An octave is exactly 1,200 cents. A semitone — one fret, one piano key — is 100 cents, and there are twelve of them in an octave. That is the whole conversion, and it never changes: not with the instrument, not with the octave, not with the key you are playing in.
The reason those numbers matter is that every chromatic tuner reports in them. Point one at any note and it answers with two things: the nearest note name, and a number of cents — “+7” or “−12” — telling you how far you are from it. Cents are the ruler that all tuning is measured with, and once you understand them, every tuner readout, every setup spec and every argument about 440 vs 432 Hz suddenly makes sense.
What a cent actually measures
A cent is 1/100 of a semitone — but the useful part is that the scale is the same everywhere on the instrument. E2 to F2 is 100 cents, and E5 to F5 is also 100 cents, even though the frequency gap in hertz is eight times larger up there. That is the whole point: cents measure musical distance, not raw frequency, which is why “−12 cents” means the same amount of flat on a bass string as on a piccolo.
How many cents is an octave?
An octave is exactly 1,200 cents — always. Twelve semitones of 100 cents each, whether the octave sits at the bottom of a bass or the top of a piccolo. And once you know that one number, every other interval in equal temperament falls out of simple multiplication:
| Interval | Semitones | Cents |
|---|---|---|
| Semitone (minor 2nd) | 1 | 100 |
| Whole tone (major 2nd) | 2 | 200 |
| Minor third | 3 | 300 |
| Major third | 4 | 400 |
| Perfect fourth | 5 | 500 |
| Perfect fifth | 7 | 700 |
| Octave | 12 | 1,200 |
| Two octaves | 24 | 2,400 |
Why pitch needs a logarithmic ruler
Our ears judge pitch by frequency ratios, not differences. Doubling any frequency raises it exactly one octave: 110 → 220 Hz is an octave, and so is 1760 → 3520 Hz. The first jump is 110 Hz wide, the second 1760 Hz wide — yet they sound like the same musical step. A ruler that measured hertz would call those wildly different distances; a logarithmic ruler calls them equal, matching what we hear.
The formula, for the curious:
cents = 1200 × log₂(f₂ ÷ f₁)
Every doubling of the ratio adds 1200 cents; a semitone is a ratio of 21/12 ≈ 1.0595, or exactly 100 cents. Plug in 440 and 432 and you get the famous 31.8-cent gap between the two concert pitches.
How many cents can you actually hear?
The honest answer: it depends on how the notes are presented.
- Two notes in sequence (play one, then the other): most listeners reliably notice differences around 5–10 cents; trained musicians often get to ~3 cents. Below that, played one after another, notes are indistinguishable to nearly everyone.
- Two notes at once: vastly more sensitive, because mistuned simultaneous notes produce audible beating — a rhythmic wobble in volume whose speed equals the frequency difference. Even a 2-cent error between two sustained tones creates a slow pulse a careful ear can catch. This is why tuning by ear works at all, and why out-of-tune chords offend ears that wouldn’t notice the same error in a melody.
- In real music: context is forgiving. Vibrato, short notes and dense arrangements mask errors of 10 cents or more, which is why a slightly off guitar can survive a band mix but sounds naked and sour playing solo arpeggios.
Don’t take our word for any of this — measure your own threshold:
Start at +25 with “Both together” — the wobble is unmissable. Then work downward and find where it disappears for you. Most people lose it somewhere between 2 and 5 cents.
Practical cent thresholds for tuning
| Error | What it sounds like | Verdict |
|---|---|---|
| ±1–3 cents | Inaudible to almost everyone, even in chords | Perfectly in tune |
| ±3–6 cents | Slow beating in sustained chords; melodies fine | Fine for nearly all playing |
| ±6–10 cents | Chords audibly “shimmer”; attentive ears notice | Re-tune before recording |
| ±10–25 cents | Clearly sour in any harmony | Out of tune |
| ±50 cents | Exactly between two notes — the tuner may even flip note names | A quarter-tone off |
| ±100 cents | A different note entirely | Wrong semitone |
Put a number on your own ears
Reading about thresholds is one thing; measuring your own is more fun. The trainer below uses the adaptive method from hearing research — twelve rounds, and it converges on the smallest difference you can reliably hear:
Two tones will play, one after the other. Your job: say whether the second one was higher or lower. Each correct answer shrinks the gap — 12 rounds zero in on the smallest difference your ear can catch. Headphones recommended.
Where else cents show up
- Intonation specs: a well set-up guitar aims for fretted 12th-fret notes within a few cents of the open-string octave. See our tuning stability guide for the harmonic-vs-fretted test.
- Temperaments: historical tuning systems differ from modern equal temperament by cent-sized amounts per note — a Pythagorean major third is 8 cents wider, a just-intonation third 14 cents narrower. (The Pano Tuner’s settings include several of these temperaments if you want to explore.)
- Vibrato and bending: a subtle vocal vibrato swings roughly ±20–50 cents; a guitar half-step bend is a 100-cent journey your ear tracks the whole way.
- Stretch tuning: piano tuners deliberately tune high notes a few cents sharp and low notes flat, because stiff piano strings produce slightly sharp overtones — cents give them the vocabulary to do it precisely.
Frequently asked questions
How many cents are there between two notes?
Between two adjacent notes — one semitone, say E to F or A to A♯ — there are exactly 100 cents. Wider intervals stack from there, as the table near the top of this guide shows: a whole tone is 200 cents, a perfect fifth 700, an octave 1,200.
How many hertz is one cent?
There’s no fixed conversion, because a cent is a ratio, not a frequency step: one cent multiplies frequency by 21/1200 ≈ 1.000578. That works out to roughly 0.05 Hz at a guitar’s low E (E2), 0.19 Hz at the high E (E4), and 0.25 Hz at A4 = 440 Hz — the same musical size, very different frequency sizes. This is exactly why tuners report cents rather than hertz: the number means the same thing on every string.
Why does my tuner's needle never sit perfectly still on zero?
Because the string itself doesn’t sit still. A plucked note starts slightly sharp during the attack, drifts as it decays, and wobbles with any finger contact. A reading that hovers within a couple of cents of center is a stable, in-tune string. Judge the settled average, not the flicker.
Do professional musicians really tune to within 1 cent?
Sustained studio work aims tight, but nobody plays within a cent — fretting pressure, temperature and attack all move pitch more than that in normal playing. What professionals actually do is tune carefully (±2–3 cents), check often, and control pitch with their hands and ears in real time. String and wind players adjust intonation continuously as they play; the tuner just sets the starting point.
What tool do I need to measure cents on my own instrument?
Any chromatic tuner with a needle or cents display — including the free Pano Tuner, which shows the nearest note and a needle calibrated in cents, and lets you change the reference pitch and temperament when you want to go deeper.