The science

Why an ordinary tuner app gets a piano wrong.

Piano strings are thick, stiff steel. The stiffness makes their overtones ring a little sharp: more at the top of the keyboard, and by a different amount on every piano.

Tune every note to the textbook and the octaves beat against each other: you hear a slow wobble where there should be none. Professional tuners know this. They stretch the octaves until they sound clean, by ear or with tuning software. An ordinary tuner app can't, because it assumes a perfect string.

Resonance works from the same science. It measures how stiff your strings are (one number per note, called B) and works out the stretch from that.

p_{n} = n F \sqrt{1 + B n^{2}}

Overtone n of a stiff string. With B = 0 you get the textbook. A typical middle C is near 4 × 10⁻⁴, which puts its eighth overtone about 21 cents sharp.

Watch this part

An interactive diagram compares the harmonic ladder of an ideal string with the partials of a real, stiff piano string, showing each partial's offset in cents.

How it works

A whole tuning, step by step.

You don't need to know how to tune. You need a tuning lever, a few mutes and some patience. The app gives you one step at a time, in plain words: which key, which string, which way to turn.

Set up
Tell it about your piano: grand or upright, and where the notes change from one string to two, and from two to three. Check that the microphone can hear it.
Survey
Play every key, about a second each. You'll see how far out the piano is, and what to do about it.
Pitch raise
Only if the piano is well below pitch. A quick rough pass that pulls each note a little too high on purpose, so it settles where it should.
Measure
Play a handful of notes the app picks. It shows which strings to mute, listens, and asks for a second strike to be sure.
Curve
From those notes it works out the right pitch for all 88 keys, and tells you when it has heard enough.
Tune
One note at a time. Tune one string until the needle turns green, then bring the note's other strings in line until the wobble stops.
Unisons
Come back to any note whose strings have drifted apart. It shows how fast they wobble and which way to turn.

iPhone · iPad · Mac

Stand it on the music desk.

The same app on iPhone, iPad and Mac. Everything you need to tune a piano fits on your phone, so you can prop it on the music desk and keep your hands free for the lever and the keys.

iPhoneThe whole tuning, start to finish: setup, the survey, a pitch raise, measuring, and every note and unison. Laid out for the phone, with a note name and needle you can read from the bench.
iPadThe same app with more room. The list of steps stays beside the one you're on, upright or sideways.
MacEverything the iPhone does, plus the curve charts, the unison numbers, the strobe and one-key shortcuts.

Each device keeps its own sessions. Nothing syncs, because nothing leaves the device.

A live copy of the Tune view at iPhone size: the note name and how far off it is, the needle, and a guide that gives one step at a time in plain words.

The Tune view at iPhone size: a live copy on made-up values.

Tune

One note. One step. Plain words.

Resonance tells you the one thing to do next, and moves on when it hears you've done it. Your hands stay on the lever.

Watch this part

A live copy of the Tune view. On the left, the note name, how far off it is in cents, and a needle. On the right, a guide that gives one step at a time in plain words: put the mutes in, tune the middle string, match the left string, match the right string. Below, an 88-key keyboard shows which notes are done. An Advanced mode switch adds the strobe, the spectrum and the numbers.

A live copy of the Tune view on made-up values, as it looks on the Mac and on a wide iPad. Turn the pin yourself, or switch on Advanced mode.

Put the mutes in. A picture shows which strings to mute. Play the note and it moves on by itself.
Tune the middle string. Turn the pin a tiny bit at a time until the needle sits in the middle and turns green. It records by itself.
Match the left string, then the right. Take out one mute and you'll hear a slow wobble. Turn the pin until it's gone.
Easy to read from the bench. A huge note name, and a word with every colour: FLAT, SHARP, IN TUNE.
It listens to the right overtone for each part of the keyboard, and stays on your note even when a string is way off.
Want the numbers? Advanced mode adds the spectrum. On the Mac it also adds a strobe for the last tenth of a cent, and the tuning plan.

Measure

It tells you which string. Then it listens.

For every note it shows which strings to mute and which one to leave open. Wedges or a felt strip, grand or upright.

Hands-free. Mute, strike, hold. It listens, checks the note and moves on by itself.
Two strikes must agree before a measurement counts.
One clear reason when a strike is no good: too loud, too quiet, died too soon — or the wrong key: That sounded like B2, not C3. C3 is one white key to the right.
It picks the next note for you: the one that helps the most.

