User:CompactStar/Ed12/5 - Revision history

BudjarnLambeth at 12:02, 18 May 2025

2025-05-18T12:02:50Z

← Older revision		Revision as of 12:02, 18 May 2025
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			{{Editable user page}}
	The '''equal division of 12/5''' ('''ed12/5''') is a [[tuning]] obtained by dividing the [[12/5\|classic minor tenth (12/5)]] into a number of [[equal]] steps.		The '''equal division of 12/5''' ('''ed12/5''') is a [[tuning]] obtained by dividing the [[12/5\|classic minor tenth (12/5)]] into a number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed12/5 to User:CompactStar/Ed12/5

2025-05-18T12:02:41Z

BudjarnLambeth moved page Ed12/5 to User:CompactStar/Ed12/5

← Older revision	Revision as of 12:02, 18 May 2025
(No difference)

BudjarnLambeth: /* Properties */

2025-04-25T01:57:20Z

Properties

← Older revision		Revision as of 01:57, 25 April 2025
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	The structural utility of 12/5 (or another minor tenth) is hinted by its being the base of so much common practice tonal harmony{{clarify}}, and being the absolute widest range most generally used in popular songs{{citation needed}}.		The structural utility of 12/5 (or another minor tenth) is hinted by its being the base of so much common practice tonal harmony{{clarify}}, and being the absolute widest range most generally used in popular songs{{citation needed}}.

	One approach to ed12/5 tunings is to ~~tteat~~ the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is a "macro-meantone"{{idiosyncratic}} as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note [[MOS]] in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.		One approach to ed12/5 tunings is to treat the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is a "macro-meantone"{{idiosyncratic}} as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note [[MOS]] in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==

BudjarnLambeth: /* Properties */ adapted wording from ed16/15

2025-04-25T01:57:08Z

Properties: adapted wording from ed16/15

← Older revision		Revision as of 01:57, 25 April 2025
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	== Properties ==		== Properties ==
	Division of 12/5 into equal parts ~~can be conceived of as to~~ directly ~~use~~ this interval as an ~~equivalence, or not. The question of~~ [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, ~~of these~~ scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.		Division of 12/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed12/5 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	~~Incidentally, one way to treat~~ 12/5 ~~as an equivalence~~ is the ~~use~~ of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is ~~literally~~ a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.		The structural utility of 12/5 (or another minor tenth) is hinted by its being the base of so much common practice tonal harmony{{clarify}}, and being the absolute widest range most generally used in popular songs{{citation needed}}.

			One approach to ed12/5 tunings is to tteat the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is a "macro-meantone"{{idiosyncratic}} as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note [[MOS]] in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==

CompactStar at 01:35, 23 May 2023

2023-05-23T01:35:29Z

← Older revision		Revision as of 01:35, 23 May 2023
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	Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.		Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==

CompactStar at 01:35, 23 May 2023

2023-05-23T01:35:25Z

← Older revision		Revision as of 01:35, 23 May 2023
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	Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by ~~about~~ 26%, you will get intervals ~~of approximately~~ 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.		Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==

CompactStar at 01:35, 23 May 2023

2023-05-23T01:35:00Z

← Older revision		Revision as of 01:35, 23 May 2023
Line 4:		Line 4:
	Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.		Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 26%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==

CompactStar at 01:34, 23 May 2023

2023-05-23T01:34:46Z

← Older revision		Revision as of 01:34, 23 May 2023
Line 4:		Line 4:
	Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25~~-30~~%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.		Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==

CompactStar at 01:15, 23 May 2023

2023-05-23T01:15:51Z

← Older revision		Revision as of 01:15, 23 May 2023
Line 4:		Line 4:
	Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, ~~thhis~~ temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.		Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==

CompactStar at 01:15, 23 May 2023

2023-05-23T01:15:46Z

← Older revision		Revision as of 01:15, 23 May 2023
Line 4:		Line 4:
	Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.		Division of 12/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

	Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, thhis temperament yields 5, 7, 12, and 19 note MOS in exactly the same families as ~~meantone~~, just with a period of 12/5 instead of 2/1.		Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, thhis temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.

	== Individual pages for ED12/5s ==		== Individual pages for ED12/5s ==