Since "The Guitarist Tunes Up" is only 8 lines long, we don't get to spend much time with the speaker. Still, we're able to get some sense of who's talking in this one.
Phrases like "attentive courtesy," "lordly conqueror," and "slight essential things" give us the feeling that this speaker is pretty refined. The language isn't particularly academic or artificially elevated in tone, but it does seem knowledgeable and subtle. And we know the speaker's observant, too, because she's noticing every little detail of this exchange between man and musical instrument.
While it is always a good idea to separate the speaker from the poet, there isn't anything in these 8 lines to make us consider a speaker other than Cornford herself. So, that makes our speaker a knowledgeable, refined woman attending some kind of music recital but imagining something much more… personal.