http://www.research.ibm.com/people/s/shearer/mgrule.html

This mentions three constructions for modular Golomb rulers--the projective plane one, for the q^2+q+1 ets, an affine plane one for

q^2-1 ets, and one of size q^2-q, constructed I know not how. Putting together all of these for primes and prime powers with the result less than 1000, I got the following list:

2, 3, 6, 7, 8, 12, 13, 15, 20, 21, 24, 31, 42, 48, 56, 57, 63, 72,

73, 80, 91, 110, 120, 133, 156, 168, 183, 240, 255, 272, 273, 288, 307, 342, 360, 381, 506, 528, 553, 600, 624, 651, 702, 728, 757, 812, 840, 871, 930, 960, 992, 993

We see the 7-et, of course, from 2^2+2+1, we have a Golomb ruler for

the 12-et coming from 4^2-4, one for the 15-et from 4^2-1, the 31-et

from 5^2+5+1, and the 72-et from 9^2-9, the 80-et from 9^2-1, and even the 342 et from 19^2-19. (I never knew about this rational point on the elliptic curve y^2-y=x^3-1 before; cute.)

Now I want to know what Robert wants these for...it seems to be they are, musically speaking, at opposite poles from what we usually contruct as scales--they are anti-scales of a sort.