What Is Equal Temperament and Why Does It Matter for Piano Tuning?

If you’ve ever wondered why a piano can play in any key without retuning — the answer is equal temperament. It’s one of the most consequential decisions in Western music history, and it’s also the central challenge in learning to tune a piano by ear.

Here’s what it actually is, where it comes from, and why every aspiring piano tuner needs to understand it deeply.

The Problem Equal Temperament Solves

In purely acoustic terms, intervals like the perfect fifth and the major third don’t divide the octave evenly. If you tune perfect fifths stacked on top of each other — the old Pythagorean tuning method — you get twelve notes, but when you return to your starting pitch, you’re slightly sharp. That error is called the Pythagorean comma.

This created a practical problem: keyboard instruments tuned in Pythagorean or meantone systems sounded beautiful in some keys and hideous in others. A piece in C major was pure and resonant; a piece in F# major was dissonant and unpleasant — the so-called “wolf” intervals.

The Solution: Deliberate Compromise

Equal temperament solves this by distributing the error equally across all twelve notes. Instead of perfect mathematical intervals, every interval except the octave is slightly out of tune — but only slightly, and by the same amount in every key.

The result:

Every major key sounds equally good (or equally compromised, depending on your philosophy)
Modulation between any two keys is possible and consistent
A single piano can accompany music in every key without retuning

This is the system essentially all modern Western instruments use. It was the dominant standard for pianos by the late 19th century.

Why “Equal” Is a Bit Misleading

The word “equal” refers to equal distribution of a mathematical error — not to equal beauty or equal resonance. In fact, the intervals in equal temperament are all slightly impure:

Octaves: The only perfectly pure interval. 2:1 frequency ratio, exact.
Perfect fifths: Slightly narrow — about 2 cents flat from a pure 3:2 ratio.
Major thirds: Noticeably wide — about 14 cents sharp from a pure 5:4 ratio.
Minor thirds: Slightly narrow.

A “cent” is 1/100th of a semitone — a unit of measurement used in tuning. The human ear can detect differences as small as 3-5 cents in direct comparison, which means these errors, while small, are audible in the right context.

How Beats Reveal Temperament

This is where ear training connects to equal temperament theory.

When two strings are close to the same pitch but not exactly, they produce a rhythmic pulsation — a beat. The rate of that beat (measured in beats per second) is proportional to the frequency difference between the strings.

In equal temperament, intervals beat at predictable rates:

A tempered fifth beats slowly — roughly 1 beat per second in the middle octave
A tempered major third beats much faster — around 7-10 beats per second
Octaves, when correctly tuned, beat at zero (beatless)

This is the key insight for aural tuning: you’re not listening for silence. You’re listening for the correct beat rate for each interval in each octave — and comparing those rates to each other to verify the temperament.

This is why equal temperament is both the goal and the measuring stick. Every interval in a correctly tuned piano has a characteristic beating pattern. Learning to hear and set those patterns is what aural tuning is.

Setting Equal Temperament Aurally

In practice, the tuner sets a temperament octave — usually the middle octave of the piano — by establishing 12 notes that form equal temperament within that octave. The rest of the piano is then tuned by octaves from that foundation.

The process for the temperament octave typically involves:

Setting a reference pitch (A4 = 440 Hz, usually from a tuning fork or electronic reference)
Tuning a temperament starting note from that reference
Building the temperament through a sequence of intervals — testing fourths, fifths, thirds, and sixths against each other
Verifying the temperament is consistent by checking multiple intervals that should have predictable beating relationships

The difficulty is that you’re simultaneously juggling multiple interval relationships, and a small error in any one note propagates through everything else. It’s a multi-variable problem that requires real pattern recognition in the ear.

The Historical Debate

Equal temperament was controversial. Many musicians and theorists in the 18th and 19th centuries argued that the impure major third was an unacceptable compromise. J.S. Bach’s Well-Tempered Clavier was actually written for a well-tempered system — not equal temperament — in which some keys were purer than others. (The name “equal temperament” for Bach’s system is a common historical misconception.)

Today, early music performers and instrument makers sometimes use historical temperaments — meantone, Kirnberger, Werckmeister — that were designed for specific repertoire. Some pianists swear that historical temperaments make Baroque music sound more alive.

For modern piano tuning in most contexts, equal temperament is standard. But understanding the historical alternatives illuminates why equal temperament makes the choices it does.

What This Means for Learning

If you’re learning to tune a piano, equal temperament is the system you’re learning to implement. That means:

You need to hear impurity accurately. Equal temperament is not just “in tune.” It’s a precisely calibrated out-of-tune system. Learning to set it means learning to hear specific degrees of impurity as correct.
Theory and ear training are inseparable. You can memorize the beat rates theoretically, but until you’ve heard them many times and internalized the pattern, the theory doesn’t produce good tuning.
The temperament octave is the core skill. Everything else in piano tuning — extensions to bass and treble, unison refinement, voicing, regulation — builds on top of a solid temperament foundation.

This is why 88 Lessons spends the first quarter of the curriculum on ear training and equal temperament theory before students ever place a tuning hammer on a pin.

You can’t build something you can’t hear.

Start learning equal temperament from the ground up with 88 Lessons — daily podcast episodes, free, starting from zero. Listen now →