Check Rufure's video for in-game version.
• Video
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Annoying Dog's "Dance of Dog" (also known as "Room of Dog", "Error Dance", ...) can be seen if, for whatever reason, your game attempts to load a room that does not exist.
It's named "mus_dance_of_dog.ogg" in the game's files. It's one of the three ways the game handles save errors that I'm aware of:
1: Dance of Dog.
2: Sigh of Dog (also known as "Room of Dog 2", "Sleep of Dog", ...). It plays "mus_sigh_of_dog.ogg".
3: The "dirty hacker" / error handling (fallback) ending.
Props to Annoying D-- Toby Fox for this game's amazing error handling!