Intervals are the building blocks of melody and harmony, measuring the distance between two notes in pitch. Every melody moves through intervals, and every chord is constructed from specific interval combinations. Understanding intervals unlocks the ability to analyze music, build chords, construct scales, and recognize patterns across all styles of music.
An interval is the distance between two pitches, measured by counting the number of letter names spanned and the exact number of half steps (semitones) between them. Intervals can be played melodically (one note after another) or harmonically (both notes sounding simultaneously).
The size of an interval is determined by two factors: the numeric distance and the quality. The numeric distance counts how many letter names are included from the first note to the second, including both endpoints. For example, from C to E spans three letter names (C-D-E), making it a third. From C to G spans five letter names (C-D-E-F-G), making it a fifth.
Perfect Fifth Interval
The interval from C to G spans five letter names and seven half steps, creating a perfect fifth
The half step count provides precision. While C to E is always called a third because it spans three letters, the exact distance in half steps determines whether it's a major third (4 half steps) or minor third (3 half steps). This combination of numeric distance and quality gives intervals their complete identity.
Understanding intervals helps you recognize melodic patterns, build chords by stacking thirds, transpose music to different keys, and develop better ear training skills. Professional musicians can often identify intervals by ear, which helps them learn music faster and improvise more effectively.
Interval quality describes the exact size of an interval in half steps, categorized as perfect, major, minor, augmented, or diminished. Different qualities create different levels of consonance, tension, and emotional character in music.
Perfect intervals (unison, fourth, fifth, octave) are the most consonant and stable intervals, occurring naturally in the overtone series. A perfect unison is 0 half steps (same note), perfect fourth is 5 half steps (C to F), perfect fifth is 7 half steps (C to G), and perfect octave is 12 half steps. These intervals sound hollow, open, and are foundational to harmony across cultures.
Major and minor intervals (seconds, thirds, sixths, sevenths) come in two sizes that differ by one half step. Major intervals are the larger version while minor intervals are one half step smaller. For example, a major third is 4 half steps (C to E) while a minor third is 3 half steps (C to Eb). Major intervals tend to sound brighter and more open, while minor intervals sound darker and more closed.
Common major intervals include: major second (2 half steps, C to D), major third (4 half steps, C to E), major sixth (9 half steps, C to A), and major seventh (11 half steps, C to B). Their minor counterparts are one half step smaller: minor second (1 half step, C to Db), minor third (3 half steps, C to Eb), minor sixth (8 half steps, C to Ab), and minor seventh (10 half steps, C to Bb).
Augmented and diminished intervals are altered versions that extend beyond major/minor. An augmented interval is one half step larger than major or perfect, while a diminished interval is one half step smaller than minor or perfect. For example, an augmented fourth (C to F#, 6 half steps) is also called a tritone and creates significant tension. A diminished fifth (C to Gb, also 6 half steps) is the tritone's enharmonic equivalent.
Interval quality determines how notes function in scales and chords. The specific combination of major and minor thirds determines chord quality—major triads use a major third followed by a minor third, while minor triads reverse this pattern.
Inverting an interval means flipping the position of the two notes so the lower note becomes the higher note, or vice versa. This creates a complementary interval that, together with the original, always spans exactly one octave (12 half steps).
When you invert an interval, the numeric value changes according to a simple rule: the original interval number plus the inverted interval number always equals nine. A second inverts to a seventh (2 + 7 = 9), a third inverts to a sixth (3 + 6 = 9), a fourth inverts to a fifth (4 + 5 = 9), and so on.
The quality also changes in predictable ways: major intervals become minor (and vice versa), perfect intervals remain perfect, augmented intervals become diminished (and vice versa). For example, a major third (C to E, 4 half steps) inverts to a minor sixth (E to C, 8 half steps). Together they span 12 half steps, completing the octave.
Interval inversion is particularly important in understanding chord voicings and counterpoint. When you rearrange chord tones across different octaves, you're creating inversions that use the same notes but create different interval relationships. A C major chord in root position (C-E-G) becomes a first inversion (E-G-C) when the C is moved up an octave.
Understanding inversions helps with voice leading in composition, recognizing chord voicings at the piano, and developing a deeper understanding of harmonic relationships. It's also useful for ear training—recognizing that a descending major third sounds similar to an ascending minor sixth.
Compound intervals are intervals larger than an octave, spanning more than 12 half steps. They're essentially simple intervals (those within an octave) extended by one or more octaves, and they function similarly to their simple interval counterparts.
The most common compound intervals have specific names. A ninth is a second extended by an octave (C to D an octave higher, 14 half steps). An eleventh is a fourth plus an octave (C to F an octave higher, 17 half steps). A thirteenth is a sixth plus an octave (C to A an octave higher, 21 half steps).
In chord theory, compound intervals are written using their actual numeric distance rather than reducing them to simple intervals. A C major 9th chord includes the ninth (D) rather than calling it a second. This distinction matters because the ninth sits above the seventh in the chord voicing, creating a specific texture and spacing.
Major Ninth Interval
From C to D spanning an octave plus a major second, creating a major ninth compound interval
Compound intervals retain the quality of their simple interval equivalent. A major ninth is a compound major second, so it's measured as 14 half steps. A perfect eleventh is a compound perfect fourth at 17 half steps. This relationship helps you calculate compound intervals quickly by adding 12 (one octave) to the simple interval's half step count.
Understanding compound intervals is essential for analyzing extended harmony in jazz, understanding chord extensions, and working with wider melodic leaps. While they span larger distances, they retain the harmonic character of their simple interval roots—a ninth has a similar quality to a second, just with more spaciousness and sophistication.