Ed5/2: Difference between revisions

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== Properties ==

Division of 5/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. 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, 5/2 being the best option for “no-threes” harmony excluding the octave. Many, though not all, ~~of these~~ scales have a perceptually important false octave, with various degrees of accuracy.

Division of 5/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/2 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.

~~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.

The structural utility of 5/2 (or another tenth) is apparent by its being the base of so much common practice tonal harmony{{clarify}}, and by 5/2 being the best option for “no-threes” harmony excluding the octave{{clarify}}.

Another option is to treat ed5/2's 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 [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.

One way to approach ed5/2 tunings 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 shares the scale shape of meantone.

[[Joseph Ruhf]] proposes the term "[[Macrodiatonic and microdiatonic scales|Macrodiatonic]]"{{idiosyncratic}} for the above approach because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the [[MOS]] scales formerly known as Middletown{{idiosyncratic}} because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.

Another option is to treat ed5/2's 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 [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of [[jubilic]] temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.

== Individual pages for ed5/2's ==

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 == Properties ==
-Division of 5/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. 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, 5/2 being the best option for “no-threes” harmony excluding the octave. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.
+Division of 5/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/2 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.
-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.
+The structural utility of 5/2 (or another tenth) is apparent by its being the base of so much common practice tonal harmony{{clarify}}, and by 5/2 being the best option for “no-threes” harmony excluding the octave{{clarify}}.
-Another option is to treat ed5/2's 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 [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.
+One way to approach ed5/2 tunings 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 shares the scale shape of meantone.
+[[Joseph Ruhf]] proposes the term "[[Macrodiatonic and microdiatonic scales|Macrodiatonic]]"{{idiosyncratic}} for the above approach because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the [[MOS]] scales formerly known as Middletown{{idiosyncratic}} because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.
+Another option is to treat ed5/2's 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 [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of [[jubilic]] temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.
 == Individual pages for ed5/2's ==