4172edo - Revision history

ArrowHead294 at 18:04, 20 February 2025

2025-02-20T18:04:40Z

← Older revision		Revision as of 18:04, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}
	==Theory==		== Theory ==
	The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament.		The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament.

Francium: changed EDO intro to ED intro

2025-02-20T06:51:20Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:51, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|4172~~}}		{{ED intro}}
	==Theory==		==Theory==
	The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament.		The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament.

BudjarnLambeth: {{todo|inline=1|explain its xenharmonic value}}

2025-01-04T00:16:19Z

← Older revision		Revision as of 00:16, 4 January 2025
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	[[Category:Equal divisions of the octave\|####]]		[[Category:Equal divisions of the octave\|####]]


			{{todo\|inline=1\|explain its xenharmonic value}}

BudjarnLambeth at 07:06, 9 July 2023

2023-07-09T07:06:42Z

← Older revision		Revision as of 07:06, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|4172}}		{{EDO intro\|4172}}
	==Theory==		==Theory==

BudjarnLambeth at 04:26, 9 July 2023

2023-07-09T04:26:47Z

← Older revision		Revision as of 04:26, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|4172}}		{{EDO intro\|4172}}
	==Theory==		==Theory==

Eliora: /* Theory */

2023-06-15T12:03:08Z

Theory

← Older revision		Revision as of 12:03, 15 June 2023
Line 2:		Line 2:
	{{EDO intro\|4172}}		{{EDO intro\|4172}}
	==Theory==		==Theory==
	The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament~~, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error)~~.		The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament.

	4172's divisors are {{EDOs\|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit~~. Therefore from a logarithmic pitch or highly composite EDO theory perspective~~, ~~4172edo can be thought of as a compound~~ of ~~28 149edos interlocked together~~.		=== Subsets and supersets ===
			4172's divisors are {{EDOs\|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit, although its approximations have long been diluted by edo of this size.

	=== Odd harmonics ===		=== Odd harmonics ===

Eliora: /* Harmonics */ oops

2023-01-18T00:01:53Z

Harmonics: oops

← Older revision		Revision as of 00:01, 18 January 2023
Line 6:		Line 6:
	4172's divisors are {{EDOs\|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.		4172's divisors are {{EDOs\|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.

	=== ~~Harmonics~~ ===		=== Odd harmonics ===
	{{~~Odd~~ harmonics in equal\|4172}}		{{harmonics in equal\|4172}}
	<!-- 4-digit number -->		<!-- 4-digit number -->

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

Eliora at 00:01, 18 January 2023

2023-01-18T00:01:34Z

← Older revision		Revision as of 00:01, 18 January 2023
Line 2:		Line 2:
	{{EDO intro\|4172}}		{{EDO intro\|4172}}
	==Theory==		==Theory==
	~~{{Harmonics in equal\|4172}}~~

	The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error).		The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error).

	4172's divisors are {{EDOs\|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.		4172's divisors are {{EDOs\|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.

			=== Harmonics ===
			{{Odd harmonics in equal\|4172}}
	<!-- 4-digit number -->		<!-- 4-digit number -->

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

Plumtree: Infobox ET added

2022-10-04T22:17:45Z

Infobox ET added

← Older revision		Revision as of 22:17, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	{{EDO intro\|4172}}		{{EDO intro\|4172}}
	==Theory==		==Theory==

Eliora: Created page with "{{EDO intro|4172}} ==Theory== {{Harmonics in equal|4172}} The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought..."

2022-09-28T18:08:53Z

Created page with "{{EDO intro|4172}} ==Theory== {{Harmonics in equal|4172}} The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought..."

New page

{{EDO intro|4172}}
==Theory==
{{Harmonics in equal|4172}}

The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error).

4172's divisors are {{EDOs|1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086}}. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.


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