Download or read book The Mathematical Theory of Tone Systems written by Jan Haluska and published by CRC Press. This book was released on 2003-12-19 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 systems are featured. Topics include Fuzziness and Sonance, Wavelets and Nonspecificity, Pitch Granulation and Ambiguity, Equal Temperaments, Mean Tone Systems. Well Tempered Systems, Ptolemy Systems, and more. Appendices include extended lists of tone systems and a catalogue of historical organs with subsemitones.
Download or read book A Mathematical Theory of Musical Combination Tones written by Julius John Vande Kopple and published by . This book was released on 1977 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics of Music written by John O'Sullivan and published by . This book was released on 2010 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics of Music, Music Theory, 12 Tone Equal Temperament and its Origins Explained and Two New Alternative Tuning Systems.
Download or read book The Mathematical Theory of Music written by Maria M. Coulson and published by . This book was released on 1995 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis and Tone Systems written by and published by . This book was released on 2001 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Mathematical Theory of Sound written by Samuel Earnshaw and published by . This book was released on 1860 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Theory of Music written by Franck Jedrzejewski and published by . This book was released on 2006 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Compendium Of Musical Mathematics written by Franck Jedrzejewski and published by World Scientific. This book was released on 2024-02-28 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide a concise introduction to the mathematical theory of music, opening each chapter to the most recent research. Despite the complexity of some sections, the book can be read by a large audience. Many examples illustrate the concepts introduced. The book is divided into 9 chapters.In the first chapter, we tackle the question of the classification of chords and scales. Chapter 2 is a mathematical presentation of David Lewin's Generalized Interval Systems. Chapter 3 offers a new theory of diatonicity in equal-tempered universes. Chapter 4 presents the Neo-Riemannian theories based on the work of David Lewin, Richard Cohn and Henry Klumpenhouwer. Chapter 5 is devoted to the application of word combinatorics to music. Chapter 6 studies the rhythmic canons and the tessellation of the line. Chapter 7 is devoted to serial knots. Chapter 8 presents combinatorial designs and their applications to music. The last chapter, chapter 9, is dedicated to the study of tuning systems.
Download or read book Mathematical Systems Theory written by Diederich Hinrichsen and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. (Amazon.com).
Download or read book Musical Scales and their Mathematics written by Karlheinz Schüffler and published by Springer. This book was released on 2024-08-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are musical scales just trivial? This book explores this question, revealing the complexity of creating "harmony" in tonal systems. Why 12 tones? Are there alternatives? Are 12 fifths equal 7 octaves? What is "consonance"? When are intervals "perfect" or "imperfect"? What is meant by "tonal characteristics", "whole tone" and "semitone"? "Ancient tuning" vs potentially new? Answers need thoughtful explanations, revealing interconnectedness. In this context, mathematics is pivotal, explaining scale generation, temperament systems, etc. Divided into three parts, this book covers: Modern interval arithmetic driven by prime numbers. Architectural principles of scales, with examples. Systematic nature of historical tunings and temperaments. Understanding only requires school knowledge, developed into algebraic tools applied musically.
Download or read book On the Origin of the Tone System and the Theory of Harmony written by Per-Olov Löwdin and published by . This book was released on 1991 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fuzzy Logic and Mathematics written by Radim Belohlavek and published by Oxford University Press. This book was released on 2017-05-03 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.
Download or read book Mathematics and Art written by Claude Bruter and published by Springer Science & Business Media. This book was released on 2002-08-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.
Download or read book Mathematical Models of Musical Scales written by Mark Lindley and published by . This book was released on 1993 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tonal Gears written by William Ostrand and published by . This book was released on 2023-11-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on building towards a broader understanding of music and its relationship to math. It seeks to explain the fundamental reason why music theory is the way it is. This book offers an explanation rooted in prime numbers and group theory, showing that the key signatures we use in music theory, as well as the chords within them, can be created with an algorithm that assumes nothing about the way things sound. Music theory and its structure stems from the structure of prime numbers. This leads to the conclusion that other musical systems are able to be used in the creation of music. For example, a system with 20 notes can be used rather than the the usual system of 12 notes. These different systems are called tonal gears. The structure of these systems is nearly identical to the overall structure of regular music theory. Perhaps the most important part of this idea is that the notes, keys, and chords created using this idea actually sound good to the extent that ones ear is able to hear a kind of tonal harmony within these systems that is similar in some ways and different in others as to offer a unique experience while making it possible to utilize known techniques to play the music with direction. Though it may seem complex, I believe this theory provides a more complete explanation for why music is the way it is today and opens up the possibility for a new kind of music to be played. The second half of the book takes a bit of a turn into developing a method for constructing certain groups that are able to generate prime numbers, among other things, developing a broader understanding of the structure of prime numbers and a relationship to graph theory.
Download or read book The Math Behind the Music with CD ROM written by Leon Harkleroad and published by Cambridge University Press. This book was released on 2006-08-07 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the math related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on - overtones, scales, and tuning systems - the musical dice game attributed to Mozart and Haydn - the several-hundred-year-old style of bell-playing known as ringing the changes - the twelve-tone school of composition that strongly influenced music throughout the 20th century and many other topics involving mathematical ideas from probability theory to Fourier series to group theory. He also relates some cautionary tales of misguided attempts to mix music and mathematics. Both the mathematical and the musical concepts are described in an elementary way, making the book accessible to general readers as well as to mathematicians and musicians of all levels. The book is accompanied by an audio CD of musical examples.
Download or read book Computational Counterpoint Worlds written by Octavio Alberto Agustín-Aquino and published by Springer. This book was released on 2015-07-08 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of counterpoint was originally aimed at simulating the composition rules described in Johann Joseph Fux’s Gradus ad Parnassum. It soon became apparent that the algebraic apparatus used in this model could also serve to define entirely new systems of rules for composition, generated by new choices of consonances and dissonances, which in turn lead to new restrictions governing the succession of intervals. 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 contrapuntal models. The book is suitable for graduates and researchers. A good command of algebra is a prerequisite for understanding the construction of the model.
