A cent is the unit for small pitch differences: 1 semitone = 100 cents and 1 octave = 1,200 cents. A tuner reading of +10 cents means the note is one tenth of a semitone sharp; −50 cents is halfway to the next note down. Cents between two frequencies = 1200 × log₂(f₂ / f₁).
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Chromatic Tuner with a cents meter
Play or sing any note and read the note name, the frequency in Hz and how many cents sharp or flat you are, with a strobe for fine tuning.
Open the chromatic tuner →What Is a Cent in Music?
The cent was introduced by the phonetician and mathematician Alexander J. Ellis in 1885 so that musicians could compare tunings from different cultures on one scale. One cent is a frequency ratio of 21/1200 ≈ 1.000578. Because it is a ratio, a cent is the same musical size everywhere: 10 cents sharp sounds equally “off” on a low bass note and on a high soprano note, even though the difference in Hz is very different. That is why tuners, pitch detectors and DAWs all show tuning errors in cents rather than in hertz.
How Many Cents in a Semitone, a Tone and an Octave?
| Interval | Cents (equal temperament) |
|---|---|
| 1 cent | 1/100 of a semitone |
| Quarter tone | 50 |
| Semitone (half step, one piano key) | 100 |
| Whole tone (whole step) | 200 |
| Minor third | 300 |
| Major third | 400 |
| Perfect fourth | 500 |
| Tritone | 600 |
| Perfect fifth | 700 |
| Octave | 1,200 |
| Two octaves | 2,400 |
A “note” in the sense of one step on the piano is therefore 100 cents, and there are 12 × 100 = 1,200 cents in every octave, whatever key you are in.
The Cents Formula: 1200 × log₂(f₂ / f₁)
To find the distance between a reference frequency f₁ and a measured frequency f₂:
cents = 1200 × log₂(f₂ / f₁) (the same as 3986.3 × log₁₀(f₂ / f₁))
To go the other way, from cents to a frequency: f₂ = f₁ × 2cents/1200. Worked examples with A4 = 440 Hz as the reference:
- 445 Hz: 1200 × log₂(445/440) = +19.6 cents (clearly sharp).
- 432 Hz: −31.8 cents, about a third of a semitone flat (see 432 Hz vs 440 Hz).
- 415 Hz, the baroque A: −101.3 cents, one semitone plus about one cent (see historical pitch standards).
- 440 Hz + 10 cents = 440 × 210/1200 = 442.55 Hz.
The frequency to note converter does this for you: type any frequency and it shows the nearest note and the offset in cents.
Cents to Hz at A4 = 440 Hz
| Offset | Frequency | Difference |
|---|---|---|
| −50 | 427.47 | −12.5 Hz |
| −20 | 434.95 | −5.1 Hz |
| −10 | 437.47 | −2.5 Hz |
| −5 | 438.73 | −1.3 Hz |
| −1 | 439.75 | −0.3 Hz |
| +1 | 440.25 | +0.3 Hz |
| +5 | 441.27 | +1.3 Hz |
| +10 | 442.55 | +2.5 Hz |
| +20 | 445.11 | +5.1 Hz |
| +50 | 452.89 | +12.9 Hz |
The size of one cent in Hz grows with pitch, which is why tuners use cents:
| Note | Frequency | 1 cent ≈ |
|---|---|---|
| A2 | 110.00 | 0.064 Hz |
| A3 | 220.00 | 0.127 Hz |
| A4 | 440.00 | 0.254 Hz |
| A5 | 880.00 | 0.508 Hz |
| A6 | 1,760.00 | 1.017 Hz |
How Many Cents Out of Tune Is Noticeable?
