Piano tuner with a stretched tuning curve
An online piano tuner that accounts for the one property that defines a piano string — inharmonicity. It breaks the sound of a strike into partials, measures the stiffness coefficient B, and builds a stretched tuning curve for your piano, showing the reading on a strobe dial: it stops exactly when the string reaches its target, and it resolves fractions of a cent that a pointer cannot.
How to use it
Choose the piano type and the pitch standard. That alone gives a sensible stretched curve — measurements refine it rather than create it.
Put the phone or laptop next to the instrument. The quieter the room, the cleaner the split into partials.
The tool tells you which key to strike, measures the stiffness and moves on. Two of the six sit either side of the bass break, where the curve bends hardest.
Pick a note on the keyboard or let the tool recognise it by ear. Turn the pin until the dial stops: stopping is arriving. Tuned keys mark themselves.
Mute the extra strings, set one, then open them one at a time and take the pulse out. The Unisons tab shows its rate as a number.
Measure your own strings and tune the instrument to its own curve
Your instrument
Your instrument's tuning curve
Horizontally, the keys from A0 to C8; vertically, the deviation from equal temperament in cents. The dashed line is the "even" tuning, the dots are notes whose stiffness you measured: between them the curve is interpolated, beyond them it follows the shape of a real instrument. The vertical line is the note you are working on.
String stiffness
Stiffness — the coefficient B — is how far a string's partials climb above the harmonic series, and it is what the stretch is built from. Strike a note and let it ring for a second: the tool finds up to ten partials and fits B by least squares, and reports the residual with it — an honest measure of whether this reading can be trusted.
Unisons
Most notes have two or three strings. Set one against the meter, then open the others one at a time: two nearly identical strings do not each sound on their own — together they pulse, and the pulse rate is the mistuning. The tool counts it for you.
Interval checks
A tuner checks their own work by ear: counting the beats of known intervals and comparing them with what they should be. Below are the rates for your curve. Thirds should accelerate smoothly upward with no dips; fifths should be nearly clean.
| Interval | Notes | Beats/s | Partials |
|---|
Spectrum of the strike
The vertical lines are where the partials should stand for a string of the measured stiffness. The point is visible at once: they do not land on whole multiples of the fundamental, and they run sharper the higher they go. The partial the reading is taken on is marked brightest.
Why a piano cannot be tuned "evenly"
A piano string is thick and stiff, so its partials sound higher than the harmonic series says they should: the n-th partial sits not at n·f₀ but at n·f₀·√(1 + B·n²), where B is the inharmonicity coefficient of that particular string. A tuner listens not to the notes themselves but to the beats between their partials, and sets each octave so that the chosen partials of the lower and upper note coincide. The finished tuning is therefore stretched: the top above equal temperament, the bottom below it — the Railsback curve. A piano tuned to strict equal temperament sounds dull in the treble and muddy in the bass, and everyone can hear it.
