Possible principles of mathematical music analysis
نویسندگان
چکیده
منابع مشابه
Principles of Mathematical Analysis
3. (a) If F is as in Theorem 10.7, put A = F′(0), F1(x) = A −1F(x). Then F1(0) = I. Show that F1(x) = Gn◦Gn−1◦. . .◦G1(x) in some neighbourhood of 0, for certain primitive mappings G1, . . . ,Gn. This gives another version of Theorem 10.7: F(x) = F(0)Gn◦Gn−1◦. . .◦G1(x). (b) Prove that the mapping (x, y) 7→ (y, x) of R onto R is not the composition of any two primitive mappings, in any neighbou...
متن کاملMathematical Morphology: Basic Principles
This paper is intended as a rst introduction into mathematical morphology, and does not require any preliminary knowledge in this eld. The paper discusses the basic morphological operators, such as dilations, erosions, openings, closings, rank operators, skeletons, and reconstruction operators. Furthermore, it introduces the complete lattice framework for morphology. The paper concludes with an...
متن کاملMathematical Principles of Data Inversion
Inverse elastic-wave scattering problems are shown to be ill-posed in general. Standard simplifying assumptions--the first Born approximation, the physical optics approximation, and the stopping power approximation of tomography--are shown to reduce to the same ill-posed mathematical problem, that of inverting a Fourier transform. Practical implications of this fact are illustrated with examples.
متن کاملMotivic Topologies: Mathematical and Computational Modelling in Music Analysis
This paper discusses a mathematical model together with its computational realization, for the motivic analysis of a piece of music. Relations between the mathematical model (motivic topologies), computational counter-part (OM-Melos), and music analysis are presented in the light of general concepts of computational music analysis, stressing the importance of neutrality and scientific rigour in...
متن کاملThe Mathematical in Music Thinking
“The Mathematical in music thinking” is based on Heidegger’s understanding of “the Mathematical” as the basic assumption of the knowledge of the things. Heidegger’s ideas are combined with Peirce’s classification of sciences, in particular, to distinguish between the Mathematical from the less abstract logical thinking and the more abstract mathematical thinking. The aim of this paper is to mak...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: New Sound
سال: 2018
ISSN: 0354-818X,1821-3782
DOI: 10.5937/newso1851153l