By comparing his beloved to a rose and a sweet-sounding melody the speaker in Robert burns a red red rose indicates that his beloved is

In both comparisons, the beloved person, as well as the affection towards they, has to do with emotions. Talking about a red rose that is fresh, lovable and that represents love, more specifically passionate, deep and intense love. The poem also says many times the word red, which is used to emphasize the intense emotions.

The second comparison about a melody makes reference to how beautiful peaceful and at the same time passionate and harmonious a melody can be, just the way the speaker and they beloved interact in their connection