1553edo - Revision history

ArrowHead294 at 13:11, 21 February 2025

2025-02-21T13:11:52Z

← Older revision		Revision as of 13:11, 21 February 2025
Line 13:		Line 13:
	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
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	\| {{monzo\| 4923 -1553 }}		\| {{monzo\| 4923 -1553 }}
	\| {{mapping\| 1553 4923 }}		\| {{mapping\| 1553 4923 }}
	\| -0.0130		\| −0.0130
	\| 0.0130		\| 0.0130
	\| 1.68		\| 1.68
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	\| {{monzo\| 93 -33 5 }}, {{monzo\| -36 -26 51 }}		\| {{monzo\| 93 -33 5 }}, {{monzo\| -36 -26 51 }}
	\| {{mapping\| 1553 4923 3606 }}		\| {{mapping\| 1553 4923 3606 }}
	\| -0.0137		\| −0.0137
	\| 0.0106		\| 0.0106
	\| 1.38		\| 1.38
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	\| {{monzo\| -5 5 5 -8 }}, {{monzo\| 2 -10 14 -1 }}, {{monzo\| 37 1 -4 -11 }}		\| {{monzo\| -5 5 5 -8 }}, {{monzo\| 2 -10 14 -1 }}, {{monzo\| 37 1 -4 -11 }}
	\| {{mapping\| 1553 4923 3606 4360 }}		\| {{mapping\| 1553 4923 3606 4360 }}
	\| -0.0225		\| −0.0225
	\| 0.0178		\| 0.0178
	\| 2.31		\| 2.31
Line 46:		Line 47:
	\| 4096/4095, 140625/140608, 28829034/28824005, {{monzo\| 4 10 -9 0 -4 }}		\| 4096/4095, 140625/140608, 28829034/28824005, {{monzo\| 4 10 -9 0 -4 }}
	\| {{mapping\| 1553 4923 3606 4360 5372 }}		\| {{mapping\| 1553 4923 3606 4360 5372 }}
	\| -0.0271		\| −0.0271
	\| 0.0184		\| 0.0184
	\| 2.38		\| 2.38

Francium: changed EDO intro to ED intro

2025-02-21T05:39:31Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:39, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1553~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: +categories

2024-02-13T18:27:45Z

+categories

← Older revision		Revision as of 18:27, 13 February 2024
Line 52:		Line 52:

	== Music ==		== Music ==
	; [[~~User:Francium\|~~Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=gdxwRJSLyvw ''Stumbling Over Mystery''] (2023)		* [https://www.youtube.com/watch?v=gdxwRJSLyvw ''Stumbling Over Mystery''] (2023)

			[[Category:Listen]]

FloraC: Cleanup

2023-10-17T07:24:00Z

Cleanup

← Older revision		Revision as of 07:24, 17 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1553}}		{{EDO intro\|1553}}

	== Theory ==		== Theory ==
	1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608.		1553edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 10:		Line 11:
	1553edo is the 245th [[prime edo]]. 3106edo, which doubles it, provides a good correction to the harmonic 3.		1553edo is the 245th [[prime edo]]. 3106edo, which doubles it, provides a good correction to the harmonic 3.

	==Regular temperament properties==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
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	\| 2.9		\| 2.9
	\| {{monzo\| 4923 -1553 }}		\| {{monzo\| 4923 -1553 }}
	\| {{~~val~~\| 1553 4923 }}		\| {{mapping\| 1553 4923 }}
	\| -0.0130		\| -0.0130
	\| 0.0130		\| 0.0130
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	\| 2.9.5		\| 2.9.5
	\| {{monzo\| 93 -33 5 }}, {{monzo\| -36 -26 51 }}		\| {{monzo\| 93 -33 5 }}, {{monzo\| -36 -26 51 }}
	\| {{~~val~~\| 1553 4923 3606 }}		\| {{mapping\| 1553 4923 3606 }}
	\| -0.0137		\| -0.0137
	\| 0.0106		\| 0.0106
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	\| 2.9.5.7		\| 2.9.5.7
	\| {{monzo\| -5 5 5 -8 }}, {{monzo\| 2 -10 14 -1 }}, {{monzo\| 37 1 -4 -11 }}		\| {{monzo\| -5 5 5 -8 }}, {{monzo\| 2 -10 14 -1 }}, {{monzo\| 37 1 -4 -11 }}
	\| {{~~val~~\| 1553 4923 3606 4360 }}		\| {{mapping\| 1553 4923 3606 4360 }}
	\| -0.0225		\| -0.0225
	\| 0.0178		\| 0.0178
Line 44:		Line 45:
	\| 2.9.5.7.13		\| 2.9.5.7.13
	\| 4096/4095, 140625/140608, 28829034/28824005, {{monzo\| 4 10 -9 0 -4 }}		\| 4096/4095, 140625/140608, 28829034/28824005, {{monzo\| 4 10 -9 0 -4 }}
	\| {{~~val~~\| 1553 4923 3606 4360 5372 }}		\| {{mapping\| 1553 4923 3606 4360 5372 }}
	\| -0.0271		\| -0.0271
	\| 0.0184		\| 0.0184
	\| 2.38		\| 2.38
	\|}		\|}
	==Music==
	* [https://www.youtube.com/watch?v=gdxwRJSLyvw Stumbling Over Mystery] ~~by Francium~~		== Music ==
			; [[User:Francium\|Francium]]
			* [https://www.youtube.com/watch?v=gdxwRJSLyvw ''Stumbling Over Mystery''] (2023)

BudjarnLambeth at 06:55, 9 July 2023

2023-07-09T06:55:11Z

← Older revision		Revision as of 06:55, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1553}}		{{EDO intro\|1553}}
	== Theory ==		== Theory ==

BudjarnLambeth at 05:05, 9 July 2023

2023-07-09T05:05:42Z

← Older revision		Revision as of 05:05, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	{{EDO intro\|1553}}		{{EDO intro\|1553}}
	== Theory ==		== Theory ==

FloraC: /* Theory */ -typo

2023-04-25T05:22:30Z

Theory: -typo

← Older revision		Revision as of 05:22, 25 April 2023
Line 2:		Line 2:
	{{EDO intro\|1553}}		{{EDO intro\|1553}}
	== Theory ==		== Theory ==
	1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a ~~reason~~ approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608.		1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608.

