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5.4.2 Just Intonation vs Equal Temperament: Musical Tuning Systems
Musicians and theorists tried all sorts of variations on the theme of just intonation, methods of tuning with simple whole-number frequency ratios. Such tuning systems—and there are many—enable the tuning of an instrument so that it’s playable in one key, or perhaps even several keys. But if you try to play in keys the instrument isn’t tuned for ... forget it. Doesn’t work.
Eventually, one of the numerous tuning solutions attempted over the centuries emerged the clear winner. The solution was to:
- Stick to an exact 2:1 octave, despite the Pythagorean comma.
- Divide the octave into 12 exactly equal semitones.
This system is called equal temperament (from temperare, the Latin root meaning to mingle or mix in due proportion).