Intervals refer to the distances between notes numerically using the major scale as the reference.

Perfect

In the major scale, notes one, four and five are called perfect, i.e. perfect prime, perfect fourth and perfect fifth. For example, when playing a C, then the same C again, that interval is a perfect prime. When playing C, then the next higher F (the fourth note of the C major scale) that interval is called a perfect fourth. When playing C, then the next higher G (the fifth note of the C major scale) that interval is called a perfect fifth.

Major

Notes two, three, six and seven are called major. For example, when playing a C, then the next higher D (the second note of the C major scale) that interval is called a major second. C to E is a major third, C to A is a major sixth, and C to B is a major seventh.

Minor

When any major interval is lowered by a semitone it becomes minor.

Augmented

When any interval of the major scale is raised by a semitone it becomes augmented.

Diminished

When a perfect or minor interval is lowered by a semitone it becomes diminished.

Descending Intervals

When naming descending intervals (i.e. going backwards) they are the same as ascending. For example, when playing a C, then the next A below the C, that interval is called a minor third. See Complimentary intervals.

Compound Intervals

A compound interval is any interval above the octave. The eighth note of the seven note major scale is the same as the first (7 + 1 = 8). For example, when playing a C, then the next C in the scale, that interval is called a perfect octave. The ninth is the same as the second (7 + 2 = 9) etc. For example, when playing a C and the D an octave above the next D in the scale, that interval is called a major ninth.

Here are some examples in different keys:

C D E F G A B C Db = a minor ninth

D E F# G A B C D E F# G# = an augmented eleventh

Eb F G Ab Bb C D Eb F Gb = a minor tenth