Equal temperament

A tuning system that divides an octave into equal logarithmic intervals. In twelve-tone equal temperament, each semitone has the same frequency ratio, making transposition consistent across keys.

Twelve-tone equal temperament: A tuning system that divides an octave into twelve equal semitones, each with a frequency ratio of the twelfth root of two. It is the familiar equal-tempered system used by most modern Western keyboards.
Just intonation: A tuning approach that builds intervals from simple whole-number frequency ratios. It can tune selected intervals more purely, but those ratios do not transfer uniformly between keys.
Aristoxenus: An ancient Greek music theorist who treated musical intervals in terms of perceived pitch distances. His approach anticipated thinking about musical intervals as divisible spans rather than only ratios.
Piano: A keyboard instrument that produces sound when hammers strike strings. Its fixed pitches make equal temperament a practical standard for moving among keys.
Cent (music): A logarithmic unit of musical interval equal to one hundredth of an equal-tempered semitone. Cents express how far equal temperament's fixed steps depart from other tunings.
Meantone temperament: A family of tuning systems that narrows fifths to improve the tuning of thirds. It favors selected thirds more than equal temperament does, at the cost of limited usable keys.
Zhu Zaiyu: A sixteenth-century Chinese prince and music theorist who calculated twelve-tone equal temperament. His precise calculations are among the earliest known mathematical treatments of the system.
Guitar: A fretted string instrument whose strings are plucked or strummed to produce musical pitches. Its frets commonly place notes at equal-tempered semitone positions.
Frequency ratio: The quotient of two sound frequencies, which determines their musical interval. Equal temperament makes each successive step correspond to the same frequency ratio.
Well temperament: A family of unequal tunings that permits music in all keys while giving each key a distinct character. Unlike equal temperament, its interval sizes vary among keys.

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