24ed5 - Revision history

Squib at 03:27, 26 May 2026

2026-05-26T03:27:38Z

← Older revision		Revision as of 03:27, 26 May 2026
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	== Theory ==		== Theory ==
	From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the very low-[[badness]] 5.7.11 [[subgroup temperament]] named as [[juggernaut]], tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]).		From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the very low-[[badness]] 5.7.11 [[subgroup temperament]] named as [[juggernaut]], tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]). 24ed5 shares 31edo's mappings for 5 and 7, but not 11.
	== Interval table ==		== Interval table ==
	{\| class="wikitable"		{\| class="wikitable"

Squib: /* 24ed5 as a generator */

2026-05-25T23:56:18Z

24ed5 as a generator

← Older revision		Revision as of 23:56, 25 May 2026
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	==24ed5 as a generator==		==24ed5 as a generator==
	24ed5 ~~can also be thought~~ of ~~as a~~ [[~~generator~~]] ~~of the 2.3.5.7.11.23 [[Subgroup temperaments\|subgroup~~ temperament~~]] which tempers out 225/224~~, ~~243/242, 385/384, and 529/528, which is~~ a [[~~cluster temperament~~]] ~~with 10 clusters~~ of ~~notes in an octave~~. ~~The small chroma interval between adjacent notes in each cluster is very versatile~~, ~~representing 45~~/~~44 ~ 46/45 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[31edo]]~~, ~~[[82edo]], [[113edo]], and [[144edo]]~~.		One step of 24ed5 is just flat of 3\31, an acceptable generator for [[miracle]] temperament, so it can be used as a [[retraction]] of miracle. However, miracle maps 5/1 to 23 secors and 3 dieses, not 24 secors.

MisterShafXen at 11:12, 17 May 2026

2026-05-17T11:12:22Z

← Older revision		Revision as of 11:12, 17 May 2026
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 24 equal parts''' (24ed5) is related to the [[Miracle\|miracle temperament]]. The step size about 116.0964 cents. It is similar to every third step of [[31edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.		'''[[Ed5\|Division of the 5th harmonic]] into 24 equal parts''' (24ed5) is related to the [[Miracle\|miracle temperament]]. The step size is about 116.0964 cents. It is similar to every third step of [[31edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.

	== Theory ==		== Theory ==

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

2025-08-01T19:21:46Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:21, 1 August 2025
Line 154:		Line 154:
	==24ed5 as a generator==		==24ed5 as a generator==
	24ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.23 [[Subgroup temperaments\|subgroup temperament]] which tempers out 225/224, 243/242, 385/384, and 529/528, which is a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44 ~ 46/45 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[31edo]], [[82edo]], [[113edo]], and [[144edo]].		24ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.23 [[Subgroup temperaments\|subgroup temperament]] which tempers out 225/224, 243/242, 385/384, and 529/528, which is a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44 ~ 46/45 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[31edo]], [[82edo]], [[113edo]], and [[144edo]].

	~~[[Category:Edonoi]]~~

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

2025-08-01T18:39:04Z

Removing from Category:Ed5 using Cat-a-lot

← Older revision		Revision as of 18:39, 1 August 2025
Line 155:		Line 155:
	24ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.23 [[Subgroup temperaments\|subgroup temperament]] which tempers out 225/224, 243/242, 385/384, and 529/528, which is a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44 ~ 46/45 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[31edo]], [[82edo]], [[113edo]], and [[144edo]].		24ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.23 [[Subgroup temperaments\|subgroup temperament]] which tempers out 225/224, 243/242, 385/384, and 529/528, which is a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 45/44 ~ 46/45 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[31edo]], [[82edo]], [[113edo]], and [[144edo]].

	~~[[Category:Ed5]]~~
	[[Category:Edonoi]]		[[Category:Edonoi]]

BudjarnLambeth: Harmonics

2024-10-06T01:20:07Z

Harmonics

@@ Line 137: / Line 137: @@
 | | just major third plus two octaves
 |}
 ==24ed5 as a generator==

CompactStar: Using the other name I decided to change it to

2023-08-02T08:33:07Z

Using the other name I decided to change it to

← Older revision		Revision as of 08:33, 2 August 2023
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	== Theory ==		== Theory ==
	From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the very low-[[badness]] 5.7.11 [[subgroup temperament]] ~~tentatively~~ named as ~~"tuatara"~~, tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]).		From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the very low-[[badness]] 5.7.11 [[subgroup temperament]] named as [[juggernaut]], tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]).
	== Interval table ==		== Interval table ==
	{\| class="wikitable"		{\| class="wikitable"

CompactStar at 08:38, 11 July 2023

2023-07-11T08:38:21Z

← Older revision		Revision as of 08:38, 11 July 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the 5.7.11 [[subgroup temperament]] tentatively named as "tuatara", tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]). ~~This temperament is in a sense a no-twos-or-threes counterpart of pajara, and one of the lowest badness temperaments of the 5.7.11 subgroup.~~		From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the very low-[[badness]] 5.7.11 [[subgroup temperament]] tentatively named as "tuatara", tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]).

	== Interval table ==		== Interval table ==
	{\| class="wikitable"		{\| class="wikitable"

CompactStar at 08:38, 11 July 2023

2023-07-11T08:38:01Z

← Older revision		Revision as of 08:38, 11 July 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the 5.7.11 [[subgroup temperament]] tentatively named as "tuatara", tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]). It is in a sense a no-twos-or-threes counterpart of pajara, and one of the lowest badness temperaments of the 5.7.11 subgroup.		From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the 5.7.11 [[subgroup temperament]] tentatively named as "tuatara", tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]). This temperament is in a sense a no-twos-or-threes counterpart of pajara, and one of the lowest badness temperaments of the 5.7.11 subgroup.

	== Interval table ==		== Interval table ==

CompactStar at 08:37, 11 July 2023

2023-07-11T08:37:25Z

← Older revision		Revision as of 08:37, 11 July 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the 5.7.11 [[subgroup temperament]] tentatively named as "tuatara", tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and ~~with~~ a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]). It is in a sense a no-twos-or-threes counterpart of pajara, and one of the lowest badness temperaments of the 5.7.11 subgroup.		From a no-twos-or-threes point of view, 24ed5 offers a particularly good tuning of the 5.7.11 [[subgroup temperament]] tentatively named as "tuatara", tempering out 125/121. This has a CTE generator of exactly [[7/5]] (in 24ed5 approximated as 5 steps) and a period of 1\[[2ed5]] or the square root of five (which is equated to [[11/5]]). It is in a sense a no-twos-or-threes counterpart of pajara, and one of the lowest badness temperaments of the 5.7.11 subgroup.

	== Interval table ==		== Interval table ==