Watch this part

A live recreation of the measurement wizard: a diagram of a three-string note with wedges muting the left and right strings and the middle string open as the reference, a ring that fills while the app listens to a strike, and a quality bar built from the number of partials found, the fit error, the signal-to-noise ratio and consistency.

A live copy of the measuring step, faster than real life, on made-up values.

Curve

A stretch curve from your strings, not from a table.

This is the stretch a good tuner builds by ear, worked out from your measurements instead. All 88 notes are solved together, so the octaves sound as clean as your strings allow, from the bottom of the keyboard to the top.

It says when it's ready. curve reliable (0.7¢) means: more measuring could still move a note by up to 0.7 cents.
Start with about nine notes. It usually asks for a few more.
It keeps learning while you tune, and notes you've already tuned stay put.
Five stretch styles, from Light to Pure twelfths, if you have a preference.

Watch this part

Two charts. The stretch curve shows each key's target in cents relative to equal temperament, from about 20 cents flat at the lowest A to about 23 cents sharp at the top C, inside a band showing the remaining uncertainty. The second chart shows the inharmonicity of each key on a logarithmic axis, with the measured notes marked and a step where the copper-wound bass strings give way to plain steel.

A live copy of the Curve view on the Mac. Made-up data: a grand with fourteen measured notes. iPhone and iPad tune to the same curve.

Survey & pitch raise

Far from pitch? Start there.

Pull a very flat piano straight up to pitch and it sinks back behind you. So Resonance checks the whole keyboard first and tells you what the piano needs.

A plain answer: Your piano is close to pitch. Or: Your piano needs a pitch raise first.
It aims a little sharp, on purpose. Aiming +8.3¢ sharp on purpose — the string will settle.
It goes gently. Never more than 30 cents sharp, or 15 on the copper-wound strings. Two passes if the piano is very flat.
It spots notes whose strings disagree while you play through.

A live recreation of the Survey view: a wide meter showing how far each key is from pitch, up to 100 cents either way, and a keyboard that fills in key by key, tinted from blue for close to pitch through amber to red for far off, ending in a verdict.

A live copy of the Survey view, faster than real life, on made-up values.

Unisons

Then pull the unisons clean.

Most notes have two or three strings. When they disagree you hear a slow wobble. Resonance hears it too, and tells you which way to turn.

Which way to turn: Turn it up a little or Turn it down a little.
How fast the wobble is, so you can see it slow down as you get close.
It tells you when it is gone: No wobble — this string matches.
On the Mac, Advanced mode adds the numbers: beats per second, the gap in cents, and a lamp that turns green when the unison is clean.

Watch this part

A live recreation of the Unison panel: two strings sounding together, their combined loudness swelling and fading as they beat, a large beat-rate readout in hertz, a direction such as LOWER the open string, and a lamp that turns green when the unison is clean.

A live copy of the Unison panel on the Mac (Advanced mode), on made-up values. Turn the pin to stop the wobble.

The maths

Show me the equations.

You don't need any of this to tune. But it's the physics professional tuning software is built on, and nothing in Resonance is a black box. Here it is, in the order the app uses it.

01
Cents: the one unit
Where in the app: Everywhere

$c (f, g) = 1200 \cdot \log_{2} (\frac{f}{g})$

The distance between two frequencies $f$ and $g$ , in cents: 100 to a semitone, 1200 to an octave. The needle, the curve and the error of every fit are all in this unit. At A4, one cent is only 0.254 Hz.
02
A stiff string’s overtones
Where in the app: Measure

$p_{n} = n \cdot F \cdot \sqrt{1 + B n^{2}}$ $f_{1} = F \cdot \sqrt{1 + B}$

$R_{n} (B) = \sqrt{\frac{1 + B n^{2}}{1 + B}}$ $p_{n} = f_{1} \cdot n \cdot R_{n} (B)$

Piano wire is stiff steel, so overtone $n$ is not exactly $n$ times the fundamental: it runs sharp, by an amount that grows with $n^{2}$ . One number per string, the inharmonicity $B$ , describes the whole series. Everything you see is anchored on the real first partial $f_{1}$ : “A4 = 440” means $f_{1}$ , never the zero-stiffness $F$ , and $R_{1} = 1$ .
03
Frequency from phase, and the strobe
Where in the app: Measure · Tune

Project short Hann-windowed blocks onto the guess $Z_{m} = \sum_{i = 0}^{N_{b} - 1} w [i] x [m H + i] e^{- j 2 π \hat{f} (m H + i) / f_{s}}$

