User:CompactStar/Ed8/5 - Revision history

Lucius Chiaraviglio: /* Music */ Change to specific example section with link to 7ed8/5, after creating that page

2025-10-20T03:30:05Z

Music: Change to specific example section with link to 7ed8/5, after creating that page

← Older revision		Revision as of 03:30, 20 October 2025
Line 9:		Line 9:


	== ~~Music~~ ==		== Specific examples ==
	; [[~~Bryan Deister]]~~		[[7ed8/5]] (includes link to music smaple)
	* [https://www.youtube.com/shorts/Ex3EKrUt8q8 ''7ed(8/5~~) improv''~~] (~~2025~~)

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed8/5]]		[[Category:Ed8/5]]

Lucius Chiaraviglio: Add Bryan Deister's ''7ed(8/5) improv'' (2025)

2025-10-18T18:43:25Z

Add Bryan Deister's ''7ed(8/5) improv'' (2025)

← Older revision		Revision as of 18:43, 18 October 2025
Line 7:		Line 7:

	[[CTE]] and near-CTE tunings of said temperament introduce pseudo-octaves, which may be considered a hindrance due to distracting from the 10:12:15:16 sonority, or it may be considered beneficial if one wants to combine that sonority with traditional octave-based harmony and melody.		[[CTE]] and near-CTE tunings of said temperament introduce pseudo-octaves, which may be considered a hindrance due to distracting from the 10:12:15:16 sonority, or it may be considered beneficial if one wants to combine that sonority with traditional octave-based harmony and melody.


			== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/Ex3EKrUt8q8 ''7ed(8/5) improv''] (2025)

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed8/5]]		[[Category:Ed8/5]]

BudjarnLambeth at 11:56, 18 May 2025

2025-05-18T11:56:52Z

← Older revision		Revision as of 11:56, 18 May 2025
Line 1:		Line 1:
			{{Editable user page}}
	'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.		'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.

BudjarnLambeth: BudjarnLambeth moved page Ed8/5 to User:CompactStar/Ed8/5

2025-05-18T11:56:40Z

BudjarnLambeth moved page Ed8/5 to User:CompactStar/Ed8/5

← Older revision	Revision as of 11:56, 18 May 2025
(No difference)

BudjarnLambeth: Adapted wording from ed16/15

2025-04-25T01:29:40Z

Adapted wording from ed16/15

← Older revision		Revision as of 01:29, 25 April 2025
Line 1:		Line 1:
	'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.		'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.

	Division of 8/5 into equal parts ~~can be conceived of as to~~ directly ~~use~~ this interval as an [[equivalence]], or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, ~~of these~~ scales have a perceptually important [[Pseudo-octave\|~~pseudo (~~false) octave]], with various degrees of accuracy.		Division of 8/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/5 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one~~ way to ~~treat 8~~/5 ~~as an equivalence~~ is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields [[MOS scale]]s of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. ~~However, this~~ temperament ~~can sometimes result in~~ pseudo-octaves ~~particularly in near~~-~~[[CTE]] tuning range~~.		One way to approach some ed8/5 tunings is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields [[MOS scale]]s of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>.

			[[CTE]] and near-CTE tunings of said temperament introduce pseudo-octaves, which may be considered a hindrance due to distracting from the 10:12:15:16 sonority, or it may be considered beneficial if one wants to combine that sonority with traditional octave-based harmony and melody.

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed8/5]]		[[Category:Ed8/5]]

BudjarnLambeth: Add links

2024-12-26T01:16:39Z

Add links

← Older revision		Revision as of 01:16, 26 December 2024
Line 1:		Line 1:
	'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.		'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.

	Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 8/5 into equal parts can be conceived of as to directly use this interval as an [[equivalence]], or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important [[Pseudo-octave\|pseudo (false) octave]], with various degrees of accuracy.

	Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS ~~scales~~ of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range.		Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields [[MOS scale]]s of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-[[CTE]] tuning range.

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed8/5]]		[[Category:Ed8/5]]

Lériendil: removed mmtm edits: 10:12:15 is not equivalent to 15:16:18

2024-11-22T05:01:05Z

removed mmtm edits: 10:12:15 is not equivalent to 15:16:18

← Older revision		Revision as of 05:01, 22 November 2024
Line 3:		Line 3:
	Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) ~~(equated to the cluster 15:16:18):~~as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range~~. As with other faster-than-octave-repeating temperament, this temperament is necessary to compromise by notating it like 64/25 (a diminished eleventh)~~.		Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range.

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed8/5]]		[[Category:Ed8/5]]

CompactStar at 02:25, 15 March 2023

2023-03-15T02:25:13Z

← Older revision		Revision as of 02:25, 15 March 2023
Line 3:		Line 3:
	Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) (equated to the cluster 15:16:18):as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range.As with other faster-than-octave-repeating temperament, this temperament is necessary to compromise by notating it like 64/25 (a diminished eleventh).		Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) (equated to the cluster 15:16:18):as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range. As with other faster-than-octave-repeating temperament, this temperament is necessary to compromise by notating it like 64/25 (a diminished eleventh).

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed8/5]]		[[Category:Ed8/5]]

Moremajorthanmajor at 01:49, 15 March 2023

2023-03-15T01:49:46Z

← Older revision		Revision as of 01:49, 15 March 2023
Line 1:		Line 1:
	'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.		'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.

	Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another sixth) as a base though, is apparent by ~~being important~~ in ~~modern~~ tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range.		Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) (equated to the cluster 15:16:18):as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range.As with other faster-than-octave-repeating temperament, this temperament is necessary to compromise by notating it like 64/25 (a diminished eleventh).

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed8/5]]		[[Category:Ed8/5]]

CompactStar at 08:21, 13 March 2023

2023-03-13T08:21:06Z

← Older revision		Revision as of 08:21, 13 March 2023
Line 1:		Line 1:
	'''~~Ed8~~/5''' is division of the just minor sixth ([[8/5]]) into n parts.		'''ED8/5''' is division of the just minor sixth ([[8/5]]) into n parts.

	Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another sixth) as a base though, is apparent by being important in modern tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another sixth) as a base though, is apparent by being important in modern tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range.		Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-CTE tuning range.

			[[Category:Equal-step tuning]]
			[[Category:Ed8/5]]