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

In what sense can instruments and bodies be said to form spaces?

My recent work is an exploration of the physical and conceptual mechanisms that interface people with instruments. Central to this investigation is a conception of the performer/instrument assemblage as a symbiosis of two parallel and interdependent systems: one – the performer – moves through space established by the other – the instrument. Each system possesses its own intrinsic properties and characteristics; each possesses capacities to affect and be affected by one another. The music emanates from this contiguous interaction. Instrument surface is understood as a compositional resource itself, a topological façade, defined by ordinal distances, that guides gestures along its contours. Within these fluctuating constellations of spatial coordinates, I consider all the relevant ways a body can move, and establish some general combinatory rules that inform the convergence of forces within the body. The traditional subjects of compositional contemplation such as form, duration, dynamic, etc. are not attributing features to the work per se but emerge as results from spatiotemporal relations of (bodily) movement’s correspondence with (instrumental) surface and mechanism. This liberation of movement is understood as a liberation of timbre, and the inherent indeterminacy of this relationship is embraced. As such, I would hypothesize that sound is, to an extent, freed from the subtractive tendencies of perception that might otherwise subvert it into generalized typological categories. Once liberated from the imagination, sound can bypass the brain and directly engage the nervous system

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

Narrating the origin of the universe through music: A case study

Our project is about the synthesis of a musical piece, based on the timeline of the Universe. We can understand music through visual and gestural analogies. In a similar way, popular descriptions of scienti c concepts also use external metaphors and visual support to help comprehension. We will use music to describe a topic from astrophysics, the birth and evolution of the Universe. We describe the compositional technique used to create the composition “Origin,” referring to recent techniques to derive music from tridimensional images and from gestures, under the light of the mathematical theory of music in the context of a narrative

Inter-Piece Sampling and Convolution: Portfolio of 5.1 Acousmatic and Electronica Compositions, Interactive Diagrams and Text

This practice-based PhD – ‘Inter-piece Sampling and Convolution’ – evolved against the background of composers such as Amon Tobin and Monty Adkins, who use techniques and workflows common to both acousmatic and electronica music. The pieces in this thesis are linked through a sustained commitment to working across these two musical contexts and through their relationships to source materials and pulses. Sound materials have been sampled from within the pieces themselves, and materials from older pieces have been convolved with newer sounds, furthering the connections between pieces. The continual feeding-forward of source material promoted the synchronous development of the conceptual tool: Input, Sculpt, Output, which brought about the evolution of intricate diagrams. All of the pieces are for fixed media, and nine of the ten are in 5.1-format surround sound. The complex web of interrelationships created by the process of sampling and convolving material from previous pieces demanded an innovative means of representation. This representation took on a diagrammatic form in order to facilitate the analysis of a sound’s continuous (re)appropriation, explicated within supporting text. The diagrams indicate the extensive use of sampling and convolution to connect pieces, and include embedded hyperlinks to audio at various stages. As a result, textual analysis of techniques and their implications takes place across multiple pieces, and results in a wider scope for individual commentaries. The hyperlinked nature of the diagrams provides a foundation for further research, and a number of conclusions are posited about the use of sampling and convolution across multiple pieces

Of epistemic tools: musical instruments as cognitive extensions

This paper explores the differences in the design and performance of acoustic and new digital musical instruments, arguing that with the latter there is an increased encapsulation of musical theory. The point of departure is the phenomenology of musical instruments, which leads to the exploration of designed artefacts as extensions of human cognition – as scaffolding onto which we delegate parts of our cognitive processes. The paper succinctly emphasises the pronounced epistemic dimension of digital instruments when compared to acoustic instruments. Through the analysis of material epistemologies it is possible to describe the digital instrument as an epistemic tool: a designed tool with such a high degree of symbolic pertinence that it becomes a system of knowledge and thinking in its own terms. In conclusion, the paper rounds up the phenomenological and epistemological arguments, and points at issues in the design of digital musical instruments that are germane due to their strong aesthetic implications for musical culture

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

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

Harmony and Technology Enhanced Learning

New technologies offer rich opportunities to support education in harmony. In this chapter we consider theoretical perspectives and underlying principles behind technologies for learning and teaching harmony. Such perspectives help in matching existing and future technologies to educational purposes, and to inspire the creative re-appropriation of technologies

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