"Sonnet 128" is a more traditional sonnet. In fact, the subject here does not even have to be the Dark Lady. The speaker could be talking about any beautiful woman. In this poem a little story is told. The speaker is watching the woman he adores play the piano, and he becomes envious or jealous of the piano keys since she is moving her fingers over them. He describes her touching the keys as kisses: the piano keys get to kiss her fingertips. The speaker wishes that his lips, instead of the piano keys, were the ones kissing the lady's fingers. The speaker somewhat comically concludes that since the piano keys get her fingers to kiss, then he should get her lips for the same purpose.
A reader might also note the metaphor in the first line. The speaker refers to his lady as "my music." She is the music of his soul. She is the one who transports him to such grand and eloquent feelings.
The idea of envying an inanimate object in this poem may remind the reader of one of the sonnets in Astrophil and Stella by Sir Philip Sidney. In that sonnet cycle (in Sonnet 45, to be exact) Astrophil envies a story that causes Stella to feel pity and cry. Just as the speaker in Shakespeare's poem wishes to trade places with the piano keys, Astrophil wishes that he could be the story that makes Stella weep.