Cents to Frequency Calculator
Cents to Frequency
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Frequency Difference in Cents
New frequency = base × 2^(cents ÷ 1200). Cents between two frequencies = 1200 × log₂(f₂ ÷ f₁). 100 cents = one semitone; 1200 cents = one octave. Related: note frequency, equal temperament.
What Your Result Means
- New Frequency: The pitch in Hz after applying your cent offset to the base frequency. Positive cents raise the pitch; negative cents lower it.
- Frequency Ratio: The multiplier between the base and new frequency. A ratio of 2.0 means one octave up; a ratio of 1.0595 is one equal-tempered semitone (100 cents).
- Cents Between: The logarithmic distance between two frequencies. Positive values mean f₂ is higher than f₁. Every 100 cents is one semitone; 1,200 cents is one octave.
How This Calculator Works
You enter a base frequency and a cent offset, or two frequencies to compare. For cents-to-frequency, the tool computes newFreq = base × 2^(cents ÷ 1200). For the difference between two frequencies, it computes cents = 1200 × log₂(f₂ ÷ f₁). Both formulas derive from the equal-temperament definition where one octave equals 1,200 cents.
Quick Questions
What exactly is a cent in music?
A cent is 1/100 of an equal-tempered semitone, or 1/1200 of an octave. It is a logarithmic unit, which means adding 100 cents always multiplies the frequency by the same ratio (~1.0595), regardless of the starting pitch.
Why use cents instead of Hz?
Hz differences are not perceptually uniform — a 10 Hz gap sounds large at low frequencies but tiny at high ones. Cents are perception-proportional: 100 cents always sounds like one semitone, whether you start at 100 Hz or 1,000 Hz.
How many cents is "out of tune"?
Most listeners can detect pitch differences of about 5–10 cents. Professional musicians often aim for accuracy within 2–3 cents. Orchestral tuning and choral intonation routinely involve adjustments of just a few cents.
Can cents be negative?
Yes. A negative cent offset means the new frequency is lower than the base. Similarly, the cents-between result is negative when f₂ is lower than f₁.
Sources
- Wikipedia — Cent (music) (definition, formulas, and history of the cent unit)
- Wikipedia — Equal Temperament (the 12-TET system and its relationship to cents)
Method & review
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.