Music

Music Interval Calculator

Pick any two notes to identify the interval, frequency ratio, semitones, and cents. Perfect 5th, minor 3rd, tritone — instantly.

Quick Answer

An interval is the pitch distance between two notes, measured in semitones. The frequency ratio = 2^(semitones/12). Cents = 1200 × log₂(ratio). Octave = 12 semitones, 2:1 ratio, 1200 cents.

Pick Two Notes

Note 1

261.63 Hz

Note 2

392.00 Hz

Interval

Perfect 5th

Semitones

7

Just Ratio

3:2

ET Ratio

1.4983

Cents

700.0

All Intervals Within an Octave

SemitonesNameSymbolRatio
0Perfect UnisonP11:1
1Minor 2ndm216:15
2Major 2ndM29:8
3Minor 3rdm36:5
4Major 3rdM35:4
5Perfect 4thP44:3
6TritoneTT45:32
7Perfect 5thP53:2
8Minor 6thm68:5
9Major 6thM65:3
10Minor 7thm716:9
11Major 7thM715:8
12Perfect OctaveP82:1

About This Tool

The Music Interval Calculator instantly identifies the musical interval between any two notes you select, complete with the frequency ratio, semitone distance, and cents value. Whether you are studying for a music theory exam, transcribing a melody, or sound designing a tuned instrument, knowing the exact interval relationship between pitches is foundational.

What Is an Interval?

An interval is simply the pitch distance between two notes. Western music names intervals by counting letter names inclusively from the lower note: C to E spans three letters (C, D, E) so it is a 3rd. The quality (major, minor, perfect, augmented, diminished) is determined by the exact number of semitones in that span. C to E (4 semitones) is a major 3rd. C to E♭ (3 semitones) is a minor 3rd.

The Math Behind the Magic

In equal temperament, every semitone is the same frequency ratio: the twelfth root of two, or about 1.05946. Multiply any frequency by this number 12 times and you double it — that is the octave. The frequency ratio for any interval is 2^(semitones/12). The cents system divides each semitone into 100 equal cents, giving a logarithmic ruler that matches our perception of pitch distance.

Just Intonation Ratios

The simple ratios you see in the table (3:2, 4:3, 5:4) are the ratios of just intonation, derived from the harmonic series. These ratios sound "pure" — when two notes vibrate at a 3:2 ratio, their waveforms align periodically and produce no beating. Equal temperament approximates these ratios so that every key sounds equally in tune (or equally out of tune, depending on perspective).

Why Intervals Matter in Composition

Intervals are the building blocks of melody and harmony. Major and minor 3rds determine whether a chord sounds happy or sad. Perfect 5ths give chords stability. Tritones create dramatic tension that demands resolution. The interval between adjacent notes in a melody (its "shape") is often more memorable than the absolute pitches. "Somewhere Over the Rainbow" opens with an octave leap; the "Star Wars" theme starts with a perfect 5th.

Compound Intervals

Intervals larger than an octave are called compound intervals. A 9th is an octave plus a 2nd, a 10th is an octave plus a 3rd, and so on. For analysis purposes, compound intervals usually function the same as their simple equivalents — a 9th chord behaves harmonically like adding a 2nd above the root.

Pair With Other Tools

Combine this with our Note Frequency Calculator to see exact Hz values, the Chord Progression Builder for harmonic context, or the Key Signature Finder if you have a melody and want to know its home key. The Circle of Fifths Tool shows how perfect 5ths organize all 12 keys, and the Chord Transposer lets you move full progressions to any key.

Frequently Asked Questions

What is a musical interval?
A musical interval is the distance in pitch between two notes. Intervals are named by their numeric size (2nd, 3rd, 4th, etc.) and their quality (perfect, major, minor, augmented, diminished). For example, the distance from C to G is a perfect 5th — five letter names apart with a frequency ratio of 3:2.
How do I calculate the frequency ratio of an interval?
In equal temperament, the ratio between two notes equals 2 raised to the power of (semitones / 12). For an octave (12 semitones) that gives exactly 2:1. For a perfect 5th (7 semitones) you get about 1.498, very close to the just intonation 3:2 ratio. The cents value equals 1200 × log₂(ratio), making one semitone = 100 cents and an octave = 1200 cents.
What are consonant vs dissonant intervals?
Consonant intervals sound stable and pleasant: octaves, perfect fifths, perfect fourths, major and minor thirds, and major and minor sixths. Dissonant intervals create tension and pull toward resolution: 2nds, 7ths, and the tritone (augmented 4th / diminished 5th). Most Western melodies and harmonies use a mix of both to create movement.
What is the difference between equal temperament and just intonation?
Equal temperament divides the octave into 12 equal semitones (each exactly 100 cents apart). Just intonation uses small whole-number ratios derived from the harmonic series (3:2, 5:4, etc.). Equal temperament makes every key playable on a fixed-tuning instrument like piano but slightly detunes most intervals from their pure ratios. The perfect 5th is 2 cents flat in equal temperament; the major 3rd is 14 cents sharp.
Why are some intervals called perfect?
The unison, 4th, 5th, and octave are called perfect because they have the simplest frequency ratios (1:1, 4:3, 3:2, 2:1) and are perceived as the most stable consonances. They cannot be major or minor — only perfect, augmented, or diminished. The 2nd, 3rd, 6th, and 7th come in major and minor flavors instead.

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