BP on the Roland HandSonic HPD-15

The Roland HandSonic HPD-15 hand drum includes some tuned percussion instruments. You can edit the pitch of each pad in cents.  The pads are grouped into 3 sets of 5, as shown:

You can edit the pitch of each pad individually, and further adjust the pitch of an entire set (A, B or C).  The pad set adjustment is very helpful when creating a patch for any HPD-15 instrument that is voiced for a higher or lower octave.

After several experiments, I finally settled on this arrangement of the Bohlen-Pierce scale notes.  It is fully chromatic from D to D'.  I didn't include a low Db as it seemed less important than the high D' for modal music. 

I tuned the notes to the C Lambda scale in just intonation with A=440 Hz (pad A2).  The first song recorded with this system was Fuse Blue.  The HPD-15 is somewhat buried in the final mix. I've created a separate MP3 file of just the HandSonic tracks so that you can hear what it sounds like: FuseBlueHandSonic.mp3.

I'm happy to answer any technical questions from other HandSonic players who are into BP or other alternate scales.  The HPD-15 isn't a real sensitive instrument, but its fine tuning capabilities make it a very useful tool for creating a variety of sounds in real time performance.

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