For those of you unfamiliar with music, we offer a (very) brief introduction into the technical aspects of music.

The sounds you hear over the airwaves and in all manner of places may be grouped into 12 superficially disparate categories. Each category is labeled a "note" and given an alphasymbolic representation. That is, the letters A through G represent seven of the notes and the other five are represented by appending either a pound sign (#, or sharp) or something that looks remarkably similar to a lower-case b (also called a flat).

Although these notes were conjured in an age where the modern theory of waves and optics was not dreamt of even by the greatest of thinkers, they share some remarkable characteristics. Namely, every note that shares its name with another (notes occupying separate "octaves," with one sounding higher or lower than the other) has a frequency that is some rational multiple of the frequency of the notes with which it shares a name. More simply, an A in one octave has a frequency twice that of an A one octave below.

As it turns out, *every* note is related to every other note by a common multiplicative factor. To run the full gamut, one need only multiply a given note by the 12th root of two n times to find the nth note "above" it (i.e. going up in frequency). Mathematically: