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Pitch Shift Calculator

Enter the original frequency and a semitone shift to find the new pitch.

How it is calculated

Equal temperament divides the octave into 12 equal ratio steps, so one semitone multiplies frequency by 21/12 (about 1.0595). For a shift of n semitones: ratio = 2^(n ÷ 12), new frequency = original frequency × ratio and cents = n × 100. Frequency is in hertz and must be above zero. The semitone shift can be positive (up), negative (down) or fractional (0.5 is a quarter-tone, 50 cents). The new frequency is rounded to two decimals, the ratio to four, and 12 semitones always gives a ratio of exactly 2, one octave. The tool works on a frequency, not a note name or a sampled audio file, and it assumes equal temperament rather than just intonation.

Worked example

Start from middle C at 261.63 Hz and shift it down 5 semitones. Ratio: 2^(−5 ÷ 12) = 2^(−0.4167) = 0.7492. New frequency: 261.63 × 0.7492 = 196.00 Hz, which is the G below middle C. The shift in cents is −5 × 100 = −500 cents. The negative ratio exponent simply means the new pitch is lower than the original.

Try this example →

Common mistakes

  • Adding the semitone count to the frequency, or multiplying by it. Pitch is exponential: each semitone is a constant ratio, not a constant number of hertz.
  • Using the wrong sign. A positive shift raises the pitch and a negative one lowers it, so −5 and +5 give 196.00 Hz and 349.23 Hz respectively from the same starting note.
  • Entering cents in the semitone field. 50 cents is 0.5 semitones; typing 50 would shift the pitch by more than four octaves.
  • Expecting the result to match a tuning that is not equal-tempered, such as just intonation or a reference of a non-440 Hz pitch. The tool only applies the 2^(n/12) rule to the frequency you give.
  • Confusing frequency ratio with playback speed in a sampler. The two are equal for varispeed shifting, but a pitch shifter that keeps duration works differently.

About this calculator

In Western music theory, each octave is divided into 12 equal semitones, and shifting a note by n semitones multiplies its frequency by 2^(n/12) — the basis of equal temperament tuning. A hundredth of a semitone is a cent, the finer unit musicians use to describe subtle tuning differences that the ear can still detect.

This calculator takes an original frequency and a semitone shift (positive to go up, negative to go down) and returns the new frequency, the resulting frequency ratio, and the shift in cents. Audio engineers use it to plan pitch-shifting effects and time-stretching in a DAW, musicians use it to transpose parts or check alternate tunings, and sound designers use it to calculate exact sample-rate or playback-speed changes needed for a target pitch.

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  • Editorial team

    Equal temperament is a compromise, and you can see it here. Seven semitones above 440 Hz gives 659.26 Hz with a ratio of 1.4983, while a pure 3:2 fifth would land at exactly 660 Hz, about two cents higher. For most mixing work the gap is inaudible, but it explains why strings tuned by ear can beat against a keyboard. Which reference pitch do you tune to: 440 Hz or something else?

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