67ed5 - Revision history

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:23:13Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:23, 1 August 2025
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	\|}		\|}

	~~[[Category:Edonoi]]~~
	[[Category:29edo]]		[[Category:29edo]]

Fredg999 category edits: Removing from Category:Ed5 using Cat-a-lot

2025-08-01T18:39:07Z

Removing from Category:Ed5 using Cat-a-lot

← Older revision		Revision as of 18:39, 1 August 2025
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	\|}		\|}

	~~[[Category:Ed5]]~~
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:29edo]]		[[Category:29edo]]

FloraC: /* Theory */ cleanup

2025-01-17T17:07:10Z

Theory: cleanup

← Older revision		Revision as of 17:07, 17 January 2025
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	== Theory ==		== Theory ==
	~~The [[patent val]]~~ has a generally sharp tendency for [[harmonic]]s up to 28. Unlike 29edo, it is only [[consistent]] up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic. ~~This tuning~~ [[tempers out]] 49/48 in the [[7-limit]]; 55/54 in the 11-limit; 65/64 and 91/90 in the 13-limit; 85/84 in the 17-limit; 77/76 in the 19-limit; 70/69 in the 23-limit; 58/57 in the 29-limit; and 93/92 in the 31-limit.		67ed5 has a generally sharp tendency for [[harmonic]]s up to 28. Unlike 29edo, it is only [[consistent]] up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic. As an equal temperament, it [[tempering out\|tempers out]] 49/48 in the [[7-limit]]; 55/54 in the 11-limit; 65/64 and 91/90 in the 13-limit; 85/84 in the 17-limit; 77/76 in the 19-limit; 70/69 in the 23-limit; 58/57 in the 29-limit; and 93/92 in the 31-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

BudjarnLambeth at 06:41, 7 January 2025

2025-01-07T06:41:50Z

← Older revision		Revision as of 06:41, 7 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents.		'''[[Ed5\|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo]], but with the [[5/1]] rather than the [[2/1]] being [[just]]. The octave is about 6.0164 cents [[Stretched octave\|stretched]] and the step size is about 41.5868 cents.

	== Theory ==		== Theory ==
	The patent val has a generally sharp tendency for ~~harmonics~~ up to 28. Unlike 29edo, it is only consistent up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic. This tuning tempers out 49/48 in the 7-limit; 55/54 in the 11-limit; 65/64 and 91/90 in the 13-limit; 85/84 in the 17-limit; 77/76 in the 19-limit; 70/69 in the 23-limit; 58/57 in the 29-limit; and 93/92 in the 31-limit.		The [[patent val]] has a generally sharp tendency for [[harmonic]]s up to 28. Unlike 29edo, it is only [[consistent]] up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic. This tuning [[tempers out]] 49/48 in the [[7-limit]]; 55/54 in the 11-limit; 65/64 and 91/90 in the 13-limit; 85/84 in the 17-limit; 77/76 in the 19-limit; 70/69 in the 23-limit; 58/57 in the 29-limit; and 93/92 in the 31-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	Compared to 29edo, 67ed5 has a much better 5/1, 7/1, 11/1, 13/1, and 17/1, at the expense of a much worse 3/1.		Compared to 29edo, 67ed5 has a much better 5/1, 7/1, 11/1, 13/1, and 17/1, at the expense of a much worse 3/1.

	The biggest argument in favor of this trade-off is that 29edo’s 7/1 is so inaccurate as to be unusable for many. So, the fact that 67ed5 makes the 3/1 not as good, but still definitely useable, and in return, replaces that ~~horrible~~ 7/1 with almost perfectly in-tune one, could be seen as a worthwhile trade-off.		The biggest argument in favor of this trade-off is that 29edo’s 7/1 is so inaccurate as to be unusable for many. So, the fact that 67ed5 makes the 3/1 not as good, but still definitely useable, and in return, replaces that unusable 7/1 with almost perfectly in-tune one, could be seen as a worthwhile trade-off.
	{{Harmonics in equal\|67\|5\|1\|intervals=prime\|columns=11}}		{{Harmonics in equal\|67\|5\|1\|intervals=prime\|columns=11}}

BudjarnLambeth at 06:38, 7 January 2025

2025-01-07T06:38:36Z

← Older revision		Revision as of 06:38, 7 January 2025
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	[[Category:Ed5]]		[[Category:Ed5]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			[[Category:29edo]]

