27720edo - Revision history

Eliora: /* Theory */ there are good highly composite edos less than 27720

2023-03-20T16:03:35Z

Theory: there are good highly composite edos less than 27720

← Older revision		Revision as of 16:03, 20 March 2023
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	27720edo is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, with a large jump from [[2520edo]] caused by the prime factor 11.		27720edo is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, with a large jump from [[2520edo]] caused by the prime factor 11.

	The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87~~. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[12edo]]~~. The mapping for 3/2 in 27720edo derives from [[1848edo]].		The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. The mapping for 3/2 in 27720edo derives from [[1848edo]].
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|27720}}		{{Harmonics in equal\|27720}}

	== Contorsion table ==		== Contorsion table ==
	{\| class="wikitable"		{\| class="wikitable"

Eliora at 01:41, 18 March 2023

2023-03-18T01:41:55Z

← Older revision		Revision as of 01:41, 18 March 2023
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	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|27720}}~~		27720edo is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, with a large jump from [[2520edo]] caused by the prime factor 11.
	27720edo ~~is a [[highly melodic EDO]]. It~~ is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, ~~and~~ with a large jump from ~~2520~~ caused by the prime factor 11.

	The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]].		The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]].
			=== Prime harmonics ===
			{{Harmonics in equal\|27720}}
	== Contorsion table ==		== Contorsion table ==
	{\| class="wikitable"		{\| class="wikitable"

Eliora: infobox et

2022-10-05T16:41:40Z

infobox et

← Older revision		Revision as of 16:41, 5 October 2022
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			{{Infobox ET}}
	The '''27720 equal divisions of the octave''' ('''27720edo'''), or the '''27720(-tone) equal temperament''' ('''27720tet''', '''27720et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 27720 [[equal]] parts of about 43 [[cent\|millicent]]s, or exactly 10/231 of a cent each.		The '''27720 equal divisions of the octave''' ('''27720edo'''), or the '''27720(-tone) equal temperament''' ('''27720tet''', '''27720et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 27720 [[equal]] parts of about 43 [[cent\|millicent]]s, or exactly 10/231 of a cent each.

Eliora at 21:10, 30 March 2022

2022-03-30T21:10:44Z

← Older revision		Revision as of 21:10, 30 March 2022
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	27720edo is a [[highly melodic EDO]]. It is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, and with a large jump from 2520 caused by the prime factor 11.		27720edo is a [[highly melodic EDO]]. It is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, and with a large jump from 2520 caused by the prime factor 11.

	The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[~~72edo\|~~12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]].		The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]].

	== Contorsion table ==		== Contorsion table ==

Eliora at 21:09, 30 March 2022

2022-03-30T21:09:56Z

← Older revision		Revision as of 21:09, 30 March 2022
Line 1:		Line 1:
	The '''27720 equal divisions of the octave''' ('''27720edo'''), or the '''27720(-tone) equal temperament''' ('''27720tet''', '''27720et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 27720 [[equal]] parts of about {{~~#expr:(1200/~~27720~~) round 3~~}} [[~~cent~~]]~~s each~~.		The '''27720 equal divisions of the octave''' ('''27720edo'''), or the '''27720(-tone) equal temperament''' ('''27720tet''', '''27720et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 27720 [[equal]] parts of about 43 [[cent\|millicent]]s, or exactly 10/231 of a cent each.

			== Theory ==
			{{Harmonics in equal\|27720}}
			27720edo is a [[highly melodic EDO]]. It is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, and with a large jump from 2520 caused by the prime factor 11.

			The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[72edo\|12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]].

			== Contorsion table ==
			{\| class="wikitable"
			\|+For 2.prime subgroups
			!Prime p
			!Contorsion order
			for 2.p subgroup
			!Meaning that
			the mapping derives from
			\|-
			\|3
			\|15
			\|[[1848edo]]
			\|-
			\|5
			\|4
			\|6930edo
			\|-
			\|7
			\|60
			\|462edo
			\|-
			\|11
			\|45
			\|616edo
			\|-
			\|13
			\|24
			\|1155edo
			\|-
			\|17
			\|24
			\|1155edo
			\|}

Eliora: need to subst for millicents

2022-03-30T20:53:23Z

need to subst for millicents

New page

The '''27720 equal divisions of the octave''' ('''27720edo'''), or the '''27720(-tone) equal temperament''' ('''27720tet''', '''27720et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 27720 [[equal]] parts of about {{#expr:(1200/27720) round 3}} [[cent]]s each.