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 and microdiatonic scales|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the MOS formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.

Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes ~~three~~ 4/3 to get to 6/5, here it takes one [[25/14]] to get to 7/4 (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, and either 11 or 13 note MOS.

Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[/57]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, and either 11 or 13 note MOS.

== 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 and microdiatonic scales|Macrodiatonic]]" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the MOS formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.
-Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes three 4/3 to get to 6/5, here it takes one [[25/14]] to get to 7/4 (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, and either 11 or 13 note MOS.
+Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[/57]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, and either 11 or 13 note MOS.
 == Individual pages for ED5/2s ==