What does III or iii represent in terms of scale degree?

The designation III or iii in the context of scale degrees indicates the mediant. In a major scale, the mediant is the third degree, which is a crucial point in establishing the harmonic framework of the scale. It represents a harmony that occurs between the tonic (first degree) and the subdominant (fourth degree), and it plays an important role in chord progressions and resolutions.

In a major scale, for example, the notes of the C major scale are C, D, E, F, G, A, and B. The third note, which is E, corresponds to the mediant. In terms of harmony, the mediant can also serve as a pivot point leading to other chords and is key in creating tension and movement in music.

The mediant’s function contrasts with that of other scale degrees, like the tonic, which is the home or resting tone, the supertonic as the second degree, and the subdominant as the fourth degree. Recognizing the mediant's role helps in understanding tonal structures and chord relationships within a given key.