User:CompactStar/Ed9/2: Difference between revisions

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The '''equal division of 9//2''' ('''ed9/2''') is a [[tuning]] obtained by dividing ~~the~~ [[9/2|~~just~~ major ~~sixteenth~~ (9/2)]] into a number of [[equal]] steps.

The '''equal division of 9//2''' ('''ed9/2''') is a [[tuning]] obtained by dividing [[9/2|two octaves and a Pythagorean major second (9/2)]] into a number of [[equal]] steps.

== Properties ==

Division of 9/2 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. Many, though not all, of these scales have a perceptually important ~~pseudo (~~false) octave, with various degrees of accuracy.

Division of 9/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

Incidentally, one way to treat 9/2 as an equivalence is the use of the 9:10:14 chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to [[5/1]], here it takes seven [[14/9]] to get to [[10/9]] (tempering out the comma 215233605/210827008 in the 9/2.5.7 fractional subgroup). This temperament yields 7, 10, 17, and 27 note ~~MOS~~.

Incidentally, one way to treat 9/2 as an equivalence is the use of the 9:10:14 chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to [[5/1]], here it takes seven [[14/9]] to get to [[10/9]] (tempering out the comma 215233605/210827008 in the 9/2.5.7 fractional subgroup). This temperament yields 7-, 10-, 17-, and 27-note [[mos scale]]s.

[[Category:Edonoi]]

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-The '''equal division of 9//2''' ('''ed9/2''') is a [[tuning]] obtained by dividing the [[9/2|just major sixteenth (9/2)]] into a number of [[equal]] steps.
+The '''equal division of 9//2''' ('''ed9/2''') is a [[tuning]] obtained by dividing [[9/2|two octaves and a Pythagorean major second (9/2)]] into a number of [[equal]] steps.
 == Properties ==
-Division of 9/2 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. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
+Division of 9/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.
-Incidentally, one way to treat 9/2 as an equivalence is the use of the 9:10:14 chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to [[5/1]], here it takes seven [[14/9]] to get to [[10/9]] (tempering out the comma 215233605/210827008 in the 9/2.5.7 fractional subgroup). This temperament yields 7, 10, 17, and 27 note MOS.
+Incidentally, one way to treat 9/2 as an equivalence is the use of the 9:10:14 chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to [[5/1]], here it takes seven [[14/9]] to get to [[10/9]] (tempering out the comma 215233605/210827008 in the 9/2.5.7 fractional subgroup). This temperament yields 7-, 10-, 17-, and 27-note [[mos scale]]s.
 [[Category:Edonoi]]