1716/1715]] in the [[13-limit]], providing the [[optimal patent val]] for 11- and 13-limit [[polypyth]] temperament; [[256/255]], [[442/441]], [[595/594]], [[715/714]], and [[936/935]] in the [[17-limit]]. It also [[support]]s the 11-limit [[unthirds]] temperament.

167edo also has a very close approximation to the [[golden magic]] scale.

Line 125:

| 78\167

| 560.48

| ~~864~~/~~625~~

| 242/175

| [[Whoops]]

|}

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 == Theory ==
-et [[tempering out|tempers out]] the [[würschmidt comma]], 393216/390625, and the leapday comma, {{monzo| 31 -21 1 }}, in the [[5-limit]]; [[2401/2400]], [[3136/3125]], and 179200/177147 in the [[7-limit]]; [[896/891]], 2200/2187, and 3388/3375 in the [[11-limit]]; [[325/324]], [[352/351]], [[364/363]], [[1001/1000]], and [[1716/1715]] in the [[13-limit]], providing the [[optimal patent val]] for 11- and 13-limit [[polypyth]] temperament; [[256/255]], [[442/441]], [[595/594]], [[715/714]], and [[936/935]] in the [[17-limit]]. It also [[support]]s the 11-limit [[unthirds]] temperament.
+et [[tempering out|tempers out]] the [[würschmidt comma]], 393216/390625, and the leapday comma, {{monzo| 31 -21 1 }}, in the [[5-limit]]; [[2401/2400]], [[3136/3125]], [[6144/6125]], and 179200/177147 in the [[7-limit]]; [[896/891]], [[2200/2187]], [[3025/3024]], [[3388/3375]], and [[4000/3993]] in the [[11-limit]]; [[325/324]], [[352/351]], [[364/363]], [[1001/1000]], and [[1716/1715]] in the [[13-limit]], providing the [[optimal patent val]] for 11- and 13-limit [[polypyth]] temperament; [[256/255]], [[442/441]], [[595/594]], [[715/714]], and [[936/935]] in the [[17-limit]]. It also [[support]]s the 11-limit [[unthirds]] temperament.
 edo also has a very close approximation to the [[golden magic]] scale.
@@ Line 125: / Line 125: @@
 | 78\167
 | 560.48
-| 864/625
+| 242/175
 | [[Whoops]]
 |}