...what's great about Theatrhythm tapping is that it feels like you're playing against your own limitations. Instead of facing off against some arbitrarily-difficult creation of some bored programmer in Osaka, you're fighting your body's lack of rhythm. And getting better requires practice, not level grinding.
A music game is a videogame where the gameplay is meaningfully and often almost entirely oriented around the player's interactions with a musical score or individual songs. Music video games may take a variety of forms and are often grouped with puzzle games due to their common use of "rhythmically generated puzzles".
Strong support for the convergence of live music and video games is evident with the success of the Video Games Live concert series. Emergent games for live concert performance, "game-scores," augment traditional western music notation with the dramatic elements of animation, interactivity, graphic elements and aleatoric principles (Anigraphical Music). The concept of incorporating Game Theory and music is not new and can be traced back to Musikalisches Würfelspiel.
Music video games are distinct from purely audio games (e.g. the 1997 Sega Saturn release Real Sound: Kaze no Regret) in that they feature a visual feedback, to lead the player through the game's soundtrack, although eidetic music games can fall under both categories.