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Ed7/4 means Division of of the septimal minor seventh (7/4) into n equal parts.


Division of 7:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. 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 pseudo (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, 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.

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

Individual pages for ED7/4s