Cents & Detune Calculator

A cent is one hundredth of an equal-temperament semitone. One octave spans 1200 cents because frequency doubles (ratio 2:1). The cents between two pitches is 1200 × log₂(f₂ ÷ f₁). Positive cents mean the second frequency is higher; negative cents mean it is lower. This logarithmic scale matches human pitch perception better than raw Hz differences — a 4 Hz gap near A440 feels similar to a 4 Hz gap near A220 in cents terms.

Cents Between mode compares two Hz values you enter — useful when measuring how far a guitar string drifts from a reference tone or how two singers unison on a held note. Detune By Cents mode starts from one frequency and applies an offset — the way synthesizer fine-tune knobs and Auto-Tune retune speed settings think about micro-adjustments.

Everyday thresholds: ±5 cents is near the just-noticeable difference for many trained listeners in quiet conditions. ±50 cents is a quarter-tone. ±100 cents is exactly one semitone. Guitar intonation setup often targets string error under ±3 cents at the twelfth fret. Pipe organs and historical keyboards may intentionally spread temperament — cents math still applies even when the target is not equal temperament.

Worked example with the default Cents Between fields: Frequency 1 = 440 Hz, Frequency 2 = 444 Hz. The ratio 444 ÷ 440 ≈ 1.00909, and log₂ of that × 1200 ≈ +15.7 cents — slightly sharp of concert A. The semitones row shows about 0.16 semitones. Switch to Detune mode with 440 Hz and +100 cents and the output is 466.16 Hz — one semitone up, matching A#4 in equal temperament.

Vocal producers use cents readouts to quantify double-track detune: pan two takes left/right with +10 and −10 cents for subtle width without obvious chorusing. Sample library developers document round-robin detune ranges in cents. When a tuner displays “+4 cents,” enter your reference Hz and the measured Hz here to confirm how close you are to the target.

Common mistakes include treating cents as linear Hz (adding 10 cents twice is not the same as adding 20 Hz), comparing cents across different reference notes without converting through Hz first, and forgetting that beat frequencies between two tones are not the same unit as cents — beats per second depend on absolute Hz difference.

Frequency ratio appears in Detune results as f_out ÷ f_in. A ratio of 1.05946 corresponds to +100 cents. For octave jumps, ratio = 2 and cents = 1200. Use ratio when configuring modular VCO exponential inputs that expect multipliers instead of cent offsets.

Limits: this assumes equal temperament mapping via log₂. It does not replace strobe tuner hardware for live stage tuning. Very low fundamentals below 40 Hz have wider absolute Hz tolerance for the same cent deviation. Inharmonic sounds (bells, gongs) may not have a single meaningful cent offset.