401edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:54Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
Line 77:		Line 77:
	\| [[Diatessic]]		\| [[Diatessic]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

Francium: changed EDO intro to ED intro

2025-02-21T06:13:59Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:13, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|401~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:59, 15 January 2025

2025-01-15T17:59:20Z

← Older revision		Revision as of 17:59, 15 January 2025
Line 5:		Line 5:
	401edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has a reasonable approximation to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation.		401edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has a reasonable approximation to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation.

	Using the [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] 283115520/282475249 and [[703125/702464]] in the 7-limit; 35156250/35153041, 2097152/2096325, 117649/117612, 226492416/226474325, 9765625/9732096, 42875/42768, 1375/1372, [[5632/5625]], 15488/15435, 202397184/201768035, 102487/102400 and 805255/802816 in the 11-limit. It provides the [[optimal patent val]] for [[diatessic]], the 140 & 261 temperament.		Using the [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] 283115520/282475249 and [[703125/702464]] in the 7-limit; 35156250/35153041, 2097152/2096325, 117649/117612, 226492416/226474325, 9765625/9732096, 42875/42768, 1375/1372, [[5632/5625]], 15488/15435, 202397184/201768035, 102487/102400 and 805255/802816 in the 11-limit. It provides the [[optimal patent val]] for [[diatessic]], the {{nowrap\|140 & 261}} temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 28:		Line 28:
	\| {{monzo\| 636 -401 }}		\| {{monzo\| 636 -401 }}
	\| {{mapping\| 401 636 }}		\| {{mapping\| 401 636 }}
	\| ~~−0~~.4060		\| −0.4060
	\| 0.4058		\| 0.4058
	\| 13.56		\| 13.56
Line 35:		Line 35:
	\| 15625/15552, {{monzo\| 107 -66 -1 }}		\| 15625/15552, {{monzo\| 107 -66 -1 }}
	\| {{mapping\| 401 636 931 }}		\| {{mapping\| 401 636 931 }}
	\| ~~−0~~.2307		\| −0.2307
	\| 0.4139		\| 0.4139
	\| 13.83		\| 13.83
Line 42:		Line 42:
	\| 10976/10935, 15625/15552, 67108864/66706983		\| 10976/10935, 15625/15552, 67108864/66706983
	\| {{mapping\| 401 636 931 1126 }}		\| {{mapping\| 401 636 931 1126 }}
	\| ~~−0~~.2400		\| −0.2400
	\| 0.3588		\| 0.3588
	\| 11.99		\| 11.99
Line 49:		Line 49:
	\| 2200/2187, 1375/1372, 5632/5625, 102487/102400		\| 2200/2187, 1375/1372, 5632/5625, 102487/102400
	\| {{mapping\| 401 636 931 1126 1387 }}		\| {{mapping\| 401 636 931 1126 1387 }}
	\| ~~−0~~.1518		\| −0.1518
	\| 0.3661		\| 0.3661
	\| 12.23		\| 12.23
Line 56:		Line 56:
	\| 325/324, 352/351, 625/624, 1375/1372, 3276800/3270267		\| 325/324, 352/351, 625/624, 1375/1372, 3276800/3270267
	\| {{mapping\| 401 636 931 1126 1387 1484 }}		\| {{mapping\| 401 636 931 1126 1387 1484 }}
	\| ~~−0~~.1431		\| −0.1431
	\| 0.3348		\| 0.3348
	\| 11.19		\| 11.19
Line 77:		Line 77:
	\| [[Diatessic]]		\| [[Diatessic]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==
Line 85:		Line 85:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) ~~–~~ diatessic in 403edo tuning		* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning

	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Diatessic]]		[[Category:Diatessic]]

ArrowHead294: Partial undo

2024-11-16T12:53:59Z

Partial undo

← Older revision		Revision as of 12:53, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 50:		Line 59:
	\| 0.3348		\| 0.3348
	\| 11.19		\| 11.19
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 60:		Line 76:
	\| 75/56		\| 75/56
	\| [[Diatessic]]		\| [[Diatessic]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

