Semitone calculator
Measure the equal-tempered interval between two frequencies, or apply a semitone shift to a starting frequency.
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An octave is a frequency ratio of two
Twelve equal-tempered semitones double a frequency. The interval formula uses a base-2 logarithm, so 440 Hz to 880 Hz is exactly 12 semitones or 1,200 cents.
Frequency math does not identify a note by itself
The result describes an interval. A note name also depends on the tuning reference and temperament used by the instrument or session.
Why the interval is logarithmic
Pitch is heard as a ratio, not as a difference in hertz. From 100 Hz to 200 Hz is one octave, and so is 1,000 Hz to 2,000 Hz, even though the second gap is ten times wider in hertz. Dividing one frequency by the other and taking a base-2 logarithm is what turns that ratio back into a musical distance.
The practical consequence is that a fixed number of hertz means different things in different registers. Twenty hertz below the top A on a piano is barely noticeable; twenty hertz below the bottom A is a different note entirely.
Frequently asked questions
What is a cent?
One hundredth of a semitone, so 1,200 cents to the octave. It is the unit tuners and pitch-correction plug-ins use, because whole semitones are far too coarse to describe how in tune something is. Trained listeners notice a steady tone that is off by roughly five to ten cents; drift of 20 cents or more reads as out of tune to almost anyone.
How different are A=440 and A=432 tuning?
About 31.8 cents, roughly a third of a semitone. That is well inside a semitone, so the notes keep their names, but it is far enough that instruments tuned to the two references cannot play together. Enter 432 as the starting frequency and 440 as the second one to see the figure yourself.
Why do equal-tempered intervals sound slightly different from pure ones?
Because equal temperament divides the octave into twelve identical steps, which is a compromise that lets every key work. A pure fifth is 702 cents against equal temperament’s 700, close enough to pass. A pure major third is 386 cents against 400, and that 14-cent gap is why a sustained major third on a piano beats slightly while the same chord sung by a choir does not.
How far can I pitch-shift audio before it sounds processed?
For a solo voice, a few semitones in either direction is usually safe with a modern algorithm, and beyond that the formants start to move with the pitch, which is what produces the chipmunk or the monster. Percussive and noisy material tolerates less; sustained tones tolerate more. Shift the whole arrangement rather than one part when you can.
Can it tell me which note a frequency is?
Not directly, because a note name depends on the tuning reference. What it does do is the arithmetic behind that answer: enter your reference, say 440 Hz for A4, and the measured frequency, and the semitone count tells you how many steps away the note is and by how many cents it misses.
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