What is an interval?

An interval is the distance between two notes. Every interval carries two labels, and they measure different things.

The number counts letters

Count the letter names from the lower note to the higher, including both ends.

C to E: C, D, E — three letters, so a third. C to G: C, D, E, F, G — five letters, a fifth. C to C: same letter, one apart in pitch — an octave.

Sharps and flats do not affect the number. C to E and C to E♭ are both thirds, because both span three letter names.

The quality measures semitones

The number alone is not enough — a third can be four semitones or three, and those sound quite different. Quality pins it down.

Two families of interval take different quality names:

Fourths, fifths, octaves and unisons are perfect. Alter them and they become augmented (one semitone wider) or diminished (one narrower).

Seconds, thirds, sixths and sevenths are major or minor. Major is the wider of the two by one semitone.

Spelling is not optional

C to F♯ and C to G♭ are both six semitones. They are not the same interval.

C to F♯ spans four letters — an augmented fourth. C to G♭ spans five — a diminished fifth.

They sound identical in equal temperament, but they behave differently in a key and resolve in different directions. Which is why the letter you write genuinely matters, and why accidentals are chosen by context rather than convenience.

Harmonic and melodic

An interval whose notes sound together is harmonic. One whose notes sound one after the other is melodic. Same interval, same name; the terms just describe how it appears.

Why everything else depends on this

A major chord is a major third with a minor third on top. A major scale is a specific sequence of tones and semitones. Key signatures exist to protect that sequence. Every one of those definitions is an interval definition.