Semitone Calculator

A semitone is the smallest standard interval in twelve-tone equal temperament, the tuning system used by most modern Western instruments. Twelve semitones form one octave. Moving up one octave doubles frequency, while moving down one octave halves it. Because pitch perception is logarithmic, equal musical steps require multiplication rather than adding a fixed number of hertz. The frequency multiplier for a semitone interval is two raised to the number of semitones divided by twelve. Starting at concert A, 440 Hz, a rise of twelve semitones gives 880 Hz. A rise of seven semitones, a perfect fifth in equal temperament, gives approximately 659.255 Hz. Negative semitone values move downward: subtracting twelve semitones from 440 Hz gives 220 Hz. The calculator preserves decimals so it can also handle microtonal intervals. The reverse calculation measures the interval between two frequencies. Divide the ending frequency by the starting frequency, take the base-two logarithm, and multiply by twelve. The answer is positive when the second pitch is higher and negative when it is lower. Multiplying semitones by one hundred expresses the same interval in cents. One hundred cents equal one equal-tempered semitone, and twelve hundred cents equal one octave. These formulas describe equal temperament, not every tuning tradition. Just intonation uses simple whole-number frequency ratios, while historical temperaments distribute tuning differences unevenly across keys. An equal-tempered perfect fifth has a ratio near 1.4983 rather than the exact just ratio of 1.5. The difference is small but relevant in tuning, synthesis, acoustics, and ensemble performance. Real instruments may also stretch octaves or vary pitch intentionally for expressive effect. Musicians can use the calculator to transpose samples, tune oscillators, compare measured pitches, plan pitch-shifting effects, and translate audio-analysis results into familiar musical intervals. Audio engineers can convert a desired transposition into a resampling ratio, while instrument makers can check frequency spacing. The calculator accepts any positive frequency, so it works beyond the range of standard piano notes and does not assume that the starting pitch is A4.