Game is balanced when it's mechanics don't lead to the dominance of a single scenario.

In the most narrow sense game balance is tied to competitive games and is examined in the context of winning. For example: do some players (for example first in the game) get higher chances of winning the game, regardless of their skill?

The above equals to balance as fairness, but that's not the only type. Jesse Schell in his The Art of Game Design stretches the notion and points out 11 more aspects. Although this typology could be contested at the theoretical level but author's aim is not to provide rigour but rather to introduce many useful terms and, as he calls them, "lenses" for game design analysis and education.

Let's list all kinds of balance according to Art of Game Design. In parentheses I add some of the related topics discussed in the book especially important for music games: fairness (symmetry and asymmetry in games), challenge vs success (too much success is boring in regular games), meaningful choices (risk/reward distribution), skill vs chance (choice vs chance), head vs hands (different types of skills), competition vs cooperation, short vs long, rewards (separately with…), punishment (…for unknown reason), freedom vs controlled experience, simple vs complex (emergence!), detail vs imagination.

For music games many aspects would need to be specified or added. Here are some examples of topics that are worth considering when making a music game and are possible to approach in the context of balance:
— Can different types of instrument participate on equal footing? Usual suspects are percussion and vocals. Can you let them play?
— Does the music always feel the same in different playthroughs? Or maybe it is so dissimilar every time that has no identity?
— Can the person that has no experience in music have an attempt on the game? What skills it requires and what it allows to develop?

Other game design terms:

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