From Xenharmonic Wiki
Jump to navigation Jump to search

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.

Steps Cents Hekts Corresponding
JI intervals
0 0.0000 0 1/1
1 475.4888 325 17/13, 21/16, 25/19, 33/25
2 950.9775 650 19/11, 45/26, 26/15, (85/49), 33/19
3 1426.4663 975 25/11, 57/25, 16/7, 39/17
4 1901.9550 1300 3/1 just perfect fifth plus an octave

Related regular temperaments

4EDT is a generator of the vulture temperament, which tempers out 10485760000/10460353203 in the 5-limit.