Is there higher-dimensional generative grammar?
Yes, there are n-dimensional grammars and in some cases specifically applied to music, see for example Grammar-based music composition by Jon McCormack, which talks about parametric extensions to L-grammars, or more generally, Regulated Array Grammars of Finite Index, Part I: Theoretical Investigations by Henning FERNAU, Rudolf FREUND and Markus HOLZER which talk about n-dimensional array grammars.