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 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 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. Many, though not all, of these scales have a perceptually important pseudo (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 10/3.3.5 subgroup). This regular temperament yields monolarge MOS with 1-12 notes, followed by a 13-note 12L 1s〈10/3〉 MOS.