ArrowHead294 at 03:19, 16 November 2024

2024-11-16T03:19:59Z

← Older revision		Revision as of 03:19, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 636 -401 }}		\| {{monzo\| 636 -401 }}
	\| {{mapping\| 401 636 }}		\| {{mapping\| 401 636 }}
	\| -0.4060		\| −0.4060
	\| 0.4058		\| 0.4058
	\| 13.56		\| 13.56
Line 34:		Line 26:
	\| 15625/15552, {{monzo\| 107 -66 -1 }}		\| 15625/15552, {{monzo\| 107 -66 -1 }}
	\| {{mapping\| 401 636 931 }}		\| {{mapping\| 401 636 931 }}
	\| -0.2307		\| −0.2307
	\| 0.4139		\| 0.4139
	\| 13.83		\| 13.83
Line 41:		Line 33:
	\| 10976/10935, 15625/15552, 67108864/66706983		\| 10976/10935, 15625/15552, 67108864/66706983
	\| {{mapping\| 401 636 931 1126 }}		\| {{mapping\| 401 636 931 1126 }}
	\| -0.2400		\| −0.2400
	\| 0.3588		\| 0.3588
	\| 11.99		\| 11.99
Line 48:		Line 40:
	\| 2200/2187, 1375/1372, 5632/5625, 102487/102400		\| 2200/2187, 1375/1372, 5632/5625, 102487/102400
	\| {{mapping\| 401 636 931 1126 1387 }}		\| {{mapping\| 401 636 931 1126 1387 }}
	\| -0.1518		\| −0.1518
	\| 0.3661		\| 0.3661
	\| 12.23		\| 12.23
Line 55:		Line 47:
	\| 325/324, 352/351, 625/624, 1375/1372, 3276800/3270267		\| 325/324, 352/351, 625/624, 1375/1372, 3276800/3270267
	\| {{mapping\| 401 636 931 1126 1387 1484 }}		\| {{mapping\| 401 636 931 1126 1387 1484 }}
	\| -0.1431		\| −0.1431
	\| 0.3348		\| 0.3348
	\| 11.19		\| 11.19
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 74:		Line 60:
	\| 75/56		\| 75/56
	\| [[Diatessic]]		\| [[Diatessic]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Scales ==		== Scales ==
Line 83:		Line 69:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning		* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning

	[[Category:Listen]][[Category:Diatessic]]		[[Category:Listen]]
			[[Category:Diatessic]]

BudjarnLambeth at 01:34, 21 September 2024

2024-09-21T01:34:09Z

← Older revision		Revision as of 01:34, 21 September 2024
Line 85:		Line 85:
	* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning		* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning

	[[Category:Listen]]		[[Category:Listen]][[Category:Diatessic]]

Francium: +categories

2024-02-13T18:06:24Z

+categories

← Older revision		Revision as of 18:06, 13 February 2024
Line 82:		Line 82:

	== Music ==		== Music ==
	; [[~~User:Francium\|~~Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning		* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning

			[[Category:Listen]]

FloraC: Rework

2023-11-06T16:05:03Z

Rework

← Older revision		Revision as of 16:05, 6 November 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|401}} It is the ~~79th~~ [[~~prime edo~~]]		{{EDO intro\|401}}
	~~==Theory==~~
	~~401et~~ tempers out 283115520/282475249 and [[703125/702464]] in the 7-limit; 35156250/35153041, 2097152/2096325, 117649/117612, 226492416/226474325, 9765625/9732096, 42875/42768, 1375/1372, [[5632/5625]], 15488/15435, 202397184/201768035, 102487/102400 and 805255/802816 in the 11-limit.		== Theory ==
	It provides the optimal patent val for diatessic temperament.		401edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has a reasonable approximation to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], and [[13/1\|13]], making it suitable for a 2.9.5.7.11.13 [[subgroup]] interpretation.

