Interval Name: The traditional Western music name for the distance between the two notes — unison, minor 2nd, major 3rd, perfect 5th, octave, etc. The name repeats every 12 semitones (one octave).
Semitones: The absolute distance in half steps between the two notes. One semitone equals one piano key (including black keys) or one guitar fret.
Frequency Ratio: The just-intonation ratio for this interval — the simplest whole-number ratio that approximates the frequency relationship. For example, a perfect 5th is 3:2, meaning the higher note vibrates 1.5 times faster.
Cents: A logarithmic unit where 100 cents equals one semitone and 1,200 cents equals one octave. Useful for measuring fine pitch differences, tuning discrepancies, and microtonal intervals.
How This Calculator Works
You pick two notes with their octave numbers. The tool converts each to a MIDI number (octave × 12 + note index), subtracts to find the semitone distance, and maps the result modulo 12 to a standard interval name. The just-intonation ratio is a reference lookup for each interval, and cents are computed as semitones × 100. All calculations use 12-tone equal temperament note numbering.
Quick Questions
What is the difference between just intonation and equal temperament?
Just intonation tunes intervals to exact whole-number frequency ratios (e.g., 3:2 for a perfect 5th), which sound pure but only work in one key. Equal temperament divides the octave into 12 equal semitones, each a ratio of 2^(1/12) ≈ 1.0595, allowing free modulation between keys at the cost of slightly impure intervals.
What is a cent in music?
A cent is 1/100 of a semitone, or 1/1,200 of an octave. It's a logarithmic unit: each semitone in equal temperament is exactly 100 cents. Musicians use cents to describe tuning deviations — for example, a note that is 15 cents sharp is slightly above the equal-tempered pitch.
Why does the octave number matter?
The octave determines the absolute pitch. C4 is middle C (261.63 Hz), while C5 is one octave higher (523.25 Hz). The interval name repeats every octave, but the semitone count increases — C4 to C5 is 12 semitones, C4 to C6 is 24.
Can I use this for guitar or other instruments?
Yes. Musical intervals are universal across instruments. Each fret on a guitar equals one semitone, so the semitone count tells you exactly how many frets apart two notes are on the same string.