Enter a frequency to find the nearest musical note and how many cents sharp or flat it is. One cent = 1/100 of a semitone. A deviation under ±5 cents is generally imperceptible; beyond ±15 cents most listeners perceive the pitch as “out of tune.”
Reverse: note → frequency
| Note | Frequency (Hz) | Wavelength |
|---|
How Frequency Maps to Musical Pitch
Western music divides each octave into twelve equal semitones using a system called twelve-tone equal temperament (12-TET). The frequency ratio between adjacent semitones is the twelfth root of two (√[12]2 ≈ 1.05946). This means that to go up one semitone, you multiply the frequency by 1.05946; to go up one octave (twelve semitones), you multiply by exactly 2.
The formula to find the frequency of a note n semitones above A4 is:
f = 440 × 2n/12
Conversely, to find how many semitones a given frequency is from A4:
n = 12 × log2(f / 440)
The fractional part of n, expressed in hundredths of a semitone, gives the cents deviation. A result of +50 cents means the frequency falls exactly between two notes.
What Are Cents?
The cent is a logarithmic unit of pitch interval. One hundred cents equal one equal-tempered semitone; 1200 cents equal one octave. Cents allow precise measurement of pitch differences regardless of the absolute frequency range. A deviation of 1 cent at 100 Hz (0.06 Hz) is far smaller in absolute terms than 1 cent at 10 kHz (5.8 Hz), but both represent the same perceptual interval.
Trained musicians can typically detect deviations of 5–10 cents. Vibrato in singing and string playing typically spans ±20–50 cents around the target pitch. Piano tuners work to tolerances of 1–2 cents.
Concert Pitch and A4 Reference
The standard reference pitch, A4 = 440 Hz, was adopted by the International Organization for Standardization (ISO 16) in 1955. However, tuning standards have varied considerably throughout history: Baroque ensembles often tune to A415 (a semitone below modern pitch), while some European orchestras prefer A442 or A443 for a brighter sound. This calculator allows you to adjust the reference frequency to match any tuning system.
Frequency Ranges of Musical Instruments
| Instrument | Lowest note | Highest note | Range (Hz) |
|---|---|---|---|
| Piano (88 keys) | A0 | C8 | 27.5–4186 |
| Guitar (standard) | E2 | E6 | 82.4–1319 |
| Bass guitar | E1 | G4 | 41.2–392 |
| Violin | G3 | E7 | 196–2637 |
| Human voice (bass) | E2 | E4 | 82–330 |
| Human voice (soprano) | C4 | C6 | 262–1047 |
Applications in Audio Engineering
- Tuning and calibration: verify oscillator frequencies, check instrument intonation, calibrate tone generators.
- EQ and mixing: identify the fundamental frequency of a problematic resonance by note name to communicate precisely with musicians (“there’s a buildup around B♭2”).
- Sound design: tune synthesiser oscillators, sample playback, and sound effects to a specific musical key.
- Acoustic analysis: correlate room mode frequencies (from the Room Mode Calculator) with musical notes to understand which pitches will be affected.