Musical Interval Calculator

What Are Musical Intervals?

A musical interval is the distance in pitch between two notes. Intervals are the building blocks of melody and harmony — every chord is a stack of intervals, and every melody is a sequence of intervals. In Western music, intervals are measured in semitones (the smallest step on a piano, one fret on a guitar) and named according to their position within the diatonic scale. The interval from C to E spans four semitones and is called a major third. From C to G spans seven semitones and is called a perfect fifth. Each interval has a distinctive sound quality that musicians learn to recognize by ear.

Intervals are classified as either harmonic (both notes sounding simultaneously) or melodic (notes sounding in sequence). Harmonic intervals are the foundation of chords and harmony, while melodic intervals shape the contour and character of melodies. A melody that moves mostly by small intervals (seconds) has a smooth, stepwise character, while one that leaps by larger intervals (fourths, fifths, octaves) has a more dramatic, angular quality.

Consonance Versus Dissonance

The concept of consonance and dissonance describes how stable or tense an interval sounds when two notes are played together. Consonant intervals — unisons, octaves, perfect fifths, and perfect fourths — have simple frequency ratios (1:1, 2:1, 3:2, 4:3) that produce a smooth, blended sound. Major and minor thirds and sixths are considered imperfect consonances — they sound pleasant but with more character and color than perfect intervals. Dissonant intervals — minor seconds, major sevenths, and tritones — have complex frequency ratios that create a sense of tension demanding resolution.

Dissonance is not inherently negative — in fact, it is essential to musical expression. Without dissonance, music would lack tension, movement, and emotional depth. The interplay between consonance and dissonance is what gives music its forward motion and emotional arc. A suspension that creates a dissonant second before resolving to a consonant third is one of the most expressive devices in all of music.

Interval Ear Training

Learning to identify intervals by ear is a cornerstone of musicianship. The standard technique is to associate each interval with the opening notes of a well-known song. A perfect fourth sounds like the beginning of "Here Comes the Bride." A perfect fifth is the start of "Star Wars" or "Twinkle, Twinkle, Little Star." A minor second is the "Jaws" theme. A major sixth opens "My Bonnie Lies Over the Ocean." By building a mental library of interval reference songs, you can quickly identify any interval you hear, whether in a concert hall, a recording studio, or a theory exam.

Intervals and Frequency Ratios

In equal temperament tuning, the frequency ratio of any interval is determined by the formula ratio = 2^(semitones/12). A perfect fifth (7 semitones) has a ratio of approximately 1.498, very close to the pure 3:2 ratio (1.5) of just intonation. An octave (12 semitones) is exactly 2:1. These ratios explain why certain intervals sound consonant — simpler ratios produce fewer beating frequencies between the harmonics of the two notes, creating a smoother, more blended sound. Complex ratios produce more interference between harmonics, generating the rough, tense quality we perceive as dissonance.

Compound Intervals

When two notes span more than an octave, the interval is called a compound interval. A ninth is an octave plus a second, a tenth is an octave plus a third, and so on. Compound intervals retain the essential character of their simple counterparts — a major ninth sounds similar to a major second but with more space and openness. Jazz harmony makes extensive use of compound intervals, with ninth, eleventh, and thirteenth chords adding richness beyond the basic triads and seventh chords of simpler styles.