Humans who look for order from chaos tend to find it.
Pareidolia (don't ask me how to pronounce it) is a word to describe the perception of seemingly intentional things (often human faces) inside of random distributions. Nearly all humans experience it to some degree, and examples often include seeing a face in the headlights of a car, or a frowning face in a wall socket.
Similarly, I posit that if musicians started to look for music notation everywhere, theyd probably find it.
Also, may I add that every bird was aligned into a space on the staff rather than a line? It's no wonder it made music; us westerners love us some stacks of thirds! It's likely not as uncommon of an effect as you'd think.
You did ask for examples, so: Algebraic (standard) chess notation contains squares from a1-h8. If you took the end squares of every move as a note and its octave, you could have a piece of music (c4, c5, g4, e5,...). Even better, use the "H" as B♮ and the "B" as B♭, as some countries do (I believe Germany?). Not quite nature, though... Ocean waves are similar to sine waves, so one could imagine music made from those. One could look at the proportional diameters of the rings on trees in an area, and use that to create rhythmic music (that'd be kind of cool, considering most trees in an area would have nearly identical songs!).