How are note frequencies calculated?

Equal temperament uses the formula f = 440 × 2^((n − 69) / 12), where n is the MIDI note number and 69 is A4. Each semitone multiplies the frequency by the twelfth root of two, roughly 1.0595, so twelve semitones double the pitch exactly one octave higher.

A4 is the A above middle C, the standard concert-pitch reference adopted by ISO 16. Fixing it at 440 Hz defines the frequency of every other note in equal temperament. Some orchestras tune to 442 or 443 Hz, and 432 Hz is a popular alternative tuning.

What is a MIDI note number?

MIDI numbers map each piano key to an integer: middle C (C4) is 60 and A4 is 69. They give a compact, octave-aware way to identify pitches in software and hardware, and they feed directly into the frequency formula.

Why is middle C4 not exactly 256 Hz?

256 Hz for middle C comes from a scientific-pitch convention where each C is a power of two. Standard concert tuning anchors A4 at 440 Hz instead, which makes C4 about 261.63 Hz. The two systems simply use different reference points.

Does this work for 432 Hz tuning?

Yes. Change the A4 reference pitch to 432 and every note rescales by the ratio 432/440. The relative intervals stay identical because equal temperament is defined by ratios, not absolute frequencies.

What is the Musical Note Frequency Reference?

Searchable reference of equal-temperament note frequencies from C0 through B8 with A4 = 440 Hz standard tuning, MIDI numbers, and a re-anchorable reference pitch for 432 Hz or 442 Hz. It runs free in your browser on Gera Tools, with nothing uploaded.

Musical Note Frequency Reference

Name: Musical Note Frequency Reference
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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Every note, every octave, in hertz

This reference lists the equal-temperament frequency of every musical note from C0 through B8 — 108 pitches in total. It is built for musicians, audio engineers, instrument builders, synthesiser designers, and developers writing tuners, tone generators, or audio analysis tools. Frequencies are recomputed live from whichever A4 reference pitch you choose, so you can read off standard 440 Hz tuning or any alternative.

How it works

In twelve-tone equal temperament, every semitone is the same frequency ratio — the twelfth root of two, approximately 1.05946. Starting from the A4 anchor, the frequency of any note is:

f = A4 × 2 ^ ((n − 69) / 12)

Here n is the MIDI note number (A4 = 69, middle C = 60) and A4 is the reference pitch in hertz. Moving up twelve semitones adds exactly 1.0 to the exponent and doubles the frequency — one octave. Moving down twelve semitones halves it. That single formula produces the entire 108-note table.

Reference pitches compared

A4 reference	Middle C (C4)	Notes
440 Hz	261.63 Hz	ISO 16 standard
432 Hz	256.87 Hz	Alternative tuning popular in some genres
442 Hz	263.12 Hz	Common in some European orchestras
443 Hz	263.71 Hz	Favoured by some string players

When you change the reference pitch, every note in the table rescales by the ratio between the new and old anchor. The relative intervals between all notes stay identical because equal temperament is defined by ratios, not absolute frequencies.

Practical uses

Synthesiser and tuner development: the formula and MIDI number column let you map a MIDI note number directly to a frequency in code. f = 440 * 2**((n-69)/12) is a one-liner in any language.

Instrument intonation: compare the table at 440 Hz against a recording at 442 Hz to understand exactly which notes drift. A violin section at 442 sits about 7.9 cents sharp relative to a digital piano at 440, which is audible on sustained unison passages.

Finding a specific pitch: searching for A4 or 69 jumps to the same row — both are middle A. Searching 60 finds middle C (C4) at 261.63 Hz.

Checking the octave relationship: A3 is 220 Hz, A4 is 440 Hz, A5 is 880 Hz — each octave exactly doubles. Two notes a tritone apart (six semitones) have a frequency ratio of the square root of two, approximately 1.414.