Ed5/3
The equal division of 5/3 (ed5/3) is a tuning obtained by dividing the just major sixth (5/3) into a number of equal steps.
Properties
Division of 5/3 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 5/3, 11/7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based sensi temperament or factoring into chord inversions. 5/3 is also the most consonant interval in the range between 3/2 and 2/1, which makes the equivalence easier to hear than for more complex ratios. Many, though not all, of these scales have a false octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.
Incidentally, one way to treat 5/3 as an equivalence is the use of the 6:7:8:(10) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note mos either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-armotonic.
If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in Blackcomb temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.
ED5/3 tuning systems that accurately represent the intervals 5/4 and 4/3 include: 7ed5/3 (7.30 cent error), 9ed5/3 (6.73 cent error), and 16ed5/3 (0.59 cent error).
7ed5/3, 9ed5/3, and 16ed5/3 are to the division of 5/3 what 5edo, 7edo, and 12edo are to the division of 2/1.
Individual pages for ed5/3's
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