October 26, 2012

7-Limit Harmonies in the Bohlen Pierce Scale

The most consonant harmonies in the Bohlen Pierce scale (to my ear) are those that fall within the gamut of Harry Partch's 7-limit just intonation system. The BP intervals 9/7 and 7/5 (steps 3 and 4) seem to be the most pleasing, and their equal temperament counterparts are less than 4 cents from just.

The step 2 interval 25/21 is 302 cents, an acceptable minor third to western ears, but equal temperament changes it to a flat-sounding 292 cents.

The step 12 interval 25/9 (B note) is totally outside of the western 12-tone system.

This chart shows the intersection between the Bohlen Pierce scale and the 7-limit just intonation system.  The D and B notes (in blue) suffer the problems mentioned above.  The difference between cents and round hundreds is a rough indicator of how alien the interval will sound compared to traditional western harmony.

steps name ratio cents cents ET 12-tone name
0 C 1/1 0 0 Unison
2 D 25/21 302 293 Minor 3rd
3 E 9/7 439 435 Dim 4th
4 F 7/5 582 585 Tritone
6 G 5/3 884 877 Major 6th
7 H 9/5 1018 1024 Minor 7th
9 J 15/7 1319 1316 Dim 9th
10 A 7/3 1467 1463 Aug 9th
12 B 25/9 1769 1755 none
13 C 3/1 1902 1902 12th

2 comments:

Igliashon Jones said...

There is an error in your chart: the 2-step interval should be 25/21, but you have it as 27/25 (which IIRC is the 1-step interval)

b0b said...

Thanks. I've corrected it.