940edo - Revision history

ArrowHead294 at 16:23, 20 February 2025

2025-02-20T16:23:54Z

← Older revision		Revision as of 16:23, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|940~~}}		{{ED intro}}

	940edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.		940edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:25:32Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:25, 2 November 2023
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	{{EDO intro\|940}}		{{EDO intro\|940}}

	940edo is ~~distinctly~~ [[consistent]] through the [[11-odd-limit]], tempering out [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.		940edo is [[consistency\|distinctly consistent]] through the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.

	The non-patent val {{val\| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363.		The non-patent val {{val\| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	940edo has subset edos {{EDOs\| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which [[94edo]] is notable.		Since 940 factors into {{factorization\|940}}, 940edo has subset edos {{EDOs\| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which 94edo is notable.

	[[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.		[[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.

BudjarnLambeth at 06:47, 9 July 2023

2023-07-09T06:47:52Z

← Older revision		Revision as of 06:47, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|940}}		{{EDO intro\|940}}

BudjarnLambeth at 05:27, 9 July 2023

2023-07-09T05:27:19Z

← Older revision		Revision as of 05:27, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|940}}		{{EDO intro\|940}}

FloraC: Cleanup; linking; rework on some assessments

2023-05-10T08:47:26Z

Cleanup; linking; rework on some assessments

← Older revision		Revision as of 08:47, 10 May 2023
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	{{EDO intro\|940}}		{{EDO intro\|940}}

	940edo is ~~uniquely~~ [[~~consistent\|~~consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[~~Breedsmic_temperaments#Decoid\|~~decoid ~~temperament~~]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[~~Optimal_patent_val\|~~optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[~~The_Archipelago#Rank tree temperaments\|~~greenland]] and [[~~The_Archipelago#Rank tree temperaments\|~~baffin]] temperaments, and for the rank ~~five temperament~~ temperament tempering out 676/675.		940edo is distinctly [[consistent]] through the [[11-odd-limit]], tempering out [[2401/2400]] in the 7-limit and [[5632/5625]] and [[9801/9800]] in the 11-limit, which means it [[support]]s [[decoid]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]] and [[4225/4224]], so that it supports and gives the [[optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for the [[greenland]] and [[baffin]] temperaments, and for the rank-5 temperament tempering out 676/675.

	The non-patent val {{val\|940 1491 2184 2638 3254 3481}} gives a tuning almost identical to the POTE tuning for the 13-limit [[~~Hemifamity_family#Pele\|~~pele ~~temperament~~]] tempering out 196/195, 352/351 and 364/363.		The non-patent val {{val\| 940 1491 2184 2638 3254 3481 }} gives a tuning almost identical to the [[POTE tuning]] for the 13-limit [[pele]] temperament, tempering out 196/195, 352/351 and 364/363.

			In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location.

	In higher limits, it is a satisfactory no-13s 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to 940edo's theory in 5-prime-limit where it has good 3/2 and 5/4, but 15/8 is one step off from the "expected" location.
	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|940}}		{{Harmonics in equal\|940}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	940edo has subset edos {{EDOs\|1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470}}, of which [[94edo]] is notable.		940edo has subset edos {{EDOs\| 2, 4, 5, 10, 20, 47, 94, 188, 235, 470 }}, of which [[94edo]] is notable.

	[[1880edo]], which doubles 940edo, provides good correction for harmonics 13 ~~and 15 and uses a new mapping for 5 which consistently leads~~ to ~~15.~~		[[1880edo]], which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.
	~~[[Category:Equal divisions~~ of the ~~octave\|###]] <!~~-- ~~3-digit number -->~~

Eliora: oops

2023-05-09T15:39:57Z

oops

← Older revision		Revision as of 15:39, 9 May 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|94}}		{{EDO intro\|940}}

	940edo is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675.		940edo is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675.

Eliora: style

2023-05-09T15:39:46Z

style

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''940 equal division''' divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments|greenland]] and [[The_Archipelago#Rank tree temperaments|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val &lt;940 1491 2184 2638 3254 3481| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele|pele temperament]] tempering out 196/195, 352/351 and 364/363.
+{{EDO intro|94}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T22:04:52Z

Infobox ET added

← Older revision		Revision as of 22:04, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The '''940 equal division''' divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val <940 1491 2184 2638 3254 3481\| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele\|pele temperament]] tempering out 196/195, 352/351 and 364/363.		The '''940 equal division''' divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val <940 1491 2184 2638 3254 3481\| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele\|pele temperament]] tempering out 196/195, 352/351 and 364/363.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Fredg999 category edits: Categories

2022-07-04T01:08:14Z

Cmloegcmluin: link to new page for Supports

2022-01-25T17:52:40Z

link to new page for Supports

← Older revision		Revision as of 17:52, 25 January 2022
Line 1:		Line 1:
	The ''940 equal division'' divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it ~~supports~~ [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val <940 1491 2184 2638 3254 3481\| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele\|pele temperament]] tempering out 196/195, 352/351 and 364/363.		The ''940 equal division'' divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val <940 1491 2184 2638 3254 3481\| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele\|pele temperament]] tempering out 196/195, 352/351 and 364/363.

← Older revision		Revision as of 01:08, 4 July 2022
Line 1:		Line 1:
	The ''940 equal division'' divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val <940 1491 2184 2638 3254 3481\| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele\|pele temperament]] tempering out 196/195, 352/351 and 364/363.		The '''940 equal division''' divides the octave into 940 equal parts of 1.277 cents each. It is uniquely [[consistent\|consistent]] through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it [[support]]s [[Breedsmic_temperaments#Decoid\|decoid temperament]] and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the [[Optimal_patent_val\|optimal patent val]] for 13-limit decoid. It also gives the optimal patent val for [[The_Archipelago#Rank tree temperaments\|greenland]] and [[The_Archipelago#Rank tree temperaments\|baffin]] temperaments, and for the rank five temperament temperament tempering out 676/675. The non-patent val <940 1491 2184 2638 3254 3481\| gives a tuning almost identical to the POTE tuning for the 13-limit [[Hemifamity_family#Pele\|pele temperament]] tempering out 196/195, 352/351 and 364/363.

			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->