Musical Interval Converter
Convert between semitones, cents and frequency ratio for any musical interval, and name the interval (Perfect 5th, Major 3rd…). Shows an equal-temperament vs just-intonation comparison and a detune (cents-to-frequency) calculator.
Input
Interval conversion
Semitones (e.g. 7), cents (e.g. 700) or a frequency ratio (e.g. 1.5).
Detune calculator
Apply a cent offset to this frequency to find the detuned result.
Output
Results
Equal temperament vs just intonation
| System | Cents | Ratio |
|---|---|---|
| No data yet | ||
Interval reference chart
| Semitones | Cents | Ratio (ET) | Interval |
|---|---|---|---|
| No data yet | |||
Guides
The Musical Interval Converter turns any musical interval between its four common representations — semitones, cents, frequency ratio, and its named interval (Perfect 5th, Major 3rd, Octave…). Type a value into whichever unit you have, pick that unit, and the tool fills in the rest instantly. It runs entirely in your browser, so nothing you enter is uploaded anywhere.
How interval math works
Everything is anchored to 12-tone equal temperament (12-TET), the tuning used by pianos, guitars and virtually all digital instruments. One octave is split into 12 equal semitones, and each semitone into 100 cents:
- Cents = semitones × 100
- Frequency ratio (ET) = 2 ^ (semitones ÷ 12)
- Semitones = 12 × log₂(ratio)
So a perfect fifth is 7 semitones = 700 cents = a ratio of 2^(7/12) ≈ 1.4983, and an octave is 12 semitones = 1200 cents = a ratio of exactly 2.0. Values that don't land exactly on a semitone are named by the nearest interval with the leftover shown in cents (for example, Major 3rd +14.0¢).
Equal temperament vs just intonation
Equal temperament spaces every semitone evenly, which keeps instruments in tune across all keys but makes most intervals slightly "impure." Just intonation instead tunes intervals to small whole-number frequency ratios that sound perfectly consonant. The comparison table shows both for the interval nearest your input:
- Perfect fifth — ET ≈ 1.4983 vs just 3:2 = 1.5 (about +2 cents)
- Major third — ET ≈ 1.2599 vs just 5:4 = 1.25 (about −14 cents)
- Octave — identical in both systems, a clean 2:1
The "Difference" row reports how far just intonation drifts from equal temperament, in cents, which is exactly the tuning error a musician hears when comparing the two systems.
Detune calculator
The built-in detune helper answers a related question: what frequency do you get when you shift a pitch by a number of cents? It applies
result Hz = base Hz × 2 ^ (cents ÷ 1200)
Enter a base frequency (A = 440 Hz by default) and a cent offset to find the detuned pitch — handy for setting up an oscillator, tuning a sampler, or checking how many cents sharp or flat a note is.
Which intervals are named?
All twelve intervals within an octave (minor 2nd through the octave) are named, plus extensions up to a double octave (9ths, 10ths, 11ths and beyond). Anything larger is expressed as a number of octaves plus the remaining interval.
Are the ratios exact?
Cents, semitones and the equal-temperament ratio are computed with full floating-point precision and rounded to the decimal places you choose (2 to 8). The just-intonation ratios are the exact whole-number fractions traditionally used for each interval.