The slope of the unwrapped phase is the error
$φ_{m} = unwrap (\arg Z_{m}) \approx φ_{0} + 2 π \cdot δ f \cdot t_{m}$ $f = \hat{f} + δ f$

The strobe draws the same phase between frames $φ (t) = φ_{0} + 2 π \cdot Δ f \cdot (t - t_{0})$

An FFT bin is far too coarse. So the app mixes the sound down against its best guess $\hat{f}$ and watches how fast the phase of the result turns: standing still means exactly on the guess, a slow rotation is the pitch error. The fit is a straight line through phase against time, weighted by ${| Z_{m} |}^{2}$ . In the strobe, $Δ f$ is the measured partial minus its target, so the band drifts at exactly that many periods per second, and only within ±15 cents.
04
One strike, one straight line
Where in the app: Measure

${(\frac{f_{n}}{n})}^{2} = F^{2} (1 + B n^{2})$ $= a + b \cdot n^{2}$

$F = \sqrt{a}$ $B = \frac{b}{a}$

Then refined on the residuals, in cents $r_{n} = c (f_{n}, n \cdot F \cdot \sqrt{1 + B n^{2}})$

Play one note. The app finds up to twelve overtones $f_{n}$ , measures each with step 03, and plots ${(f_{n} / n)}^{2}$ against $n^{2}$ : a straight line whose intercept gives $F$ and whose slope over intercept is $B$ . A weighted least-squares fit, then a few Gauss–Newton steps on the cents residuals; partials that miss by more than about 1.5 cents are dropped.
05
The stretch curve: every interval at once
Where in the app: Curve
One equation per pair of partials that should meet (m of key i, n of key j) $x_{j} - x_{i} = 1200 \cdot \log_{2} (\frac{R_{m} (B_{i})}{R_{n} (B_{j})}) + ε$

All of them, weighted, plus a smoothness penalty, with A4 pinned
$\min_{x} \sum_{c} w_{c} {(x_{j} - x_{i} - d_{c})}^{2} + λ \sum_{k = 2}^{87} {(x_{k + 1} - 2 x_{k} + x_{k - 1})}^{2}$ $with x_{49} = 0$
$x_{k}$ is how many cents key $k$ ’s first partial sits above its equal-tempered (or chosen temperament) pitch. No single “correct” octave exists on a real piano: the 2nd, 4th and 6th partials of the lower note each want a slightly different upper note. The solver writes down every such wish across the keyboard, weights them by register the way a tuner listens, asks for a smooth curve, and solves all 87 unknowns exactly. A4 is not an unknown: $x_{49} = 0$ is a hard anchor.
- 2:1 · 4:2 · 6:3 · 8:4 · 10:5 octaves
- 4:1 double octaves
- 3:2 fifths
$d_{c}$ is the right-hand side of the interval equation and $w_{c}$ its weight; $λ = 0.05$ . $ε$ is a width asked for on purpose: zero for every octave family and for fifths, so with $B = 0$ the curve is exactly flat; the Pure twelfths style instead adds 3:1 twelfths with $ε = + 1.955$ ¢. A family is only used where its partials are measurable (below 6 kHz). While you tune, the notes you have finished are pinned into the same system and the rest re-solves around them.
06
Overpull: sharp on purpose
Where in the app: Pitch raise

$Φ_{eff} = 0.85 \cdot {\overline{Φ}}_{k} + 0.15 \cdot Φ_{k}$ ${target}_{k} = x_{k} + ρ (k) \cdot Φ_{eff}$

Raising a flat piano loads the frame, so strings tuned early sag as the rest come up. $Φ_{k}$ is how far key $k$ has to rise (curve minus survey); ${\overline{Φ}}_{k}$ is the same for its neighbours within 8 semitones, averaged with a Gaussian weight and never across the wound/plain break. The app aims sharp by a fraction $ρ$ of that, between 0.12 and 0.33 depending on the register.

An estimate, not a simulation of your frame and soundboard: fixed constants, halved for strings that are already sharp, and clamped to −15 … +30 ¢ (+15 ¢ at most on wound strings). Very flat pianos get two passes instead of a bigger overpull.
07
Two strings, one note
Where in the app: Unison

$offset = 1200 \cdot \log_{2} (1 + \frac{Δ f}{f_{ref}})$ $beat @ fundamental = \frac{| Δ f |}{n^{*} \cdot R_{n^{*}} (B)}$

Two nearly identical strings make a slow wobble. The app isolates the partial it is listening to ( $n^{*}$ ), flattens out the natural decay and fits two pure tones to what is left; $Δ f$ is the gap between them. That gives the cents between the strings, the beat at that partial ( $| Δ f |$ ) and at the fundamental, and which way to turn the pin, even when the wobble is slower than one cycle per listening window.

