Scale degrees, and the names that describe relationships
The seven places in a scale, each with a name saying what it does in relation to the tonic; thinking in degrees instead of notes is what lets you play the same piece in any key.
A scale has seven notes, and their names change from key to key: the C scale starts on C, the G scale starts on G. What does not change is the place each note occupies, and that place has a name. The degrees are those names, and they are what make a piece the same piece in any key.
Seven places, seven numbers
The simplest way to name a degree is by number: first, second, up to seventh, counted from the note that gives the scale its name. In C major, the fifth degree is G; in G major, the fifth degree is D. The number describes the position, and the position is what repeats from key to key.
Sing the C scale with numbers instead of names — "one, two, three, four, five, six, seven, one" — and then the G scale with the same numbers. The melody of the numbers is the same; only the pitch moved.
The names say what each degree does
Besides the number, each degree has a name, and the names are not arbitrary: each describes the degree's relationship to the tonic.
- Tonic — the first degree, the note that names the scale and the place of rest.
- Supertonic — the second, just above the tonic.
- Mediant — the third, midway between the tonic and the dominant.
- Subdominant — the fourth, a fifth below the tonic, mirror of the dominant.
- Dominant — the fifth, a fifth above the tonic, the degree that pulls back hardest.
- Submediant — the sixth, midway down between tonic and subdominant.
- Leading tone — the seventh, a semitone below the tonic, which "leads" to it and wants to rise.
Notice that subdominant does not mean "a little below the dominant": it means the fifth below the tonic, just as the dominant is the fifth above. The two degrees are symmetrical about the tonic, and that is why the two have the roles they have in harmony.
The leading tone
The seventh degree deserves a paragraph. In the major scale it sits a semitone from the tonic, and that semitone is what makes the scale seem to "want" to finish: sing C, D, E, F, G, A, B, and stop. The B hangs in the air, asking for the C. That pull is why the fifth degree, which contains the leading tone, is the dominant, and why the natural minor scale, whose seventh degree is a whole tone from the tonic, sounds so much less conclusive.
When the seventh degree sits a whole tone from the tonic, it changes name: it is the subtonic, and it does not pull. The name changes because the relationship changed.
Thinking in degrees
A musician who thinks in degrees transposes without effort. A melody that goes "five, three, one" in C major is G, E, C; in F major it is C, A, F; in E flat major it is B flat, G, E flat. Nothing needs recalculating: the degrees are the melody, the key is only the pitch it comes out at.
The same holds for chords: saying "the fourth-degree chord" says the same chord in any key, and that is how the harmonic field is memorised once for all twelve.
What to take from here
The degrees are the seven places in a scale, numbered from the tonic, and their names describe relationships: the dominant is the fifth above, the subdominant the fifth below, the leading tone the semitone that pulls home. Thinking in degrees is what lets you sing, play and transpose the same piece in any key, and it is the vocabulary the whole of harmony is written in.