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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 Bartók 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.
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 Bartók 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.
| Empfohlen (von): | 22 |
|---|---|
| Erscheinungsjahr: | 2016 |
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 320 |
| Inhalt: | Gebunden |
| ISBN-13: | 9781421419183 |
| ISBN-10: | 1421419181 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC gerader Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Roberts, Gareth E |
| Hersteller: | Johns Hopkins University Press |
| Maße: | 260 x 183 x 22 mm |
| Von/Mit: | Gareth E Roberts |
| Erscheinungsdatum: | 01.02.2016 |
| Gewicht: | 0,801 kg |
| Empfohlen (von): | 22 |
|---|---|
| Erscheinungsjahr: | 2016 |
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 320 |
| Inhalt: | Gebunden |
| ISBN-13: | 9781421419183 |
| ISBN-10: | 1421419181 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC gerader Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Roberts, Gareth E |
| Hersteller: | Johns Hopkins University Press |
| Maße: | 260 x 183 x 22 mm |
| Von/Mit: | Gareth E Roberts |
| Erscheinungsdatum: | 01.02.2016 |
| Gewicht: | 0,801 kg |
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