Lets say a state is defined by the minimal amount of independent variables to completely describe a system. One would come up with the (q,p)-phase-space for a point mass and as another example the Hilbert-space for quantum-states. Consider the very simple case of a standing wave in string where f1, f2 etc are the fundamental and the harmonics. Question: Could one define a 'state-space' of the frequencies f1, f2 etc.?