Convert any note to its exact frequency, or any frequency to the nearest note with its offset in cents. Equal temperament, A440 by default, reference pitch adjustable.
exactly in tune · nearest note = 261.63 Hz
Equal temperament divides the octave into 12 identical ratios of 2^(1/12). Every note is therefore f = A4 × 2^(n/12), with n counted in semitones from A4. Going the other way, n = 12 × log₂(f ÷ A4), and whatever fraction of a semitone is left over is expressed in cents (hundredths of a semitone).
Want to hear any of these numbers? The tone generator plays arbitrary frequencies to 0.1 Hz precision - type the value in and listen.
Equal temperament spaces every semitone by a factor of 2^(1/12) ≈ 1.05946. From the A4 = 440 Hz reference: f = 440 × 2^(n/12), where n is the number of semitones from A4. Middle C (C4) is 9 semitones below A4: 440 × 2^(-9/12) ≈ 261.63 Hz. Each octave doubles the frequency.
Invert the formula: n = 12 × log2(f ÷ 440) semitones from A4; round to the nearest whole number for the note, and the remainder × 100 is the offset in cents. Example: 250 Hz → about 8.8 semitones below A4 → closest note B3 (246.94 Hz), 21 cents sharp.
A cent is 1/100 of a semitone - the standard unit for tuning error. Most people hear a pitch difference around 5-10 cents in direct comparison; ±5 cents is a common "in tune" tolerance for instrument tuners. 100 cents = 1 semitone, 1200 cents = 1 octave.
A440 is the modern standard, but baroque ensembles commonly tune to A415, some orchestras to A442-443, and the "432 Hz" tuning has its own following. Changing the reference shifts every note proportionally - the converter recalculates the whole grid from whatever A4 you set.
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