Interval Calculator
This interval calculator and musical interval finder doubles as a handy music theory calculator: find the musical interval between any two notes and see the interval name, the number of semitones between notes, cents, frequency ratio, consonance rating, and listen with melodic or harmonic playback.
Select Two Notes
Interval Result
Complete Interval Reference Table
| Interval Name | Short | Semitones | Cents | Ratio | Quality | Consonance |
|---|
How to Use the Interval Calculator
Understanding Musical Intervals
A musical interval is the distance in pitch between two notes. Intervals are measured in semitones (half steps) and can be described by their quality (perfect, major, minor, augmented, diminished) and their numerical size (unison, 2nd, 3rd, etc.). The frequency ratio between two notes determines the interval's acoustic character and its perceived consonance or dissonance. Understanding intervals is foundational to music theory: they are the building blocks of chords, scales, and harmonic progressions. For example, stacking a major 3rd (4 semitones) on top of a minor 3rd (3 semitones) produces a major triad — the most common chord structure in Western music. You can hear real-world interval relationships at any reference pitch by generating a pure tone with the online tone generator and comparing it against a second note to listen for beat frequencies.
Consonance and Dissonance
- Perfect consonance — Unison, perfect 4th, perfect 5th, and octave. These intervals have the simplest frequency ratios (1:1, 4:3, 3:2, 2:1) and sound the most stable.
- Imperfect consonance — Major and minor 3rds and 6ths. These intervals are pleasing but have a warmer, more complex quality than perfect consonances.
- Mild dissonance — Major 2nd and minor 7th. These intervals create gentle tension that is common in many musical styles.
- Sharp dissonance — Minor 2nd, major 7th, and tritone. These intervals produce strong tension and are often used for dramatic effect or to create a sense of instability.
Equal Temperament vs Just Intonation
The frequency ratios shown in this calculator are the just intonation ratios — pure mathematical relationships between harmonics that sound most "in tune" acoustically. However, modern Western instruments are tuned to 12-tone equal temperament (12-TET), where every semitone is exactly 21/12 times the previous one. This means equal temperament intervals are slight approximations of the just ratios: a 12-TET perfect 5th is 700 cents, very close to the just ratio of 701.96 cents, but a 12-TET major 3rd at 400 cents is noticeably wider than the just 3rd at 386.31 cents. The cents column in the reference table reflects 12-TET values; pure just intonation intervals would differ slightly. If you want to compare the exact frequency of a specific note in equal temperament, the note-to-Hz converter gives you the precise Hz value for any note in any octave.
Why are pianos not perfectly in tune?
In just intonation (JI), intervals are built from small whole-number ratios: the perfect fifth is 3:2 and the major third is 5:4. Those ratios produce pure, beatless chords in one key, but when you stack them across all 12 keys the errors accumulate and some intervals end up badly out of tune. Equal temperament resolves this by making every semitone an identical ratio of 21/12 (about 1.0595), so every key is equally usable. The cost is a slight compromise on purity: the ET major third lands at 400 cents, roughly 14 cents sharper than the pure JI major third at 386 cents, which is enough to produce audible beating when held as a sustained chord. The ET perfect fifth, at 700 cents, is only about 2 cents flat of the pure 3:2 ratio, so it remains nearly beatless in practice. Pianos are not "out of tune" in a haphazard sense; they are deliberately tempered so that every key sounds equally acceptable. To hear the effect of individual cent deviations for yourself, explore the chromatic tuner or experiment with specific pitches using the note-to-Hz converter.