How to use the musical interval calculator
- Type the first note and the second note with an octave number, such as C4 and G4. Use a # or b for sharps and flats, and x for a double sharp. C4 is middle C.
- Read the interval name, the number of semitones, whether it goes up or down, and its inversion.
- For an interval wider than an octave, the page also gives the simple interval.
- The frequency ratio is for equal temperament, and a just intonation ratio is shown for the simple pure intervals.
Formula
number = letter names counted from the lower note to the upper note, with octaves (C to G is a fifth)
quality = compare the semitones with the major or perfect interval of that number
equal temperament frequency ratio = 2^(semitones / 12)
Perfect intervals are the unison, fourth, fifth and octave. A second, third, sixth or seventh is major, or minor when one semitone smaller. One semitone more than major or perfect is augmented, and one less than minor or perfect is diminished. An inversion turns the interval upside down: the numbers add to 9 and major swaps with minor, augmented with diminished.
Names and sizes above C4
C4 to G4 is a perfect fifth of 7 semitones, with a frequency ratio of 1.49831 in equal temperament and 3:2 in just intonation. Its inversion is a perfect fourth. C4 to E4 is a major third (4 semitones), C4 to Eb4 a minor third (3), C4 to F#4 an augmented fourth and C4 to Gb4 a diminished fifth, though both span 6 semitones.
C4 to E5 is a major tenth, whose simple interval is a major third, and G4 down to C4 is a descending perfect fifth. C#4 to Db4 spans no semitones but is a diminished second, because the letters C and D are a second apart. Ab3 to F#4 is an augmented sixth of 10 semitones.
Spelling matters
Two intervals that sound identical on a piano can have different names because of how the notes are spelled. The augmented fourth and diminished fifth are the classic pair. The name tells a musician how the interval behaves in the music: where it came from and where it tends to go.
The page names an interval from the spelling you give, so enter the notes the way they are written in the score. A note with three or more sharps or flats is not accepted, and combinations needing more than a doubled accidental have no common name.
Related music tools
To turn notes into frequencies use the Note Frequency Converter. To list the notes of a scale, the Musical Scale Generator spells them out, the Circle of Fifths shows how keys relate, and the Key Finder suggests the key of a set of notes.
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Assumptions and limits
- Notes are named with a letter A to G, up to two sharps or flats, and an octave number from -1 to 9.
- Octave numbers follow the usual convention in which middle C is C4.
- The frequency ratio is for equal temperament, with 12 equal semitones to the octave.
- Just intonation ratios are listed only for the simple intervals up to the octave.
- The example notes are an illustration. Replace them with your own.
Frequently asked questions
Why is C to F# not a diminished fifth?
The letters C and F are a fourth apart, so the interval is some kind of fourth. A fourth with one extra semitone is an augmented fourth. A diminished fifth would be C to Gb.
What is the inversion?
It is the interval you get by moving the lower note up an octave. A fifth becomes a fourth, a third becomes a sixth, and quality flips: major to minor and perfect stays perfect.
How are compound intervals named?
An interval larger than an octave keeps its number, such as a tenth, and has the same quality as its simple form. A major tenth is a major third plus an octave.
Can I put the second note below the first?
Yes. The page names the interval between them and says the motion is downward. Distance and name are the same as going up between the same two notes.