Musical Interval Frequency Ratio Calculator
Find the frequency ratio and cents of the interval between two pitches, with the nearest named interval and a just-intonation vs equal-temperament comparison. Runs in your browser.
The interval between two pitches is their frequency ratio; in cents it is 1200·log₂(ratio), where 100 cents = one equal-tempered semitone and 1200 = an octave. Just intonation tunes intervals to simple whole-number ratios (a perfect fifth is exactly 3:2 = 701.96¢, a major third 5:4 = 386.31¢) that sound especially consonant, while equal temperament rounds every semitone to 100¢ so music can change key freely — which is why an equal-tempered major third sits about 14 cents sharp of the pure 5:4. Everything runs in your browser.
About this tool
A musical interval is the distance in pitch between two notes, and at its root it is a ratio of their frequencies. This calculator takes two frequencies and reports the interval three ways: the raw frequency ratio, the size in cents (where 1200·log₂(ratio) gives the cents, 100 cents equal one equal-tempered semitone, and 1200 cents equal an octave), and the nearest named interval such as a perfect fifth or major third. Its most illuminating feature is the side-by-side comparison of the two great tuning philosophies. Just intonation builds intervals from simple whole-number frequency ratios — a perfect fifth is exactly 3:2, a major third exactly 5:4, an octave 2:1 — and these pure ratios produce the smooth, beat-free consonance that a cappella groups and string quartets gravitate toward. Equal temperament instead divides the octave into twelve mathematically identical semitones of exactly 100 cents each; this sacrifices the purity of most intervals (an equal-tempered major third is about 14 cents sharper than the pure 5:4, noticeably 'brighter' and slightly restless) in exchange for the ability to play in any key and modulate freely without retuning — the compromise that made the piano and modern Western harmony possible. The tool shows how many cents your measured interval deviates from both the equal-tempered grid and the pure just ratio of the nearest named interval, which is exactly the information you need to understand why a perfectly tuned guitar can still sound slightly off on certain chords, or to tune a synth, analyze a recording, or explore historical temperaments. It handles intervals larger than an octave by folding the octaves out and naming the residual interval. Everything runs in your browser; nothing is uploaded.
How to use it
- Enter the lower note's frequency in Hz.
- Enter the upper note's frequency in Hz.
- Read the frequency ratio, the size in cents, and the nearest named interval.
- Compare how far the interval sits from equal temperament and from the pure just-intonation ratio.
Frequently asked questions
- How is a musical interval converted to cents?
- Cents = 1200 · log₂(f2 ÷ f1). 100 cents is one equal-tempered semitone and 1200 cents is an octave. A 3:2 ratio (perfect fifth) is about 701.96 cents.
- What is just intonation?
- A tuning system using simple whole-number frequency ratios — perfect fifth 3:2, major third 5:4, octave 2:1. These pure ratios sound maximally consonant (beat-free) but make changing key difficult.
- How does equal temperament differ?
- Equal temperament divides the octave into 12 identical 100-cent semitones, so every key sounds the same and modulation is free. The trade-off: most intervals are slightly impure — the major third is about 14 cents sharp of the pure 5:4.
- Why does an in-tune piano sound slightly off on some chords?
- Because equal temperament compromises every interval except the octave. Thirds in particular deviate from their pure just ratios, which trained ears hear as a faint brightness or beating — the price of being able to play in all keys.
- What ratio is a perfect fifth?
- In just intonation exactly 3:2 (701.96 cents). In equal temperament it is 700 cents — only about 2 cents flatter, which is why fifths sound nearly pure on a piano while thirds are more noticeably tempered.
- Can it handle intervals larger than an octave?
- Yes. It removes whole octaves and names the remaining interval (e.g. "1 oct + perfect fifth"), while the cents and ratio reflect the full interval.