420edo - Revision history

ArrowHead294 at 22:53, 20 February 2025

2025-02-20T22:53:00Z

← Older revision		Revision as of 22:53, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|420~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
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	\| 2401/2400, 4000/3993, 5120/5103, 15625/15552		\| 2401/2400, 4000/3993, 5120/5103, 15625/15552
	\| {{mapping\| 420 666 975 1179 1453 }}		\| {{mapping\| 420 666 975 1179 1453 }}
	\| -0.051		\| −0.051
	\| 0.278		\| 0.278
	\| 9.74		\| 9.74
	\|-		\|- style="border-top: double;"
	\| style="border-top: double;" \| 2.5.7.11.13.19.23		\| 2.5.7.11.13.19.23
	~~\| style="border-top: double;"~~ \| 875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976		\| 875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976
	~~\| style="border-top: double;"~~ \| {{mapping\| 420 975 1179 1453 1554 1784 1900 }}		\| {{mapping\| 420 975 1179 1453 1554 1784 1900 }}
	\| ~~style="border-top: double;" \|~~ 0.069		\| +0.069
	~~\| style="border-top: double;"~~ \| 0.104		\| 0.104
	~~\| style="border-top: double;"~~ \| 3.62		\| 3.62
	\|}		\|}

Francium: +categories

2024-02-13T18:08:43Z

+categories

← Older revision		Revision as of 18:08, 13 February 2024
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	; [[Mandrake]]		; [[Mandrake]]
	* [https://youtu.be/X1deLLCJD64?si=baHHYZQV9VFMaJZs ''Follow In Is''] (2022) – a superset of [[12edo]], [[5edo]], and [[7edo]], least common multiple of which is 420edo.		* [https://youtu.be/X1deLLCJD64?si=baHHYZQV9VFMaJZs ''Follow In Is''] (2022) – a superset of [[12edo]], [[5edo]], and [[7edo]], least common multiple of which is 420edo.

			[[Category:Listen]]

CompactStar: 666 != 69

2023-11-11T00:40:08Z

666 != 69

← Older revision		Revision as of 00:40, 11 November 2023
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	== Trivia ==		== Trivia ==
	The approximation to the third harmonic, which derives from 70edo, constitutes 666 steps of 420edo~~. Nice~~.		The approximation to the third harmonic, which derives from 70edo, constitutes 666 steps of 420edo.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Cleanup

2023-11-06T13:58:42Z

Cleanup

← Older revision		Revision as of 13:58, 6 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	420edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning of [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] as [[140edo]]. The [[13/1\|13th~~]] [[~~harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1\|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only 11 and 17 have step ~~correspondences~~ coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups.		420edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning of [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] as [[140edo]]. The [[13/1\|13th harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1\|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only the harmonics 11 and 17 have step numbers coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups.

	420edo is good at the 2.5.7.11.13.19.23 [[subgroup]], and has a great potential as a near-just xenharmonic system. It also works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].		420edo is good at the 2.5.7.11.13.19.23 [[subgroup]], and has a great potential as a near-just xenharmonic system. It also works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	420 is a largely composite number, being ~~divisible by~~ {{EDOs\| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210 }}. For this reason 420edo is rich in modulation circles.		420 is a largely composite number, its nontrivial subset edos being {{EDOs\| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210 }}. For this reason 420edo is rich in modulation circles.

	== Trivia ==		== Trivia ==
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 4000/3993, 5120/5103, 15625/15552		\| 2401/2400, 4000/3993, 5120/5103, 15625/15552
	\| [{{~~val~~\| 420 666 975 1179 1453 }}]		\| {{mapping\| 420 666 975 1179 1453 }}
	\| -0.051		\| -0.051
	\| 0.278		\| 0.278
	\| 9.74		\| 9.74
	\|-		\|-
	\|style="border-top: double;" \|2.5.7.11.13.19.23		\| style="border-top: double;" \| 2.5.7.11.13.19.23
	\|style="border-top: double;" \|875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976		\| style="border-top: double;" \| 875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976
	\|style="border-top: double;" \|[{{~~val~~\|420 975 1179 1453 1554 1784 1900}}]		\| style="border-top: double;" \| {{mapping\| 420 975 1179 1453 1554 1784 1900 }}
	\|style="border-top: double;" \|0.069		\| style="border-top: double;" \| 0.069
	\|style="border-top: double;" \|0.104		\| style="border-top: double;" \| 0.104
	\|style="border-top: double;" \|3.62		\| style="border-top: double;" \| 3.62
	\|}		\|}

	== Music ==		== Music ==
	; [[Mandrake]]		; [[Mandrake]]
	* ''[https://~~www~~.~~youtube.com~~/~~watch~~?v=~~X1deLLCJD64~~ Follow In Is]'' – a superset of [[12edo]], [[5edo]], and [[7edo]], least common multiple of which is 420edo.		* [https://youtu.be/X1deLLCJD64?si=baHHYZQV9VFMaJZs ''Follow In Is''] (2022) – a superset of [[12edo]], [[5edo]], and [[7edo]], least common multiple of which is 420edo.

