Frequency to Musical Note Converter

Musical note frequency is the precise number of vibrations per second (Hz) that a sound wave produces to create a specific pitch. The relationship between notes follows a mathematically elegant pattern based on the twelfth root of 2.

Standard tuning frequency: A4 = 440 Hz (concert pitch; international standard since 1939) Some orchestras use A4 = 441 to 444 Hz; some early music ensembles use 415 Hz.

Frequency formula (equal temperament): f(n) = 440 × 2^(n/12)

Where n = number of semitones above or below A4:

• A4 is semitone 0
• Each semitone above = n+1; each semitone below = n-1
• A5 (one octave up) = n+12 → 440 × 2^(12/12) = 440 × 2 = 880 Hz
• A3 (one octave down) = n-12 → 440 × 2^(-1) = 220 Hz

Octave relationship: Frequency doubles with each octave up; halves with each octave down

Interval frequency ratios (equal temperament):

• Unison: 1:1
• Semitone: 1 : 2^(1/12), so 1:1.0595
• Whole step (major 2nd): 1 : 2^(2/12), so 1:1.1225
• Perfect 4th: 1 : 2^(5/12), so 1:1.3348
• Perfect 5th: 1 : 2^(7/12), so 1:1.4983
• Octave: 1:2 (exact)

What each variable means:

• Equal temperament divides the octave into 12 exactly equal semitones, so every instrument plays together in any key with minimal beating
• Just intonation uses pure frequency ratios (5:4 major third, 3:2 perfect fifth). It sounds purer, but only in one key at a time, which makes it impractical for modern fixed-pitch instruments
• Hz (Hertz) means cycles per second. Human hearing runs roughly 20 Hz to 20,000 Hz, and musical notes occupy a much narrower band, about 27.5 Hz (A0, the lowest piano key) to 4,186 Hz (C8, the highest)

Reference: frequency of all C notes (piano range):

Worked example:

Find the frequency of E4, the E above middle C.

The only thing to get right is the direction. E4 sits below A4, not above it, so n is negative. Count down from A4 and you pass G♯4, G4, F♯4, F4, E4, which is five semitones.

• n = -5
• f(E4) = 440 × 2^(-5/12) = 440 × 0.74915 = 329.63 Hz

That is the guitar’s open first string in standard tuning, and it is also the note the calculator returns if you type E4 above.

Sign errors are the usual failure here. Enter +5 by mistake and you get 587.33 Hz, which is D5, a minor seventh away from the note you wanted.