Guitar and piano use equal temperament because it's the only system that divides the octave into twelve exactly equal half steps, which makes every key equally playable. The price you pay is that the intervals aren't perfectly pure the way they are in just intonation, the system built on ratios of simple whole numbers. It's a compromise, but it's exactly what lets you play and modulate into any key without retuning.
In short: equal temperament divides the octave into twelve identical half steps of 100 cents each; it trades a sliver of interval purity for the freedom to play in every key.
What equal temperament is
In equal temperament, the octave is divided into twelve half steps that are all equal. Each half step is worth exactly 100 cents (a cent is a hundredth of a half step), and the frequency ratio between two consecutive half steps is always the same: the twelfth root of 2, about 1.0595. Multiplying this ratio twelve times gets you exactly to double the starting frequency — the octave.
The key point is uniformity: every half step is identical to every other one, regardless of which note you start from. A C# sits 100 cents from C exactly as a G# sits 100 cents from G. That's why, once the instrument is tuned, all twelve keys work the same way. The reference frequencies start from A440: you'll find the detail in hertz and musical notes.
Just intonation: ratios of whole numbers
Just intonation builds intervals on ratios of simple whole numbers. The perfect fifth has a ratio of 3:2, the major third a ratio of 5:4. These are the ratios the ear perceives as purest: when two notes stand in such a simple proportion, their vibrations lock together and the chord sounds clean, with no beating.
The problem is that these pure intervals don't combine consistently across all twelve notes. If you tune an instrument to have perfect thirds and fifths in one key, those same notes come out out of tune in another. Just intonation is gorgeous in one key, but it traps you in that key.
The compromise: the major third
This is the heart of the compromise. The equal-temperament major third is about 14 cents higher than the just-intonation major third, the one with a 5:4 ratio. Fourteen cents isn't much, but a trained ear catches it: that's why certain major chords, on guitar just as on piano, sound a touch sharp compared to pure, with a faint underlying shimmer.
| Interval | Just intonation | Equal temperament |
|---|---|---|
| Half step | — | exactly 100 cents |
| Major third | 5:4 ratio | about 14 cents higher |
| Perfect fifth | 3:2 ratio | slightly narrower |
In exchange for this small imperfection, you get a huge advantage: every key is equally usable. None sounds better or worse than the others, so you can modulate freely from one piece to another, from one section to another, without ever retuning.
Why fixed frets force equal temperament
On the guitar, this isn't even optional — it's built into the neck. Frets are fixed metal bars that run across all six strings, and their position is calculated according to equal temperament. Every fret serves six strings and every key at once, so it can't shift to favor the pure intonation of a single chord.
A fretless instrument, like the violin, can adjust the pitch of every note on the fly and get closer to just intonation. The guitar can't: once the frets are placed, the intonation of every fretted note is already decided. That's why a small departure from pure is baked into the instrument's DNA, not a flaw in your tuning. For why the guitar still tends to go out of tune regardless, there's more in why guitars go out of tune.
What changes when you play
In practice, even with the guitar perfectly tuned to standard EADGBE, certain chords will always sound a touch different from pure: the slightly sharp major third is the sonic signature of equal temperament, not a mistake on your part or the instrument's.
The most reliable way to bring every string to its target note remains a chromatic tuner: a tool like EasyGuitarTuner runs in your browser, listens to the string, and tells you how far you are from the equal-tempered note, whether you're playing an open string or a fretted one.
Understanding this compromise helps you stop chasing an impossible perfection: equal temperament is the solution that has, for centuries, balanced harmonic freedom and playability on every fretted or keyboard instrument.