Music Interval Calculator

Pick two notes and octaves to find the interval between them: semitones, frequency ratio, cents, and the standard interval name in 12-tone equal temperament.

Quick Facts

Method
12-tone equal temperament (12-TET)
1 octave = 12 semitones = 1200 cents; each semitone is a frequency ratio of 2^(1/12) ≈ 1.05946 (about 5.95%).

Your Results

Calculated
Interval name
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Named interval, equal temperament
Semitones
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Distance in half-steps
Frequency ratio
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Second note ÷ first note
Interval size
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In cents (100 cents = 1 semitone)

Ready

Pick two notes and octaves, then press Calculate.

Understanding Musical Intervals

A musical interval is the distance in pitch between two notes. This calculator uses 12-tone equal temperament (12-TET) — the tuning system behind virtually every modern piano, guitar, and fretted instrument — where an octave is divided into 12 equal semitones and each semitone is a frequency ratio of 21/12 ≈ 1.05946.

The formula

Each note and octave (using scientific pitch notation, where middle C is C4) is converted to a MIDI-style note number n, where A4 = 69. From there the calculator finds the interval three equivalent ways:

  • Semitones: the difference between the two notes' positions on the 12-note chromatic scale — every half step, counting both black and white piano keys.
  • Frequency ratio: f₂ ÷ f₁, where each note's frequency is f = A4 × 2(n − 69) / 12, with A4 the concert-pitch reference (440 Hz by default).
  • Cents: 1200 × log₂(f₂ ÷ f₁). A cent is 1/100 of a semitone, so 100 cents = 1 semitone and 1200 cents = 1 octave.

Naming the interval

The semitone count, reduced to within one octave (0–11), maps to a standard interval name: 0 = unison, 1 = minor 2nd, 2 = major 2nd, 3 = minor 3rd, 4 = major 3rd, 5 = perfect 4th, 6 = tritone, 7 = perfect 5th, 8 = minor 6th, 9 = major 6th, 10 = minor 7th, 11 = major 7th, and 12 = octave. Intervals larger than an octave (compound intervals, like a 10th or 12th) are named by their remainder plus the number of extra octaves — for example, 19 semitones is a perfect 5th plus one octave.

Consonance and dissonance

In common-practice tonal theory, unisons, octaves, perfect fifths, and thirds and sixths are generally treated as consonant (stable-sounding), while seconds, sevenths, and the tritone are treated as dissonant (tense, wanting resolution). This is a long-standing convention, not a physical law — perceived consonance also depends on timbre, voicing, and musical context.

Frequently Asked Questions

How is the interval between two notes calculated?
The calculator converts each note and octave to a MIDI-style note number, subtracts to get the number of semitones, and derives each note's frequency as A4 × 2^((n − 69) / 12). The frequency ratio and the interval size in cents (1200 × log₂ of the ratio) follow directly from those two frequencies.
What is a cent in music theory?
A cent is 1/100 of an equal-tempered semitone, so there are 1200 cents in an octave. Cents let you measure tuning differences finer than a semitone — useful for comparing temperaments, describing microtonal intervals, or checking how far a note is out of tune.
Why does the A4 reference pitch matter?
A4 is the "concert pitch" reference note that every other note's frequency is calculated from. The modern standard is 440 Hz, though some orchestras tune slightly higher, such as 442 Hz, for a brighter sound. Changing A4 shifts every frequency proportionally but does not change the semitone or cent distance between two notes.
What is the difference between a perfect fifth and a tritone?
A perfect fifth spans 7 semitones (700 cents). A tritone (augmented fourth or diminished fifth) spans exactly 6 semitones (600 cents) — the only interval that splits the octave precisely in half under equal temperament.

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