over-equal and under-equal series

OVER-EQUAL SERIES:

Where "n" and "x" are any given numbers, an over to under series is
defined as 2n*x with a sequential numerator rule of +2 and a
sequential denominator rule of -(x-1).

Letting x=1 gives a corresponding n-over series.

Letting x=(sqrt(2)+1) gives an "over-equal series" with symmetry at
the half octave. [For a rational variation that converts the 1:2^(1/2)
into a 17:24 let x=2.5.]

UNDER-EQUAL SERIES:

Where "n" and "x" are any given numbers, an under to over series is
defined as n*x with a sequential numerator rule of +(x-2) and a
sequential denominator rule of -1.

Letting x=2 gives a corresponding n-under series.

Letting x=(sqrt(2)+2) gives an "under-equal series" with symmetry at
the half octave. [For a rational variation that converts the 1:2^(1/2)
into a 12:17 let x=3.5.]

--Dan Stearns