User:CompactStar/Super-pitch

Super-pitch is a quantity that is equal to the super-logarithm (inverse tetration) of frequency, just as pitch is the logarithm of frequency.

Tetration and super-logarithm

Tetration (most commonly represented with ↑↑) is iterated exponentiation, like how exponentiation is iterated multiplication. Tetration can be defined recursively as:

a↑↑b = 1 if b = 0

a↑↑b = a^a↑(b-1) if b > 0

For example, a↑↑1 = a, a↑↑2 = a^a, and a↑↑3 = a^aa.