3 edition of **The Mathematical Theory of Tone Systems (Pure and Applied Mathematics)** found in the catalog.

- 31 Want to read
- 32 Currently reading

Published
**December 19, 2003** by CRC .

Written in English

- Science/Mathematics,
- Mathematics,
- Advanced,
- Applied,
- Mathematics / General

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 380 |

ID Numbers | |

Open Library | OL8125653M |

ISBN 10 | 0824747143 |

ISBN 10 | 9780824747145 |

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The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics.

Hundreds of examples of past and prevalent tone 5/5(1). Book Description. The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory.

This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular.

The Mathematical Theory of Tone Systems patterns a unified theory defining the The Mathematical Theory of Tone Systems book system in functional terms based on the principles and forms of uncertainty theory.

This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory.

This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular by: ISBN: OCLC Number: Description: pages.

Contents: I Fundamentals 1 Tone systems and uncertainty theory 3 A piece of metaphysics 3 Practical manners of the tone system description 4 Current trends 6 America 7 Europe 9 Africa 13 Uncertainty-based information theory 16.

The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory.

This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular by: Tone systems and uncertainty theory --Fuzziness and sonance --Wavelets and nonspecificity --Pitch granulation and ambiguity --Equal temperaments --Mean tone systems --Well tempered systems and 10 granulations --Ptolemy system --Bibliography --Appendix A: Extended lists of tone systems --Appendix B: Catalogue of historical organs with.

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Reviewed by David Miller, Professor, West Virginia University on 4/18/ Comprehensiveness rating: 5 see less. This textbook is very comprehensive. Covers a basic review of sets and set operations, The Mathematical Theory of Tone Systems book and logical statements, all the proof techniques, set theory proofs, relation and functions, and additional material that is helpful for upper-level proof course preparation (like a chapter /5(6).

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All in all, the book is well written and accessible to any interested mathematicians and mathematical graduates.” Brand: Springer-Verlag New York. The modern Arab tone system, or system of musical tuning, is based upon the theoretical division of the octave into twenty-four equal divisions or tone equal temperament (TET), the distance between each successive note being a quarter tone (50 cents).Each tone has its own name not repeated in different octaves, unlike systems featuring octave equivalency.

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The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are.

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Shannon’s paper, published the same year as the invention of the transistor, instantaneously created the field of information theory, with broad applications in engineering and computer : Geoffrey Nunberg.

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While the book attempts to be self-contained, much of the content would not be accessible without a reasonably advanced background both in rigorous dynamical systems theory and mathematical thermodynamics.

A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a tone example, C is adjacent to C ♯; the interval between them is a semitone.

In a note approximately equally divided scale Abbreviation: m2; A1. This is the first book bringing together recent developments and perspectives on mathematical counterpoint theory in detail.

The authors include recent theoretical results on counterpoint worlds, the extension of counterpoint to microtonal pitch systems, the singular homology of counterpoint models, and the software implementation of. In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.

It is a result of studies of linear algebra and the solutions of systems of linear equations and their generalizations. The theory is connected to that of analytic.

Mathematical Foundations of Quantum Theory is a collection of papers presented at the conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues.

This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and.

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Langlands to unify number theory with the geometry of Lie groups, the systems of symmetries that are also central to mathematical physics. An Introduction to the Mathematical Theory of Knots. Colin Adams, well-known for his advanced research in topology and knot theory, is the author of this new book that brings his findings and his passion for the subject to a more general audience.

Product Information. The central topic of this book is the mathematical analysis of social systems, understood in the following rather classical way: social systems consist of social actors who interact according to specific rules of interactions; the dynamics of social systems is then the consequences of these interactions, viz., the self-organization of social systems.

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