100edo - Revision history

Overthink: /* Subsets and supersets */ + supersets

2026-02-08T18:44:44Z

Subsets and supersets: + supersets

← Older revision		Revision as of 18:44, 8 February 2026
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 100 factors into {{factorization\|100}}, 100edo has subset edos {{EDOs\| 2, 4, 5, 10, 20, 25, and 50 }}.		Since 100 factors into {{factorization\|100}}, 100edo has subset edos {{EDOs\| 2, 4, 5, 10, 20, 25, and 50 }}. [[200edo]], which doubles it, corrects the perfect fifth to near-just quality. [[400edo]] further corrects many harmonics, making for a strong 19-limit system. [[1600edo]] and [[2000edo]] do very well in high prime limits.

	== Intervals ==		== Intervals ==

Overthink: added subgroup suitable for use

2025-09-22T06:11:22Z

added subgroup suitable for use

← Older revision		Revision as of 06:11, 22 September 2025
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	100edo is closely related to [[50edo]], but the [[patent val]]s differ on the mapping for [[7/1\|7]]. It tempers out [[6144/6125]] in the 7-limit, [[99/98]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit, and like 50edo [[81/80]] in the 5-limit. It provides the [[optimal patent val]] for the 11- and 13- limit {{nowrap\|43 & 57}} temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.		100edo is closely related to [[50edo]], but the [[patent val]]s differ on the mapping for [[7/1\|7]]. It tempers out [[6144/6125]] in the 7-limit, [[99/98]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit, and like 50edo [[81/80]] in the 5-limit. It provides the [[optimal patent val]] for the 11- and 13- limit {{nowrap\|43 & 57}} temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.

	Like [[6edo\|6-]], [[35edo\|35-]], [[47edo\|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].		Like [[6edo\|6-]], [[35edo\|35-]], [[47edo\|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. It is therefore a strong 2.9.5.7.11.13.17.19 system for its size. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].

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

Lucius Chiaraviglio: /* Music */ Add normal link to Iceface H. Wakabayashi's ''Microtonal Piano in 100 tone equal temperament (100EDO) (Microtonal Music)'' (2016) in case the embedded video won't play

2025-08-12T22:45:37Z

Music: Add normal link to Iceface H. Wakabayashi's ''Microtonal Piano in 100 tone equal temperament (100EDO) (Microtonal Music)'' (2016) in case the embedded video won't play

← Older revision		Revision as of 22:45, 12 August 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022)		* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022)

			; [[Iceface H. Wakabayashi]] (微分音チャンネル)
			* [https://www.youtube.com/watch?v=shcrw2vtmJU ''Microtonal Piano in 100 tone equal temperament (100EDO) (Microtonal Music)''] (2016) (this is the same as the video linked above, to use in case the embedded video refuses to play)

Yourmusic Productions: Add lumatone mapping link.

2025-08-12T21:12:02Z

Add lumatone mapping link.

← Older revision		Revision as of 21:12, 12 August 2025
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	== Instruments ==		== Instruments ==
			=== Lumatone ===
			[[Lumatone mapping for 100edo]]
	=== Skip fretting ===		=== Skip fretting ===
	One way to play 100edo on a [[20edo]] guitar is to tune the strings 13\100 apart, or 156 [[cents]]. All examples on this page are for 7-string guitar.		One way to play 100edo on a [[20edo]] guitar is to tune the strings 13\100 apart, or 156 [[cents]]. All examples on this page are for 7-string guitar.
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022)		* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022)

	~~{{Todo\|add lumatone mapping}}~~

Lucius Chiaraviglio: /* Music */ Todo|add lumatone mapping

2025-07-24T09:19:47Z

Music: Todo|add lumatone mapping

← Older revision		Revision as of 09:19, 24 July 2025
Line 223:		Line 223:
	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022)		* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022)

			{{Todo\|add lumatone mapping}}

Lucius Chiaraviglio: /* Music */ Fix year of Bryan Deister's 100edo composition

2025-06-21T09:55:18Z

Music: Fix year of Bryan Deister's 100edo composition

← Older revision		Revision as of 09:55, 21 June 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (~~2023~~)		* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2022)

Lucius Chiaraviglio: /* Video */ Insert music section after this, starting with Bryan Deister's ''100edo'' (2023)

2025-06-21T07:44:32Z

Video: Insert music section after this, starting with Bryan Deister's ''100edo'' (2023)

← Older revision		Revision as of 07:44, 21 June 2025
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	== Video ==		== Video ==
	<youtube>shcrw2vtmJU</youtube>		<youtube>shcrw2vtmJU</youtube>

			== Music ==

			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/37bFvBsKXqo ''100edo''] (2023)

BudjarnLambeth at 05:28, 26 April 2025

2025-04-26T05:28:57Z

← Older revision		Revision as of 05:28, 26 April 2025
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	61/32: string 3 fret 16		61/32: string 3 fret 16

	~~[[Category:Skip fretting]][[Category:100edo]]~~

	== Video ==		== Video ==
	<youtube>shcrw2vtmJU</youtube>		<youtube>shcrw2vtmJU</youtube>

BudjarnLambeth: /* Instruments */ Merge into EDO page as voted on XA Discord #wiki channel

2025-04-26T05:27:32Z

Instruments: Merge into EDO page as voted on XA Discord #wiki channel

@@ Line 173: / Line 173: @@
 == Instruments ==
-[[Skip fretting system 100 5 13]]
+=== Skip fretting ===
 == Video ==
 <youtube>shcrw2vtmJU</youtube>

ArrowHead294 at 17:50, 11 March 2025

2025-03-11T17:50:35Z

← Older revision		Revision as of 17:50, 11 March 2025
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	== Theory ==		== Theory ==
	100edo is closely related to [[50edo]], but the [[patent val]]s differ on the mapping for [[7/1\|7]]. It tempers out [[6144/6125]] in the 7-limit, [[99/98]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit, and like 50edo [[81/80]] in the 5-limit. It provides the [[optimal patent val]] for the 11- and 13- limit 43 & 57 temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.		100edo is closely related to [[50edo]], but the [[patent val]]s differ on the mapping for [[7/1\|7]]. It tempers out [[6144/6125]] in the 7-limit, [[99/98]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit, and like 50edo [[81/80]] in the 5-limit. It provides the [[optimal patent val]] for the 11- and 13- limit {{nowrap\|43 & 57}} temperament tempering out 81/80, 99/98, 1350/1331, and in the 13-limit, 144/143.

	Like [[6edo\|6-]], [[35edo\|35-]], [[47edo\|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].		Like [[6edo\|6-]], [[35edo\|35-]], [[47edo\|47-]] and [[88edo]], 100edo possesses two approximations of the perfect fifth (at 58\100 and 59\100 respectively), each almost exactly six cents from just. One interesting consequence of this property is that one may have a closed circle of twelve good fifths (four wide, eight narrow) that bears little resemblance to [[12edo]].