Ed10/3

The equal division of 10/3 (ed10/3) is a tuning obtained by dividing the just major thirteenth (10/3) into a number of equal steps.

Properties

Division of 10/3 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 10/3 or another thirteenth as a base though, is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the tritave and the double octave. 10/3 is also the complete ambitus of three, later five, of the church modes ^{[clarification needed ]}. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

Incidentally, one way to treat 10/3 as an equivalence is the use of the 2:3:6 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/4, here it takes eight 3/1 to get to 3/2 (tempering out the comma 5000000/4782969 in the 5-limit). This regular temperament yields monolarge mos with 1–12 notes, followed by a 13-note 12L 1s〈10/3〉 mos.