346edo: Difference between revisions

Revision as of 07:19, 15 November 2023

346edo is consistent to the 7-odd-limit, but the errors of harmonics 3, 5, and 7 are all quite large, commending itself as a 2.9.15.21.11 subgroup temperament. Using the patent val nonetheless, the equal temperament tempers out 243/242, 441/440, 540/539, 2401/2400, 4000/3993, 9801/9800 and 19683/19600. It is an excellent tuning for the 11-limit version of harry, the 72 & 274 temperament, as well as the rank-3 temperament jove, which tempers out 243/242 and 441/440.

Approximation of odd harmonics in 346edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.38	-1.34	-1.20	+0.71	+0.13	-1.22	+0.75	-0.91	+0.75	+0.90	-0.53
Error	Relative (%)	-39.7	-38.7	-34.5	+20.6	+3.7	-35.2	+21.6	-26.2	+21.7	+25.8	-15.2
Steps (reduced)		548 (202)	803 (111)	971 (279)	1097 (59)	1197 (159)	1280 (242)	1352 (314)	1414 (30)	1470 (86)	1520 (136)	1565 (181)

Since 346 factors into 2 × 173, 346edo contains 2edo and 173edo as subsets.

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 {{Infobox ET}}
-'''346edo''' divides the octave into 346 equal parts of size 3.468 cents each. While that is a lot of parts, not all of them must be used to gain the benefits of the tuning, which tempers out 19683/19600, 2401/2400, 243/242, 441/440, 540/539, 4000/3993 and 9801/9800. It is an excellent tuning for the 11-limit version of harry, the 72&amp;130 temperament, as well as the rank three temperament jove which tempers out 243/242 and 441/440.
+{{EDO intro|346}}
+edo is [[consistent]] to the [[7-odd-limit]], but the errors of [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all quite large, commending itself as a 2.9.15.21.11 [[subgroup]] temperament. Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[243/242]], [[441/440]], [[540/539]], [[2401/2400]], [[4000/3993]], [[9801/9800]] and [[19683/19600]]. It is an excellent tuning for the 11-limit version of [[harry]], the 72 &amp; 274 temperament, as well as the rank-3 temperament [[jove]], which tempers out 243/242 and 441/440.
+=== Odd harmonics ===
+{{Harmonics in equal|346}}
+=== Subsets and supersets ===
+Since 346 factors into {{factorization|346}}, 346edo contains [[2edo]] and [[173edo]] as subsets.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Nano]]