There is no single threshold: it depends on the listener, the note, the loudness and whether the notes sound together (where beating reveals tiny errors) or one after another. These are widely used rules of thumb, not strict standards:
| Offset | What it means in practice |
|---|---|
| 0 to ±2 cents | Effectively perfect; the target for recording and fixed-pitch instruments. |
| ±3 to ±5 cents | Most tuners show “in tune” (green) in this zone; hard to hear on a single note. |
| ±5 to ±10 cents | Around the smallest difference many listeners can detect; trained ears notice it, especially in held chords. |
| ±10 to ±25 cents | Audibly out of tune to most musicians; the chord starts to sound sour. |
| ±25 to ±50 cents | Clearly wrong; at ±50 cents you are halfway to the neighbouring note and the tuner may flip to it. |
Singers move more than instruments, so on held notes a few cents of drift is normal and vibrato swings much wider. How to read these numbers in your own takes is explained in how to interpret pitch detector results; causes and fixes are in why singers go sharp or flat, and the pitch accuracy checker scores your average cents error.
Cents in Equal Temperament vs Just Intonation
Equal temperament makes every semitone exactly 100 cents. Pure (just) intervals from simple frequency ratios are slightly different, and cents show by how much:
| Interval | Equal temperament | Just ratio (cents) | ET − just |
|---|---|---|---|
| Minor second | 100 | 111.7 (16:15) | −11.7 |
| Major second (whole tone) | 200 | 203.9 (9:8) | −3.9 |
| Minor third | 300 | 315.6 (6:5) | −15.6 |
| Major third | 400 | 386.3 (5:4) | +13.7 |
| Perfect fourth | 500 | 498.0 (4:3) | +2.0 |
| Tritone | 600 | 590.2 (45:32) | +9.8 |
| Perfect fifth | 700 | 702.0 (3:2) | −2.0 |
| Minor sixth | 800 | 813.7 (8:5) | −13.7 |
| Major sixth | 900 | 884.4 (5:3) | +15.6 |
| Minor seventh | 1000 | 1017.6 (9:5) | −17.6 |
| Major seventh | 1100 | 1088.3 (15:8) | +11.7 |
| Octave | 1200 | 1200.0 (2:1) | 0 |
The equal-tempered major third is about 14 cents wider than a pure one, which is why a held major chord on a piano beats slightly while a good choir or string quartet can tune it pure. More in intonation and temperament explained.
Cents on Tuners, Pitch Shifters and Synths
- Tuners and pitch detectors: the needle or bar runs from −50 to +50 cents around the nearest note; 0 is perfectly in tune. The online pitch detector shows the live cents offset for voice and instruments.
- Pitch shifters and DAWs: the coarse control moves in semitones and the fine control in cents (100 cents = 1 semitone). Moving a 440-tuned song to 432 Hz is a −31.8 cent shift in the pitch shifter.
- Synth detune: two oscillators detuned by a few cents beat against each other and sound thicker, the basis of chorus and “supersaw” sounds.
- Reference pitch: tuning to A4 = 442 Hz instead of 440 raises everything by 7.9 cents; why 440 is the default is covered in A440 explained.
- Vibrato: a singer’s vibrato is measured as its width in cents above and below the note; see what is vibrato.
Cents FAQ
Is 100 cents a semitone?
Yes. In equal temperament one semitone (half step) is exactly 100 cents, a whole step is 200 cents and an octave is 1,200 cents.
How many cents is out of tune?
As a rule of thumb, within ±5 cents counts as in tune on most tuners, 10 cents or more is noticeable to trained listeners, and 20 cents or more sounds clearly out of tune.
What is a cent in guitar tuning?
It is the tuner’s measure of how far a string is from its target note. Tune each string to within a few cents of 0, then check chords, because fretting and string height add small errors of their own.
How do I convert cents to Hz?
Multiply the reference frequency by 2cents/1200. At A4 one cent is about 0.25 Hz, so +10 cents is about 442.55 Hz.
Related: see every note’s exact frequency in the musical note frequency chart, or all tuners and tuning guides in the instrument tuning hub.
Ornella is a music technology writer and vocal tools specialist at Pitch Detector. She creates practical content around pitch detection, note recognition, vocal analysis, and singing education tools for beginners, singers, and audio creators.