generalizing non-octave scales

(LOG(N/D))*(P/LOG(2))

where P is any desired periodicity in cents results in a ratio in the
form of

N^(P/O)
---------
D^(P/O)

where P = any given periodicity and O = 1:2

(This allows one to alter the proportions of any ratio, or sets of
ratios, relative to a given periodicity.)

--Dan Stearns

I wrote,

<<(LOG(N/D))*(P/LOG(2)) where P is any desired periodicity>>

Periodicity in this case can also be applied to rhythm. Though the
garden variety drum machine is eminently more capable of a faithful
execution than the flesh and blood virtuosi (less likely to complain
anyway).

Say a 4/4 measure = 384. Six 8:9s would overshoot the measure in the
exact same way they'd overshoot the octave. So in 9/8s you'd have a
particular flavor of liner sextuplets. (Note the analogy to Lou
Harrison's free style JI here.)

Personally I'm very much drawn to mixing the two; the linear and
logarithmic.

Many strange things can be done. But without the aid of tailor-made
click tracks I think linear ratios as rhythms and vice versa are best
left to the professionals amongst us -- polyrhythmiconic machinery (or
in my case, cheap polyrhythmiconic machinery).

--Dan Stearns