Music Interval Calculator
Find the interval in semitones between two pitches.
Measure the musical distance between two frequencies.
How the Math Works
The Music Interval Calculator uses the mathematical relationship between frequencies to determine how many semitones separate two pitches. The formula semitones = 12 × log₂(f₂ ÷ f₁) works because equal temperament divides the octave into 12 equal parts, where each semitone represents a frequency ratio of 2^(1/12). By taking the base-2 logarithm of the frequency ratio and multiplying by 12, we convert the multiplicative relationship between frequencies into the additive counting system of semitones that musicians use.
Practical Applications
To use this calculator, simply enter the frequency values (in Hz) of any two pitches you want to compare. For instance, if you input f₁ as 440 Hz (standard tuning pitch A) and f₂ as 880 Hz (the A one octave higher), the calculator will output 12 semitones, confirming the perfect octave. This tool is invaluable for composers verifying chord spacing, DJs matching harmonic tracks, or audio engineers troubleshooting frequency relationships in recordings.
Day-to-Day Use
Understanding musical intervals helps us recognize why certain sounds feel pleasing together while others create tension. Whether you're tuning a guitar, analyzing your favorite songs, or simply appreciating how melodies flow, this calculator reveals the mathematical foundation of music that surrounds us. It bridges the gap between the physics of sound and our emotional response to harmony, making the science behind music accessible to anyone curious about how the world sounds.
Worked example
440 → 660 Hz → ~7 semitones (a perfect fifth).
FAQ
Cents?
A finer unit — 100 cents per semitone, used for tuning.