Interval
An interval is the distance between two notes. Its size is counted in letter names, both ends included: from C to E there are three (C, D, E), so C–E is a third.
The intervals are named after numbers. Counting up from C: unison (the same note twice), second (C–D), third (C–E), fourth (C–F), fifth (C–G), sixth (C–A), seventh (C–B) and octave (C to the next C). Up or down, the size is counted the same way.
On the staff an interval is written in two ways. When the notes sound one after the other, the interval is melodic: the notes stand side by side, as in a tune. When they sound together, it is harmonic: one note is written above the other. The size is the same either way.
Half steps (semitones) are the finer measure. Intervals with the same name can differ by a half step: C–E is four half steps, a major third; D–F is three, a minor third. A perfect fifth is seven half steps, an octave twelve. Every tune and every chord is built from intervals: a triad is two thirds stacked up.
What it sounds like
Each interval has its own sound: a second is close and tense, a third sweet and warm, a fifth open and wide, and an octave blends into one sound.
Where it is taught: the studio’s interactive textbook, chapter 15, “Intervals: unison to octave”.