133edo: Difference between revisions

133edo is only consistent to the 5-odd-limit. The equal temperament tempers out 393216/390625 (würschmidt comma) and 131072000/129140163 (rodan comma) in the 5-limit.

Using the patent val, it tempers out 245/243, 1029/1024 and 395136/390625 in the 7-limit; 385/384, 441/440, 896/891 and 43923/43750 in the 11-limit; 196/195, 325/324, 352/351, 364/363 and 3146/3125 in the 13-limit. It supports rodan and superenneadecal.

Using the 133d val, it tempers out 1728/1715, 4000/3969 and 4375/4374. It supports enneadecal.

Approximation of prime harmonics in 133edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+1.80	+1.66	-3.41	-0.94	-1.43	+3.32	+0.23	+3.30	-1.01	+0.83
Error	Relative (%)	+0.0	+20.0	+18.4	-37.8	-10.4	-15.8	+36.7	+2.6	+36.6	-11.1	+9.2
Steps (reduced)		133 (0)	211 (78)	309 (43)	373 (107)	460 (61)	492 (93)	544 (12)	565 (33)	602 (70)	646 (114)	659 (127)

Since 133 factors into 7 × 19, 133edo contains 7edo and 19edo as its subsets.

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 {{EDO intro}}
-The equal temperament [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and 131072000/129140163 (rodan comma) in the 5-limit.
+edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and 131072000/129140163 (rodan comma) in the 5-limit.
 Using the [[patent val]], it tempers out [[245/243]], [[1029/1024]] and 395136/390625 in the 7-limit; [[385/384]], [[441/440]], [[896/891]] and 43923/43750 in the 11-limit; [[196/195]], [[325/324]], [[352/351]], [[364/363]] and 3146/3125 in the 13-limit. It [[support]]s [[rodan]] and [[superenneadecal]].

Revision as of 16:22, 27 May 2024