Counting intervals

C up to E is a third, not a second, because you count both notes: C is one, D is two, E is three.

Size: count the letters, both ends included

Every interval has a size and a quality. The size is the number you get by counting letter names from the lower note to the upper note, including both. F to C is a fifth: F is one, G two, A three, B four, C five. It is tempting to start from zero and get four, and that is the most common mistake beginners make. Two notes on the same line or space are a unison, not a "first", and eight letters apart is an octave, not an "eighth".

On the staff there is a quick check. Lines and spaces alternate, so an interval with both notes on lines, or both in spaces, is always an odd number: a third, fifth or seventh. One note on a line and the other in a space gives an even number: a second, fourth, sixth or octave. A third looks like two notes on neighbouring lines, a fifth like notes two lines apart with one line between them.

Melodic and harmonic, up and down

When the two notes sound one after the other, the interval is melodic. When they sound together, it is harmonic. The size is the same either way, and so is the size going up or coming down: G down to C is still a fifth. Musicians say "a fifth up" or "a fifth down" when direction matters, as it does in a melody. Accidentals do not change the size either. C to E, C to E♭ and C♯ to E are all thirds, because the letters are still C, D, E.

Quality: the exact size in half steps

Because accidentals leave the number alone, the number cannot be the whole story. C to E is four half steps; C to E♭ is three. The quality word tells them apart. Seconds, thirds, sixths and sevenths come in major and minor forms, a minor one being a half step smaller. Unisons, fourths, fifths and octaves are called perfect. An interval a half step larger than major or perfect is augmented, and one a half step smaller than minor or perfect is diminished.

Open Music Theory recommends a shortcut called the major scale method. Imagine the lower note as the first note of a major scale. If the upper note belongs to that scale, the interval is major (for seconds, thirds, sixths, sevenths) or perfect (for unisons, fourths, fifths, octaves). If it is a half step lower than the scale note, a major interval becomes minor. In C major every note above C gives a major or perfect interval, which is why the table above reads so neatly.

Interval names may look like bookkeeping, but they make musical conversation fast. A singer told that the next note is a fifth higher can find it without a score, and a guitarist can move a chord shape up a fourth without thinking about each string. Intervals also explain why a melody still sounds like itself when it starts on a different note: the distances between the notes stay the same, and only the starting point moves.