			Using the [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] 283115520/282475249 and [[703125/702464]] in the 7-limit; 35156250/35153041, 2097152/2096325, 117649/117612, 226492416/226474325, 9765625/9732096, 42875/42768, 1375/1372, [[5632/5625]], 15488/15435, 202397184/201768035, 102487/102400 and 805255/802816 in the 11-limit. It provides the [[optimal patent val]] for [[diatessic]], the 140 & 261 temperament.

			=== Odd harmonics ===
	{{Harmonics in equal\|401}}		{{Harmonics in equal\|401}}
	==Regular temperament properties==
			=== Subsets and supersets ===
			401edo is the 79th [[prime edo]]

			== 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		\| 2.3
	\|{{monzo\| 636 -401 }}		\| {{monzo\| 636 -401 }}
	\|[{{~~val~~\| 401 636 }}]		\| {{mapping\| 401 636 }}
	\| -0.4060		\| -0.4060
	\|0.4058		\| 0.4058
	\|13.56		\| 13.56
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|15625/15552, {{monzo\| 107 -66 -1 }}		\| 15625/15552, {{monzo\| 107 -66 -1 }}
	\|[{{~~val~~\| 401 636 931}}]		\| {{mapping\| 401 636 931 }}
	\| -0.2307		\| -0.2307
	\|0.4139		\| 0.4139
	\|13.83		\| 13.83
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|10976/10935, 15625/15552, 67108864/66706983		\| 10976/10935, 15625/15552, 67108864/66706983
	\|[{{~~val~~\| 401 636 931 1126}}]		\| {{mapping\| 401 636 931 1126 }}
	\| -0.2400		\| -0.2400
	\|0.3588		\| 0.3588
	\|11.99		\| 11.99
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|2200/2187, 1375/1372, 5632/5625, 102487/102400		\| 2200/2187, 1375/1372, 5632/5625, 102487/102400
	\|[{{~~val~~\|401 636 931 1126 ~~1387~~}}]		\| {{mapping\| 401 636 931 1126 1387 }}
	\| -0.1518		\| -0.1518
	\|0.3661		\| 0.3661
	\|12.23		\| 12.23
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|325/324, 352/351, 625/624, 1375/1372, 3276800/3270267		\| 325/324, 352/351, 625/624, 1375/1372, 3276800/3270267
	\|[{{~~val~~\|401 636 931 1126 1387 1484}}]		\| {{mapping\| 401 636 931 1126 1387 1484 }}
	\| -0.1431		\| -0.1431
	\|0.3348		\| 0.3348
	\|11.19		\| 11.19
	\|}		\|}

Line 56:		Line 64:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|169\401		\| 169\401
	\|505.74		\| 505.74
	\|75/56		\| 75/56
	\|Diatessic		\| [[Diatessic]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Scales ==
			* [[Starlingtet11]]
			* [[Diatessic27]]

	==~~Scales~~==		== Music ==
	*[[~~Starlingtet11]]~~		; [[User:Francium\|Francium]]
	*[[Diatessic27]]		* [https://www.youtube.com/watch?v=hh-cgGe_zas ''Diana Tessa''] (2023) – diatessic in 403edo tuning
	~~==Music==~~
	*[https://www.youtube.com/watch?v=hh-cgGe_zas Diana Tessa] ~~by Francium~~

BudjarnLambeth at 06:32, 9 July 2023

2023-07-09T06:32:00Z

← Older revision		Revision as of 06:32, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|401}} It is the 79th [[prime edo]]		{{EDO intro\|401}} It is the 79th [[prime edo]]
	==Theory==		==Theory==

BudjarnLambeth at 05:57, 9 July 2023

2023-07-09T05:57:47Z

← Older revision		Revision as of 05:57, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|401}} It is the 79th [[prime edo]]		{{EDO intro\|401}} It is the 79th [[prime edo]]
	==Theory==		==Theory==