A small mathematical lie about frequency lets every key be playable. The Western musical scale is a compromise — twelve equally spaced notes per octave, each separated by a frequency ratio of the twelfth root of two — that no acoustically pure interval is exactly right, but every interval is close enough to sound good. The system, equal temperament, replaced earlier tuning systems that sounded perfectly in tune in some keys at the cost of being unusable in others. Bach's Well-Tempered Clavier (1722, 1742) — twenty-four preludes and fugues, one in each major and minor key — was the demonstration project for a tempered system in which all keys were musically usable.
The acoustic problem is geometric: pure musical intervals correspond to small whole-number frequency ratios (octave 2:1, fifth 3:2, fourth 4:3, major third 5:4). If you tune one key perfectly, modulating to another key produces out-of-tune intervals (the wolf fifth of medieval music). Earlier tuning systems — Pythagorean, just intonation, meantone — preserved purity in some intervals at the cost of others; performers had to retune between keys, or accept that some keys sounded badly. Equal temperament spreads the deviation evenly: every fifth is slightly narrow, every third is slightly wide, but none is unbearable, and the listener's ear adjusts. The system's adoption was gradual through the 17th and 18th centuries, was contested (Werckmeister's well temperament — the title of Bach's collection — was technically a slightly different scheme that preserved subtle key-character differences), and was effectively universal by the late 19th. The mathematical elegance enabled the modulation-rich harmonic language of late Beethoven, Wagner, Debussy, and the entire jazz tradition. Most non-Western musical systems — Indian classical music, Arabic maqam, Indonesian gamelan, Chinese pentatonic — do not use equal temperament, and their preservation in the digital era has involved active resistance to Western tuning's hegemony.
The digital sampling, MIDI, and Auto-Tune infrastructure of the recording industry has cemented equal temperament globally; pop music in any country is now produced on a Western-tuned 12-tone grid. The microtonal movement (Harry Partch, Wendy Carlos, La Monte Young, modern just-intonation enthusiasts) is a small but persistent counter-current that uses tunings outside equal temperament for expressive ends digital tools cannot easily produce. The AI-generation of music currently produces equal-tempered output by default because the training data is overwhelmingly equal-tempered. The acoustic compromise of 1700 is the inherited operating system of the global musical economy of 2025.