Music: a mathematical offering
Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBW01 Volltext |
| Zusammenfassung: | Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiii, 411 pages) |
| ISBN: | 9780511811722 |
| DOI: | 10.1017/CBO9780511811722 |
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| 505 | 8 | 0 | |g Preface |g Acknowledgements |g Introduction |g 1 |t Waves and harmonics |g 1.1 |t What is sound? |g 1.2 |t The human ear |g 1.3 |t Limitations of the ear |g 1.4 |t Why sine waves? |g 1.5 |t Harmonic motion |g 1.6 |t Vibrating strings |g 1.7 |t Sine waves and frequency spectrum |g 1.8 |t Trigonometric identities and beats |g 1.9 |t Superposition |g 1.10 |t Damped harmonic motion |g 1.11 |t Resonance |g 2 |t Fourier theory |g 2.1 |t Introduction |g 2.2 |t Fourier coefficients |g 2.3 |t Even and odd unctions |g 2.4 |t Conditions for convergence |g 2.5 |t The Gibbs phenomenon |g 2.6 |t Complex coefficients |g 2.7 |t Proof of Fejér's theorem |g 2.8 |t Bessel functions |g 2.9 |t Properties of Bessel functions |g 2.10 |t Bessel's equation and power series |g 1.11 |t Fourier series for FM feedback and planetary motion |g 2.12 |t Pulse streams |g 2.13 |t The Fourier transform |g 2.14 |t Proof of the inversion formula |g 2.15 |t Spectrum |g 2.16 |t The Poisson summation formula |g 2.17 |t The Dirac delta function |g 2.18 |t Convolution |g 2.19 |t Cepstrum |g 2.20 |t The Hilbert transform and instantaneous frequency |g 3 |t A mathematician's guide to the orchestra |g 3.1 |t Introduction |g 3.2 |t The wave equation for strings |g 3.3 |t Initial conditions |g 3.4 |t The bowed string |g 3.5 |t Wind instruments |g 3.6 |t The drum |g 3.7 |t Eigenvalues of the Laplace operator |g 3.8 |t The horn |g 3.9 |t Xylophones and tubular bells |g 3.10 |t The mbira |g 3.11 |t The gong |g 3.12 |t The bell |g 3.13 |t Acoustics |g 9 |t Symmetry in music |g 9.1 |t Symmetries |g 9.2 |t The harp of the Nzakara |
| 505 | 8 | 0 | |g 9.3 |t Sets and groups |g 9.4 |t Change ringing |g 9.5 |t Cayley's theorem |g 9.6 |t Clock arithmetic and octave equivalence |g 9.7 |t Generators |g 9.8 |t Tone rows |g 9.9 |t Cartesian products |g 9.10 |t Dihedral groups |g 9.11 |t Orbits and cosets |g 9.12 |t Normal subgroups and quotients |g 9.13 |t Burnside's lemma |g 9.14 |t Pitch class sets |g 9.15 |t Pólya's enumeration theorem |g 9.16 |t The Mathieu group M₁₂ |t Appendix A : Bessel functions |t Appendix B : Equal tempered scales |t Appendix C : Frequency and MIDI chart |t Appendix D : Intervals |t Appendix E : Just, equal and meantone scales compared |t Appendix F : Music theory |t Appendix G : Recordings |g References |g Bibliography |g Index |g 7 |t Digital music |g 7.1 |t Digital signals |g 7.2 |t Dithering |g 7.3 |t WAV and MP3 files |g 7.4 |t MIDI |g 7.5 |t Delta functions and sampling |g 7.6 |t Nyquist's theorem |g 7.7 |t The z-transform |g 7.8 |t Digital filters |g 7.9 |t The discrete Fourier transform |g 7.10 |t The fast Fourier transform |g 8 |t Synthesis |g 8.1 |t Introduction |g 8.2 |t Envelopes and LFOs |g 8.3 |t Additive synthesis |g 8.4 |t Physical modelling |g 8.5 |t The Karplus-Strong algorithm |g 8.6 |t Filter analysis for the Karplus-Strong algorithm |g 8.7 |t Amplitude and frequency modulation |g 8.8 |t The Yamaha DX7 and FM synthesis |g 8.9 |t Feedback, or self-modulation |g 8.10 |t CSound |
| 520 | |a Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Musik | |
| 650 | 4 | |a Music / Acoustics and physics | |
| 650 | 4 | |a Music theory / Mathematics | |
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Datensatz im Suchindex
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| author | Benson, D. J. 1955- |
| author_facet | Benson, D. J. 1955- |
| author_role | aut |
| author_sort | Benson, D. J. 1955- |
| author_variant | d j b dj djb |
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| bvnumber | BV043943786 |
| classification_rvk | LR 57780 SK 990 |
