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This paper introduces an extension of the Rubato Composer software's BigBang rubette module for gestural composition. The extension enables composers and improvisers to operate BigBang using the Leap Motion controller, which uses two cameras to detect hand motions in three-dimensional space. The low latency and high precision of the device make it a good fit for BigBang's functionality, which is based on immediate visual and auditive feedback. With the new extensions, users can define an infinite variety of musical objects, such as oscillators, pitches, chord progressions, or frequency modulators, in real-time and transform them in order to generate more complex musical structures on any level of abstraction.

The mathematical theory of counterpoint was originally aimed at simulating the composition rules described in Johann Joseph Fux’s Gradus ad Parnassum. It soon became apparent that the algebraic apparatus used in this model could also serve to define entirely new systems of rules for composition, generated by new choices of consonances and dissonances, which in turn lead to new restrictions governing the succession of intervals. This is the first book bringing together recent developments and perspectives on mathematical counterpoint theory in detail. The authors include recent theoretical results on counterpoint worlds, the extension of counterpoint to microtonal pitch systems, the singular homology of counterpoint models, and the software implementation of contrapuntal models. The book is suitable for graduates and researchers. A good command of algebra is a prerequisite for understanding the construction of the model.

Il punto di partenza di questo lavoro e l'interpretazione delle topologie di Grothendieck nel linguaggio dei sistemi relazionali (cfr. [5]); cio permette uno studio aritmetico di tali topologie. Attraverso nuove tecniche, qui introdotte, si ottengono risultati non privi di interesse, tra i quali una caratterizzazione degli spazi topologici noetheriani, ed ulteriori strutture topologiche di tipo locale (siti tangenti), per le quali vengono dimostrate numerose proprieta. Vengono, infine, date alcune applicazioni alla teoria degli schemi, utilizzando il funtore inviluppo affine. The starting point of this paper is the interpretation of Grothendieck's topologies in the language of relational systems (cfr. [5]); this permits an arithmetical study of these topologies. By applying new techniques introduced here, we have achieved interesting results. These include a new characterization of Noetherian topological spaces, and further topological structures of local type (tangent sites) for which we have shown numerous properties. Finally, we have used the affine-envelope functor to illustrate some applications to the theory of schemes.