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

Francium: Added music section

2023-04-24T10:12:33Z

Added music section

← Older revision		Revision as of 10:12, 24 April 2023
Line 49:		Line 49:
	\| 2.38		\| 2.38
	\|}		\|}
			==Music==
			* [https://www.youtube.com/watch?v=gdxwRJSLyvw Stumbling Over Mystery] by Francium

FloraC: /* Theory */ the prime subgroup doesn't look any useful. 2.9.5.7.13 arguably makes more sense

2023-04-18T04:41:55Z

Theory: the prime subgroup doesn't look any useful. 2.9.5.7.13 arguably makes more sense

← Older revision		Revision as of 04:41, 18 April 2023
Line 2:		Line 2:
	{{EDO intro\|1553}}		{{EDO intro\|1553}}
	== Theory ==		== Theory ==
	1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. ~~Assume~~ the [[~~patent val~~]], ~~1553et~~ tempers out ~~200120949~~/200000000 in the 7-limit; 102487/102400, 759375/758912, 2359296/2358125, and 369140625/369098752 in the 11-limit; 1716/1715, 40656/40625, 59535/59488, 105644/105625, 196625/196608, 200000/199927, 823875/823543, 8859375/8859136, 34034175/34027136, and ~~75000000~~/~~74942413, in the 13-limit~~.		1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reason approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608.

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

FloraC: /* Regular temperament properties */ rework as a dual-fifth temp

2023-04-18T04:39:49Z

Regular temperament properties: rework as a dual-fifth temp

← Older revision		Revision as of 04:39, 18 April 2023
Line 12:		Line 12:
	==Regular temperament properties==		==Regular temperament properties==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.9
	\|{{monzo\|-~~2461~~ 1553}}		\| {{monzo\| 4923 -1553 }}
	\|{{val\|1553 ~~2461~~}}		\| {{val\| 1553 4923 }}
	\| 0.~~1089~~		\| -0.0130
	\| 0.~~1089~~		\| 0.0130
	\| 14.09		\| 1.68
	\|-		\|-
	\|2.3.5		\| 2.9.5
	\|~~1224440064/1220703125~~, {{monzo\|-~~201 99 19~~}}		\| {{monzo\| 93 -33 5 }}, {{monzo\| -36 -26 51 }}
	\|{{val\|1553 ~~2461~~ 3606}}		\| {{val\| 1553 4923 3606 }}
	\| 0.~~0675~~		\| -0.0137
	\| 0.~~1064~~		\| 0.0106
	\| 13.77		\| 1.38
	\|-		\|-
	\|2.3.5.7		\| 2.9.5.7
	\|~~200120949/200000000~~, ~~2579890176/2573571875~~, ~~23066015625/23018340352~~		\| {{monzo\| -5 5 5 -8 }}, {{monzo\| 2 -10 14 -1 }}, {{monzo\| 37 1 -4 -11 }}
	\|{{val\|1553 ~~2461~~ 3606 4360}}		\| {{val\| 1553 4923 3606 4360 }}
	\| 0.~~0384~~		\| -0.0225
	\| 0.~~1051~~		\| 0.0178
	\| 13.60		\| 2.31
	\|-		\|-
	\|2.3.5.7.11		\| 2.9.5.7.13
	\|~~24057~~/~~24010~~, ~~759375~~/~~758912~~, ~~2359296~~/~~2358125~~, ~~992436543/991232000~~		\| 4096/4095, 140625/140608, 28829034/28824005, {{monzo\| 4 10 -9 0 -4 }}
	\|{{~~val\|1553 2461 3606 4360 5372}}~~		\| {{val\| 1553 4923 3606 4360 5372 }}
	\| 0~~.0529~~		\| -0.0271
	~~\| 0.0984~~		\| 0.0184
	~~\| 12.73~~		\| 2.38
	\|-
	~~\|2.3.5.7.11.13~~
	~~\|729/728, 1716/1715, 40656/40625, 196625/196608, 14085981/14080000~~
	~~\|{{val\|1553 2461 3606 4360 5372 5747~~}}
	~~\| 0.0366~~
	~~\| 0.0970~~
	~~\| 12.55~~
	\|-
	~~\|2.3.5.7.11.13.17~~
	~~\|729/728, 1716/1715, 1089/1088, 14400/14399, 27648/27625, 14085981/14080000~~
	\|{{val\|1553 ~~2461~~ 3606 4360 5372 ~~5747 6348~~}}
	\| 0.~~0267~~
	\| 0.~~0930~~
	~~\| 12.04~~
	\|-
	\|2.~~3.5.7.11.13.17.19~~
	~~\|729/728, 1716/1715, 1089/1088, 5985/5984, 4200/4199, 21888/21875, 287469/287375~~
	~~\|{{val\|1553 2461 3606 4360 5372 5747 6348 6597}}~~
	~~\| 0.0241~~
	~~\| 0.0872~~
	~~\| 11.29~~
	\|}		\|}