52 research outputs found
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
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
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
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
Comparison of non-Markovianity criteria in a qubit system under random external fields
We give the map representing the evolution of a qubit under the action of
non-dissipative random external fields. From this map we construct the
corresponding master equation that in turn allows us to phenomenologically
introduce population damping of the qubit system. We then compare, in this
system, the time-regions when non-Markovianity is present on the basis of
different criteria both for the non-dissipative and dissipative case. We show
that the adopted criteria agree both in the non-dissipative case and in the
presence of population damping.Comment: 8 pages, 1 figure. Some changes made. In press on Physica Scripta T
(special issue
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
Embryo of a Quantum Vocal Theory of Sound
Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study of human voice, considered as a probe to investigate the world of sounds. We present a theoretical framework that is based on observables of vocal production, and on some measurement apparati that can be used both for analysis and synthesis. In analogy to the description of spin states of a particle, the quantum-mechanical formalism is used to describe the relations between the fundamental states associated with phonetic labels such as phonation, turbulence, and slow myoelastic vibrations. The intermingling of these states, and their temporal evolution, can still be interpreted in the Fourier/Gabor plane, and effective extractors can be implemented. This would constitute the basis for a Quantum Vocal Theory of sound, with implications in sound analysis and design
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