C-110-N-220-D-440, eh?

i see you found 220 from 110 using revision1

(<--these are important-->)

derp1200 cents are equal to one octave — a frequency ratio of 2:1 — and an equally tempered semitone (the interval between two adjacent piano keys) is equal to 100 cents. This means that the ratio of one cent is precisely equal to 21/1200, the 1200th root of 2, which is approximately 1.0005777895.

RATIONAL("the devil's interval") = FALSE

on to your problem -

given the pairs [x1, y1], [x2, y2], . . . , [xn, yn]

(are you making quarter tones? i rather enjoy talvin singh)

f(x) = see: general formula for linear or nonlinear regression

thousands of beers have obscured the data, but

f(x) = ()/() + ()/() + . . . + ()/() seems like the right direction

f(x) = (y1)/(x - x1) + (y2)/(x - x2) + . . . + (yn)/(x-xn) ??

constipated mathematician

f(x) = y1*[(x-x2)(x-x3)...(x-xn)] + . . . + yn*[(x-x1)(x-x2)...(x - x(n-1))]

i'll work more on it later if i have time.

what I don't get is C# = C*2

^{1/12} but F=E*2

^{1/12}and why not C# = C*2

^{1/13}?