Edit 6: Longing

[RiverNotch]

Longing --- Here are some thoughts that haven't yet been spoken, I agree with much of what dukealien said regarding flow. As for this piece being part of a collection --- well, I can't say anything about that, but the thought will definitely hang over me.
 
Cicadas sing the artless words that two 
familiar strangers stifle with esprit, With "esprit de corps", I always think of esprit as something inclusive, which stifling words is not. "familiar strangers" is a nice wording, but it sets a sort of subject confusion, as it might lead to the reader thinking those strangers were familiar to the cicadas. Now, that might be what you're going for in the first place, but the wording is only nice if the "both of us" were those "familiar strangers".
to both of us in soothing secrecy. I do find "soothing secrecy" an especially luscious wording.
It isn't through a cithara—but through The em-dashes are completely unnecessary: the first mark should be gone, the last replaced with a comma. 
a sycamore, the dappled grass and dew—The comparison between the musical instrument and the nature is a little disjoint, as it detaches the music of the cicadas from the cicadas themselves. I think, even with how magical their music is, it's obvious that a cicada's song comes not from the plantlife all around, or perhaps if a comparison is to be made it's the plantlife as some other acoustic device, like say an echo chamber.
the two misapprehend the chances we The problem of who the subject referred to by "the two" seeps into this sentence, but a closer reading clarifies things. Still, I bet an easier reading exists.
provoke, for clay; but through their artistry "artistry" does feel a little lazy, the focus is more on the response of the listeners or the thoughts and equipment of the players rather than the players' music itself.
I sense those artless words belong to you 
 
and me. I wish to watch the clouds again On the flow, I agreed. On how the sonnet is structured --- quatrain quatrain tercet tercet, not quite, but eight and six I somehow felt.
for possibilities we'd ponder till 
we rot alone into ourselves. And then "alone" intrudes. Remove it, then complete the thought some other way.
we're in the shade and hear the flowing creek There's also the division between the two tercets, which as far as I know isn't as necessary, but now I've noticed that the octave does not rely on imagery as much as the sestet, the crux of that portion is personification with a bit of 'philosophy'. That might not be what you want.
and ravenous cicadas, on the hill. The blatant mention of the cicadas here feels too much like it blurs the already subtle distinction between octave and sestet.
I nudge your leg with mine and now I speak. It's crickets that sing with their legs. Sly point aside, with this act "Longing" might not be an entirely appropriate title. The act itself, however, is quite lovely.

Slightly edited.