And why your tuner shows “−7” instead of telling you how many hertz you're off.
A cent is one hundredth of a semitone. Since an octave has twelve semitones, an octave is 1200 cents. It measures the distance between two notes, not absolute pitch: “you're at −7 cents” means “you're seven hundredths of a semitone below where you should be.”
Because your ear doesn't hear hertz: it hears ratios. Going up an octave always means doubling the frequency, which means the same interval is worth a different number of hertz depending on where you are.
| Note | Frequency | One semitone up | Difference |
|---|---|---|---|
| E2 (open 6th string) | 82.41 Hz | 87.31 Hz | 4.9 Hz |
| A4 (reference pitch) | 440.00 Hz | 466.16 Hz | 26.2 Hz |
| E6 | 1318.51 Hz | 1396.91 Hz | 78.4 Hz |
The same semitone is 5 Hz down low and 78 Hz up high. If your tuner measured in hertz, “3 Hz flat” would be a disaster on the sixth string and inaudible on the first. In cents, on the other hand, 7 cents sound just as out of tune anywhere on the instrument. It's the unit that matches what you hear.
cents = 1200 × log₂(f_measured / f_target).
A semitone is always a factor of 21/12 ≈ 1.0595, wherever it falls.
| Deviation | What happens |
|---|---|
| 1–3 cents | Inaudible on a single note. It only shows up as very slow beating if two instruments hold the same note. |
| ±5 cents | The threshold tuners use to call a string good. A trained ear starts to notice it on long notes. |
| 10–15 cents | You can hear it. A chord sounds “muddy” without it being clear which string is to blame. |
| 25 cents | A quarter tone. Clearly wrong to anyone. |
| 100 cents | A whole semitone: you're on a different note. |
Because a plucked string doesn't have a single frequency. During the attack the tension is higher and the note comes out a few cents sharp; as it dies away, it drops. On top of that, the low strings of a guitar have inharmonicity: because of their stiffness, their overtones don't land on exact multiples of the fundamental, and the detector receives a mix that keeps shifting.
That's why the needle on a good tuner is always smoothed —averaging several readings, throwing out the erratic ones— and why the criterion is a band of ±5 cents rather than a single point. A tuner that stayed pinned at exactly zero would be lying to you.
The tuner shows cents and hertz at the same time, with a smoothed needle and the string turning green within ±5 cents. Adjustable reference pitch from 415 to 466 Hz. Free, no account, works offline.
Get it on Google Play Download on the App StoreBecause of the inharmonicity of its strings, a piano is tuned to the Railsback curve: the bass somewhat lower and the treble somewhat higher than the math would dictate, by up to 30 cents at the extremes. It's done because a “correctly” tuned piano sounds wrong. If you tune a guitar with a tuner and then play with a piano up in the treble, that's part of the explanation.
Equal temperament spreads the error of pure intervals across the whole neck: a major third on a guitar is about 14 cents above the pure third that the harmonic series would produce. It isn't a flaw in your instrument; it's the price of being able to play in any key with the same frets.
In equal temperament, it is. In the just intonation a choir or a string quartet uses when holding a chord, it isn't: there the intervals settle into simple ratios (3:2, 5:4) and the notes shift by several cents relative to the piano. That's why a singer who is in tune with their group can sound out of tune against a keyboard.