User:Xenllium/Ed7/4

The equal division of 7/4 (ed7/4) is a tuning obtained by dividing the 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. Many, though not all, ed7/4 scales have a perceptually important false octave, with various degrees of accuracy.

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 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 scales, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. Joseph Ruhf proposed the name "microdiatonic"^{[idiosyncratic term]} 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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