Illustrative numbers: A4 heard at partial 2 (about 880 Hz) with the open string 0.50 Hz high reads +0.98 ¢, 0.50 Hz at partial 2, 0.25 Hz at the fundamental.

Worked example · equation 02

Middle C, eight partials up.

C4 · $f_{1}$ = 261.63 Hz
$B$ = 4.0e-4

The textbook column is what an ideal, perfectly flexible string would give. The real column is equation 02. By the eighth partial the string is more than a fifth of a semitone sharp of the textbook, which is why an octave tuned to an exact 2 : 1 beats.

Illustrative — the app’s default model, not a specific piano. Offsets are $c (p_{n}, n \cdot f_{1})$ from equation 01.
Partial n	Textbook n · f₁, Hz	Real pₙ, Hz	Offset cents
1	261.63	261.63	0.00
2	523.26	523.57	+1.04
3	784.89	786.14	+2.76
4	1046.52	1049.65	+5.18
5	1308.15	1314.41	+8.27
6	1569.78	1580.73	+12.03
7	1831.41	1848.90	+16.46
8	2093.04	2119.24	+21.53

The details

Made for an afternoon at the piano.

Reference pitch: A4 from 415 to 466 Hzin 0.1 Hz steps; 440.0 by default.
Temperaments: Equal · Werckmeister III · Kirnberger III · Vallotti · Young II · ¼-comma meantone
Stretch styles: Standard · Light · Bass wide · Treble wide · Pure twelfthsPure twelfths with equal temperament. Bass and treble trims on top.
Sessions: One per piano, saved as you workLayout, survey, measurements and progress. Never deleted automatically; export any session as a zip. Each device keeps its own.
At the bench: Dark, big type, one step at a timeReadable from the bench on every screen. On the Mac, also one-key shortcuts: ← → note · Space lock · M mark tuned · ? all of them. Respects Reduce Motion.
Shows its work: Nothing is hiddenThe Curve view shows every measured note, how sure the app is, and how far a note could still move, in cents.

Privacy

What your microphone hears stays in the room.

Resonance never goes online. No account, no tracking, no cloud. It listens on your iPhone, iPad or Mac and sends nothing anywhere.

It does keep short clips of the notes it measures, a few seconds each, stored with that piano's session on your device. Delete the session and the clips go with it.

Read the privacy policy

What you need

An iPhone, iPad or Mac, and a tuning lever.

Resonance shows where each string is and where it should be. Turning the pin is your job, and like any hand skill it gets easier with practice.

iPhone and iPad: iOS 18 or iPadOS 18, or later
Mac: macOS 15 or later
Microphone: Built-in, wired or USBPick it in Settings. A good microphone helps. Bluetooth headsets are not used.
Piano: Grand or upright88 keys, or 85 (A0–A7).
Tools: Tuning lever and mutesA felt strip or rubber wedges.
Version: 1.0 · EnglishMusic · App Store and Mac App Store

Questions

Before you reach for the lever.

Can I really tune my own piano?

Yes, with patience. The hard part to learn is hearing exactly where a string is and where it should be, and that's the part Resonance does for you. What's left is the hand work: small, steady turns of the tuning lever.

That takes practice, and your first tuning will take a while. Start with a piano that's close to pitch, go gently, and don't force a pin that feels wrong. If something feels off, stop and call a tuner. The app won't turn the pins for you, and it can't teach you lever technique; that comes with time.

Will it replace my piano tuner?

No, and it isn't meant to. A tuner does more than tune: they set each pin so the tuning holds, regulate the action, voice the hammers, and fix loose pins, buzzing strings and sticking keys.

Resonance is for the times you can't get one: between visits, far from the nearest tuner, or when a visit isn't in the budget. When something needs a repair, call a professional.

Does it work on iPhone and iPad?

Yes. The same app runs on iPhone and iPad with iOS 18 or later, and on the Mac with macOS 15 or later.

You can do a whole tuning on your phone: setup, the survey, a pitch raise, measuring, and every note and unison. The Mac adds a few extras for the curious: the curve charts, the unison numbers and the strobe.

What do I need besides the app?

An iPhone or iPad with iOS 18 or later, or a Mac with macOS 15 or later. A tuning lever, and mutes: a felt strip or rubber wedges. The muting pictures in the app assume you have one or the other.

