Every interval up to an octave

Number, then type

1. Number: count the letter names from the lower note to the upper one, counting both.
2. Type: compare with the major scale of the lower note. If the upper note is in it, the interval is major (2nds, 3rds, 6ths, 7ths) or perfect (4ths, 5ths, octaves). A major interval one semitone smaller is minor.

To write an interval above a note, work the same way round: count up the letter names first, then choose the sign that gives the right number of semitones.