Titlebook: Mathematics and Music; A Diderot Mathematic Gerard Assayag,Hans Georg Feichtinger,Jose Francis Book 2002 Springer-Verlag Berlin Heidelberg

Flavouring

Musical Analysis Using Mathematical Proceedings in the XXth Century, or philosophers such as Mersenne, Descartes, Rameau, D’Alembert, Euler were essentially concerned with the problem of finding out the numerical relationship hidden in music or in sound. Their basic assumption was the direct link between the use of ratio 3/2 or a limited number of simple intervals i

果仁

Universal Prediction Applied to Stylistic Music Generation,have appeared in the literature. These models do not provide an intentional description of some musical theory but rather use statistical techniques to capture regularities that are typical of certain music experience. A standard procedure in this approach is to assume a particular model for the dat

Commodious

Ethnomusicology, Ethnomathematics. The Logic Underlying Orally Transmitted Artistic Practices,n. This domain consists in the study of mathematical ideas shared by orally transmitted cultures. Such ideas are related to number, logic and spatial configurations [9,11]. My purpose is to show how ethnomusicology could turn musical materials in this direction. Music will be considered here as a me

宠爱

Expressing Coherence of Musical Perception in Formal Logic,s in the formal language to an underlying interpretation in terms of musical images and image transformations. Such an interpretation characterizes truth within a framework of spatio-temporal representations and perception-based musical information processing. The framework provides a way for defini

cornucopia

The Topos Geometry of Musical Logic,functorial algebraic geometry and Lawvere’s topos theory of logic. We give an account of these theoretical connections, discuss and illustrate their formalization and implementation on music software. Three issues are particularly interesting in this context: First, the crucial insight of Grothendie

弄皱

Computing Musical Sound,has also played a significant scientific role. Musical notation seems to have inspired the use of cartesian coordinates..But the intervention of numbers within the human senses should not be taken for granted. In the Antiquity, while the pythagorician conception viewed harmony as ruled by numbers, A

Accessible

gait-cycle

The Musical Communication Chain and its Modeling,ll not make justice to its amazing richness. However, this cannot prevent us from trying to explain and formalize some aspects. In this way we also contribute to its understanding and develop new tools to create and enjoy new musical artwork. This in turn can be seen as a form of further enrichment

LAP

Computational Models for Musical Sound Sources,even though their performance and quality is rarely satisfactory. For the specific needs of music production and multimedia art, sound models are needed which are versatile, responsive to user’s expectations, and having high audio quality. Moreover, for human-machine interaction model flexibility is

葡萄糖

Computing Musical Sound,culating numbers specifying sound waves. Beyond composing with sounds, synthesis permits to compose the sound itself, opening new resources for musicians. Digital sound has been popularized by compact discs, synthesizers, samplers, and also by the activity of institutions such as IRCAM. Mathematics