1517edo - Revision history

ArrowHead294 at 23:13, 20 February 2025

2025-02-20T23:13:34Z

← Older revision		Revision as of 23:13, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1517~~}}		{{ED intro}}

	1517edo is only [[consistent]] to the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are quite large. To start with, we may consider the [[patent val]] and 1517d [[val]] up to the 11-limit. Otherwise, it has a reasonable approximation to the 2.9.15.7.11.17 [[subgroup]] with optional additions of either [[13/1\|13]] or [[19/1\|19]].		1517edo is only [[consistent]] to the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are quite large. To start with, we may consider the [[patent val]] and 1517d [[val]] up to the 11-limit. Otherwise, it has a reasonable approximation to the 2.9.15.7.11.17 [[subgroup]] with optional additions of either [[13/1\|13]] or [[19/1\|19]].

FloraC: Rework theory; adopt template: Factorization

2023-10-31T09:04:40Z

Rework theory; adopt template: Factorization

← Older revision		Revision as of 09:04, 31 October 2023
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	{{EDO intro\|1517}}		{{EDO intro\|1517}}

	1517edo is a [[~~dual~~-~~fifth system~~]] with a [[~~consistency~~\|~~consistency limit~~]] ~~of only 5~~.		1517edo is only [[consistent]] to the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are quite large. To start with, we may consider the [[patent val]] and 1517d [[val]] up to the 11-limit. Otherwise, it has a reasonable approximation to the 2.9.15.7.11.17 [[subgroup]] with optional additions of either [[13/1\|13]] or [[19/1\|19]].

	~~The~~ first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 [[subgroup]], 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{monzo\| 18 -12 2 1 1 0 }}, {{monzo\| 44 -4 -9 1 0 -1 }}}.		For higher harmonics, the first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 [[subgroup]], 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{monzo\| 18 -12 2 1 1 0 }}, {{monzo\| 44 -4 -9 1 0 -1 }}}.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1517}}		{{Harmonics in equal\|1517}}

			=== Subsets and supersets ===
			Since 1517 factors into {{factorization\|1517}}, 1517edo contains [[37edo]] and [[41edo]] as subsets.

FloraC: Adopt template: EDO intro; cleanup; -redundant categories

2023-10-17T07:44:03Z

Adopt template: EDO intro; cleanup; -redundant categories

← Older revision		Revision as of 07:44, 17 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~1517 equal divisions of the octave''', or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.		{{EDO intro\|1517}}

	~~== Theory ==~~		1517edo is a [[dual-fifth system]] with a [[consistency\|consistency limit]] of only 5.

	~~1517edo is a dual fifths system with a consistency limit of only 5.~~		The first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 [[subgroup]], 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{monzo\| 18 -12 2 1 1 0 }}, {{monzo\| 44 -4 -9 1 0 -1 }}}.

	The first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 subgroup, 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{~~Monzo~~\|18 -12 2 1 1 0}}, {{monzo\|44 -4 -9 1 0 -1}}}.

			=== Odd harmonics ===
	{{Harmonics in equal\|1517}}		{{Harmonics in equal\|1517}}

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

BudjarnLambeth at 06:54, 9 July 2023

2023-07-09T06:54:31Z

← Older revision		Revision as of 06:54, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''1517 equal divisions of the octave''', or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.		The '''1517 equal divisions of the octave''', or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.

BudjarnLambeth at 05:07, 9 July 2023

2023-07-09T05:07:58Z

← Older revision		Revision as of 05:07, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	The '''1517 equal divisions of the octave''', or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.		The '''1517 equal divisions of the octave''', or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.

Eliora at 14:40, 22 December 2022

2022-12-22T14:40:10Z

← Older revision		Revision as of 14:40, 22 December 2022
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	== Theory ==		== Theory ==

	1517edo~~, despite its size,~~ is a dual fifths system with a consistency limit of only 5.		1517edo is a dual fifths system with a consistency limit of only 5.

			The first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 subgroup, 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{Monzo\|18 -12 2 1 1 0}}, {{monzo\|44 -4 -9 1 0 -1}}}.

	{{Harmonics in equal\|1517}}		{{Harmonics in equal\|1517}}

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

Aura at 14:26, 8 December 2022

2022-12-08T14:26:33Z

← Older revision		Revision as of 14:26, 8 December 2022
Line 6:		Line 6:
	1517edo, despite its size, is a dual fifths system with a consistency limit of only 5.		1517edo, despite its size, is a dual fifths system with a consistency limit of only 5.

	[[Category:Equal divisions of the octave\|####]]		{{Harmonics in equal\|1517}}
	<!-- 4-digit number -->
			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Aura: I was curious, so I created this article, it needs cleanup though...

2022-12-08T14:25:02Z

I was curious, so I created this article, it needs cleanup though...

New page

{{Infobox ET}}
The '''1517 equal divisions of the octave''', or the 1517-tone equal temperament (1517tet), 1517 equal temperament (1517et) when viewed from a regular temperament perspective, divides the octave into 1517 equal parts of about 0.791 cents each.

== Theory ==

1517edo, despite its size, is a dual fifths system with a consistency limit of only 5.

[[Category:Equal divisions of the octave|####]]

← Older revision		Revision as of 09:04, 31 October 2023
Line 2:		Line 2:
	{{EDO intro\|1517}}		{{EDO intro\|1517}}

	1517edo is a [[~~dual~~-~~fifth system~~]] with a [[~~consistency~~\|~~consistency limit~~]] ~~of only 5~~.		1517edo is only [[consistent]] to the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are quite large. To start with, we may consider the [[patent val]] and 1517d [[val]] up to the 11-limit. Otherwise, it has a reasonable approximation to the 2.9.15.7.11.17 [[subgroup]] with optional additions of either [[13/1\|13]] or [[19/1\|19]].

	~~The~~ first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 [[subgroup]], 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{monzo\| 18 -12 2 1 1 0 }}, {{monzo\| 44 -4 -9 1 0 -1 }}}.		For higher harmonics, the first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 [[subgroup]], 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, {{monzo\| 18 -12 2 1 1 0 }}, {{monzo\| 44 -4 -9 1 0 -1 }}}.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1517}}		{{Harmonics in equal\|1517}}

			=== Subsets and supersets ===
			Since 1517 factors into {{factorization\|1517}}, 1517edo contains [[37edo]] and [[41edo]] as subsets.