Diagrams, gestures and formulae in music
read more
Citations
REVIEWS-Modern algebra and the rise of mathematical structures
The Topos of Music III: Gestures : Musical Multiverse Ontologies
The Topos of Music I: Theory: Geometric Logic, Classification, Harmony, Counterpoint, Motives, Rhythm
The Topos of Music II: Performance : Theory, Software, and Case Studies
References
Categories for the Working Mathematician
Gesture and Thought
Moduli of representations of finite dimensional algebras
Representations and Cohomology
Introduction to Topological Manifolds
Related Papers (5)
Frequently Asked Questions (13)
Q2. What are the morphisms of the R-gestoids?
The objects, called gestoids, are the R-linear categories G, i.e. the authors have bilinear composition, addition, and scalar multiplication of morphisms on the R-modules x@y of morphisms.
Q3. What is the simplest way to calculate the fundamental group of a digraph?
The fundamental gestoid Gg(G) of a digraph G is easily calculated: it is well known [31 Theorem10.7] that the fundamental group of a graph is free, the number of generators being given by the number of edges added to a spanning tree.
Q4. What is the topological construction of the fundamental gestoid /Gg(1)?
On the one hand, the topological construction of the fundamental gestoid /Gg(1) is the category IRZ, the group algebra over IR of the group of integers, and the latter comes in via the generator of the fundamental group of the circle S1.
Q5. What is the case of gesture theory?
The case of gesture theory suggests that the authors can naturally transfer Mac Lane’s conception of mathematics as ‘an elaborate tightly connected network of formalsystems, axiom systems, rules, and connections’ [10, p. 417] to music.
Q6. What is the morphism of the spatial digraphs?
if f : d0/g is a morphism of gestures, then the associated morphism of spatial digraphs are not uniquely determined, but the induced functors on the R-gestoids of the given gestures are well defined.
Q7. What is the meaning of gestural approach?
In this spirit, the gestural approach is an enrichment of musical object categories, which enables a refinement of the conceptual anatomy and at the same time a rapprochement to the human reality of making music.
Q8. What is the definition of a gesture’s curve coordinate?
A gesture’s curve coordinate is an abstract parametrization of the curvein a given space, not the material time coordinate, which may also be absent, as shown in the dance gesture from figure 6.
Q9. What is the meaning of category theory?
Category theory is more than a useful universal language, eventually providing the theoretical setting for the foundations of mathematics.
Q10. What is the importance of embodiment of sounds?
The important role of embodiment of sounds is rightly testified by the strong need for concerts, where performance is not only heard, but also experienced from the musicians’ bodies in movement.
Q11. What is the IR-linear dual of the local ring?
In algebraic geometry, the Zariski tangent space TX,x of an IR-rational point of an IR-scheme is the IR-linear dual (m/m2)* of the quotient m/m2 of the maximal ideal m of the local ring /OX,x.
Q12. How is the meaning of music enhanced?
Understanding music is strongly enhanced if not enabled by means of its presentation in moving bodies, or, to put it more concisely, in musical gestures.
Q13. What is the meaning of the term adjoint?
Far from being isomorphic, music and mathematics seem to involve some common structures that can be related by one of the most powerful concepts of category theory: the notion of adjoint functors.