One Cent Is a Hundredth of a Half Step
Modern tuning splits the octave into 12 equal half steps, and each half step into 100 cents. The physicist Joe Wolfe of the University of New South Wales (UNSW) gives the formula: a note's distance in cents from A4 is 1,200 × log2(f ÷ 440 Hz). An octave doubles the frequency, so it is 1,200 cents.
Cents are a ratio, not a fixed number of hertz. One cent raises a frequency by about 0.058%, and one half step by about 5.9%. That is why the same cents reading means the same thing on a bass string and a piccolo. At A4 (440 Hz):
- +1 cent: 440.25 Hz
- +5 cents: 441.27 Hz
- +10 cents: 442.55 Hz
- +50 cents: 452.89 Hz, halfway to the next note
- +100 cents: 466.16 Hz, which is A♯4 (B♭4)
How to Read the Needle
Most tuners show the nearest note name and a needle or bar from −50 to +50 cents. Fifty cents is halfway to the next note, so a note more than 50 cents sharp is shown as the next note up, flat. Peterson's StroboFlip manual, for example, sets its cents range at ±50 cents in 0.1-cent steps.
- A plus number, or a needle right of center: the note is sharp. Lower it (loosen a string, or pull out a tuning slide or barrel).
- A minus number, or a needle left of center: the note is flat. Raise it (tighten a string, or push the slide or barrel in).
- A reading near ±50 cents: check the note name first. You may be closer to the next note than the one you want.
On a strobe tuner the same idea is shown as motion. Peterson's manual says the strobe image moves up when the note is sharp, down when it is flat, and stands still when it is in tune.
How Close Counts as In Tune
Tuners are far more precise than any player needs. Boss rates its TU-3 pedal tuner as accurate to ±1 cent, and Peterson rates the StroboFlip at 1/10 of a cent, which its manual notes is a thousandth of a half step.
Our chromatic tuner says In tune once your note stays within 3 cents of the target for half a second. A few cents is a small change: at A4, 3 cents is 0.76 Hz.
Some tunings move notes away from zero on purpose. Tuning A4 to 442 Hz puts every note 7.9 cents sharp of standard, and 432 Hz puts every note 31.8 cents flat. See 432 Hz vs 440 Hz for more.
Check Your Own Notes
Open the online tuner, tap Start Tuning, and play or sing one note at a time. It shows the note, its frequency, and how many cents sharp or flat you are, using your phone or computer mic. For a guitar, the guitar tuner adds a button for each string, and tuning a guitar without a tuner shows how to get close by ear first.