Semitone Interval Frequency Calculator
Move a frequency up or down by any number of semitones and see the new pitch, the exact frequency ratio and the interval in cents.
How it works
f₂ = f₁ × 2^(n ÷ 12), where n is the number of semitones · Cents = 100 × n · One octave = 12 semitones = 1200 cents
In equal temperament every semitone multiplies frequency by 2^(1/12) ≈ 1.0595, so an interval of n semitones scales the starting pitch by 2^(n/12). Twelve semitones double the frequency (one octave); seven give a perfect fifth with a ratio very close to the pure 3:2. Cents are a finer unit — 100 per semitone, 1200 per octave — handy for describing tuning offsets and how far tempered intervals drift from their just-intonation ideals.
Worked example
A perfect fifth above 440 Hz is 7 semitones: 440 × 2^(7/12) ≈ 659.26 Hz. The ratio is 1.4983, only 0.1% below the pure 3:2 (1.5000) of just intonation — that tiny difference is the price of equal temperament.
Frequently asked questions
What is a cent?
A cent is one hundredth of an equal-tempered semitone, so an octave spans 1200 cents. Human ears can just detect differences of about 5–10 cents, which is why tuners display pitch in cents.
Why is a tempered fifth not exactly 3:2?
Just intonation uses simple whole-number ratios like 3:2, but stacking them never returns cleanly to the octave. Equal temperament compromises by making every semitone identical, so the tempered fifth (1.4983) sits about 2 cents flat of the pure 3:2.
Can I go down instead of up?
Yes — enter a negative number of semitones. Down 12 halves the frequency (an octave lower), and down 7 gives a perfect fifth below the starting note.
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This calculator is for educational purposes. Double-check important results before acting on them.