Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts.Comment: The final version of this paper has been published by the Journal of Mathematics and Musi

Parametric Natura Morta

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Location of high speed rail stations in French medium-size city and their mobility and territorial implications

International audienceIn France, the extension of High Speed Rail network has come with the creation of new stations and a diversification of territorial configurations in which the stations fit. If the reduction in travel time allowed by high speed train increases mobility and contributes to the economic development of metropolitan areas, the implications of these stations on local mobility and territorial development depend on the station's location. The example of midsized cities allows us to analyze the part played by the location of stations in spatial organization. The impact of HST on local mobility and territorial development differed depending on whether the metropolitan area is served by a central station, a peripheral one or if it is connected to the high speed rail network by both station

Quels effets territoriaux pour les nouvelles gares de la LGV Rhin-Rhône?

Deux gares TGV ont été construites en Franche-Comté pour desservir Besançon et Belfort-Montbéliard. Or, le degré de centralité des gares influence la réussite des stratégies adoptées dans la mesure où il conditionne la capacité des acteurs locaux à coordonner leurs actions autour de projets d'aménagement conformes aux dynamiques spatiales préexistantes. La localisation de ces gares périphériques, largement dictées par des contraintes techniques et financières, ont peu pris en compte ces dynamiques, et il s'avère difficile de mobiliser l'ensemble des acteurs autour de projets situés aux marges de leurs compétences territoriales

Networks of Music and Images

Powerful abstraction of mathematical category theory can be used to describe musical procedures and structures. The same mathematical theory can be applied to visual shapes and their transformations, including computational applications. Since we can connect music and images through mappings, we can also connect their networks step by step, describing progressive shape modifications. We propose a new approach to music composition based on these ideas, composing music from a network of images “sonifying” each step, as well as creating a parallel sequence of visual and musical variations.Reti di musica e immaginiIl potere di astrazione della teoria delle categorie può essere utilizzato per descrivere procedure e strutture musicali. La stessa teoria matematica può essere applicata alle forme visuali e alle loro trasformazioni, comprese le applicazioni computazionali. Poiché è possibile associare musica e immagini attraverso apposite mappature (mappings), è anche possibile connettere reti (networks) di frammenti musicali e di immagini descrivendo progressivamente le modifiche apportate alle forme musicali e visuali. In questo articolo si intende proporre un nuovo approccio alla scrittura musicale secondo questi principi, ovvero componendo musica a partire da una rete di immagini in grado di “sonorizzare” ogni passaggio e creando una sequenza parallela di variazioni musicali e visuali.Powerful abstraction of mathematical category theory can be used to describe musical procedures and structures. The same mathematical theory can be applied to visual shapes and their transformations, including computational applications. Since we can connect music and images through mappings, we can also connect their networks step by step, describing progressive shape modifications. We propose a new approach to music composition based on these ideas, composing music from a network of images “sonifying” each step, as well as creating a parallel sequence of visual and musical variations.Reti di musica e immaginiIl potere di astrazione della teoria delle categorie può essere utilizzato per descrivere procedure e strutture musicali. La stessa teoria matematica può essere applicata alle forme visuali e alle loro trasformazioni, comprese le applicazioni computazionali. Poiché è possibile associare musica e immagini attraverso apposite mappature (mappings), è anche possibile connettere reti (networks) di frammenti musicali e di immagini descrivendo progressivamente le modifiche apportate alle forme musicali e visuali. In questo articolo si intende proporre un nuovo approccio alla scrittura musicale secondo questi principi, ovvero componendo musica a partire da una rete di immagini in grado di “sonorizzare” ogni passaggio e creando una sequenza parallela di variazioni musicali e visuali

Parametric Natura Morta

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students

cARTegory Theory: Framing Aesthetics of Mathematics

Mathematics can help investigate hidden patterns and structures in music and visual arts. Also, math in and of itself possesses an intrinsic beauty. We can explore such a specific beauty through the comparison of objects and processes in math with objects and processes in the arts. Recent experimental studies investigate the aesthetics of mathematical proofs compared to those of music. We can contextualize these studies within the framework of category theory applied to the arts (cARTegory theory), thanks to the helpfulness of categories for the analysis of transformations and transformations of transformations. This approach can be effective for the pedagogy of mathematics, mathematical music theory, and STEAM

Networks of Music and Images

Powerful abstraction of mathematical category theory can be used to describe musical procedures and structures. The same mathematical theory can be applied to visual shapes and their transformations, including computational applications. Since we can connect music and images through mappings, we can also connect their networks step by step, describing progressive shape modifications. We propose a new approach to music composition based on these ideas, composing music from a network of images “sonifying” each step, as well as creating a parallel sequence of visual and musical variations

Gestural similarity, mathematics, psychology: Hints from a first experiment and some applications between pedagogy and research

Can music and drawings be thought of as the results of physical gestures, and thus be compared? In this paper we summarize the conjecture of „gestural similarity“ developed in the framework of the mathematical theory of musical gestures. Then, we outline the history of an experiment involving mathematics, music, drawing, and psychology, aiming to evaluate the cognitive relevance of the conjecture. A simple visual form and a short homophonic musical sequence can be considered „similar“ if they can be thought of as produced by the same movements. Participants in an experiment were asked to assess the degree of similarity between given music examples and simple visuals (three visuals for each sound stimulus). Results were analyzed and con rmed the theoretical expectations. In addition, we describe some creative applications of this conjecture, including pedagogical and creative developments. In particular, we describe the music derived from a natural form, the essential structure of an ammonite, and the illusion of a „mathematical ocean“ with sounds and images. We discuss challenges of these techniques and the characteristics of spectrograms in relation with gestural similarity