BudjarnLambeth at 06:33, 9 July 2023

2023-07-09T06:33:26Z

← Older revision		Revision as of 06:33, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|420}}		{{EDO intro\|420}}

BudjarnLambeth at 05:54, 9 July 2023

2023-07-09T05:54:48Z

← Older revision		Revision as of 05:54, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|420}}		{{EDO intro\|420}}

Eliora: /* Regular temperament properties */

2023-05-25T14:23:57Z

Regular temperament properties

← Older revision		Revision as of 14:23, 25 May 2023
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	\| 9.74		\| 9.74
	\|-		\|-
	\|2.5.7.11.13.19.23		\|style="border-top: double;" \|2.5.7.11.13.19.23
	\|875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976		\|style="border-top: double;" \|875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976
	\|[{{val\|420 975 1179 1453 1554 1784 1900}}]		\|style="border-top: double;" \|[{{val\|420 975 1179 1453 1554 1784 1900}}]
	\|0.069		\|style="border-top: double;" \|0.069
	\|0.104		\|style="border-top: double;" \|0.104
	\|3.62		\|style="border-top: double;" \|3.62
	\|}		\|}

Eliora: /* Regular temperament properties */ added subgroup at which 420edo is best at

2023-05-25T14:23:08Z

Regular temperament properties: added subgroup at which 420edo is best at

← Older revision		Revision as of 14:23, 25 May 2023
Line 33:		Line 33:
	\| 0.278		\| 0.278
	\| 9.74		\| 9.74
			\|-
			\|2.5.7.11.13.19.23
			\|875/874, 5635/5632, 10241/10240, 12103/12100, 11875/11858, 10985/10976
			\|[{{val\|420 975 1179 1453 1554 1784 1900}}]
			\|0.069
			\|0.104
			\|3.62
	\|}		\|}

Eliora: /* Theory */ elaborate

2023-05-25T14:19:19Z

Theory: elaborate

← Older revision		Revision as of 14:19, 25 May 2023
Line 5:		Line 5:
	420edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning of [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] as [[140edo]]. The [[13/1\|13th]] [[harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1\|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only 11 and 17 have step correspondences coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups.		420edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning of [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] as [[140edo]]. The [[13/1\|13th]] [[harmonic]] is also present in 140edo, and ultimately derives from [[10edo]]. The [[29/1\|29th harmonic]], while having significantly drifted in terms of [[relative interval error]], has retained its step position from [[7edo]]. In addition, in the 29-limit, only 11 and 17 have step correspondences coprime with 420. This means that all other approximations are preserved from smaller edos, thus enabling edo mergers and mashups.

	420edo is ~~better~~ at the 2.5.7.11.13.19.23 [[subgroup]], and works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].		420edo is good at the 2.5.7.11.13.19.23 [[subgroup]], and has a great potential as a near-just xenharmonic system. It also works satisfactorily with the 29-limit as a whole, though in[[consistent]]. In the 11-limit, it notably tempers out [[4000/3993]], and in the 13-limit, [[10648/10647]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	420 is a largely composite number, being divisible by {{EDOs\| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210 }}. For this reason 420edo is rich in modulation circles.		420 is a largely composite number, being divisible by {{EDOs\| 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, and 210 }}. For this reason 420edo is rich in modulation circles.

	== Trivia ==		== Trivia ==

FloraC: Ez comma basis

2023-05-15T06:38:21Z

Ez comma basis

@@ Line 15: / Line 15: @@
 == Trivia ==
 The approximation to the third harmonic, which derives from 70edo, constitutes 666 steps of 420edo. Nice.
 == Music ==
 ; [[Mandrake]]
-* ''[https://www.youtube.com/watch?v=X1deLLCJD64 Follow In Is]'' - a superset of [[12edo]], [[5edo]], and [[7edo]], least common multiple of which is 420edo.
+* ''[https://www.youtube.com/watch?v=X1deLLCJD64 Follow In Is]'' – a superset of [[12edo]], [[5edo]], and [[7edo]], least common multiple of which is 420edo.