1793edo - Revision history

ArrowHead294 at 23:12, 20 February 2025

2025-02-20T23:12:43Z

← Older revision		Revision as of 23:12, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1793~~}}		{{ED intro}}

	1793edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. Nonetheless, it is a good 2.3.5.11.13.17 [[subgroup]] system, in which it has a [[comma basis]] [[4225/4224]], [[6656/6655]], 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.		1793edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. Nonetheless, it is a good 2.3.5.11.13.17 [[subgroup]] system, in which it has a [[comma basis]] [[4225/4224]], [[6656/6655]], 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.

FloraC: Rework theory; adopt template: Factorization

2023-10-30T12:54:22Z

Rework theory; adopt template: Factorization

← Older revision		Revision as of 12:54, 30 October 2023
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	{{EDO intro\|1793}}		{{EDO intro\|1793}}

	1793edo is a good 2.3.5.11.13.17 [[subgroup]] system, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.		1793edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. Nonetheless, it is a good 2.3.5.11.13.17 [[subgroup]] system, in which it has a [[comma basis]] [[4225/4224]], [[6656/6655]], 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.

	If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000. It provides the [[optimal patent val]] for the [[luminal]] temperament.		If a mapping for 7 is added, this gives two interpretations. First is the [[patent val]], which has a comma basis {[[2080/2079]], [[3025/3024]], 4225/4224, [[5832/5831]], 14875/14872, 108086/108085}. The 1793d val has a comma basis {[[1225/1224]], 8624/8619, [[12376/12375]], [[14400/14399]], 42500/42471, 29755593/29744000}. It provides the [[optimal patent val]] for the [[luminal]] temperament.

	1793edo tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo\| -176 23 -2 35 }}.		1793edo [[tempering out\|tempers out]] the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is {6656/6655, {{monzo\| -176 23 -2 35 }}}.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	1793edo ~~has~~ [[11edo]] and [[163edo]] as ~~its~~ subsets.		Since 1793 factors into {{factorization\|1793}}, 1793edo contains [[11edo]] and [[163edo]] as subsets.

FloraC: Cleanup; -redundant categories

2023-10-15T14:29:59Z

Cleanup; -redundant categories

← Older revision		Revision as of 14:29, 15 October 2023
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	{{EDO intro\|1793}}		{{EDO intro\|1793}}

	~~== Theory ==~~		1793edo is a good 2.3.5.11.13.17 [[subgroup]] system, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.
	1793edo is a good 2.3.5.11.13.17 subgroup system, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.

	If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000. It provides the optimal patent val for the [[luminal]] temperament.		If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000. It provides the [[optimal patent val]] for the [[luminal]] temperament.

	1793edo tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo\| -176 23 -2 35 }}.		1793edo tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo\| -176 23 -2 35 }}.

	~~1793edo has divisors {{EDOs\| 1, 11, 163 }}.~~

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1793\|columns=11}}		{{Harmonics in equal\|1793\|columns=11}}

	[[~~Category:Equal divisions of the octave\|####~~]] ~~<!-- four-digit number -->~~		=== Subsets and supersets ===
			1793edo has [[11edo]] and [[163edo]] as its subsets.

BudjarnLambeth at 06:57, 9 July 2023

2023-07-09T06:57:23Z

← Older revision		Revision as of 06:57, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1793}}		{{EDO intro\|1793}}

BudjarnLambeth at 04:52, 9 July 2023

2023-07-09T04:52:32Z

← Older revision		Revision as of 04:52, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1793}}		{{EDO intro\|1793}}

FloraC: "Naively consistent" isn't defined anywhere, replaced with a more reasonable statement. Misc cleanup

2022-11-08T15:24:14Z

"Naively consistent" isn't defined anywhere, replaced with a more reasonable statement. Misc cleanup

← Older revision		Revision as of 15:24, 8 November 2022
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1793}}		{{EDO intro\|1793}}
	==Theory==
	1793edo is ~~naively consistent in the~~ 2.3.5.11.13.17 subgroup, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.		== Theory ==
			1793edo is a good 2.3.5.11.13.17 subgroup system, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.

	If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000. It provides the optimal patent val for the [[luminal]] temperament.		If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000. It provides the optimal patent val for the [[luminal]] temperament.

	1793edo tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo\|-176 23 -2 35}}.		1793edo tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo\| -176 23 -2 35 }}.

			1793edo has divisors {{EDOs\| 1, 11, 163 }}.

			=== Odd harmonics ===
			{{Harmonics in equal\|1793\|columns=11}}

	~~1793edo has divisors {{EDOs\|1, 11, 163}}.~~		[[Category:Equal divisions of the octave\|####]] <!-- four-digit number -->
	~~===Odd harmonics===~~
	~~{{harmonics in equal\|1793}}~~
	[[Category:Equal divisions of the octave]]

Eliora at 00:57, 8 November 2022

2022-11-08T00:57:15Z

← Older revision		Revision as of 00:57, 8 November 2022
Line 4:		Line 4:
	1793edo is naively consistent in the 2.3.5.11.13.17 subgroup, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.		1793edo is naively consistent in the 2.3.5.11.13.17 subgroup, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.

	If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000.		If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000. It provides the optimal patent val for the [[luminal]] temperament.

	It tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo\|-176 23 -2 35}}.		1793edo tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo\|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo\|-176 23 -2 35}}.

	1793edo has divisors {{EDOs\|1, 11, 163}}.		1793edo has divisors {{EDOs\|1, 11, 163}}.

Eliora: Created page with "{{Infobox ET}} {{EDO intro|1793}} ==Theory== 1793edo is naively consistent in the 2.3.5.11.13.17 subgroup, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 478..."

2022-11-07T20:24:20Z

Created page with "{{Infobox ET}} {{EDO intro|1793}} ==Theory== 1793edo is naively consistent in the 2.3.5.11.13.17 subgroup, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 478..."

New page

{{Infobox ET}}
{{EDO intro|1793}}
==Theory==
1793edo is naively consistent in the 2.3.5.11.13.17 subgroup, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.

If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000.

It tempers out the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo|-176 23 -2 35}}.

1793edo has divisors {{EDOs|1, 11, 163}}.
===Odd harmonics===
{{harmonics in equal|1793}}
[[Category:Equal divisions of the octave]]