Note Frequency Calculator

In short Two definitions fix every note frequency in music. A4 is 440 hertz by international agreement, and an octave is exactly a doubling of frequency. Equal temperament divides that doubling into twelve equal ratios, so one semitone multiplies the frequency by the twelfth root of two — about 1.059463 — and the formula for any note is 440 × 2^((n − 69) ÷ 12), where n is the MIDI note number and 69 is A4. That gives middle C, MIDI 60, as 261.63 Hz, the lowest key of a piano as exactly 27.5 Hz, and the top key as 4,186 Hz. The consequence people find counter-intuitive is that pitch is geometric, not linear. The octave from A0 to A1 spans 27.5 Hz; the octave from A6 to A7 spans 1,760 Hz. The same musical distance covers sixty-four times as much frequency at the top of the piano as at the bottom, which is why frequency graphs of music are drawn on a logarithmic axis and why cents — 100 to a semitone, 1,200 to an octave — exist as a unit at all. Concert pitch is also a convention rather than a constant. A4 = 440 was standardised in 1939; many European orchestras tune to 442 or 443 for a brighter sound, and baroque ensembles commonly use 415, which is almost exactly a semitone below modern pitch.