Pitch Bend Cents Calculator
Cents are the universal fine ruler of pitch: one hundredth of a semitone, twelve hundred to the octave. Any change in frequency, whether a deliberate pitch bend, a tuning offset, or an intonation error, can be expressed in cents by taking the base-two logarithm of the frequency ratio. This calculator takes an original frequency and a bent or measured frequency and returns the interval in cents, the equivalent in semitones, and the raw frequency ratio. Use it to quantify a guitar bend, check how far a note is sharp or flat, or convert between tuning systems with a single, even measure.
Cents formula
Ratio = bent frequency / original frequency
Cents = 1200 * log2(ratio)
Semitones = cents / 100
Frequency change (percent) = (ratio - 1) * 100
The base-two logarithm turns the multiplicative frequency ratio into an additive cents measure. Positive cents mean the pitch rose (sharp); negative cents mean it fell (flat).
Cents and bending context
- An octave is 1,200 cents; an equal-tempered semitone is exactly 100 cents.
- A full-tone guitar bend raises pitch by 200 cents; a typical blues bend is around 300 cents.
- Differences under a few cents are barely audible; over ten cents is clearly noticeable.
- MIDI pitch bend range is set per instrument, commonly plus or minus two semitones.
- Tuners show the same cents deviation to indicate sharp or flat notes.
Pitch bend cents: frequently asked questions
How are cents calculated from two frequencies?
Cents equal 1,200 times the base-two logarithm of the ratio of the two frequencies. Because an octave is a 2:1 ratio and spans 1,200 cents, the logarithm turns any frequency ratio into a precise interval measure. A ratio of 1 gives 0 cents, no change.
What is a cent in tuning?
A cent is one hundredth of an equal-tempered semitone, so a semitone is 100 cents and an octave is 1,200 cents. Cents give a fine, even scale for comparing pitches. A few cents of error is hard to hear; more than about ten cents is clearly noticeable to trained ears.
How does this relate to MIDI pitch bend?
MIDI pitch bend is a 14-bit value with a centre at no change, and the bend range in semitones is set per instrument, often two semitones. To find the cents a given bend produces, work out the semitone shift the bend represents and multiply by 100, or compare the bent and original frequencies directly here.
Can I check an instrument's intonation with this?
Yes. Measure the played frequency and compare it with the target frequency. The cents result is the tuning error: positive means sharp, negative means flat. Many tuners display this same cents deviation from the nearest note.
Why use a logarithm for pitch?
Human pitch perception is roughly logarithmic: equal musical intervals correspond to equal frequency ratios, not equal frequency differences. The logarithm converts multiplicative ratios into additive cents, so intervals add up the way our ears expect.
Official sources
- UNSW School of Physics: Note names, MIDI numbers and frequencies.
- MIDI Association: MIDI pitch bend specification.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.