4edt

4EDT is the equal division of the third harmonic into four parts of 475.4888 cents each, corresponding to 2.5237 edo.

The 4th root of 3, might be viewed alternately as a degenerate form or a fundamental building block of Bohlen-Pierce harmony, analogous to how 5edo relates to diatonic music. The situation is different however, as in this case both 5 and 7 are relatively well represented (opposed to just 3 in 5edo). While the approximations may seem excessively vague, and some might say impossible, they are nevertheless categorically important to the perception of the scale, and, may even be heard as those harmonies given the width of the "scale". It is doubtful however, that this scale could recieve much melodic treatment, and is more useful as a harmonic entity, either to demonstrate BP harmony, or as a component of scales like 8edt.

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	475.4888	17/13, 21/16, 25/19, 33/25
2	950.9775	19/11, 45/26, 26/15, (85/49), 33/19
3	1426.4663	25/11, 57/25, 16/7, 39/17
4	1901.9550	exact 3/1	just perfect fifth plus an octave

Related regular temperaments

4EDT is a generator of the rank-three regular temperament which tempers out 120/119, 171/170, 176/175, 325/323, and 363/361 in the 19-limit, which is supported by 15edo (15g val), 43edo, and 53edo. Using two equal divisions of the interval which equals an octave minus the step interval of 4EDT as a generator, it leads the interpental temperament, which tempers out 99/98, 120/119, 169/168, 171/170, 176/175, and 325/323 in the 19-limit.

19-limit 15g&43&53

Commas: 120/119, 171/170, 176/175, 325/323, 363/361

POTE generator: ~17/13 = 475.455

Map: [<1 0 0 4 0 -1 -1 0|, <0 4 0 -3 -3 6 7 -1|, <0 0 1 0 2 1 1 2|]

EDOs: 5egh, 10e, 15g, 38f, 43, 53

19-limit interpental (43&53)

Commas: 99/98, 120/119, 169/168, 171/170, 176/175, 325/323

POTE generator: ~16/13 = 362.440

Map: [<1 4 -1 1 -5 4 5 -3|, <0 -8 11 6 28 -1 -3 24|]

EDOs: 10e, 43, 53