What is a cent in music?

A cent is one hundredth of an equal-tempered semitone, which makes an octave 1200 cents. Because it is a logarithmic unit, a cent describes a ratio rather than a fixed number of hertz: the same 10 cents is a wide gap at the bottom of a piano and a barely audible one at the top.

It is a 20th-century standard, not a physical fact. The pitch called A has been fixed at 415 Hz for Baroque organs, 426 Hz in eighteenth-century France, 435 Hz under the 1939 international compromise and 440 Hz since the 1974 ISO 16 standard. Some European orchestras still use 442 or 443 Hz, and early-music ensembles deliberately play at 415 or even lower.

How many cents apart are two notes a semitone apart?

Exactly 100 cents, by definition, since equal temperament defines the semitone that way. A thousand cents is a semitone, and 1200 is an octave. Any deviation from 100 means the interval is not equal-tempered — which is exactly what distinguishes just intonation from the tempered scale.

Is 5 cents out of tune?

For a trained listener in a sustained context, 5 cents is noticeable; 2 cents is audible in a slow passage but easily masked in a fast one. Whether it matters depends on the context: a beating fifth is deliberate in some tuning traditions, and inconsequential in a pop mix. Under sustained exposure the threshold drops by roughly half.

Should I tune to 440 or 442 Hz?

Tune to 440 unless you know the ensemble expects otherwise. Moving to 442 is a 7.9-cent change, well above the just-noticeable difference, so it is audible as a shift and it will need every other part retuned to match. The 7.9 cents between them is small enough that a player may not consciously notice, but a recording made at one pitch will play audibly sharp at the other.

Cents and tuning: how far off is that note?

A cent is not a number of hertz. It is a ratio, which is why 5 cents is a wide gap at the bottom of a piano and a barely-audible one at the top. Once you read a tuner as a ratio rather than a distance, the number stops being mysterious — and the question of what to tune to stops being a preference.

Cents and tuning calculator

Enter a frequency to find the nearest note and how far off it is, or set a reference to retune the whole table.

Frequency (Hz) Tuning reference for A4 (Hz) Or a target note

Nearest note

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Also spelled

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Offset

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Direction

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MIDI note

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Exact frequency of that note

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Difference

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Period

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Reference in use

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Shift from 440 Hz

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A4 at 440 Hz would be

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What a cent actually is

Equal temperament divides an octave into twelve equal semitones. A cent is a hundredth of one of those, which fixes two things at once:

1 semitone = 100 cents · 1 octave = 1200 cents

The important consequence is that a cent is a ratio, not an absolute step. The number of hertz a cent represents grows with pitch, because the relationship is exponential. At A4 = 440 Hz one cent is about 0.25 Hz. At A2, two octaves down, it is about 0.063 Hz. At A7, three octaves up, it is about 2 Hz.

Note	Frequency	Size of 1 cent
A2	110.00 Hz	0.063 Hz
A3	220.00 Hz	0.127 Hz
A4	440.00 Hz	0.254 Hz
A5	880.00 Hz	0.508 Hz
A6	1760.00 Hz	1.016 Hz
A7	3520.00 Hz	2.032 Hz

So "5 cents flat" means something quite different depending on register. On a low bass note it is a shift of 0.3 Hz, which the ear may not resolve at all. On a high treble note it is 1 Hz, which is plainly audible under sustained conditions. This is the whole reason tuning is hardest at the extremes of the keyboard, and why a piano technician's job gets harder toward the treble.

Reading a tuner

A chromatic tuner shows the nearest note, how far off you are in cents, and which way. The number is circular: there is no wrap-around at 50 cents, because anything more than half a semitone belongs to a different note.

What each reading means in practice:

Under 2 cents — inaudible in context. Do not chase it; a tuner reading that close is as likely to be its own noise floor as your playing.
2 to 5 cents — audible in a slow, sustained passage, easy to miss in a fast one. Worth fixing if the context allows.
5 to 15 cents — plainly out. You will hear it as a pitch shift rather than as wrongness.
Over 20 cents — a different note is a plausible reading, or the instrument is genuinely mistuned.

