Is My Keyboard Truly Well-Tempered?

First things first… what is a temperament?

The word may sound surprising, but here it has nothing to do with human character. A temperament refers to a way of tuning notes in relation to each other. When we speak of equal temperament or well-tempered keyboard, we’re talking about different ways of organizing the intervals between notes in the musical scale.

Pythagoras discovering harmonic fifths…

Simple sounds, complex sounds

A musical note is never pure: it consists of a fundamental (the note we perceive) and a series of harmonics, higher-pitched sounds that give it its color or timbre. These harmonics follow specific rules. For example, when you play a C, you often hear the third harmonic — which corresponds to a G. And when you play that G, its third harmonic will be a D. These successions form what are called fifths. Pythagoras had already discovered this phenomenon back in the 6th century BCE.

The problem with perfect fifths…

If we build note by note, moving up in perfect fifths according to this natural logic, we eventually go full circle — twelve fifths should (in theory) bring us back to the original note. But… not quite! The final C ends up a little higher than the one we started with. This tiny difference is called the Pythagorean comma, and it’s enough to cause an imbalance that the ear can detect.So if we want everything to sound in tune, we need to compromise.

The art of compromise: temperaments

Over the centuries, musicians and instrument makers devised many different temperaments to distribute this imbalance. Some keep the fifths very pure, at the cost of distorted thirds. Others favor the thirds, or aim to balance the discrepancies.Each method gives every key its own distinctive flavor and color. There are dozens of these so-called unequal temperaments: meantone, Werckmeister, Vallotti, Young, and many more.

Equal temperament: a modern solution

From the 19th century onward, one temperament eventually won out: equal temperament.Its principle is simple and mathematically flawless: the octave is divided into 12 equal semitones, and the famous Pythagorean comma is evenly distributed across all of them — by slightly adjusting each note using the twelfth root of 2.

– Oops! I said I wouldn’t get too technical… 🤭

In equal temperament, no fifth or third is perfectly in tune — but every key sounds the same. That’s the system used on all modern pianos.

The other side of the coin?

Equal temperament is mathematically impeccable — but some musicians find it too smooth, too uniform. It erases the natural differences between keys, whereas in older temperaments, each key had its own mood, tension, and expressive quality.

And what about The Well-Tempered Clavier?

Contrary to popular belief, Bach’s Well-Tempered Clavier was not written for an instrument in equal temperament! The exact tuning he used isn’t known for sure, but it was an unequal temperament (probably Werckmeister), chosen to allow playing in all keys while preserving expressive contrasts between them.

That’s the genius of this collection: it shows that, even with compromises, music can still sound harmonious — in every key.

In short

• A temperament is a way of distributing intervals between notes.

• Equal temperament divides the octave into 12 perfectly equal parts.

• It’s the system we use today, but older temperaments offer richer variety.

• Bach didn’t use equal temperament — his keyboard was just well… well-tempered!

  
  

👉 Any questions?

I’d be delighted to discuss this with you — and of course, to tune your piano according to its needs.

Feel free to get in touch through the Contact page.