Ed5/2: Difference between revisions

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Division of 5/2 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. The utility of 5:2, (or another tenth) as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Incidentally, one way to treat 5/2 as an equivalence is the use of the 4:6:7:(10) 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 ~~four [[7~~/~~4]]~~ to get to ~~75/8 = 3~~/~~2 * (~~5~~/2)<sup>2</sup>~~ (tempering out the comma ~~2401~~/~~2400~~). So, doing this yields ~~2, 3,~~ 5, ~~8, 13~~, and 18 note MOS. While the notes are rather ~~farther apart~~, the scheme is ~~uncannily similar~~ to meantone.

Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 3/2 to get to 6/5 (tempering out the comma 27/25). So, doing this yields 5, 7, and 12 note MOS, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Macrodiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched.

== Individual pages for ED5/2s ==

* 5 - [[5ed5/2|Fifth root of 5/2]]

* 7 - [[7ed5/2|Seventh root of 5/2]]

* 9 - [[9ed5/2|Ninth root of 5/2]] ([[9edX]])

* 12 - [[12ed5/2|12th root of 5/2]]

* 16 - [[16ed5/2|16th root of 5/2]] ([[16edX]])

* 18 - [[18ed5/2|18th root of 5/2]]

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 Division of 5/2 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. The utility of 5:2, (or another tenth) as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
-Incidentally, one way to treat 5/2 as an equivalence is the use of the 4:6:7:(10) 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 four [[7/4]] to get to 75/8 = 3/2 * (5/2)<sup>2</sup> (tempering out the comma 2401/2400). So, doing this yields 2, 3, 5, 8, 13, and 18 note MOS. While the notes are rather farther apart, the scheme is uncannily similar to meantone.
+Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 3/2 to get to 6/5 (tempering out the comma 27/25). So, doing this yields 5, 7, and 12 note MOS, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Macrodiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched.
 == Individual pages for ED5/2s ==
+* 5 - [[5ed5/2|Fifth root of 5/2]]
+* 7 - [[7ed5/2|Seventh root of 5/2]]
 * 9 - [[9ed5/2|Ninth root of 5/2]] ([[9edX]])
+* 12 - [[12ed5/2|12th root of 5/2]]
 * 16 - [[16ed5/2|16th root of 5/2]] ([[16edX]])
 * 18 - [[18ed5/2|18th root of 5/2]]