Music: a mathematical offering
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 411 S. Ill., graph. Darst., Notenbeisp. |
| ISBN: | 0521853877 9780521853873 0521619998 9780521619998 |
Staff View
MARC
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| 245 | 1 | 0 | |a Music |b a mathematical offering |c Dave Benson |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XIII, 411 S. |b Ill., graph. Darst., Notenbeisp. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 650 | 7 | |a Natuurkunde |2 gtt | |
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| 650 | 7 | |a Wiskundige methoden |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Musik | |
| 650 | 4 | |a Physik | |
| 650 | 4 | |a Music |x Acoustics and physics | |
| 650 | 4 | |a Music theory |x Mathematics | |
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Record in the Search Index
| _version_ | 1804136264541143040 |
|---|---|
| adam_text | Contents
Preface
page
Acknowledgements
xiii
Introduction
1
Waves and harmonics
5
1.1
What is sound?
5
1.2
The human ear
7
1.3
Limitations of the ear
13
1.4
Why sine waves?
17
1.5
Harmonic motion
18
1.6
Vibrating strings
19
1.7
Sine waves and frequency spectrum
21
1.8
Trigonometric identities and beats
23
1.9
Superposition
26
1.10
Damped harmonic motion
28
1.11
Resonance
31
Fourier theory
36
2.1
Introduction
37
2.2
Fourier coefficients
38
2.3
Even and odd functions
44
2.4
Conditions for convergence
46
2.5
The Gibbs phenomenon
50
2.6
Complex coefficients
54
2.7
Proof of
55
2.8
Bessel functions
58
2.9
Properties of Bessel functions
61
2.10
Bessel s equation and power series
63
2.11
Fourier series for
68
2.12
Pulse streams
71
VII
viii Contents
2.13
73
2.14
77
2.15
80
2.16
81
2.17
82
2.18
86
2.19
88
2.20
89
A mathematician s guide to the orchestra
91
3.1
91
3.2
92
3.3
100
3.4
103
3.5
107
3.6
112
3.7
117
3.8
120
3.9
122
3.10
130
3.11
133
3.12
138
3.13
142
Consonance and dissonance
144
4.1
144
4.2
145
4.3
148
4.4
151
4.5
152
4.6
153
4.7
155
4.8
158
Scales and temperaments: the fivefold way
161
5.1
162
5.2
162
5.3
164
5.4
165
5.5
167
5.6
168
5.7
170
5.8
171
Contents ix
5.9 Eitz s
5.10
5.11
5.12
5.13
5.14
5.15
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11 FM
Contents
8.12
300
8.13
304
8.14
308
8.15
309
8.16
309
9
312
9.1
312
9.2
322
9.3
324
9.4
329
9.5
331
9.6
333
9.7
335
9.8
337
9.9
339
9.10
340
9.11
342
9.12
343
9.13
345
9.14
348
9.15
353
9.16
358
Appendix A Bessel functions
361
Appendix
365
Appendix
367
Appendix
368
Appendix
372
Appendix
374
Appendix
381
References
386
Bibliography
389
Index
393
|
| adam_txt |
Contents
Preface
page
Acknowledgements
xiii
Introduction
1
Waves and harmonics
5
1.1
What is sound?
5
1.2
The human ear
7
1.3
Limitations of the ear
13
1.4
Why sine waves?
