Ed5/2

Ed5/2 means Division of the classic major tenth (5/2) into n equal parts.

Properties

Division of 5/2 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 5:2, (or another tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, 5:2 being the best option for “no-threes” harmony excluding the octave. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) 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 3/2 to get to 6/5 (tempering out the comma 3125/3048). 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. "Macrodiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the MOS formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.

Another option is to treat ED5/2s as "no-threes" systems (like how EDTs are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four 4/3 to get to 6/5, here it takes one 10/7 to get to 7/5 (tempering out the comma 50/49 in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5, 8, 13, and 21 note MOS.

Individual pages for ED5/2s

0…49

0	1	2	3	4	5	6	7	8	9
10	11	12	13	14	15	16	17	18	19
20	21	22	23	24	25	26	27	28	29
30	31	32	33	34	35	36	37	38	39
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