3684edo: Difference between revisions
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{{EDO intro|3684}} | |||
3684 = 12 * 307, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments. From that point of view, one might note that 81/80 is 66 steps, 531441/524288, the Pythagorean comma, 72 steps, and 32805/32768, the schisma, 6 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Raider, |71 -99 37 | 3684edo is an extraordinarily strong 5-limit system, tempering out senior, {{monzo|-17 62 -35}}, gross, {{monzo|144 -22 -47}}; and the Kirnberger atom, {{monzo|161 -84 -12}};. It is uniquely consistent through the 9 odd limit, and in the 7-limit, it tempers out the landscape comma, 250047/250000, and so [[support]]s the 7-limit [[atomic]]. | ||
3684 = 12 * 307, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments. From that point of view, one might note that 81/80 is 66 steps, 531441/524288, the Pythagorean comma, 72 steps, and 32805/32768, the schisma, 6 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Raider, {{monzo|71 -99 37}};, pirate, {{monzo|-90 -15 49}}; and the monzisma, {{monzo|54 -37 2}};, are all one step of 3684et. | |||
{{Primes in edo|3684|prec=4}} | {{Primes in edo|3684|prec=4}} | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
Revision as of 15:20, 12 June 2023
| ← 3683edo | 3684edo | 3685edo → |
3684edo is an extraordinarily strong 5-limit system, tempering out senior, [-17 62 -35⟩, gross, [144 -22 -47⟩; and the Kirnberger atom, [161 -84 -12⟩;. It is uniquely consistent through the 9 odd limit, and in the 7-limit, it tempers out the landscape comma, 250047/250000, and so supports the 7-limit atomic.
3684 = 12 * 307, and is potentially of use as a device for constructing 5-limit 12-note circulating temperaments. From that point of view, one might note that 81/80 is 66 steps, 531441/524288, the Pythagorean comma, 72 steps, and 32805/32768, the schisma, 6 steps, making it exactly 1/12 of a Pythagorean comma and 1/11 of a syntonic comma, useful approximations when dealing with this problem. Raider, [71 -99 37⟩;, pirate, [-90 -15 49⟩; and the monzisma, [54 -37 2⟩;, are all one step of 3684et.
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