What is the significance of ending on scale degrees ^1 and ^3 in a melody?

Ending a melody on scale degrees ^1 (the tonic) and ^3 (the mediant) carries significant meaning within tonal music. The tonic, or the first scale degree, serves as a foundational element of a key, providing a sense of resolution and closure. When a melody concludes on ^1, it solidifies that sense of home and stability, which is a hallmark of well-structured musical phrases.

Scale degree ^3, while not as stable as ^1, still contributes positively to the harmony and mood of the melody. When employed at the end of a piece or phrase, ^3 can enrich the final sound, offering a sense of brightness and leaving the listener with a pleasant, resolved feeling.

In contrast, ending on less stable degrees or creating tension by using degrees that lead back to the tonic might leave the listener anticipating further musical development. Therefore, the decision to conclude a melody on degrees ^1 and ^3 typically signifies a satisfying resolution, encapsulating the tonal center of the piece while promoting an overall sense of completion.