Music Interval Calculator

A musical interval is the distance between two pitches or notes. In Western music, intervals are measured in semitones, which are the smallest unit of pitch in the standard 12-tone equal temperament system. Intervals have both size (distance) and quality (perfect, major, minor, augmented, diminished).

Perfect intervals (unison, fourth, fifth, octave) have a pure and stable sound quality and are considered the most consonant. Major and minor intervals apply to seconds, thirds, sixths, and sevenths. The major version is one semitone larger than its minor counterpart. For example, a major third is 4 semitones, while a minor third is 3 semitones.

The perfect unison (same note) and perfect octave are considered the most consonant intervals, with a frequency ratio of either 1:1 or 2:1. The perfect fifth (ratio 3:2) is also highly consonant, followed by the perfect fourth (4:3). Consonance generally correlates with simpler frequency ratios.

Traditionally, the tritone (augmented fourth or diminished fifth, spanning 6 semitones) has been considered the most dissonant interval, even called "diabolus in musica" (the devil in music) during medieval times. Minor seconds and major sevenths are also highly dissonant intervals with complex frequency ratios.

Intervals are fundamental building blocks in music theory. They are used to construct scales, melodies, and chords. Different intervals evoke different emotional responses. For example, major thirds often sound bright and happy, while minor thirds tend to sound sad or melancholic. Musicians also practice interval recognition as part of ear training.

An inverted interval is created by moving the lower note up an octave or the upper note down an octave. When intervals are inverted, perfect intervals remain perfect, major intervals become minor, minor become major, augmented become diminished, and diminished become augmented. The original and inverted intervals always add up to 9 (e.g., a perfect fifth inverted becomes a perfect fourth: 5 + 4 = 9).

Each musical interval corresponds to a specific frequency ratio between the two notes. In just intonation, these ratios are simple fractions: octave (2:1), perfect fifth (3:2), perfect fourth (4:3), major third (5:4), etc. In 12-tone equal temperament (used on modern pianos), these ratios are slightly adjusted to allow for consistent intervals in all keys.

A compound interval is an interval larger than an octave. For example, a major ninth is a compound interval consisting of an octave plus a major second. To analyze compound intervals, you can reduce them by subtracting octaves until you have a simple interval (within one octave), then identify that interval and add the appropriate number of octaves.