3684edo: Difference between revisions

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The '''3684 equal division''' divides the octave into 3684 steps of 0.325733 cents each, which means that one cent is exactly 3.07 steps of 3684 edo. It 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 [[support]]s the 7-limit version of the 612&1848 temperament.

~~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&gt~~; and the ~~monzisma~~, |54 -~~37 2&gt~~;, ~~are all one step of 3684et~~.

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.

[[Category:Equal divisions of the octave|####]]

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-The '''3684 equal division''' divides the octave into 3684 steps of 0.325733 cents each, which means that one cent is exactly 3.07 steps of 3684 edo. It is an extraordinarily strong 5-limit system, tempering out senior, |-17 62 -35&gt;, gross, |144 -22 -47&gt; and the Kirnberger atom, |161 -84 -12&gt;. 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 version of the 612&amp;1848 temperament.
+{{Infobox ET}}
+{{ED intro}}
-= 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&gt;, pirate, |-90 -15 49&gt; and the monzisma, |54 -37 2&gt;, are all one step of 3684et.
+edo 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]].
-{{Primes in edo|3684|prec=4}}
+= 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.
+{{Harmonics in equal|3684|columns=10|prec=4}}
 [[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->