Someone read a poem I wrote and interpreted it in a way that transcended my intent. It was a beautiful interpretation and hung together very nicely on its own terms and with the text. Did I misread it? Is that what you meant? the person asked.
I didn’t answer in any meaningful way, I didn’t think I should.
It occurs to me that poems and their readers are like the two players on either side of a log xylophone, each playing a different melody. If everything comes together as it should – if the players are mutually aware and mutually sensitive -, they work in counterpoint, “slipping notes in the gaps of each other’s parts” and out of that (it always seems so miraculous to me) the audience begins to hear a third melody, knocking and throbbing and hanging out there in a phantom-like but very moving way.
No-one “wrote” the third melody. It is born of the interaction between the two players.