Intervals

What is an interval?

An interval describes how far one note is above (or below) another. Musicians use two ideas together:

• Chromatic distance — counted in semitones (half steps). Twelve semitones make one octave.
• Diatonic name — a number (second, third, fifth …) from counting letter names from the lower note to the higher, and a quality (major, minor, perfect, augmented, or diminished) that matches the semitone size.

For example, from C up to E is a major third: three letter steps (C–D–E) and four semitones. From C up to Eb is still three letters but only three semitones, so it is a minor third.

Simple intervals within an octave

These are the building blocks. Examples use C as the lower note; any root follows the same semitone pattern.

Interval qualities

Perfect intervals are unisons, fourths, fifths, and octaves (and their compounds). In the major scale, these are stable, open sounds.

Major and minor apply to seconds, thirds, sixths, and sevenths. In a major scale built on the lower note, the scale degrees form major 2nds, 3rds, 6ths, and 7ths above the tonic; the minor scale versions use minor qualities where the semitone count is one smaller.

Augmented and diminished raise or lower a perfect or major/minor interval by one semitone (written +1 or −1 from the “natural” size for that number). The tritone is six semitones and can spell as an augmented fourth or a diminished fifth depending on letter names.

Intervals and triads

Stacking thirds from a root builds the basic chords you use in every style:

• Major triad — major third, then perfect fifth from the root (4 + 7 semitones from root to fifth, or think M3 + m3 stacked).
• Minor triad — minor third, perfect fifth (3 + 7 semitones from root to fifth).
• Diminished — minor third, diminished fifth.
• Augmented — major third, augmented fifth.

Seventh chords add another third above the fifth: for example, a dominant seventh is a minor seventh above the root combined with a major triad.

Compound intervals

When the upper note sits more than an octave above the lower note, you keep the same quality but add 7 to the number for each octave spanned. A major ninth is an octave plus a major second (14 semitones). An eleventh is an octave plus a fourth; a thirteenth is an octave plus a sixth. Jazz charts often label extensions as 9, 11, and 13 because those compound names match how players hear them over a chord.

Inversions

Move the lower note up an octave (or the higher note down) so the former top note is now on the bottom: the interval is inverted. The two interval numbers always add to 9 (second ↔ seventh, third ↔ sixth, fourth ↔ fifth). Unison and octave swap with each other. Qualities swap in a fixed way: major ↔ minor, perfect ↔ perfect, augmented ↔ diminished.