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| contents | Waves and harmonics What is sound? The human ear Limitations of the ear Why sine waves? Harmonic motion Vibrating strings Sine waves and frequency spectrum Trigonometric identities and beats Superposition Damped harmonic motion Resonance Fourier theory Introduction Fourier coefficients Even and odd unctions Conditions for convergence The Gibbs phenomenon Complex coefficients Proof of Fejér's theorem Bessel functions Properties of Bessel functions Bessel's equation and power series Fourier series for FM feedback and planetary motion Pulse streams The Fourier transform Proof of the inversion formula Spectrum The Poisson summation formula The Dirac delta function Convolution Cepstrum The Hilbert transform and instantaneous frequency A mathematician's guide to the orchestra The wave equation for strings Initial conditions The bowed string Wind instruments The drum Eigenvalues of the Laplace operator The horn Xylophones and tubular bells The mbira The gong The bell Acoustics Symmetry in music Symmetries The harp of the Nzakara Sets and groups Change ringing Cayley's theorem Clock arithmetic and octave equivalence Generators Tone rows Cartesian products Dihedral groups Orbits and cosets Normal subgroups and quotients Burnside's lemma Pitch class sets Pólya's enumeration theorem The Mathieu group M₁₂ Appendix A : Bessel functions Appendix B : Equal tempered scales Appendix C : Frequency and MIDI chart Appendix D : Intervals Appendix E : Just, equal and meantone scales compared Appendix F : Music theory Appendix G : Recordings Digital music Digital signals Dithering WAV and MP3 files MIDI Delta functions and sampling Nyquist's theorem The z-transform Digital filters The discrete Fourier transform The fast Fourier transform Synthesis Envelopes and LFOs Additive synthesis Physical modelling The Karplus-Strong algorithm Filter analysis for the Karplus-Strong algorithm Amplitude and frequency modulation The Yamaha DX7 and FM synthesis Feedback, or self-modulation CSound |
| ctrlnum | (ZDB-20-CBO)CR9780511811722 (OCoLC)992933282 (DE-599)BVBBV043943786 |
| dewey-full | 781.2 |
| dewey-hundreds | 700 - The arts |
| dewey-ones | 781 - General principles and musical forms |
| dewey-raw | 781.2 |
| dewey-search | 781.2 |
| dewey-sort | 3781.2 |
| dewey-tens | 780 - Music |
| discipline | Mathematik Musikwissenschaft |
| doi_str_mv | 10.1017/CBO9780511811722 |
| format | Electronic eBook |
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code="t">Bessel functions</subfield><subfield code="g">2.9</subfield><subfield code="t">Properties of Bessel functions</subfield><subfield code="g">2.10</subfield><subfield code="t">Bessel's equation and power series</subfield><subfield code="g">1.11</subfield><subfield code="t">Fourier series for FM feedback and planetary motion</subfield><subfield code="g">2.12</subfield><subfield code="t">Pulse streams</subfield><subfield code="g">2.13</subfield><subfield code="t">The Fourier transform</subfield><subfield code="g">2.14</subfield><subfield code="t">Proof of the inversion formula</subfield><subfield code="g">2.15</subfield><subfield code="t">Spectrum</subfield><subfield code="g">2.16</subfield><subfield code="t">The Poisson summation formula</subfield><subfield code="g">2.17</subfield><subfield code="t">The Dirac delta function</subfield><subfield code="g">2.18</subfield><subfield code="t">Convolution</subfield><subfield code="g">2.19</subfield><subfield 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code="g">9.8</subfield><subfield code="t">Tone rows</subfield><subfield code="g">9.9</subfield><subfield code="t">Cartesian products</subfield><subfield code="g">9.10</subfield><subfield code="t">Dihedral groups</subfield><subfield code="g">9.11</subfield><subfield code="t">Orbits and cosets</subfield><subfield code="g">9.12</subfield><subfield code="t">Normal subgroups and quotients</subfield><subfield code="g">9.13</subfield><subfield