1001edo - Revision history

ArrowHead294 at 22:56, 20 February 2025

2025-02-20T22:56:18Z

← Older revision		Revision as of 22:56, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1001~~}}		{{ED intro}}

	1001edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], [[19/1\|19]], and [[23/1\|23]], making it suitable for a 2.9.7.11.13.19.23 [[subgroup]] interpretation, with an optional addition of either [[5/1\|5]], or [[15/1\|15]]. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832.		1001edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], [[19/1\|19]], and [[23/1\|23]], making it suitable for a 2.9.7.11.13.19.23 [[subgroup]] interpretation, with an optional addition of either [[5/1\|5]], or [[15/1\|15]]. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832.

FloraC: Rework theory; adopt template: Factorization

2023-10-31T11:03:35Z

Rework theory; adopt template: Factorization

← Older revision		Revision as of 11:03, 31 October 2023
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	{{EDO intro\|1001}}		{{EDO intro\|1001}}

	~~The best prime~~ [[~~subgroup~~]] for ~~1001edo is~~ 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the [[parakleisma]].		1001edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], [[19/1\|19]], and [[23/1\|23]], making it suitable for a 2.9.7.11.13.19.23 [[subgroup]] interpretation, with an optional addition of either [[5/1\|5]], or [[15/1\|15]]. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832.

			Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the [[parakleisma]].

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	1001 factorizes as ~~7 × 11 × 13~~, ~~and~~ has subset edos {{EDOs\| 7, 11, 13, 77, 91, and 143 }}.		Since 1001 factorizes as {{factorization\|1001}}, 1001edo has subset edos {{EDOs\| 7, 11, 13, 77, 91, and 143 }}.

FloraC: Style; formatting; -redundant categories

2023-10-19T15:39:57Z

Style; formatting; -redundant categories

← Older revision		Revision as of 15:39, 19 October 2023
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	{{EDO intro\|1001}}		{{EDO intro\|1001}}

	The best prime subgroup for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the [[parakleisma]].		The best prime [[subgroup]] for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the [[parakleisma]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|1001}}		{{Harmonics in equal\|1001}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	1001 factorizes as 7 x 11 x 13, and has subset ~~EDOs~~ {{EDOs\|7, 11, 13, 77, 91, and 143}}.		1001 factorizes as 7 × 11 × 13, and has subset edos {{EDOs\| 7, 11, 13, 77, 91, and 143 }}.
	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~

BudjarnLambeth at 06:49, 9 July 2023

2023-07-09T06:49:14Z

← Older revision		Revision as of 06:49, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1001}}		{{EDO intro\|1001}}

BudjarnLambeth at 05:24, 9 July 2023

2023-07-09T05:24:06Z

← Older revision		Revision as of 05:24, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1001}}		{{EDO intro\|1001}}

Eliora: cleanup

2023-03-14T22:28:31Z

cleanup

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''1001edo''' divides the octave into parts of 1.(19880) cents each.
+{{EDO intro|1001}}
 [[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->

Plumtree: Infobox ET added

2022-10-04T22:06:36Z

Infobox ET added

← Older revision		Revision as of 22:06, 4 October 2022
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			{{Infobox ET}}
	'''1001edo''' divides the octave into parts of 1.(19880) cents each.		'''1001edo''' divides the octave into parts of 1.(19880) cents each.

Fredg999 category edits: Categories

2022-07-04T01:10:28Z

Eliora at 15:49, 26 December 2021

2021-12-26T15:49:16Z

← Older revision		Revision as of 15:49, 26 December 2021
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	== Theory ==		== Theory ==
			{{primes in edo\|1001\|columns=15}}
	1001 factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It's composite divisors are 77, 91, and 143.		1001 factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It's composite divisors are 77, 91, and 143.

			The best prime subgroup for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775.

			Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520.

Eliora: Created page with "1001edo divides the octave into parts of 1.(19880) cents each. == Theory == 1001 factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It'..."

2021-12-26T15:43:15Z

Created page with "1001edo divides the octave into parts of 1.(19880) cents each. == Theory == 1001 factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It'..."

New page

1001edo divides the octave into parts of 1.(19880) cents each.

== Theory ==
1001 factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It's composite divisors are 77, 91, and 143.

← Older revision		Revision as of 01:10, 4 July 2022
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	1001edo divides the octave into parts of 1.(19880) cents each.		'''1001edo''' divides the octave into parts of 1.(19880) cents each.

	== Theory ==		== Theory ==
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	Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520.		Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520.

			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->