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 = 441–444 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) ≈ 1:1.0595
• Whole step (major 2nd): 1: 2^(2/12) ≈ 1:1.1225
• Perfect 4th: 1: 2^(5/12) ≈ 1:1.3348
• Perfect 5th: 1: 2^(7/12) ≈ 1:1.4983
• Octave: 1:2 (exact)

What each variable means:

• Equal temperament — divides the octave into 12 exactly equal semitones; every instrument plays together in any key with minimal “beating”
• Just intonation — uses pure frequency ratios (5:4 major third, 3:2 perfect fifth); sounds “purer” but only in one key at a time; impractical for modern instruments
• Hz (Hertz) — cycles per second; the human hearing range is approximately 20 Hz to 20,000 Hz; musical notes occupy roughly 27.5 Hz (A0, lowest piano key) to 4,186 Hz (C8, highest piano key)

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

Worked example: Calculate the frequency of E4 (the E above Middle C). E4 is 4 semitones above A4? No — let’s count from A4: A4(0), A#4(1), B4(2), C5(3)… actually E4 is 5 semitones below A4.

• n = −5 (E4 is 5 semitones below A4)
• f(E4) = 440 × 2^(−5/12) = 440 × 0.7492 = 329.63 Hz

The guitar’s open first string (high E) vibrates at exactly 329.63 Hz when in standard A440 tuning.