Play a Real Number on a Monochord

This is a little tool so that one can 'play' a real number given by some sort of Cauchy sequence, or really any sequence of either fractions or ratios. These operate by multiplying by middle A (440hz) to produce the next sound.

One can write their own number-generating functions and hit the 'user' button to play it. With enough Javascript knowledge the given example might give you enough of a background to get it started, but generally you just write a function user_iterator() to return an iterator, which gives fractions as an object with a numerator n and denominator d (as in {n: 4,d: 5}). Functions available for your convenience include gcd(m,n) for integers m, n, frac_add(a,b) for fractions (as given above) a, b, frac_mul(a,b) for fractions again, and frac_pow(a,n), where a is a fraction and n is an integer.

The given examples play the harmonic sequence, play the sequence of superparticular ratios, plays a major scale, and plays Leibniz's series for approximating π/4.