Non-isochronous Metre in Music from Mali

The basic building blocks for rhythmic structure in music are widely believed to be universally confined to small-integer ratios. In particular, basic metric processes such as pulse perception are assumed to depend on the recognition and anticipation of even, categorically equivalent durations or inter-onset intervals, which are related by the ratio of 1:1 (isochrony). Correspondingly, uneven (non-isochronous) beat subdivisions are theorized as instances of expressive microtiming variation, i.e. as performance deviations from some underlying, categorically isochronous temporal structure. By contrast, ethnographic experience suggests that the periodic patterns of uneven beat subdivision timing in various styles of music from Mali themselves constitute rhythmic and metric structures. The present chapter elaborates this hypothesis and surveys a series of empirical research projects that have found evidence for it. These findings have implications for metric theory as well as for our broader understanding of how human perception relates to cultural environments. They suggest that the bias towards isochrony, which according to many accounts of rhythm and metre underlies pulse perception, is culturally specific rather than universal. Claims regarding cultural diversity in the study of music typically concern styles and meanings of performance practices. In this chapter, I will claim that basic structures of perception can vary across cultural groups too.

Taut contact hyperbolas on three-manifolds

In this paper, we introduce the notion of taut contact hyperbola on three-manifolds. It is the hyperbolic analogue of the taut contact circle notion introduced by Geiges and Gonzalo (Invent. Math., 121: 147–209, 1995), (J. Differ. Geom., 46: 236–286, 1997). Then, we characterize and study this notion, exhibiting several examples, and emphasizing differences and analogies between taut contact hyperbolas and taut contact circles. Moreover, we show that taut contact hyperbolas are related to some classic notions existing in the literature. In particular, it is related to the notion of conformally Anosov flow, to the critical point condition for the Chern–Hamilton energy functional and to the generalized Finsler structures introduced by R. Bryant. Moreover, taut contact hyperbolas are related to the bi-contact metric structures introduced in D. Perrone (Ann. Global Anal. Geom., 52: 213–235, 2017).

Pseudo-Parallel Characteristic Jacobi Operators on Contact Metric 3 Manifolds

We prove that the characteristic Jacobi operator on a contact metric three manifold is semiparallel if and only if it vanishes. We determine Lie groups of dimension three admitting left invariant contact metric structures such that the characteristic Jacobi operators are pseudoparallel.

Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness

In this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.