Note to Frequency Calculator

Sound frequency and pitch are directly related: frequency (measured in Hz — cycles per second) determines what pitch we hear. The Western musical scale is built on a logarithmic system where each octave doubles the frequency, and each of the 12 semitones within an octave divides this doubling equally.

Frequency of any note formula: f = f₀ × 2^(n/12)

Where:

• f = frequency of the target note (Hz)
• f₀ = reference frequency (standard tuning: A4 = 440 Hz)
• n = number of semitones above (+) or below (−) the reference note
• 2^(1/12) = the twelfth root of 2 ≈ 1.05946 — the frequency ratio between adjacent semitones

Frequency ratios of musical intervals:

• Unison: 1:1
• Minor 2nd (1 semitone): 1.0595:1
• Major 2nd: 1.1225:1
• Minor 3rd: 1.1892:1
• Major 3rd: 1.2599:1
• Perfect 4th: 1.3348:1
• Perfect 5th: 1.4983:1
• Octave: 2:1 exactly

Standard note frequencies (A440 tuning):

• A3: 220 Hz; A4: 440 Hz; A5: 880 Hz
• Middle C (C4): 261.63 Hz
• B4: 493.88 Hz; C5: 523.25 Hz

Wavelength formula: λ = v ÷ f Where v = speed of sound ≈ 343 m/s at 20°C, f = frequency in Hz.

Worked example: Find the frequency of C5 (middle C is C4 = 261.63 Hz, C5 is one octave above):

• C5 = C4 × 2^(12/12) = 261.63 × 2 = 523.25 Hz

Find the frequency of D4 (D is 2 semitones above A4? No — D4 is a specific note): n from A4 to D4: A4 → A#4 → B4 → C5… wait, going DOWN: A4 → G#4 → G4 → F#4 → F4 → E4 → D#4 → D4 = −7 semitones f(D4) = 440 × 2^(−7/12) = 440 × 0.6674 = 293.66 Hz