code="t">Burnside's lemma</subfield><subfield code="g">9.14</subfield><subfield code="t">Pitch class sets</subfield><subfield code="g">9.15</subfield><subfield code="t">Pólya's enumeration theorem</subfield><subfield code="g">9.16</subfield><subfield code="t">The Mathieu group M₁₂</subfield><subfield code="t">Appendix A : Bessel functions</subfield><subfield code="t">Appendix B : Equal tempered scales</subfield><subfield code="t">Appendix C : Frequency and MIDI chart</subfield><subfield code="t">Appendix D : Intervals</subfield><subfield code="t">Appendix E : Just, equal and meantone scales compared</subfield><subfield code="t">Appendix F : Music theory</subfield><subfield code="t">Appendix G : Recordings</subfield><subfield code="g">References</subfield><subfield code="g">Bibliography</subfield><subfield code="g">Index</subfield><subfield code="g">7</subfield><subfield code="t">Digital music</subfield><subfield code="g">7.1</subfield><subfield code="t">Digital signals</subfield><subfield code="g">7.2</subfield><subfield code="t">Dithering</subfield><subfield code="g">7.3</subfield><subfield code="t">WAV and MP3 files</subfield><subfield code="g">7.4</subfield><subfield code="t">MIDI</subfield><subfield code="g">7.5</subfield><subfield code="t">Delta functions and sampling</subfield><subfield code="g">7.6</subfield><subfield code="t">Nyquist's theorem</subfield><subfield code="g">7.7</subfield><subfield code="t">The z-transform</subfield><subfield code="g">7.8</subfield><subfield code="t">Digital filters</subfield><subfield code="g">7.9</subfield><subfield code="t">The discrete Fourier transform</subfield><subfield code="g">7.10</subfield><subfield code="t">The fast Fourier transform</subfield><subfield code="g">8</subfield><subfield code="t">Synthesis</subfield><subfield code="g">8.1</subfield><subfield code="t">Introduction</subfield><subfield code="g">8.2</subfield><subfield code="t">Envelopes and LFOs</subfield><subfield code="g">8.3</subfield><subfield code="t">Additive synthesis</subfield><subfield code="g">8.4</subfield><subfield code="t">Physical modelling</subfield><subfield code="g">8.5</subfield><subfield code="t">The Karplus-Strong algorithm</subfield><subfield code="g">8.6</subfield><subfield code="t">Filter analysis for the Karplus-Strong algorithm</subfield><subfield code="g">8.7</subfield><subfield code="t">Amplitude and frequency modulation</subfield><subfield code="g">8.8</subfield><subfield code="t">The Yamaha DX7 and FM synthesis</subfield><subfield code="g">8.9</subfield><subfield code="t">Feedback, or self-modulation</subfield><subfield code="g">8.10</subfield><subfield code="t">CSound</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. 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| id | DE-604.BV043943786 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:20Z |
| institution | BVB |
| isbn | 9780511811722 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029352757 |
| oclc_num | 992933282 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-20 |
| owner_facet | DE-12 DE-92 DE-20 |
| physical | 1 online resource (xiii, 411 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBW_PDA_CBO_Kauf_2023 |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Benson, D. J. 1955- Verfasser aut Music a mathematical offering Dave Benson Cambridge Cambridge University Press 2007 1 online resource (xiii, 411 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Preface Acknowledgements Introduction 1 Waves and harmonics 1.1 What is sound? 1.2 The human ear 1.3 Limitations of the ear 1.4 Why sine waves? 