The catch is that the threshold depends on exposure. A beat-frequency fifth is audible at 3 cents in a held chord and inaudible in a passage moving every 200 ms, because the ear has no time to resolve it. Sustained exposure roughly halves the noticeable figure.

Why A4 is 440 and who says otherwise

The pitch called A has no fixed frequency. It was about 415 Hz in the Baroque, roughly 426 Hz in eighteenth-century France, and the modern value is the result of two twentieth-century decisions. In 1939 an international conference settled on 435 Hz. Then in 1974 ISO 16 moved it to 440, largely to give the Western pitch a single fixed reference for measurement and to simplify cassette and record manufacture.

A4	Called	Used by	Shift from 440
415 Hz	Baroque pitch	Handel, Bach-era ensembles	−101.3 cents
421 Hz	Classical pitch	Mozart-era Viennese pitch	−76.4 cents
426 Hz	Diapason normal	French eighteenth century	−56.0 cents
435 Hz	Concert pitch	The 1939 compromise	−19.8 cents
440 Hz	Modern standard	ISO 16 since 1974	—
442 Hz	German concert	Still current in some orchestras	+7.9 cents
443 Hz	Bright pitch	A few European orchestras	+11.8 cents
466 Hz	Ottoman / court	Historical court practice	+99.4 cents

The 7.9 cents between 440 and 442 is the interesting one, because it is small enough that a player switching to 442 may not consciously notice, yet large enough that a recording made at one pitch sounds audibly sharp at the other. This is the argument for deciding deliberately and for tuning every track to an explicit reference rather than to whatever the piano happened to be.

Changing the reference shifts everything

The reference is not one number that affects one note. Because every pitch is defined as a ratio to A4, moving A4 moves the entire keyboard. Switching from 440 to 415 does not just detune the A above middle C; it detunes all 88 keys by the same 101.3 cents, which is about 101 cents.

That is why ensemble tuning is a conversation rather than a setting. Moving a string quartet from 440 to 415 for a Baroque programme means every player re-tunes by the same amount, and the harpsichord or organ has to be adjusted too. Getting it wrong by 20 cents leaves the ensemble in a worse place than either starting point.

Five mistakes worth avoiding

Reading cents as hertz. 5 cents is 1.3 Hz at A4 but only 0.32 Hz at A2, so the same reading means different things in different registers.
Tuning to 440 when the ensemble expects 442. The 7.9-cent difference is above the threshold for sustained tones and will be heard as the session slipping.
Chasing a 1-cent reading. Below about 2 cents the tuner is as likely to be reporting its own noise as your pitch.
Assuming a cent is a percentage. 100 cents is a ratio of 2^(1/12), which is 5.946%, not 5% and not 1%.
Retuning by ear against an already-drifting piano. If the reference instrument is 15 cents out, matching it bakes the error into everything recorded from then on. Check the reference first.

Formulas worth keeping

Quantity	Expression
Frequency from MIDI note	f = f_ref × 2^(n−69)/12
MIDI note from frequency	n = 69 + 12 · log₂(f ÷ f_ref)
Cents between two pitches	1200 · log₂(f₂ ÷ f₁)
Transpose by semitones	f₂ = f₁ × 2^n/12
Period	T = 1 ÷ f
Cents for a frequency ratio	c = 1200 · log₂(ratio)

Summary

A cent is a hundredth of a semitone, which makes it a ratio: the same number is worth a quarter of a hertz at A4 and two hertz at A7. A4 = 440 Hz is a 1974 standard, not a physical constant, and moving it moves the whole keyboard by the same amount — so 415 for Baroque and 442 for a German concert are not details, they are decisions. Set the reference deliberately, read the cents as ratios, and leave anything under 2 alone.