1955edo - Revision history

ArrowHead294 at 23:16, 20 February 2025

2025-02-20T23:16:08Z

← Older revision		Revision as of 23:16, 20 February 2025
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	1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.		1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.

	In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 {{monzo\| 80 -8 -13 1 }}, and 2.15.17.21 {{monzo\| 73 -15 4 -7 }}}. The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 ~~cents~~ per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo\| -101 -12 48 -11 }}}.		In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 {{monzo\| 80 -8 -13 1 }}, and 2.15.17.21 {{monzo\| 73 -15 4 -7 }}}. The {{nowrap\|1955 & 6003}} temperament in the 2.15.17.21 subgroup has only 0.000396{{c}} per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo\| -101 -12 48 -11 }}}.

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

ArrowHead294 at 23:15, 20 February 2025

2025-02-20T23:15:51Z

← Older revision		Revision as of 23:15, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1955~~}}		{{ED intro}}

	1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.		1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.

FloraC: Rework theory; adopt template: Factorization

2023-10-30T12:13:45Z

Rework theory; adopt template: Factorization

← Older revision		Revision as of 12:13, 30 October 2023
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	{{EDO intro\|1955}}		{{EDO intro\|1955}}

	1955edo ~~represents well~~ the 2.9.11~~.15~~.17~~.21~~ subgroup, with a comma basis {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.		1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.

	In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 {{monzo\|80 -8 -13 1}}, and 2.15.17.21 {{monzo\|73 -15 4 -7}}}.		In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 {{monzo\| 80 -8 -13 1 }}, and 2.15.17.21 {{monzo\| 73 -15 4 -7 }}}. The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 cents per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo\| -101 -12 48 -11 }}}.

	The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 cents per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo\|-101 -12 48 -11}}}.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1955 factors ~~as 5 x 17 x 23~~, 1955edo has ~~subsete~~ edos {{EDOs\| 5, 17, 23, 85, 115, 391 }}.		Since 1955 factors into {{factorization\|1955}}, 1955edo has subset edos {{EDOs\| 5, 17, 23, 85, 115, 391 }}.

FloraC: Cleanup

2023-10-15T14:00:12Z

Cleanup

← Older revision		Revision as of 14:00, 15 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1955}}		{{EDO intro\|1955}}

	~~== Theory ==~~
	~~{{Harmonics in equal\|1955}}~~

	1955edo represents well the 2.9.11.15.17.21 subgroup, with a comma basis {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.		1955edo represents well the 2.9.11.15.17.21 subgroup, with a comma basis {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.
Line 11:		Line 8:
	The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 cents per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo\|-101 -12 48 -11}}}.		The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 cents per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo\|-101 -12 48 -11}}}.

	=== ~~Miscellany~~ ===		=== Odd harmonics ===
			{{Harmonics in equal\|1955}}

	1955 factors as 5 x 17 x 23, ~~and~~ has ~~divisors~~ {{EDOs\|1, 5, 17, 23, 85, 115, 391}}.		=== Subsets and supersets ===
			Since 1955 factors as 5 x 17 x 23, 1955edo has subsete edos {{EDOs\| 5, 17, 23, 85, 115, 391 }}.

BudjarnLambeth at 06:59, 9 July 2023

2023-07-09T06:59:08Z

← Older revision		Revision as of 06:59, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1955}}		{{EDO intro\|1955}}

BudjarnLambeth at 04:48, 9 July 2023

2023-07-09T04:48:30Z

← Older revision		Revision as of 04:48, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1955}}		{{EDO intro\|1955}}

Eliora at 13:15, 4 January 2023

2023-01-04T13:15:05Z

@@ Line 1: / Line 1: @@
 {{EDO intro|1955}}
 == Theory ==
 {{Harmonics in equal|1955}}

Eliora: Created page with "{{EDO intro|1955}} == Theory == {{Harmonics in equal|1955}}"

2023-01-04T13:01:57Z

Created page with "{{EDO intro|1955}} == Theory == {{Harmonics in equal|1955}}"

New page

{{EDO intro|1955}}

== Theory ==
{{Harmonics in equal|1955}}