Tuning and Temperament
Your piano is deliberately slightly out of tune, and every piano in the world is out of tune in exactly the same way. The compromise is called equal temperament, and once you hear the pure version next to it you understand both what was given up and why.
- 12 equal steps
- every key usable
- every third slightly wide
Where you run into this
- Piano
- Choral music
- Early music
- Electronic music
In short
Pure intervals come from simple whole-number ratios, and a pure major third is the ratio five to four. Stack pure intervals around a circle of fifths and they do not meet: you end up with more than an octave. Something has to give. Equal temperament spreads the error evenly over all twelve steps, which makes every third a little wide and every key equally usable. Earlier systems made some keys beautiful and others unplayable.
The pure third sounds still, almost like one sound. The tempered third has a slow shimmer in it. Most listeners have never heard the difference side by side, and it is quietly shocking the first time.
How it works
This is why a barbershop quartet or a string section can sound purer than a piano: singers and string players adjust to whatever is around them, while a keyboard is stuck with its compromise.
Where you run into this
- A choir locking into a chord that suddenly rings
- An orchestra tuning, which is pure, against a piano, which is not
- Historical instruments in a tuning where some keys sound noticeably different
Our own examples
One held major chord, switchable between equal and just intonation, plus the third on its own where the difference is largest. Both are synthesis, so nothing but the tuning changes between the two versions.
Keep going
Everything in sound and hearing
- Sound and Vibration
- The Harmonic Series
- Waveforms and Timbre
- Resonance and Formants
- Tuning and Temperament