HesapHanem

Semitone Frequency Calculator

Note frequency from any semitone offset

Result

261.63

How it is calculated

The tool uses equal temperament: f = ref × 2n/12, where n is the number of semitones above (positive) or below (negative) the reference note A4, ref is the reference frequency in Hz and f is the result in Hz. If you leave the reference blank it defaults to 440 Hz. A reference of zero or less is rejected and no result is shown. Fractional semitone values work too, so 0.5 gives a quarter-tone above A4. The result is rounded to two decimals.

Worked example

Find middle C (C4), which is 9 semitones below A4. With n = -9 and the default 440 Hz: the exponent is -9/12 = -0.75, 2-0.75 ≈ 0.5946, and 440 × 0.5946 gives 261.63 Hz.

Try this example →

Common mistakes

  • Counting the wrong direction: notes below A4 need a negative number, so C4 is -9, not 9.
  • Counting from the wrong octave: C5 is +3 from A4, while C4 is -9. Octave numbers change at C, not at A.
  • Entering the distance in whole tones or octaves instead of semitones; one octave is 12 semitones, one whole tone is 2.
  • Forgetting to change the reference when the ensemble tunes to something other than 440 Hz, such as 432 or 442 Hz.
  • Expecting a just-intonation value; this is equal temperament, so intervals like a perfect fifth are slightly off the pure 3:2 ratio.

About this calculator

In equal temperament — the tuning system behind virtually all modern Western instruments — the octave is divided into 12 equal semitones on a logarithmic scale, so any note's frequency can be found from its distance in semitones (n) from the reference pitch A4 = 440 Hz: f = 440 × 2^(n/12). Each semitone step multiplies frequency by the twelfth root of two (about 1.0595), which is why doubling frequency always corresponds to exactly 12 semitones — one full octave.

This formula is the mathematical backbone of every electronic tuner, digital synthesizer, and MIDI system in use today, since MIDI note numbers are just semitone offsets that get converted to frequencies with exactly this equation before being sent to a speaker or synthesizer voice.

Piano tuners and instrument technicians verifying pitch, synth programmers and sound designers building custom scales, and music theory students studying equal temperament all use this relationship to move fluently between note names, semitone offsets, and physical frequency in Hz.

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Comments (1)

  • Editorial team

    The reference box matters for ensembles that tune above 440. With A4 at 442, middle C (minus 9 semitones) comes out at 262.81 Hz, while a 432 reference gives 256.87 Hz, so a few hertz separates the pitch standards. Fractions work too: a single cent is 0.01 of a semitone. If you tune by ear or a clip-on tuner, which A do you use as your reference?

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