1,721,010 research outputs found
Klein Concert: A Report from a Math-Musical Classroom Experience
No full textCan music help mathematical education? Can some shapes, that challenge visual imagination, be translated into music? I present a pedagogical application of my interdisciplinary research. This concerns a cycle of seminars about mathematics and music I gave in Italy at the Music Conservatory of Palermo and that, in a shortened version, I also gave at Ca’ Foscari University in Venice, at the Conservatory of Livorno, and in the UK, at the University of Greenwich. Seminars included a theoretical section and a workshop. Mathematical concepts helped students formalize their musical knowledge, and music provided an intuitive understanding of mathematical concepts, such as the dualism continuous/discrete, the concept of envelope, and the abstraction of categories. Then, the students were given the Klein bottle, and they translated it into music. The resulting musical compositions were different but they shared general structures highlighting the bottle’s features: e.g., counterpoint represented multiple simultaneous paths on the bottle, and quadraphony recreated a feeling of an additional dimension through spatialization and time variations. Musical cyclicity and inversions rendered the non-orientability of the Klein surface. The final output was a string orchestra concert
Libellule, Fiori, Origami: momenti matematici al Joint Mathematics Meetings 2020
No full text“Welcome in the Mile High City”, benvenuti nella città a un miglio di altitudine, è la scritta che accoglie i visitatori a Denver, nello stato del Colorado, nella profonda America delle Montagne Rocciose. Denver è nota agli amanti di sport ed esplorazioni, nonché agli appassionati di paleontologia, per i numerosi fossili di dinosauri. Ed è nota agli studiosi per il gigantesco Convention Center, scelto come sede per il Joint Mathematics Meetings dello scorso gennaio 2020 (JMM 2020)
Have Fun with Math and Music!
No full textIf abstraction makes mathematics strong, it often makes it also hard to learn, if not discouraging. If math pedagogy suffers from the lack of engaging strategies, the pedagogy of mathematical music theory must deal with the additional difficulty of double fields and double vocabulary. However, games and interdisciplinary references in a STEAM framework can help the learner break down complex concepts into essential ideas, and gain interest and motivation to approach advanced topics. Here we present some general considerations, followed by two examples which may be applied in a high-school or early college level course. The first is a musical application of a Rubik’s cube, the CubeHarmonic, to approach group theory and combinatorics jointly with musical chords; the second is an application of category theory to investigate simple musical variations together with transformations on a visual shape
Knots, Music and DNA
Full text linkMusical gestures connect the symbolic layer of the score to the physical layer of sound. I focus here on the mathematical theory of musical gestures, and I propose its generalization to include braids and knots. In this way, it is possible to extend the formalism to cover more case studies, especially regarding conducting gestures. Moreover, recent developments involving comparisons and similarities between gestures of orchestral musicians can be contextualized in the frame of braided monoidal categories. Because knots and braids can be applied to both music and biology (they apply to knotted proteins, for example), I end the article with a new musical rendition of DNA
Reversing arrows: Duality
Full text linkWhat do you get reversing all arrows? The drawing ‘Duality’ is an homage to mirrors, classical art themes, and abstract mathematics
Seeds, Brains, and Bridges: Allegory of Venice, Arts, and Science for a Vision of the Future
No full textWhat could the Venice of the future look like? A project for an ideal city can take off from an allegory: arts and sciences inside a seed of Lodoicea maldivica, whose bipartition reminds us of a human brain. From the seeds left by the past, we derive the vision of the future. The ideal city certainly needs brains able to conceptualize images and develop ideas, and bridges to strengthen connections and in- teractions. A well-working brain needs “bridges” as connections between ideas and techniques. My vision for a future city contains a livable and stimulating space enhancing at one time creativity, enthusiasm, and scientific development. To this aim, I use the image and the metaphor of cerebral hemispheres, specialized in activities of different typologies yet interconnected.
The image of the brain is one of the symbols of cognition. The right hemisphere deals with artistic expression, while the left hemisphere refers to logic thinking, mathematics, scientific attitude toward the world.
Different cerebral areas, which contribute to the complex and rich life of an individual, are a metaphor for different places in a city, contributing to the completeness of a community life.
Separation between hemispheres, also as a homage to Venice, is seen as a sort of Canal Grande, and connections are represented by bridges. The whole brain is seen as a giant seed of Lodoicea maldivica: the city of the future needs to develop from seeds, that is, knowledge inherited from the past and new ideas from our minds and thoughts. Thoughts that, in turn, are fed upon the Science of Complexity
Theoretical Physics and Category Theory as Tools for Analysis of Musical Performance and Composition
No full text(There is no abstract
Simmetrie fra Matematica e Musica
No full textCos’è la simmetria in musica? Come investigare suoni e strutture musicali alla luce della simmetria? E quale può essere, in questa ricerca, il ruolo della matematica?
Il premio Nobel per la Fisica F. Wilczek definisce la simmetria come un “cambiamento senza cambiamento”, un’invarianza rispetto a una trasforma- zione. La ricerca di simmetria e di bellezza può essere intesa come la ricerca di equilibrio fra regolarità e variazione. Se la regolarità aiuta la memoria, è invece la varietà a stimolare l’attenzione e la curiosità. Argomenti fisico-ma- tematici come la teoria dei gruppi, l’acustica e la teoria dei segnali fornisco- no strumenti di indagine anche all’estetica musicale.
Il tema della simmetria fra matematica e musica è il filo conduttore dei testi di fisici, matematici, teorici della musica e compositori presenti in questa antologia, scelti e tradotti da Federico Favali e Maria Mannone.
Il volume comprende scritti di D. Kempf, G. Rochberg, J. W. Bernard, D. Wilson, R. Donnini, D. Tymoczko, V. Hart, O. Fernández Herrero, G. W. Don - K. K. Muir - G. B. Volk - J. S. Walker.
Prefazione di David Fontanesi; postafzione di Giovanni Albini
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
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