1,721,002 research outputs found
Categories, Color Gestures, and the "Souvenir Theorem": using Math to navigate the Complexity of Music and the Visual Arts
No full textArts, including music, seem to be far away from mathematical rigor. However, some mathematical constructions can well describe artistic forms and features and image/music translations. With the language of categories, in fact, we can describe forms as morphisms connecting points in space; form transformations, as natural transformations; visual-to-music form and structure mappings, as functors (mappings between categories). Effective translations verify gestural similarity: `similar' visual sketches and articulations/melodic profiles appear as being generated by the same gesture. We can define color gestures as mappings between points in the RGB space, and timbre gestures as mappings between timbres. Timbre-color correspondence requires equivalence classes and quotient categories. A timbre is mapped onto a color-class of colors and vice versa, satisfying a perceptive analogy between color and timbre bands (e.g., tension/relaxation feeling). We also present here the Souvenir Theorem (ST) and the Art Conjecture (AC). According to AC, the same idea can be identifiable and well-defined through its embodiments in similar artworks from different media. ST, with practical implications, is a condition of minimal recognizability of a form, allowing the creation of musical souvenirs
Mathematics, Nature, Art
No full textWhen we think of 'concrete' things, we first think of the earth, with trees and plants. When we think of art, we think of shapes, colors, and sounds. When we think of 'abstract' things, one of the first ideas that comes to mind is probably higher mathematics.
This short book proposes hints from mathematics, and in particular from the language of category theory and some of its structures, as a tool for a unified perspective on forms from nature and art, in particular music and the visual arts. Mathematics, moreover, offers a way to map these shapes into sounds and to make music out of it.
In this way, the so-called 'abstract nonsense' of categories can be connected with its opposite, the concreteness of nature
cARTegory Theory: Framing Aesthetics of Mathematics
Full text linkMathematics 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
Gestural similarity, mathematics, psychology: Hints from a first experiment and some applications between pedagogy and research
Full text linkCan 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
M. Mannone, Dalla Musica all'Immagine, dall'Immagine alla Musica - Relazioni matematiche fra composizione musicale e arte figurativa
No full textNella composizione di un brano musicale, oltre all’ispirazione spontanea e al messaggio che si intende trasmettere, intervengono molteplici fattori, fra cui lo studio delle forme musicali, la scelta della tecnica compositiva, il metodo di lavoro. Contano inoltre gli influssi che le varie arti possono esercitare scambievolmente, insieme ai nessi con la letteratura, la filosofia, la natura, la scienza.
Un’opera può anche ispirarsi a un’altra di diverso genere. È possibile però realizzare una vera e propria traduzione formale da un’opera d’arte visiva in un’altra in linguaggio musicale, e viceversa? E il linguaggio intermedio di raccordo potrebbe identificarsi nel linguaggio matematico?
“Si tratta di una sfida affascinante, nuovi orizzonti si schiudono di fronte alla possibilità di analizzare le tecniche di una composizione musicale” (M. Betta)
Alberi e Sinfonie: matematica, musica e complessità della natura
No full textDalle nervature di una foglia all’intricato disegno di una foresta, è possibile guardare forme, strutture e sviluppi naturali in termini matematici, in particolare utilizzando il formalismo astratto di punti, frecce e diagrammi della teoria delle categorie. Lo stesso formalismo ben si adatta allo studio delle strutture musicali, e dunque al confronto tra forme musicali e forme naturali. Nell’articolo vengono presentati degli esempi di composizione, improvvisazione e analisi musicale
Trajectory-based and Sound-based Medical Data Clustering
No full textChallenges in medicine are often faced as interdisciplinary endeav- ors. In such an interdisciplinary view, sonification of medical data provides an additional sensory dimension to highlight often hard- to-find information and details. Some examples of sonification of medical data include Covid genome mapping [5], auditory repre- sentations of tridimensional objects as the brain [4], enhancement of medical imagery through the use of sound [1]. Here, we focus on kidney filtering-efficiency time-evolution data. We consider the estimated glomerular filtration rate (eGFR), the main indicator of kidney efficiency in diabetic kidney disease patients.1 We propose a technique to sonify the eGFR trajectories with time, frequency, and timbre to distinguish amongst patients (Figure 1). Multiple pitch tra- jectories can be formally investigated with the tools of counterpoint (Figure 2), and computationally analyzed with sound-processing techniques. Patients who present similar patterns of eGFR behavior can be more easily spotted through musical similarities. We use the Fréchet distance, which evaluates the shape similarity between curves [2], to cluster patients with similar eGFR behavior. We thus compare the information gathered through sonification and shape- based analysis. We find the mean curves in each trajectory cluster and we compare them with the characteristics of sonified curves. Clustering methods have also been applied to sound analysis: it is the case of k-means to cluster sound data [3]. The Fréchet-based clustering technique is a development of k-means taking shape into account. Thus, we sketch a sound-based clustering approach for medical data, as an additional tool to find patterns of behavior. This study can foster new research between computer science, medicine, and sound processing
Networks of Music and Images
Full text linkPowerful 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 immagini
Il 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
Quantum computing for swarm robotics: a local-to-global approach
No full text: Quantum computing is a branch of computer science derived from the fundamental laws of quantum mechanics, such as state superposition, multi-value logic and destructive measure. An open challenge in itself is to re-think in quantum terms classic problems and solving techniques. Another nature-inspired field is the development of swarm-based robotic applications, where the challenge is catching the fundamental laws governing swarm dynamics, such as pattern formation and target reaching. Here, we review some recent approaches on swarm dynamics, the organizational rules of which are formalized according to quantum computing. In this way, the shades of probability in decision-making for multiple-robot systems can be expressed according to the multi-value logic underlying quantum computing. In our review, specific quantum circuits are sketched to give an idea of how these problems have been faced in computational terms. The article is enriched by references to sonification, a strategy adding one more sensory dimension to data representation, a human-friendly tool to navigate the complexity of swarm-robotic movements in a given arena.This article is part of the theme issue 'The road forward with swarm systems'
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