1984edo - Revision history

Overthink: Some improvements (This page was clearly biased toward 2.3.5.7.11.17 and direct approximations)

2025-12-19T01:14:03Z

Some improvements (This page was clearly biased toward 2.3.5.7.11.17 and direct approximations)

← Older revision		Revision as of 01:14, 19 December 2025
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	{{ED intro}}		{{ED intro}}

	1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[~~3/1\|3]], [[5~~/1\|5]]~~, [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all~~ tuned sharp. ~~Harmonics~~ 9 ~~and~~ 15, ~~though~~, ~~are tuned~~ flat, which results in [[consistency\|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and {{nowrap\|3145 + 3145 {{=}} 6290}}, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and {{nowrap\|3145 + 4607 {{=}} 7752}}, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.		1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with all primes up to [[23/1\|23]] tuned sharp. However, harmonics 9, 15, and 21 are more than 50% of a step sharp by patent val, and flat by direct approximation, which results in [[consistency\|inconsistencies]]; that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and {{nowrap\|3145 + 3145 {{=}} 6290}}, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and {{nowrap\|3145 + 4607 {{=}} 7752}}, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.

	In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).		In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).

ArrowHead294 at 12:49, 21 February 2025

2025-02-21T12:49:53Z

← Older revision		Revision as of 12:49, 21 February 2025
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	{{ED intro}}		{{ED intro}}

	1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[consistency\|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and 3145 + 3145 = 6290, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and 3145 + 4607 = 7752, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.		1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[consistency\|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and {{nowrap\|3145 + 3145 {{=}} 6290}}, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and {{nowrap\|3145 + 4607 {{=}} 7752}}, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.

	In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).		In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).

Francium: changed EDO intro to ED intro

2025-02-21T05:59:52Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:59, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1984~~}}		{{ED intro}}

	1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[consistency\|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and 3145 + 3145 = 6290, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and 3145 + 4607 = 7752, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.		1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[consistency\|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and 3145 + 3145 = 6290, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and 3145 + 4607 = 7752, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.

FloraC: Fix links (one being wrong way around and the other linked to the plural)

2024-05-26T08:14:35Z

Fix links (one being wrong way around and the other linked to the plural)

← Older revision		Revision as of 08:14, 26 May 2024
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	{{EDO intro\|1984}}		{{EDO intro\|1984}}

	1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[inconsistencies~~\|consistency~~]], that is, their [[direct ~~approximations~~]] are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and 3145 + 3145 = 6290, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and 3145 + 4607 = 7752, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.		1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[consistency\|inconsistencies]], that is, their [[direct approximation]]s are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and 3145 + 3145 = 6290, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and 3145 + 4607 = 7752, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.

	In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).		In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).

Cmloegcmluin at 01:51, 25 May 2024

2024-05-25T01:51:39Z

← Older revision		Revision as of 01:51, 25 May 2024
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	{{EDO intro\|1984}}		{{EDO intro\|1984}}

	1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. ~~Though, the harmonics~~ 9 and 15 are tuned flat ~~and~~ in ~~consistent mapping they are one step off~~ their [[direct ~~approximation~~]]. ~~In higher limit~~, ~~1984edo approximates well~~ the 2.9.19.31.33 [[subgroup]].		1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Harmonics 9 and 15, though, are tuned flat, which results in [[inconsistencies\|consistency]], that is, their [[direct approximations]] are not the same as the sum of their constituent odd harmonics' direct approximations: 9/1 is 6289 steps while 3/1 is 3145 steps (and 3145 + 3145 = 6290, ≠ 6289), and 15/1 is 7751 steps while 5/1 is 4607 steps (and 3145 + 4607 = 7752, ≠ 7751). 1984edo does, however, approximate the 2.9.19.31.33 [[subgroup]] well.

	In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).		In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).

FloraC: +subsets and supersets

2024-05-24T07:59:52Z

+subsets and supersets

← Older revision		Revision as of 07:59, 24 May 2024
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	{{EDO intro\|1984}}		{{EDO intro\|1984}}

	1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and in consistent mapping they are one step off their [[direct approximation]]. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.		1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and in consistent mapping they are one step off their [[direct approximation]]. In higher limit, 1984edo approximates well the 2.9.19.31.33 [[subgroup]].

	In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).		In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1984}}		{{Harmonics in equal\|1984}}

			=== Subsets and supersets ===
			Since 1984 factors into {{factorization\|1984}}, 1984edo has subset edos {{EDOs\| 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, and 992 }}.

FloraC: Improve linking and style; misc. cleanup

2024-05-24T07:58:09Z

Improve linking and style; misc. cleanup

← Older revision		Revision as of 07:58, 24 May 2024
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	{{EDO intro\|1984}}		{{EDO intro\|1984}}

	1984edo is consistent in the [[7-odd-limit]] and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and in consistent mapping they are one step off their direct ~~mapping~~. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.		1984edo is [[consistent]] in the [[7-odd-limit]] and is a mostly sharp system, with [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[17/1\|17]] all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and in consistent mapping they are one step off their [[direct approximation]]. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.

			In the 7-limit the equal temperament [[tempering out\|tempers out]] the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).

	~~In the 7-limit it tempers out the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).~~
	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|1984}}		{{Harmonics in equal\|1984}}

Eliora at 15:50, 1 November 2023

2023-11-01T15:50:06Z

← Older revision		Revision as of 15:50, 1 November 2023
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	{{EDO intro\|1984}}		{{EDO intro\|1984}}

	1984edo is consistent in the [[7-odd-limit]] and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and are one step off their ~~combined steps, which limits the edo's consistency~~. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.		1984edo is consistent in the [[7-odd-limit]] and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and in consistent mapping they are one step off their direct mapping. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.

	In the 7-limit it tempers out the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).		In the 7-limit it tempers out the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).
	=== Odd harmonics ===		=== Odd harmonics ===
	{{harmonics in equal\|1984}}		{{harmonics in equal\|1984}}

Eliora at 15:49, 1 November 2023

2023-11-01T15:49:18Z

← Older revision		Revision as of 15:49, 1 November 2023
Line 5:		Line 5:

	In the 7-limit it tempers out the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).		In the 7-limit it tempers out the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).
			=== Odd harmonics ===
	{{harmonics in equal\|1984~~\|columns=20~~}}		{{harmonics in equal\|1984}}

Eliora: Created page with "{{Infobox ET}} {{EDO intro|1984}} 1984edo is consistent in the 7-odd-limit and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonic..."

2023-11-01T15:48:55Z

Created page with "{{Infobox ET}} {{EDO intro|1984}} 1984edo is consistent in the 7-odd-limit and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonic..."

New page

{{Infobox ET}}
{{EDO intro|1984}}

1984edo is consistent in the [[7-odd-limit]] and it is a mostly sharp system, with 3, 5, 7, 11, and 17 all tuned sharp. Though, the harmonics 9 and 15 are tuned flat and are one step off their combined steps, which limits the edo's consistency. In higher limit, 1984edo approximates well the 2.9.19.31.33 subgroup.

In the 7-limit it tempers out the [[wizma]] (420175/419904), the [[garischisma]] (33554432/33480783), and the [[pessoalisma]] (2147483648/2144153025).

{{harmonics in equal|1984|columns=20}}