17
1.5
Harmonic motion
18
1.6
Vibrating strings
19
1.7
Sine waves and frequency spectrum
21
1.8
Trigonometric identities and beats
23
1.9
Superposition
26
1.10
Damped harmonic motion
28
1.11
Resonance
31
Fourier theory
36
2.1
Introduction
37
2.2
Fourier coefficients
38
2.3
Even and odd functions
44
2.4
Conditions for convergence
46
2.5
The Gibbs phenomenon
50
2.6
Complex coefficients
54
2.7
Proof of
55
2.8
Bessel functions
58
2.9
Properties of Bessel functions
61
2.10
Bessel's equation and power series
63
2.11
Fourier series for
68
2.12
Pulse streams
71
VII
viii Contents
2.13
73
2.14
77
2.15
80
2.16
81
2.17
82
2.18
86
2.19
88
2.20
89
A mathematician's guide to the orchestra
91
3.1
91
3.2
92
3.3
100
3.4
103
3.5
107
3.6
112
3.7
117
3.8
120
3.9
122
3.10
130
3.11
133
3.12
138
3.13
142
Consonance and dissonance
144
4.1
144
4.2
145
4.3
148
4.4
151
4.5
152
4.6
153
4.7
155
4.8
158
Scales and temperaments: the fivefold way
161
5.1
162
5.2
162
5.3
164
5.4
165
5.5
167
5.6
168
5.7
170
5.8
171
Contents ix
5.9 Eitz's
5.10
5.11
5.12
5.13
5.14
5.15
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11 FM
Contents
8.12
300
8.13
304
8.14
308
8.15
309
8.16
309
9
312
9.1
312
9.2
322
9.3
324
9.4
329
9.5
331
9.6
333
9.7
335
9.8
337
9.9
339
9.10
340
9.11
342
9.12
343
9.13
345
9.14
348
9.15
353
9.16
358
Appendix A Bessel functions
361
Appendix
365
Appendix
367
Appendix
368
Appendix
372
Appendix
374
Appendix
381
References
386
Bibliography
389
Index
393 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Benson, David J. 1955- |
| author_GND | (DE-588)110324714 |
| author_facet | Benson, David J. 1955- |
| author_role | aut |
| author_sort | Benson, David J. 1955- |
| author_variant | d j b dj djb |
| building | Verbundindex |
| bvnumber | BV022263501 |
| callnumber-first | M - Music |
| callnumber-label | ML3805 |
| callnumber-raw | ML3805 |
| callnumber-search | ML3805 |
| callnumber-sort | ML 43805 |
| callnumber-subject | ML - Literature on Music |
| classification_rvk | LR 57780 SK 990 |
| ctrlnum | (OCoLC)69484257 (DE-599)BVBBV022263501 |
| 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 |
| discipline_str_mv | Mathematik Musikwissenschaft |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV022263501 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:43:34Z |
| indexdate | 2024-07-09T20:53:38Z |
| institution | BVB |
| isbn | 0521853877 9780521853873 0521619998 9780521619998 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015474103 |
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| owner_facet | DE-12 DE-525 DE-188 DE-739 DE-824 DE-29T DE-20 |
| physical | XIII, 411 S. Ill., graph. Darst., Notenbeisp. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Benson, David J. 1955- Verfasser (DE-588)110324714 aut Music a mathematical offering Dave Benson 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XIII, 411 S. Ill., graph. Darst., Notenbeisp. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Musique - Acoustique et physique Musique - Mathématiques Muziektheorie gtt Natuurkunde gtt Perception de la musique Wiskundige methoden gtt Mathematik Musik Physik Music Acoustics and physics Music theory Mathematics Musiktheorie (DE-588)4040876-0 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Musik (DE-588)4040802-4 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 DE-604 Musiktheorie (DE-588)4040876-0 s Mathematik (DE-588)4037944-9 s Digitalisierung BSBMuenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015474103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benson, David J. 1955- Music a mathematical offering Musique - Acoustique et physique Musique - Mathématiques Muziektheorie gtt Natuurkunde gtt Perception de la musique Wiskundige methoden gtt Mathematik Musik Physik Music Acoustics and physics Music theory Mathematics Musiktheorie (DE-588)4040876-0 gnd Physik (DE-588)4045956-1 gnd Musik (DE-588)4040802-4 gnd Mathematik (DE-588)4037944-9 gnd Akustik (DE-588)4000988-9 gnd |
| subject_GND | (DE-588)4040876-0 (DE-588)4045956-1 (DE-588)4040802-4 (DE-588)4037944-9 (DE-588)4000988-9 |
| title | Music a mathematical offering |
| title_auth | Music a mathematical offering |
| title_exact_search | Music a mathematical offering |
| title_exact_search_txtP | 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 | Musique - Acoustique et physique Musique - Mathématiques Muziektheorie gtt Natuurkunde gtt Perception de la musique Wiskundige methoden gtt Mathematik Musik Physik Music Acoustics and physics Music theory Mathematics Musiktheorie (DE-588)4040876-0 gnd Physik (DE-588)4045956-1 gnd Musik (DE-588)4040802-4 gnd Mathematik (DE-588)4037944-9 gnd Akustik (DE-588)4000988-9 gnd |
| topic_facet | Musique - Acoustique et physique Musique - Mathématiques Muziektheorie Natuurkunde Perception de la musique Wiskundige methoden Mathematik Musik Physik Music Acoustics and physics Music theory Mathematics Musiktheorie Akustik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015474103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bensondavidj musicamathematicaloffering |