6000000edo - Revision history

FloraC: - category

2025-06-03T11:07:21Z

- category

← Older revision		Revision as of 11:07, 3 June 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	6'000'000 factorizes as 2<sup>7</sup> × 3 × 5<sup>6</sup>. It has 112 divisors, most notable being {{EDOs\|128 and 3125}}.		6'000'000 factorizes as 2<sup>7</sup> × 3 × 5<sup>6</sup>. It has 112 divisors, most notable being {{EDOs\|128 and 3125}}.

	~~[[Category:Extreme]]~~

FloraC: Linking and misc. improvements

2024-11-23T05:53:09Z

Linking and misc. improvements

← Older revision		Revision as of 05:53, 23 November 2024
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	{{Novelty}}		{{Novelty}}
	{{Infobox ET}}		{{Infobox ET}}
	The '''6 million equal divisions of the octave,''' or '''literal microtonal system''', divides the ~~2/1~~ into steps of exactly 0.0002 cent, or 200 microcents each.		The '''6 million equal divisions of the octave,''' or '''literal microtonal system''', divides the [[octave]] into steps of exactly 0.0002 cent, or 200 microcents each.

	While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[~~Microtonal~~\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable.		While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[microtone (interval size measure)\|''microtonal'']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the {{w\|metric prefix\|SI prefix}} "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get approximately 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable.

	If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes. In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.		If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes. In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.

FloraC: Cleanup (2/2)

2024-11-23T05:48:37Z

Cleanup (2/2)

← Older revision		Revision as of 05:48, 23 November 2024
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	While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable.		While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable.

	~~== Theory ==~~		If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes. In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.

	If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes.		Remarkably, it has a perfect fifth that differs from just by 1 part in 231, which ultimately derives from [[80000edo]]. In a twist of irony, it provides good approximations for the 2.3.17.19 [[subgroup]], which is typically associated with [[12edo]].

	~~In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.~~

	Remarkably, it has a perfect fifth that differs from just by 1 part in 231, which ultimately derives from [[80000edo]].

	In a twist of irony, it provides good approximations for the 2.3.17.19 [[subgroup]], which is typically associated with [[12edo]].

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Cleanup (1/)

2024-11-23T05:47:13Z

Cleanup (1/)

← Older revision		Revision as of 05:47, 23 November 2024
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	{{~~novelty~~}}		{{Novelty}}
	{{Infobox ET}}		{{Infobox ET}}
	The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 ~~microcent~~ each.		The '''6 million equal divisions of the octave,''' or '''literal microtonal system''', divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcents each.

	While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable. ~~(The factorization of 11769898 is 2 * 7<sup>2</sup> * 83 * 1447.)~~		While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable.

	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|6000000}}~~
	~~6'000'000 factorizes as <math>2^7 \cdot 3 \cdot 5^6</math>. It has 112 divisors, most notable being {{EDOs\|128 and 3125}}.~~

	If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes.		If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes.

	In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' mean free path's width.		In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.

			Remarkably, it has a perfect fifth that differs from just by 1 part in 231, which ultimately derives from [[80000edo]].

			In a twist of irony, it provides good approximations for the 2.3.17.19 [[subgroup]], which is typically associated with [[12edo]].

	~~Remarkably, it has a perfect fifth that differs from just by 1 part~~ in ~~231, which ultimately derives from 80000edo.~~		=== Prime harmonics ===
			{{Harmonics in equal\|6000000}}

	~~In a twist of irony, it proveds good approximations for the~~ 2.3.~~17.19 subgroup~~, ~~which is typically associated with [[12edo]]~~.		=== Subsets and supersets ===
			6'000'000 factorizes as 2<sup>7</sup> × 3 × 5<sup>6</sup>. It has 112 divisors, most notable being {{EDOs\|128 and 3125}}.

	~~[[Category:Equal divisions of the octave\|#######]] <!-- 7-digit number -->~~
	[[Category:Extreme]]		[[Category:Extreme]]

Godtone at 21:06, 22 November 2024

2024-11-22T21:06:21Z

← Older revision		Revision as of 21:06, 22 November 2024
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	While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable. (The factorization of 11769898 is 2 * 7<sup>2</sup> * 83 * 1447.)		While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable. (The factorization of 11769898 is 2 * 7<sup>2</sup> * 83 * 1447.)

	~~This title can be contested by 1000000ed9/8, approx. 5884949edo, if a "tone" is defined to be a just [[9/8]] interval instead of an octave fraction.~~

	== Theory ==		== Theory ==

Godtone at 21:05, 22 November 2024

2024-11-22T21:05:28Z

← Older revision		Revision as of 21:05, 22 November 2024
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	The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.		The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.

	While this system is absurdly large for any human application, from a technical standpoint it is the ~~only one~~ that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts.		While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal\|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable. (The factorization of 11769898 is 2 * 7<sup>2</sup> * 83 * 1447.)

	This title can be contested by 1000000ed9/8, approx. 5884949edo, if a "tone" is defined to be a just [[9/8]] interval instead of an octave fraction.		This title can be contested by 1000000ed9/8, approx. 5884949edo, if a "tone" is defined to be a just [[9/8]] interval instead of an octave fraction.

CellularAutomaton at 12:30, 9 July 2023

2023-07-09T12:30:28Z

← Older revision		Revision as of 12:30, 9 July 2023
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			{{novelty}}
	{{Infobox ET}}		{{Infobox ET}}
	The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.		The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.

BudjarnLambeth at 07:22, 9 July 2023

2023-07-09T07:22:12Z

← Older revision		Revision as of 07:22, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.		The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.

BudjarnLambeth: Adding novelty and stub tags to Edo pages where appropriate (will mark the rest of these edits as minor)

2023-07-09T03:56:26Z

Adding novelty and stub tags to Edo pages where appropriate (will mark the rest of these edits as minor)

← Older revision		Revision as of 03:56, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.		The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.

Plumtree: Infobox ET added

2022-10-04T22:32:16Z

Infobox ET added

← Older revision		Revision as of 22:32, 4 October 2022
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			{{Infobox ET}}
	The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.		The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.