Pitch and Frequency Formula
Calculate note frequency from MIDI note number: f = 440 × 2^((n-69)/12).
Equal temperament tuning explained with frequency table.
The Formula
Every musical note has a precise frequency in Hz. In standard equal temperament tuning, A4 (concert A) is defined as 440 Hz. All other notes are calculated relative to this reference.
In this formula, n is the MIDI note number. A4 = note 69. Each semitone up raises frequency by a factor of 2^(1/12) ≈ 1.05946 — the 12th root of 2. Going up 12 semitones (one octave) doubles the frequency.
The formula works in both directions: higher MIDI numbers give higher frequencies, lower numbers give lower frequencies. Middle C (C4) is MIDI note 60, giving f = 440 × 2^(-9/12) ≈ 261.63 Hz.
Reference frequencies for common notes: C4 (middle C) = 261.63 Hz. A4 = 440 Hz. C5 = 523.25 Hz. A3 = 220 Hz. The lowest note on a standard piano (A0) = 27.5 Hz. The highest (C8) = 4,186 Hz.
This system is called equal temperament because all 12 semitones are equally spaced on a logarithmic scale. It is a compromise — pure mathematical intervals (just intonation) sound more harmonious in a single key but create dissonance when modulating to other keys.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| f | Frequency of the note | Hz |
| n | MIDI note number | integer (0–127) |
| 440 | Frequency of A4 (concert A) | Hz |
| 69 | MIDI number of A4 | — |
Example 1
Calculate the frequency of C4 (middle C), MIDI note 60.
f = 440 × 2^((60 − 69) / 12) = 440 × 2^(−9/12) = 440 × 2^(−0.75)
f ≈ 261.63 Hz
Example 2
What frequency is A5 (one octave above concert A)? MIDI = 81.
f = 440 × 2^((81 − 69) / 12) = 440 × 2^(12/12) = 440 × 2
f = 880 Hz (exactly double A4, as expected for one octave)
When to Use It
- Synthesizer and audio software development
- Tuning instruments to specific frequencies
- Music theory coursework and ear training
- Building frequency tables for signal processing