It can be realized as a ruled surface. All we need to prove it is one heavy item and a whole bunch of light items! You have to pay close attention to every move! Already have one drawn? As Tymoczko says, "Human pitch perception is both logarithmic and periodic.
Becuase you said we, so there must be other people.
For three or four-note chords the topology becomes more complicated. Wow, it sounds like you've really researched this topic, David! They use these axioms to construct a Markov-chain model for the distribution of polygonal types. This branch of mathematics, in its various guises, studies abstract groups by representing them as groups of linear transformations of vector spaces. Is a mobius strip a torus?