Ed5/2: Difference between revisions

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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 3125/3048). 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.

Alternatively, we can continue to use 4:5:6 as the fundamental complete sonority as in meantone. In this case, it takes five 3/2 to get to 5/4, tempering out the comma [[250/243]] in the 5-limit. This produces [[MOS scales]] of the families 2L 3s<5/2>, 2L 5s<5/2>, 2L 7s<5/2> ~~and~~ 2L 9s<5/2>.

Alternatively, we can continue to use 4:5:6 as the fundamental complete sonority as in meantone. In this case, it takes five 3/2 to get to 5/4, tempering out the comma [[250/243]] in the 5-limit. This produces [[MOS scales]] of the families 2L 3s<5/2>, 2L 5s<5/2>, 2L 7s<5/2>, 2L 9s<5/2>, and 9L 11s<5/2>.

== Individual pages for ED5/2s ==

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 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 3125/3048). 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.
-Alternatively, we can continue to use 4:5:6 as the fundamental complete sonority as in meantone. In this case, it takes five 3/2 to get to 5/4, tempering out the comma [[250/243]] in the 5-limit. This produces [[MOS scales]] of the families 2L 3s<5/2>, 2L 5s<5/2>, 2L 7s<5/2> and 2L 9s<5/2>.
+Alternatively, we can continue to use 4:5:6 as the fundamental complete sonority as in meantone. In this case, it takes five 3/2 to get to 5/4, tempering out the comma [[250/243]] in the 5-limit. This produces [[MOS scales]] of the families 2L 3s<5/2>, 2L 5s<5/2>, 2L 7s<5/2>, 2L 9s<5/2>, and 9L 11s<5/2>.
 == Individual pages for ED5/2s ==