Riemannian

̂A(M)=√((R/2)/(sinh (R/2)))

where R is the Riemannian curvature of the metric g, regarded as an operatorname End(TM)-valued two form, and √ is the Pfaffian, which is an invariant polynomial defined on the Lie algebra of skew symmetric matrices in even dimensions.

And not only theory: most central European composers of this century were schooled in Riemannian doctrine of one type or another.