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

Narrow and wide understanding

In the most narrow sense game balance is tied to competitive games and is examined in the context of winning. Designers have to ask themselves if some player (for example first to make a move in a turn-based 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. Imbalance can appear at any level of the game when an element is too desirable for players in comparison to alternatives. Players seemingly stop having a choice in the matter when only one option is "good". It's usually better to give players choices that are equally desirable.

The analysis of applying different types of balance to music games can be found in:
Game pieces as games — article in the journal Improvised Music - Open Scores.

Music games design

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 at the game? What skills it requires and what it allows to develop?

Other game design terms:

Mark for clarification

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