3684edo - Revision history

ArrowHead294 at 16:38, 20 February 2025

2025-02-20T16:38:51Z

← Older revision		Revision as of 16:38, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|3684~~}}		{{ED intro}}

	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]].		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]].

BudjarnLambeth: Replace deprecated template

2024-01-25T08:17:20Z

Replace deprecated template

← Older revision		Revision as of 08:17, 25 January 2024
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	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.		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}}		{{Harmonics in equal\|3684\|columns=10\|prec=4}}

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

BudjarnLambeth at 07:05, 9 July 2023

2023-07-09T07:05:47Z

← Older revision		Revision as of 07:05, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|3684}}		{{EDO intro\|3684}}

BudjarnLambeth at 04:28, 9 July 2023

2023-07-09T04:28:24Z

← Older revision		Revision as of 04:28, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|3684}}		{{EDO intro\|3684}}

Eliora at 15:20, 12 June 2023

2023-06-12T15:20:14Z

← Older revision		Revision as of 15:20, 12 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~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.		{{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~~&gt~~;, 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.

	{{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 -->

Plumtree: Infobox ET added

2022-10-04T22:17:32Z

Infobox ET added

← Older revision		Revision as of 22:17, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	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.		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.

Fredg999 category edits: Categories

2022-07-04T01:27:49Z

Cmloegcmluin: link to new page for Supports

2022-01-25T18:34:54Z

link to new page for Supports

← Older revision		Revision as of 18:34, 25 January 2022
Line 1:		Line 1:
	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 ~~supports~~ the 7-limit version of the 612&1848 temperament.		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> and the monzisma, \|54 -37 2>, are all one step of 3684et.		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.

	{{Primes in edo\|3684\|prec=4}}		{{Primes in edo\|3684\|prec=4}}

Inthar at 07:47, 23 April 2021

2021-04-23T07:47:29Z

← Older revision		Revision as of 07:47, 23 April 2021
Line 2:		Line 2:

	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.		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.

			{{Primes in edo\|3684\|prec=4}}

Xenllium: Created page with "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..."

2018-12-07T06:55:13Z

Created page with "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..."

New page

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 supports 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> and the monzisma, |54 -37 2>, are all one step of 3684et.

← Older revision		Revision as of 08:17, 25 January 2024
Line 6:		Line 6:
	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.		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}}		{{Harmonics in equal\|3684\|columns=10\|prec=4}}

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

← Older revision		Revision as of 15:20, 12 June 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~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.		{{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~~&gt~~;, 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.

	{{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 -->

← Older revision		Revision as of 01:27, 4 July 2022
Line 1:		Line 1:
	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.		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> and the monzisma, \|54 -37 2>, are all one step of 3684et.		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.

	{{Primes in edo\|3684\|prec=4}}		{{Primes in edo\|3684\|prec=4}}

			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->