1.5 Harmonic motion 1.6 Vibrating strings 1.7 Sine waves and frequency spectrum 1.8 Trigonometric identities and beats 1.9 Superposition 1.10 Damped harmonic motion 1.11 Resonance 2 Fourier theory 2.1 Introduction 2.2 Fourier coefficients 2.3 Even and odd unctions 2.4 Conditions for convergence 2.5 The Gibbs phenomenon 2.6 Complex coefficients 2.7 Proof of Fejér's theorem 2.8 Bessel functions 2.9 Properties of Bessel functions 2.10 Bessel's equation and power series 1.11 Fourier series for FM feedback and planetary motion 2.12 Pulse streams 2.13 The Fourier transform 2.14 Proof of the inversion formula 2.15 Spectrum 2.16 The Poisson summation formula 2.17 The Dirac delta function 2.18 Convolution 2.19 Cepstrum 2.20 The Hilbert transform and instantaneous frequency 3 A mathematician's guide to the orchestra 3.1 Introduction 3.2 The wave equation for strings 3.3 Initial conditions 3.4 The bowed string 3.5 Wind instruments 3.6 The drum 3.7 Eigenvalues of the Laplace operator 3.8 The horn 3.9 Xylophones and tubular bells 3.10 The mbira 3.11 The gong 3.12 The bell 3.13 Acoustics 9 Symmetry in music 9.1 Symmetries 9.2 The harp of the Nzakara 9.3 Sets and groups 9.4 Change ringing 9.5 Cayley's theorem 9.6 Clock arithmetic and octave equivalence 9.7 Generators 9.8 Tone rows 9.9 Cartesian products 9.10 Dihedral groups 9.11 Orbits and cosets 9.12 Normal subgroups and quotients 9.13 Burnside's lemma 9.14 Pitch class sets 9.15 Pólya's enumeration theorem 9.16 The Mathieu group M₁₂ Appendix A : Bessel functions Appendix B : Equal tempered scales Appendix C : Frequency and MIDI chart Appendix D : Intervals Appendix E : Just, equal and meantone scales compared Appendix F : Music theory Appendix G : Recordings References Bibliography Index 7 Digital music 7.1 Digital signals 7.2 Dithering 7.3 WAV and MP3 files 7.4 MIDI 7.5 Delta functions and sampling 7.6 Nyquist's theorem 7.7 The z-transform 7.8 Digital filters 7.9 The discrete Fourier transform 7.10 The fast Fourier transform 8 Synthesis 8.1 Introduction 8.2 Envelopes and LFOs 8.3 Additive synthesis 8.4 Physical modelling 8.5 The Karplus-Strong algorithm 8.6 Filter analysis for the Karplus-Strong algorithm 8.7 Amplitude and frequency modulation 8.8 The Yamaha DX7 and FM synthesis 8.9 Feedback, or self-modulation 8.10 CSound Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between Mathematik Musik Music / Acoustics and physics Music theory / Mathematics Musik (DE-588)4040802-4 gnd rswk-swf Musiktheorie (DE-588)4040876-0 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Akustik (DE-588)4000988-9 gnd rswk-swf Musik (DE-588)4040802-4 s Akustik (DE-588)4000988-9 s Physik (DE-588)4045956-1 s 1\p DE-604 Musiktheorie (DE-588)4040876-0 s Mathematik (DE-588)4037944-9 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-61999-8 Erscheint auch als Druckausgabe 978-0-521-85387-3 https://doi.org/10.1017/CBO9780511811722 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Benson, D. J. 1955- Music a mathematical offering Waves and harmonics What is sound? The human ear Limitations of the ear Why sine waves? Harmonic motion Vibrating strings Sine waves and frequency spectrum Trigonometric identities and beats Superposition Damped harmonic motion Resonance Fourier theory Introduction Fourier coefficients Even and odd unctions Conditions for convergence The Gibbs phenomenon Complex coefficients Proof of Fejér's theorem Bessel functions Properties of Bessel functions Bessel's equation and power series Fourier series for FM feedback and planetary motion Pulse streams The Fourier transform Proof of the inversion formula Spectrum The Poisson summation formula The Dirac delta function Convolution Cepstrum The Hilbert transform and instantaneous frequency A mathematician's guide to the orchestra The wave equation for strings Initial conditions The bowed string Wind instruments The drum Eigenvalues of the Laplace operator The horn Xylophones and tubular bells The mbira The gong The bell Acoustics Symmetry in music Symmetries The harp of the Nzakara Sets and groups Change ringing Cayley's theorem Clock arithmetic and octave equivalence Generators Tone rows Cartesian products Dihedral groups Orbits and cosets Normal subgroups and quotients Burnside's lemma Pitch class sets Pólya's enumeration theorem The Mathieu