User:CompactStar/Ed12/5: Difference between revisions

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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.

== 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 5:2, (or another 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 yields 5, 7, 12, 19, and 31 note MOS ~~(coincidentally similar to meantone)~~.

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 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 ==

* [[12ed12/5]]

[[Category:Edonoi]]

[[Category:Ed12/5]]

[[Category:Equal-step tuning]]

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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.
 == 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 5:2, (or another 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 yields 5, 7, 12, 19, and 31 note MOS (coincidentally similar to meantone).
+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 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 ==
+* [[12ed12/5]]
+[[Category:Edonoi]]
+[[Category:Ed12/5]]
+[[Category:Equal-step tuning]]