And a quiet room. Fans, fridges and open windows are the usual trouble.

Do I need an external microphone?

No. The app can use the built-in microphone of your iPhone, iPad or Mac, or a wired or USB microphone or audio interface. You pick it in Settings. Bluetooth headsets aren't used, because they aren't good enough for tuning.

A good microphone helps, and Resonance was designed around one. We make no promise about how well a built-in microphone does. Setup shows a level bar so you can check: play a note and the bar should jump to about three quarters. With Advanced mode on, Setup also has a quiet check.

Does it work on an upright?

Yes. Setup asks whether the piano is a grand or an upright, and the muting instructions change to suit: on an upright the mutes go in from the front, above the hammers. Pianos with 85 keys, which stop at A7, work too.

Each layout starts with a typical guess for where the two-string, three-string and copper-wound notes are, and you correct it for your piano. To be plain about it: the app was developed on a grand.

What is inharmonicity, in one paragraph?

An ideal string's overtones sit at exactly 2, 3, 4… times its fundamental. A piano string is stiff steel, and the stiffness pushes each overtone a little sharp, more so the higher the overtone. How much is one number per note, called B, and it differs from note to note and from piano to piano. Octaves sound clean when the overtones of the two notes line up, so the right pitch for each note depends on B. Resonance measures B on your piano and works out the stretch from it.

How many notes do I have to measure?

Not all of them. Start with about nine, spread over the keyboard. The app picks them, then usually asks for a few more where they help most. Each note takes two strikes that agree.

It tells you when it has enough. curve reliable (0.7¢) means more measuring could still move a note by up to 0.7 cents. Notes you haven't measured are filled in from the ones you have, and the app keeps learning from clean strikes while you tune.

What is a pitch raise, and do I need one?

Only if the piano is well below pitch. Raising many strings adds tension to the frame and the soundboard, and that pulls the strings you've already tuned flat again. So a pitch raise is a quick rough pass that aims each string a little sharp on purpose. The careful tuning comes afterwards.

You don't have to guess. Play through the Survey and it tells you: no pitch raise, one pass, or two. It goes gently, never aiming more than 30 cents sharp, or 15 on the copper-wound strings. It warns you when a string is at risk, but it can't stop a string from breaking, so take an old piano slowly.

How accurate is it?

The needle reads to a tenth of a cent, and IN TUNE means within half a cent, held for half a second.

Our accuracy figures come from synthetic test signals, where the right answer is known exactly: there the app holds ±0.1 cent and recovers B to within 2 %. We don't quote a figure for real pianos. On a real piano the string is the limit, not the software: it drifts a little as it rings, and no two strikes are quite the same.

Can I use historical temperaments, or a different A4?

Yes. Six temperaments are built in: Equal, Werckmeister III, Kirnberger III, Vallotti, Young II and ¼-comma meantone. A4 can be anywhere from 415 to 466 Hz, in steps of 0.1 Hz.

There are five stretch styles too, from Light to Pure twelfths. Pure twelfths needs equal temperament. You can't define a temperament of your own.

Does any sound leave my iPhone, iPad or Mac?

No. The app makes no network connections at all. There's no account, no analytics and no cloud.

It does save some sound on the device: a clip of up to about 4 seconds for each note it measures. The clips stay inside that piano's session and nowhere else. The privacy policy has the details.

Where are my sessions?

On the device you used, one folder per piano, saved automatically as you work. Sessions are never deleted automatically.

On the Mac, Reveal in Finder in Sessions shows the folder, and Tuner › Export session folder (zip)… makes a copy you can keep. On iPhone and iPad the folders are in the Files app, under On My iPhone (or iPad) › Resonance, and Settings › Export session makes a zip you can save or send.

Do my sessions move between my iPhone and my Mac?

No. Each device keeps its own sessions. There's no account and no cloud, so nothing syncs. Measure and tune a piano on one device.

Something else? Visit support.

When a tuner can't come, tune it yourself.

Download on theApp Store Download on theMac App Store

iPhone and iPad with iOS 18 or later · Mac with macOS 15 or later

Tune your own piano.

Resonance — the film

Why an ordinary tuner app gets a piano wrong.

Set up

Survey

Pitch raise

Measure

Curve

Tune

Unisons

Stand it on the music desk.

It tells you which string. Then it listens.

A stretch curve from your strings, not from a table.

Far from pitch? Start there.

Then pull the unisons clean.

Middle C, eight partials up.

What your microphone hears stays in the room.

When a tuner can't come, tune it yourself.