Psalm 137

The rivers of Babylon were mostly canals. Babylonia was flat alluvial country farmed by a huge irrigation network cut off the Tigris and Euphrates, and the deported communities were settled along them — Ezekiel names the Chebar canal as the place his group lived. Poplars and willows grew on those banks, which is where the instruments were hung.

The request for a song of Zion was not friendliness. Captured musicians were a normal spoil of war; Assyrian records boast of carrying off singers, and one of Sennacherib's inscriptions lists male and female musicians among the tribute taken from Hezekiah's Jerusalem. Being told to perform your homeland's temple music for the men who burned the temple was a form of mockery.

The oath in the middle is a musician's oath, and it costs him his trade: let my right hand forget its skill and my tongue stick to the roof of my mouth. He would rather lose the hand and the voice than use them to entertain.

Edom is named because Edom was there. Judah's neighbors to the southeast, descended from Esau, egged the Babylonians on when the city fell and moved into the emptied southern territory; the prophet Obadiah's whole book is about that day.

The last lines are brutal, and they are quoting a sentence already passed. Smashing a city's infants against the stones was the standard horror of an ancient sack — Israel's own prophets describe it happening to Israel — and Isaiah had already announced that it would be done to Babylon. The psalmist is not issuing an instruction; he is calling for the judgment written to fall, and leaving the doing of it to God and to the empire God had already named.