Yantras

Yantras are an idea of Ernest McClain which he modestly attributes to
anyone over the age of 2000. We can define them in general as
follows--first, define a function for the nth smallest p-limit odd
integer. If we order the p-limit odd integers in ascending order of
size, we may call the nth number in the sequence pl_p(n). For instance
the 5-limit sequence begins 1, 3, 5, 9, 15, 25 ... so pl_5(4)=9. We
then may define the n-note p-limit yantra, yantra_p(n), as the
reduction to an octave of pl_p(1) through pl_p(n).

Yantras have interesting properties. Yantra_p(n) is a scale of n
notes, and if n<m then yantra_p(n) is strictly contained in
yantra_p(m). Any note which is octave equivalent to pl_p(n), where
n<=floor(pl_p(m)/p), will have a complete p-limit otonality for which
it is the root.