User:Xenllium/Ed7/4: Difference between revisions

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The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.

== Properties ==

Division of 7/4 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 7/4 (or another seventh) 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 false octave, with various degrees of accuracy.

Division of 7/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/4 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.

~~Incidentally, one way to treat 7~~/~~4 as an equivalence~~ is the ~~use of the 4:5:6:(7) 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 5/4~~ to ~~get to 7~~/~~6 (tempering out the comma 392~~/~~375). So, doing this yields~~ 5~~-, 7-, and~~ 12~~-note~~ [[~~mos scale~~]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Microdiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely compressed.

The structural importance of 16/9 is suggested by its being the most common width for a [[tetrad]] in Western harmony, though it could be argued that this distinction belongs instead to [[16/9]] or [[9/5]] depending how one converts [[12edo|10\12]] into [[JI]].

~~Where examples~~ of this ~~particular temperament in use are concerned~~, ~~they are already everywhere~~, just ~~with~~ notes ~~which~~ are rather ~~farther apart~~.

One approach to ed7/4 tunings is the use of the 4:5:6:(7) 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 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the name "microdiatonic"{{idiosyncratic}} for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.

== Individual pages for ed7/4's ==

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[[Category:Ed7/4| ]]

[[Category:Ed7/4's| ]]

~~[[Category:Edonoi]]~~

[[Category:Lists of scales]]

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+{{Editable user page}}
 The '''equal division of 7/4''' ('''ed7/4''') is a [[tuning]] obtained by dividing the [[7/4|septimal minor seventh (7/4)]] in a certain number of [[equal]] steps.
 == Properties ==
-Division of 7/4 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 7/4 (or another seventh) 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 false octave, with various degrees of accuracy.
+Division of 7/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/4 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.
-Incidentally, one way to treat 7/4 as an equivalence is the use of the 4:5:6:(7) 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 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Microdiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely compressed.
+The structural importance of 16/9 is suggested by its being the most common width for a [[tetrad]] in Western harmony, though it could be argued that this distinction belongs instead to [[16/9]] or [[9/5]] depending how one converts [[12edo|10\12]] into [[JI]].
-Where examples of this particular temperament in use are concerned, they are already everywhere, just with notes which are rather farther apart.
+One approach to ed7/4 tunings is the use of the 4:5:6:(7) 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 5/4 to get to 7/6 (tempering out the comma 392/375). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the name "microdiatonic"{{idiosyncratic}} for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.
 == Individual pages for ed7/4's ==
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 |}
-[[Category:Ed7/4| ]] <!-- main article -->
+[[Category:Ed7/4's| ]] <!-- main article -->
-[[Category:Edonoi]]
 [[Category:Lists of scales]]