Note Frequency Calculator

How the Note Frequency Calculator works

Note frequency calculator: equal temperament

Western tuning divides the octave into twelve equal semitones, so each note is the previous one multiplied by the twelfth root of two, about 1.0595. Everything hangs off one reference, the A above middle C, fixed by international agreement at 440 Hz. From that, any note's frequency is 440 × 2^(n ÷ 12) where n is the number of semitones from A4, and the MIDI note number is simply 69 plus n. The calculator does this both ways.

Naming notes. Scientific pitch notation gives each note a letter, an optional sharp or flat, and an octave number that increments at C. Middle C is C4, the A above it is A4, and the lowest note on a piano is A0 at 27.5 Hz. The calculator accepts sharps and flats interchangeably (C#4 and Db4 are the same key) and understands E#, Fb, B# and Cb. Guitar low E is E2, a bass low E is E1, and a soprano's top C is C6.

Frequency to note. Enter a frequency to find what note it is closest to and by how much it misses. The offset is in cents, hundredths of a semitone; a trained ear notices five to ten cents, and a tuner aims within a couple. This is how to identify a hum, a resonant frequency in a room, or a sample of unknown pitch, and to check whether a synth oscillator or a sample is tuned. Mains hum at 50 Hz is a slightly flat G1; at 60 Hz it is a flat B1.

Concert pitch. Not every ensemble uses 440 Hz. Many European orchestras tune to 442 or 443 Hz, baroque groups often use 415 Hz (roughly a semitone lower), and some old recordings and instruments sit anywhere in between. Changing the A4 field shifts every result proportionally. The frequently repeated claim that 432 Hz is a special or natural tuning has no acoustic basis; it is just A4 32 cents flat, and the calculator will show it as such.

MIDI numbers, wavelength and period. MIDI numbers run from 0 (C-1, 8.18 Hz) to 127 (G9, 12,544 Hz); middle C is 60. Wavelength in air at room temperature is 343 m/s divided by the frequency, and it matters for speaker placement, room modes and pipe lengths: A2 at 110 Hz has a wavelength of about 3.1 m, close to the dimensions of a small room, which is why bass notes around there boom. The period in milliseconds is the length of one cycle, useful for setting delays that reinforce a pitch or for sample-accurate loop lengths.

Equal temperament versus just intonation. The frequencies here are equal-tempered, as on a piano or a synth by default. Just intonation tunes intervals to simple ratios, so a pure major third is 14 cents flatter than the equal-tempered one, and singers and string players drift towards those ratios in sustained chords. The music interval calculator shows both figures for any interval.

Note frequencies, C4 to B5

Equal temperament with A4 at 440 Hz.

Frequency, MIDI number and wavelength for two octaves from middle C

Note frequency worked examples

The formula: f = A4 × 2^((MIDI − 69) ÷ 12) with A4 = 440 Hz; nearest MIDI note = 69 + 12 × log2(f ÷ A4); wavelength = 343 ÷ f metres; period = 1000 ÷ f milliseconds.

First example. Middle C (C4, MIDI 60) is 440 × 2^(−9 ÷ 12) = 261.63 Hz, with a wavelength of 1.31 m in air and a period of 3.82 ms.

Second example. A 100 Hz tone gives 69 + 12 × log2(100 ÷ 440) = 43.35, so the nearest note is G2 (98 Hz) and the tone sits about 35 cents sharp of it. Its wavelength is 3.43 m.

How many hertz is one semitone? It depends on the pitch: each semitone multiplies the frequency by about 1.0595, so the gap is 15.6 Hz near middle C and double that an octave higher.

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