Equal Temperament

Equal temperament is the tuning system underlying Western music. It dictates what notes your instrument can produce — and you have probably never heard music in any other system.

Instruments could be tuned in many ways. Frequencies exist on a continuous spectrum, yet instruments like the guitar or piano let you pick from only a finite number of pitches. Which pitches are available is defined by the tuning system.

Equal temperament's guiding principle is to enable harmony and transposition while maximizing consonance and playability. This requires two choices.

First, notes are spread out evenly across the frequency spectrum. This makes every note equivalent — each has the same intervals around it as any other — creating an explosion of harmonic possibilities. The compromise is that it cannot produce perfectly consonant sounds: even spacing leaves you slightly off the perfect frequency ratios of the harmonic series.

Second, given even spacing, you must choose how far apart to space the notes. Ideally each note would have others available at consonant intervals (those from the harmonic series, like the octave and perfect 5th) — but with even spacing that is never exact, so the goal is to land as close to as many of the most consonant intervals as possible. Splitting the octave into 12 happens to do this well, getting close to many consonant intervals while staying far simpler than, say, 31 notes (as in the Huygens system). Fewer divisions give poor consonance.

Worth reiterating: the compromise on consonance only counts as a compromise if harmony isn't a priority — if it is, uneven tuning systems are simply ineffective.