Bohlen-Pierce

Here's what I think is an interesting RI take on the Bohlen-Pierce
scale as it adds just fifths and octaves (i.e., 2:3s and 1:2s) while
retaining some semblance of the 3:5:7s and 5:7:9s as well -- six of
each in fact if you allow for equivalencies at the 118098/117649.

729/343--81/49----9/7-----1/1
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
243/98---27/14----3/2-----7/6----49/18

0 267 435 702 870 1137 1305 1572 1734 1902
0 168 435 603 870 1038 1305 1467 1635 1902
0 267 435 702 870 1137 1299 1467 1734 1902
0 168 435 603 870 1032 1200 1467 1635 1902
0 267 435 702 864 1032 1299 1467 1734 1902
0 168 435 597 765 1032 1200 1467 1635 1902
0 267 428 597 864 1032 1299 1467 1734 1902
0 162 330 597 765 1032 1200 1467 1635 1902
0 168 435 603 870 1038 1305 1473 1740 1902

The above lattice is only a lattice in the sense that it allows the
standard two-dimensional harmonic lattice to function as a rough sort
of template where the second dimension is the first altered by a
comma.

The following "triad" shows how this scale is constructed:

18/7
/ \
/ \
/ \
/ \
(1/1,3/1)----7/3

This scale is also trivalent, though the difference between stepsizes
A and B are meant to be practically nonexistent. And in this sense
it's a JI (or RI) scale that functions more like a temperament.

--Dan Stearns