group M₁₂ Appendix A : Bessel functions Appendix B : Equal tempered scales Appendix C : Frequency and MIDI chart Appendix D : Intervals Appendix E : Just, equal and meantone scales compared Appendix F : Music theory Appendix G : Recordings Digital music Digital signals Dithering WAV and MP3 files MIDI Delta functions and sampling Nyquist's theorem The z-transform Digital filters The discrete Fourier transform The fast Fourier transform Synthesis Envelopes and LFOs Additive synthesis Physical modelling The Karplus-Strong algorithm Filter analysis for the Karplus-Strong algorithm Amplitude and frequency modulation The Yamaha DX7 and FM synthesis Feedback, or self-modulation CSound Mathematik Musik Music / Acoustics and physics Music theory / Mathematics Musik (DE-588)4040802-4 gnd Musiktheorie (DE-588)4040876-0 gnd Physik (DE-588)4045956-1 gnd Mathematik (DE-588)4037944-9 gnd Akustik (DE-588)4000988-9 gnd |
| subject_GND | (DE-588)4040802-4 (DE-588)4040876-0 (DE-588)4045956-1 (DE-588)4037944-9 (DE-588)4000988-9 |
| title | Music a mathematical offering |
| title_alt | Waves and harmonics What is sound? The human ear Limitations of the ear Why sine waves? Harmonic motion Vibrating strings Sine waves and frequency spectrum Trigonometric identities and beats Superposition Damped harmonic motion Resonance Fourier theory Introduction Fourier coefficients Even and odd unctions Conditions for convergence The Gibbs phenomenon Complex coefficients Proof of Fejér's theorem Bessel functions Properties of Bessel functions Bessel's equation and power series Fourier series for FM feedback and planetary motion Pulse streams The Fourier transform Proof of the inversion formula Spectrum The Poisson summation formula The Dirac delta function Convolution Cepstrum The Hilbert transform and instantaneous frequency A mathematician's guide to the orchestra The wave equation for strings Initial conditions The bowed string Wind instruments The drum Eigenvalues of the Laplace operator The horn Xylophones and tubular bells The mbira The gong The bell Acoustics Symmetry in music Symmetries The harp of the Nzakara Sets and groups Change ringing Cayley's theorem Clock arithmetic and octave equivalence Generators Tone rows Cartesian products Dihedral groups Orbits and cosets Normal subgroups and quotients Burnside's lemma Pitch class sets Pólya's enumeration theorem The Mathieu group M₁₂ Appendix A : Bessel functions Appendix B : Equal tempered scales Appendix C : Frequency and MIDI chart Appendix D : Intervals Appendix E : Just, equal and meantone scales compared Appendix F : Music theory Appendix G : Recordings Digital music Digital signals Dithering WAV and MP3 files MIDI Delta functions and sampling Nyquist's theorem The z-transform Digital filters The discrete Fourier transform The fast Fourier transform Synthesis Envelopes and LFOs Additive synthesis Physical modelling The Karplus-Strong algorithm Filter analysis for the Karplus-Strong algorithm Amplitude and frequency modulation The Yamaha DX7 and FM synthesis Feedback, or self-modulation CSound |
| title_auth | Music a mathematical offering |
| title_exact_search | Music a mathematical offering |
| title_full | Music a mathematical offering Dave Benson |
| title_fullStr | Music a mathematical offering Dave Benson |
| title_full_unstemmed | Music a mathematical offering Dave Benson |
| title_short | Music |
| title_sort | music a mathematical offering |
| title_sub | a mathematical offering |
| topic | Mathematik Musik Music / Acoustics and physics Music theory / Mathematics Musik (DE-588)4040802-4 gnd Musiktheorie (DE-588)4040876-0 gnd Physik (DE-588)4045956-1 gnd Mathematik (DE-588)4037944-9 gnd Akustik (DE-588)4000988-9 gnd |
| topic_facet | Mathematik Musik Music / Acoustics and physics Music theory / Mathematics Musiktheorie Physik Akustik |
| url | https://doi.org/10.1017/CBO9780511811722 |
| work_keys_str_mv | AT bensondj musicamathematicaloffering |