From Music to Mathematics: Exploring the Connections by Gareth E. Roberts (Engli

Description: From Music to Mathematics by Gareth E. Roberts From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description Taking a "music first" approach, Gareth E. Robertss From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational.Topics discussed in the book include Rhythm Introductory music theory The science of sound Tuning and temperament Symmetry in music The Bartok controversy Change ringing Twelve-tone music Mathematical modern music The Hemachandra-Fibonacci numbers and the golden ratio Magic squares Phase shifting Featuring numerous musical excerpts, including several from jazz and popular music, each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition, with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop students analytical skills and reinforce the material in the text. From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity. Author Biography Gareth E. Roberts is an associate professor of mathematics at the College of the Holy Cross. Table of Contents PrefaceAcknowledgmentsIntroduction1. Rhythm1.1. Musical Notation and a Geometric Property1.1.1. Duration1.1.2. Dots1.2. Time Signatures1.2.1. Musical examples1.2.2. Rhythmic repetition1.3. Polyrhythmic Music1.3.1. The least common multiple1.3.2. Musical examples1.4. A Connection with Sanskrit PoetryReferences for Chapter 12. Introduction to Music Theory2.1. Musical Notation2.1.1. The common clefs2.1.2. The piano keyboard2.2. Scales2.2.1. Chromatic scale2.2.2. Whole-tone scale2.2.3. Major scales2.2.4. Minor scales2.2.5. Why are there 12 major scales?2.3. Intervals and Chords2.3.1. Major and perfect intervals2.3.2. Minor intervals and the tritone2.3.3. Chords2.4. Tonality, Key Signatures, and the Circle of Fifths2.4.1. The critical tonic-dominant relationship2.4.2. Key signatures2.4.3. The circle of fifths2.4.4. Transposition2.4.5. The evolution of polyphonyReferences for Chapter 23. The Science of Sound3.1. How We Hear3.1.1. The magnificent ear-brain system3.2. Attributes of Sound3.2.1. Loudness and decibels3.2.2. Frequency3.3. Sine Waves3.3.1. The sine function3.3.2. Graphing sinusoids3.3.3. The harmonic oscillator3.4. Understanding Pitch3.4.1. Residue pitch3.4.2. A vibrating string3.4.3. The overtone series3.4.4. The starting transient3.4.5. Resonance and beats3.5. The Monochord LabReferences for Chapter 34. Tuning and Temperament4.1. The Pythagorean Scale4.1.1. Consonance and integer ratios4.1.2. The spiral of fifths4.1.3. The overtone series revisited4.2. Just Intonation4.2.1. Problems with just intonation4.2.2. Major versus minor4.3. Equal Temperament4.3.1. A conundrum and a compromise4.3.2. Rational and irrational numbers4.3.3. Cents4.4. Comparing the Three Systems4.5. Strähles Guitar4.5.1. An ingenious construction4.5.2. Continued fractions4.5.3. On the accuracy of Strähles method4.6. Alternative Tuning Systems4.6.1. The significance of log2(3/2)4.6.2. Meantone scales4.6.3. Other equally tempered scalesReferences for Chapter 45. Musical Group Theory5.1. Symmetry in Music5.1.1. Symmetric transformations5.1.2. Inversions5.1.3. Other examples5.2. The Bartók Controversy5.2.1. The Fibonacci numbers and nature5.2.2. The golden ratio5.2.3. Music for Strings, Percussion and Celesta5.3. Group Theory5.3.1. Some examples of groups5.3.2. Multiplication tables5.3.3. Symmetries of the square5.3.4. The musical subgroup of D4References for Chapter 56. Change Ringing6.1. Basic Theory, Practice, and Examples6.1.1. Nomenclature6.1.2. Rules of an extent6.1.3. Three bells6.1.4. The number of permissible moves6.1.5. Example6.1.6. Example6.2. Group Theory Revisited6.2.1. The symmetric group Sn6.2.2. The dihedral group revisited6.2.3. Ringing the cosets6.2.4. ExampleReferences for Chapter 67. Twelve-Tone Music7.1. Schoenbergs Twelve-Tone Method of Composition7.1.1. Notation and terminology7.1.2. The tone row matrix7.2. Schoenbergs Suite fÜr Klavier, Op. 257.3. Tone Row Invariance7.3.1. Using numbers instead of pitches7.3.2. Further analysis7.3.3. Tritone symmetry7.3.4. The number of distinct tone rows7.3.5. Twelve-tone music and group theoryReferences for Chapter 78. Mathematical Modern Music8.1. Sir Peter Maxwell Davies8.1.1. Magic squares8.1.2. Some examples8.1.3. The magic constant8.1.4. A Mirror of Whitening Light8.2. Steve Reich8.2.1. Clapping Music8.2.2. Phase shifts8.3. Xenakis8.3.1. A Greek architect8.3.2. Metastasis and the Philips Pavilion8.3.3. Pithoprakta8.4. Final Project8.4. References for Chapter 8CreditsIndex Review Overall, From Music to Mathematics is a pleasing and well-written book that is accessible for everyone who wants to explore the connections between music and mathematics. Gareth Roberts does a great job of making numerous suggestions on how music can be used to illuminate mathematical concepts... From Music to Mathematics is very enjoyable to read - not only for students, but for anyone who loves music and mathematics. Musicae Scientiae Overall, I strongly recommend this as an excellent basis for teaching. MathSciNet Promotional A guided tour of the mathematical principles inherent in music. Long Description Taking a "music first" approach, Gareth E. Robertss From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include: ? Rhythm ? Introductory music theory ? The science of sound ? Tuning and temperament ? Symmetry in music ? The Bart Review Text ""The fact that most of the aspects of music discussed seem to be relatively peripheral to the immediate experience of music emphasises that nobody has yet provided a convincing justification for the universal belief that ""mathematics and music go together"". Recommended to anyone with an interest in the precise details of both the music and the mathematics."" Review Quote "The fact that most of the aspects of music discussed seem to be relatively peripheral to the immediate experience of music emphasises that nobody has yet provided a convincing justification for the universal belief that "mathematics and music go together". Recommended to anyone with an interest in the precise details of both the music and the mathematics." Promotional "Headline" A guided tour of the mathematical principles inherent in music. Details ISBN1421419181 Author Gareth E. Roberts Short Title FROM MUSIC TO MATHEMATICS Pages 320 Publisher Johns Hopkins University Press Language English ISBN-10 1421419181 ISBN-13 9781421419183 Media Book Format Hardcover Year 2016 Imprint Johns Hopkins University Press Subtitle Exploring the Connections Place of Publication Baltimore, MD Country of Publication United States DEWEY 780.0519 Birth 1970 Illustrations 216 Line drawings, black and white; 13 Illustrations, black and white; 1 Illustrations, black and white Affiliation College of the Holy Cross Position Associate Professor NZ Release Date 2016-04-11 US Release Date 2016-04-11 Publication Date 2016-04-11 UK Release Date 2016-04-11 Alternative 9781421419190 Audience Tertiary & Higher Education AU Release Date 2016-02-14 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:161819270;

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