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Math

Music Note Frequency Calculator

Pick a note (C, C♯, …, B), an octave in scientific pitch notation (middle C is C4) and the A4 tuning reference, and the tool applies the twelve-tone equal-temperament formula f = A4 × 2^((n − 69)/12) to give the frequency in Hz, the MIDI note number, the wavelength in air (using 343 m/s) and the period. A4 defaults to 440 Hz (the ISO 16 international standard); switch to 432 Hz for Verdi tuning or 415 Hz for baroque pitch.

Frequency

440.00

A4 · MIDI 69

MIDI number
69
Wavelength in air
Period

Wavelength uses the speed of sound in dry air at 20 °C (343 m/s). Period = 1 / f.

Formula

f = A4 × 2^((n − 69) / 12), where n is the MIDI number (C4 = 60, A4 = 69).

Formula

f(n) = A4 × 2^((n − 69) / 12) n = MIDI number = (octave + 1) × 12 + pitch class // C = 0, C♯ = 1, …, B = 11 Wavelength λ = c / f // c = speed of sound in air ≈ 343 m/s at 20 °C Period T = 1 / f

Frequently asked

What does the octave number mean — what is the "4" in "C4"?

This is "Scientific Pitch Notation" (SPN): each note name is followed by an integer indicating which octave it sits in. C4 is the C in the middle of a piano, known as "middle C"; C5 is one octave higher (frequency × 2) and C3 is one octave lower (frequency ÷ 2). An octave runs from one C up to the B just before the next C — so C4, C♯4, D4, …, B4 are all in octave 4, and the next note up is C5 in a new octave. A piano runs from A0 (27.5 Hz) at the bottom to C8 (≈ 4186 Hz) at the top — 88 keys in all.

Is A4 = 432 Hz really "more pleasant" than 440 Hz?

There is no scientific evidence that 432 Hz is more beneficial or more "natural" for the human body than 440 Hz. The 440 Hz standard was set by an international tuning conference in 1939 and formalised as ISO 16 in 1955. Verdi's late-19th-century proposal for 432 Hz was driven by the vocal range of Italian opera singers of the time, not by any physics or biology. Listeners who prefer 432 Hz are usually responding to the fact that it is slightly lower than 440 Hz (about 31.8 cents, or one-third of a semitone), which gives an overall softer, mellower tone — but any tuning a third of a semitone lower would feel similar. This tool accepts any A4 reference from 380 Hz to 500 Hz.

Why is one semitone a factor of 2^(1/12) ≈ 1.05946 instead of a nice integer ratio?

It is a compromise so that all 12 keys sound equally in tune on a fixed-pitch instrument like a piano or fretted guitar. "Just intonation" and "Pythagorean tuning" use nice integer ratios like 3:2, 4:3, and 5:4 — these sound exceptionally pure in one key but go badly out of tune when you modulate. Twelve-tone equal temperament, popularised in J. S. Bach's time, splits the octave (a 2:1 ratio) into 12 mathematically equal steps of 2^(1/12). The major third and perfect fifth are then slightly off compared to just intonation (12-TET's fifth is about 2 cents flat), but every key sounds equally consonant. Modern electronic tuners, MIDI, and digital pianos all assume 12-TET by default.

What is a MIDI note number for, and what are the lowest and highest notes?

MIDI (Musical Instrument Digital Interface) is a 1983 electronic-music protocol. Every note is sent as a single integer from 0 to 127: MIDI 0 = C-1 (about 8.18 Hz, well below the limit of human hearing), MIDI 60 = C4 (middle C), MIDI 69 = A4 (the 440 Hz tuning reference) and MIDI 127 = G9 (about 12,544 Hz). The 88 keys of a piano span MIDI 21 (A0) to MIDI 108 (C8). MIDI notes are usually paired with a velocity value (0–127) and are the lingua franca of synthesisers, digital audio workstations (DAWs) and music software for recording, editing and playback.

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