Equal Temperament Frequency Calculator
In 12-tone equal temperament (12-TET), all semitones are equal, and the octave ratio is exactly 2:1. The frequency of any note is given by f = 440 x 2^((n-69)/12), where n is the MIDI note number (A4 = 69, middle C = 60). This is the definitive formula for tuning any equal-tempered instrument. The reference A4 = 440 Hz is defined by ISO 16:1975. Enter a MIDI note number or the number of semitones above or below A4 (440 Hz) to find the frequency.
Equal temperament formula
f = fA4 × 2n/12
Where f_A4 is the reference frequency (440 Hz) and n is the number of semitones above A4 (negative for below). Each semitone multiplies the frequency by 2^(1/12) approximately 1.05946.
Key note frequencies in 12-TET (A4 = 440 Hz)
- C4 (middle C): 261.63 Hz (n = -9)
- A4: 440.00 Hz (n = 0, reference)
- A3: 220.00 Hz (n = -12)
- A5: 880.00 Hz (n = +12)
- C5: 523.25 Hz (n = +3)
Frequently asked questions
What is 12-tone equal temperament?
12-TET (twelve-tone equal temperament) divides the octave into 12 equal semitones, each separated by a frequency ratio of 2^(1/12) approximately 1.0595. A4 is defined as 440 Hz (ISO 16). This tuning system is the standard for all modern Western music and most electronic instruments.
What is the formula for equal temperament frequencies?
f = 440 x 2^((n-49)/12), where n is the piano key number (1-88) or equivalently the MIDI note number minus 20. A4 is key 49, or f = 440 x 2^((n-69)/12) where n is the MIDI note number and A4 = MIDI 69.
How many semitones above A4 is middle C?
Middle C (C4) is 9 semitones below A4. In 12-TET: f = 440 x 2^(-9/12) = 440 x 2^(-0.75) approximately 261.63 Hz.
What is A4 = 440 Hz?
A4 = 440 Hz is the international standard tuning reference adopted by ISO 16:1975. It is the A above middle C. Some orchestras and period-instrument ensembles use 415 Hz (Baroque) or 442-444 Hz (slightly higher modern pitch) for different acoustic effects.
How do I convert semitone offset to frequency?
Multiply the reference frequency by 2^(semitones/12). Up one semitone: multiply by 2^(1/12) = 1.0595. Up one octave (12 semitones): multiply by 2. Down an octave: multiply by 0.5.
Official sources
- ISO 16:1975: Acoustics, standard tuning frequency for musical pitch (A4 = 440 Hz).
- AES: Audio Engineering Society.
- NIST: NIST physical measurement laboratory.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.