346edo: Difference between revisions

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''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.

[[~~Category:Equal divisions of the octave~~]]

[[~~Category:nano~~]]

346edo 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, in which it tempers out [[3025/3024]], [[4375/4374]] and [[5632/5625]], [[support]]ing the 76 & 270 temperament i.e. every other step of [[vishnu]].

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 a possible 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. The 346e val tempers out [[385/384]] and [[1375/1372]], and provides a possible tuning for [[fibo]], the 103 & 243 temperament.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 346 factors into primes as {{nowrap| 2 × 173 }}, 346edo contains [[2edo]] and [[173edo]] as subsets.

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-''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.
+{{Infobox ET}}
-[[Category:Equal divisions of the octave]]
+{{ED intro}}
-[[Category:nano]]
+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, in which it tempers out [[3025/3024]], [[4375/4374]] and [[5632/5625]], [[support]]ing the 76 & 270 temperament i.e. every other step of [[vishnu]].
+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 a possible 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. The 346e val tempers out [[385/384]] and [[1375/1372]], and provides a possible tuning for [[fibo]], the 103 & 243 temperament.
+=== Odd harmonics ===
+{{Harmonics in equal|346}}
+=== Subsets and supersets ===
+Since 346 factors into primes as {{nowrap| 2 × 173 }}, 346edo contains [[2edo]] and [[173edo]] as subsets.