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 or 1, / 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.