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Guerino Mazzola and Moreno Andreatta

We present some basic aspects of Klumpenhouwer transformation theory by describing an abstraction process leading to the formalization of this analytical approach in the functorial conceptual model of denotators. After summarizing the main idea about recursive construction in music theory, we show that a Klumpenhouwer network is formally equivalent to a very special limit of a diagram and give natural generalizations thereof. We end with the discussion of some problematic aspects of a group-theoretical model of music theoretical constructions.

Jon Wild

We recap some results of tiling problems in a non-cyclic homogeneous pitch-space. We then attempt to generalise to subsets of the usual chromatic, considering the subsets variously as _warped_ or _gapped_. Tiling sets may be obtained from different kinds of equivalence classes; transformations are illustrated that map one space to itself or to another space, and that map one equivalence class of tiles to another, creating isomorphism classes of tilings. Special attention is given to tilings of the diatonic implied in various music-theoretical historical sources.