Here is a fundamental quality of music. Note names repeat because of a perceptual phenomenon that corresponds to the doubling and halving of frequencies. When we double or halve a frequency, we end up with a note that sounds remarkably similar to the one we started out with. This relationship, a frequency ratio of 2:1 or 1:2, is called the octave. It is so important that, in spite of the large differences that exist between musical cultures, every culture we know of has the octave as the basis for its music, even if it has little else in common with other musical traditions. This phenomenon leads to the notion of circularity in pitch perception, and is similar to circularity in colors. Although red and violet fall at opposite ends of the continuum of visible frequencies of electromagnetic energy, we see them as perceptually similar. The same is true in music, and music is often described as having two dimensions, one that accounts for tones going up in frequency and another that accounts for the perceptual sense that we’ve come back home again each time we double a tone’s frequency.