Ed7/3

Todo: cleanup, explain edonoi Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property other than equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.

The equal division of 7/3 (ed7/3) is a tuning obtained by dividing the septimal minor tenth (7/3) in a certain number of equal steps.

Applications

Division of 7/3 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed7/3 scales have a perceptually important false octave, with various degrees of accuracy.

The structural utility of 7/3 (or another tenth) is apparent by being the absolute widest range most generally used in popular songs^{[citation needed]} (and even the range of a dastgah^{[citation needed]}).

Chords and harmonies

Main article: Pseudo-traditional harmonic functions of enneatonic scale degrees

Enneatonic scales, especially those equivalent at 7/3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) 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 two 28/15 to get to 7/2 (tempering out the comma 225/224). So, doing this yields 15-, 19-, and 34-note mos 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. Joseph Ruhf named this scheme "macrobichromatic".

Individual pages for ed7/3's

0…99

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
40	41	42	43	44	45	46	47	48	49
50	51	52	53	54	55	56	57	58	59
60	61	62	63	64	65	66	67	68	69
70	71	72	73	74	75	76	77	78	79
80	81	82	83	84	85	86	87	88	89
90	91	92	93	94	95	96	97	98	99