1. Lattices in Euclidean Space 3 1.1. Discrete vector groups 3 1.2. Hermite and Smith Normal Forms 5 1.3. Fundamental regions, covolumes and sublattices 6 1.4. The Classification of Vector Groups 12 1.5. The space of all lattices 13 2. The Lattice Point Enumerator 14 2.

Harmony theory has been essential in composing, analysing, and performing music for centuries. Since Western tonal harmony exhibits a considerable amount of structure and regularity, it lends itself to formalisation. In this paper we present HARMTRACE, a system that, given a sequence of symbolic chord labels, automatically derives the harmonic function of a chord in its tonal context. Among oth...

Fitelson and Waterman (2004)’s principal objection to Strevens (2001)’s Bayesian treatment of auxiliary hypotheses rests on a misinterpretation of Strevens’s central claim about the negligibility of certain small probabilities. The present paper clarifies and proves a very general version of the claim.