This appears to be a poem about death, or specifically, the thoughts of someone remembering and thinking of someone who has died. It is a subtle poem, so one must read it closely and examine the imagery to understand it is full of metaphors and symbols, even though it seems fairly straightforward.
For example, there are several images referring to carved stone: a granite counter, a marble floor, and a white stone building of silence. These could all be said to conjure the image of a tombstone, especially the first two images, which are also connected to the person the speaker is thinking of: their wineglass set down on the granite counter, their cut hair falling to the marble floor. The white stone building of silence is a powerful image that also describes a tomb.
The poem is also about sounds and silences. It describes soft sounds made when the speaker (the listener) makes efforts to be quiet, such as turning down the jazz on the radio, or sitting and waiting for the poem's subject to wake from their dream. The domestic sounds described portray an intimate relationship (a cough from the bedroom, the rustle of a blanket), and this further reinforces the idea that the poem describes a loved one—a family member or spouse, perhaps—who has died. In the last line, the speaker said he will listen to an ant who beats his dead comrade across the floor, the "noble sounds of his tread and his low keening," and we know this signifies the speaker's attempt to identity with the ant, who is also mourning a loss ("keening" being a word that refers specifically to the intentional sounds made during mourning).