Semitone Calculator

Each semitone multiplies frequency by the twelfth root of two.

How the Math Works

The Semitone Calculator uses the formula f = start * 2^(semitones / 12) to determine how frequencies shift when moving between musical notes. This formula is based on the equal temperament tuning system, where an octave (a doubling of frequency) is divided into 12 equal parts called semitones. Each semitone represents a frequency multiplier of 2^(1/12), approximately 1.059. When you know the starting frequency and how many semitones to shift, the calculator applies this exponential relationship to find the resulting frequency precisely.

Practical Applications

To use this calculator, first identify your starting frequency - this could be a reference note like A4 at 440 Hz or any other pitch you're working with. Next, determine how many semitones away you want to move: positive numbers shift upward (sharper), negative numbers shift downward (flatter). For example, moving 7 semitones up from 440 Hz gives you 440 * 2^(7/12), which equals approximately 659.26 Hz - that's the frequency of the note A above middle C. You can also work backwards to find how many semitones separate two frequencies.

Day-to-Day Use

This calculation is invaluable for musicians, audio engineers, and anyone working with sound. Whether you're tuning a guitar, adjusting a piano, or creating electronic music, knowing exact frequencies helps ensure harmonics blend properly. Music teachers can use it to explain why certain notes sound good together, while DJs might calculate key-compatible tracks for seamless mixing. Even if you're not a musician, understanding frequency relationships helps with audio production, speaker placement, or simply appreciating how different instruments create their distinctive sounds.

Worked example

440 Hz up 7 semitones (a fifth) is about 659.3 Hz.

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