BudjarnLambeth at 06:37, 7 January 2025

2025-01-07T06:37:56Z

← Older revision		Revision as of 06:37, 7 January 2025
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	{{Harmonics in equal\|29\|columns=11}}		{{Harmonics in equal\|29\|columns=11}}

	==Intervals==		=== 67ed5 as a generator ===
			67ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19 [[Subgroup temperaments\|subgroup temperament]] which tempers out 441/440, 513/512, 4000/3993, and 10125/10108, which is a [[cluster temperament]] with 29 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 205821/204800 ~ 210/209 ~ 225/224 ~ 7448/7425 ~ 361/360 ~ 400/399 ~ 1375/1372 ~ 200704/200475 all tempered together. This temperament is supported by [[29edo]], [[202edo]], and [[231edo]].

			== Intervals ==
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
	\|+ Intervals of 67ed5		\|+ Intervals of 67ed5
Line 364:		Line 367:
	\| \| just major third plus two octaves		\| \| just major third plus two octaves
	\|}		\|}

	~~==67ed5 as a generator==~~
	67ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19 [[Subgroup temperaments\|subgroup temperament]] which tempers out 441/440, 513/512, 4000/3993, and 10125/10108, which is a cluster temperament with 29 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 205821/204800 ~ 210/209 ~ 225/224 ~ 7448/7425 ~ 361/360 ~ 400/399 ~ 1375/1372 ~ 200704/200475 all tempered together. This temperament is supported by [[29edo]], [[202edo]], and [[231edo]].

	[[Category:Ed5]]		[[Category:Ed5]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
	~~{{todo\|expand}}~~

BudjarnLambeth: Add detailed comparsion to 29edo

2025-01-07T06:34:25Z

Add detailed comparsion to 29edo

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''[[Ed5|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo|29 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents.
+'''[[Ed5|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents.
 == Theory ==
 The patent val has a generally sharp tendency for harmonics up to 28. Unlike 29edo, it is only consistent up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic. This tuning tempers out 49/48 in the 7-limit; 55/54 in the 11-limit; 65/64 and 91/90 in the 13-limit; 85/84 in the 17-limit; 77/76 in the 19-limit; 70/69 in the 23-limit; 58/57 in the 29-limit; and 93/92 in the 31-limit.
 ==Intervals==
@@ Line 354: / Line 364: @@
 | | just major third plus two octaves
 |}
 ==67ed5 as a generator==

BudjarnLambeth: /* Intervals */ table title

2025-01-07T05:18:32Z

Intervals: table title

← Older revision		Revision as of 05:18, 7 January 2025
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	==Intervals==		==Intervals==
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 67ed5
	\|-		\|-
	! \| degree		! \| degree

MisterShafXen at 17:03, 26 December 2024

2024-12-26T17:03:40Z

← Older revision		Revision as of 17:03, 26 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo\|29 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents. The patent val has a generally sharp tendency for harmonics up to 28. Unlike 29edo, it is only consistent up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic.		'''[[Ed5\|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo\|29 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents.

			== Theory ==
			The patent val has a generally sharp tendency for harmonics up to 28. Unlike 29edo, it is only consistent up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic. This tuning tempers out 49/48 in the 7-limit; 55/54 in the 11-limit; 65/64 and 91/90 in the 13-limit; 85/84 in the 17-limit; 77/76 in the 19-limit; 70/69 in the 23-limit; 58/57 in the 29-limit; and 93/92 in the 31-limit.

	==Intervals==		==Intervals==

BudjarnLambeth: Misleading link, collapsible, todo

2024-12-22T04:09:33Z

Misleading link, collapsible, todo

← Older revision		Revision as of 04:09, 22 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo\|29 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents. The patent val has a generally sharp tendency for harmonics up to 28. Unlike 29edo, it is only consistent up to the [[~~7-odd-limit\|8-~~integer-limit]], with discrepancy for the 9th harmonic.		'''[[Ed5\|Division of the 5th harmonic]] into 67 equal parts''' (67ed5) is related to [[29edo\|29 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents. The patent val has a generally sharp tendency for harmonics up to 28. Unlike 29edo, it is only consistent up to the 8-[[integer-limit]], with discrepancy for the 9th harmonic.

	==Intervals==		==Intervals==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
	\|-		\|-
	! \| degree		! \| degree
Line 370:		Line 370:
	[[Category:Ed5]]		[[Category:Ed5]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			{{todo\|expand}}