Note Frequency Chart

Where the numbers come from

Every frequency in the table is calculated, not looked up. Modern tuning uses twelve-tone equal temperament, in which the octave is divided into twelve equal ratios. Each semitone is therefore the twelfth root of two — about 1.059463 — times the one below it.

f = 440 × 2^{(n − 69) / 12}

where n is the MIDI note number and 69 is A4. Twelve semitones multiply out to exactly 2, so an octave up is exactly double the frequency. That is the one interval equal temperament gets perfectly right.

Every other interval is slightly wrong, on purpose

A pure perfect fifth is a 3:2 frequency ratio. In equal temperament it is 2^7/12, which is 1.4983 rather than 1.5 — about two cents flat. A pure major third is 5:4, or 1.25; equal temperament gives 1.2599, which is fourteen cents sharp and genuinely audible as a slight beating in a sustained chord.

This is a deliberate compromise. Tuning systems that make some intervals pure make others badly out, and only work in a few keys. Equal temperament makes every key equally slightly imperfect, which is what allows a piano to play in all twenty-four of them without retuning.

The wavelengths are there for a reason

The second figure in each cell is the wavelength in air at roughly 20 °C, where sound travels at about 343 metres per second.

It matters for anyone dealing with rooms. A 50 Hz tone has a wavelength of nearly seven metres, comparable to the dimensions of a room, which is why bass produces standing waves and why the bass in a small room is uneven as you move around. At 5 kHz the wavelength is under seven centimetres, so treble behaves much more like light — directional, easily blocked, easily absorbed.

Numbers worth carrying

• A4 = 440 Hz — the reference.
• An octave doubles the frequency. A5 is 880, A3 is 220.
• Middle C is C4, at 261.63 Hz.
• The lowest piano note is A0 at 27.5 Hz; the highest is C8 at 4,186 Hz.
• A semitone is about 5.9 % higher than the note below it.

Common uses

• Setting a synthesiser or oscillator to an exact pitch.
• Ear training — click a cell and try to sing it.
• Audio engineering, where an EQ frequency needs translating into a musical note.
• Checking an instrument against a known reference.
• Room acoustics, using the wavelengths.

Questions people ask

What frequency is middle C?

261.63 Hz, written C4, with A4 at 440 Hz.

Why is a semitone not a round number?

Because equal temperament divides the octave into twelve equal ratios, each the twelfth root of two — about 1.059463.

Why does the chart let me change A4?

Because 440 Hz is a modern convention rather than a law. Many European orchestras use 442 or 443, and baroque ensembles often play at 415.

What is the wavelength column for?

Room acoustics. A 50 Hz wave is nearly seven metres long, comparable to a room, which is why bass is uneven in small spaces.

Why do chords sound slightly beaty?

Equal temperament makes every interval except the octave slightly impure. A major third is fourteen cents sharp, which is audible as gentle beating.