Scale degree
A scale degree is the number of a note in its scale, written in Roman numerals from I to VIII. In C major, C is degree I, D is II, E is III and so on; degree VIII is C again, an octave higher.
Degrees are counted from the tonic, so the same note has a different number in different keys: in C major, G is degree V; in G major it is degree I. Degrees I and VIII are the same note an octave apart, so a scale has seven different degrees.
Three degrees matter most. Degree I is the tonic, home, where the music comes to rest. Degree IV is the subdominant. Degree V is the dominant, which pulls back towards the tonic. The main chords stand on these degrees: in C major, C, F and G.
Degrees let you talk about music regardless of key: “the tune starts on V and ends on I” is true in C major and in G major alike. The relative minor starts on degree VI of the major scale: in C major degree VI is A, hence A minor.
What it sounds like
Each degree has its own pull: VII is left hanging and strains up to VIII, while I sounds settled, like home.
Where it is taught: the studio’s interactive textbook, chapter 6, “The C major scale”.