The core requirement for “programmability” is a machine whose behavior can be changed by altering symbolic instructions without rebuilding the machine.

The Banu Musa automatic flute player doesn’t meet this bar. The flute player was mechanically configured, not symbolically programmed. It had no conditional logic or flow control. No stored symbolic instructions.

To contrast, the Jacquard Loom used an externally stored instructions (punch cards). It allowed arbitrary-length instruction sequences, which is a primitive form of control flow.