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.

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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.

The structural importance of 7/4 is ~~hinted~~ by its being the most common width for a [[tetrad]] in Western harmony.

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]].

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" for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.

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.
@@ Line 4: / Line 5: @@
 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.
-The structural importance of 7/4 is hinted by its being the most common width for a [[tetrad]] in Western harmony.
+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]].
-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" for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.
+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]]