Why can’t you tune your guitar?
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Guitar tuning is fundamentally impossible to perfect due to the mathematics of prime numbers. When building a tuning system from natural harmonics, intervals derived from multiplying by 3 (perfect fifths) conflict with those derived from multiplying by 5 (major thirds) because these primes don't divide evenly into each other. This creates unavoidable tuning conflicts across a guitar's six strings. The modern solution, 12-tone equal temperament (12-TET), divides the octave into 12 equal semitones, making every interval slightly out of tune but consistently so across all keys. Alternatives like just intonation offer pure intervals but prevent key changes without retuning. Composers like Bach preferred well-temperament for its key-specific character, while Harry Partch used primes up to 11 to create a 43-tone scale. The post also touches on how blues music may involve bending 12-TET pitches back toward natural harmonic ratios.
Table of contents
The math of harmonics is really simpleHarmonics give you a good-sounding collection of pitchesGuitars can’t be perfectly in tuneThe standard tuning system is an unsatisfying compromiseYou don’t have to use 12-TET, thoughSort: