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) if it has not been named yet.
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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