A piano has a vexing difficulty that many other musical instruments do not: fixed pitch.
In contrast, instruments such as the violin, trumpet, clarinet, or the human voice have flexible pitch. A skilled musician intuitively alters the pitch of each note as she plays — “tuning” it — so it sounds best with the rest of the music.
Why “In Tune” Is More Complicated Than It Sounds
But why? Isn’t C always C, A always A? It turns out not. Let’s do a little experiment: Imagine you’re a violinist playing in a string quartet. When you all play a C major chord together, you each instinctively adjust your pitch so the chord sounds perfectly harmonious — clear and resonant, with no roughness. (Tuned in this way, intervals are called “pure.”) Now the music shifts to an Ab major chord and you’re still playing that same C note. You notice something: to sound harmonious in this new context, that C needs to be played at a slightly different pitch. Your fingers shift almost unconsciously.
Being “in tune” is fundamentally relational. A note can’t be in tune all by itself — only in relationship to the notes around it. Musical harmony isn’t a set of fixed numbers — it’s a web, constantly adjusting and alive.
The Problem With Fixed Pitch
But on a piano, we have to crystallize this fluid, living system into something fixed. Every note of the scale must be assigned a singular pitch. A C tuned on the piano to sound perfectly pure in a C major chord will sound noticeably out of tune when played in an Ab major chord — but we can’t retune it mid-performance like we can on a violin. It’s clear that we will have to make a compromise.
So how do we tune a piano with a fixed set of pitches that can still serve this fluid, relational harmonic web? This is where temperament comes in. Temperament is the choice about the exact pitch of each note — and which compromises to make, since all of our harmonies can’t be pure at the same time. It’s a question tuners have been exploring for centuries, with many different answers. But before we get to those solutions, let’s understand a little more deeply why this problem exists in the first place.
Why the Math Doesn’t Quite Work Out
Consider leap years. We need them because an Earth year is 365.2422 days — not a neat number! Musical tuning has the same problem. If we tune each note to sound perfectly pure with the one before it, stepping around all twelve notes of the octave, we’d expect to land right back where we started. But we don’t. The circle doesn’t quite close — we’re slightly off, even though every step was perfect. So we have to make tiny adjustments to those perfect intervals. These adjusted intervals are called tempered intervals. Temperament is like that leap day: those small adjustments let the whole cycle line up.
Of course, with leap years we just add one day in one place. Musical temperament is more nuanced — we have to distribute tiny adjustments across all the intervals. And how we distribute them is where the art comes in.
There are two options: (1) unequal temperaments, where we spread the tempering of the intervals unevenly to create more pure harmony in certain keys and more tension in others (and there are many possible variations on this), or (2) equal temperament, where we spread the tempering uniformly across all the intervals, making every key sound exactly the same.
Unequal Temperament: Color and Character by Key
Unequal temperaments were the norm from the 14th century through the 19th century. Early versions distributed the tempering drastically — eight keys were nearly pure, while the remaining four were unusably harsh. Over time, refinements led to the so-called well temperaments, which made all keys usable while still preserving subtle differences in color and personality.
Equal Temperament: The Modern Compromise
Toward the end of the 19th century, the practice of equal temperament emerged. In this system, every interval is tempered equally so that all the keys are identical — none very pure, but none very edgy either. This is the temperament used almost exclusively today. Equal temperament has some major advantages: it makes it possible to play freely in any key, compose modulating harmonies, and explore music across all tonalities without ever hitting a “sour” key. It’s a clever compromise that gives us maximum flexibility. Our modern ears have become thoroughly accustomed to this system, and the intervals in equal temperament are “in tune enough” for us to hear them as correct.
What Gets Lost?
But equal temperament comes with sacrifices too. In well temperaments, as we mentioned, the keys with fewer sharps or flats (like C, G, D, F, and Bb major) have close to pure intervals, making these keys feel calm, stable, and peaceful — a quality lost in equal temperament. Similarly, the keys with more sharps and flats are more “colorful” than their equivalents in equal temperament. The German composer Christian Friedrich Daniel Schubart published an essay in 1806 in which he described the characteristics of the keys. C major is described as “Completely pure. Its character is: innocence, simplicity, naïvety, children’s talk.” Db major, in contrast, is “A leering key, degenerating into grief and rapture. It cannot laugh, but it can smile; it cannot howl, but it can at least grimace its crying.” Composers of the 18th and 19th centuries chose keys carefully, utilizing each one’s emotional color to convey a specific emotional landscape. Modulating from one key to another was a journey. These effects are lost when we play music of these composers in modern equal temperament.
Which Temperament Is Right for Your Piano?
In recent decades, there has been a resurgence of interest in unequal temperaments, as well as the development of many new ones. These temperaments range from 18th-century-style well temperaments, with stark differences in character between keys, to versions that are nearly equal temperament but still preserve subtle color variations. And with modern computer technology, we can precisely design and tune unequal temperaments, shaping the character of each key, in ways that weren’t possible in previous times. A skilled tuner can tailor the temperament to bring out the best in each piano.
Understanding temperament is more than just a historical curiosity — it affects how a piano sounds and feels today. When you tune your piano, you have options: you can stick with standard equal temperament for maximum flexibility, or explore an unequal temperament to bring out the distinctive character of different keys. Your choice of temperament affects the personality of your instrument. Most piano owners have never been asked which they’d prefer — but it’s a real choice, and yours to make. By working together, we can decide what approach best fits your music and your ears, giving you a piano that’s not only in tune, but alive with the relationships between its notes.