Music through Fourier space: discrete Fourier transform in music theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2016]
|
| Schriftenreihe: | Computational music science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XV, 206 Seiten Illustrationen, Diagramme, Notenbeispiele (teilweise farbig) |
| ISBN: | 9783319455808 9783319833231 |
Internformat
MARC
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|---|---|---|---|
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| 020 | |a 9783319833231 |c pbk |9 978-3-319-83323-1 | ||
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| 100 | 1 | |a Amiot, Emmanuel |d 1961- |e Verfasser |0 (DE-588)1119480930 |4 aut | |
| 245 | 1 | 0 | |a Music through Fourier space |b discrete Fourier transform in music theory |c Emmanuel Amiot |
| 264 | 1 | |a Cham |b Springer |c [2016] | |
| 264 | 4 | |c ©2016 | |
| 300 | |a XV, 206 Seiten |b Illustrationen, Diagramme, Notenbeispiele (teilweise farbig) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Computational music science | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Music | |
| 650 | 4 | |a Computer science / Mathematics | |
| 650 | 4 | |a User interfaces (Computer systems) | |
| 650 | 4 | |a Application software | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Computer Science | |
| 650 | 4 | |a Computer Appl. in Arts and Humanities | |
| 650 | 4 | |a Mathematics in Music | |
| 650 | 4 | |a Mathematics of Computing | |
| 650 | 4 | |a User Interfaces and Human Computer Interaction | |
| 650 | 4 | |a Signal, Image and Speech Processing | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Musik | |
| 650 | 0 | 7 | |a Musiktheorie |0 (DE-588)4040876-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskrete Fourier-Transformation |0 (DE-588)4150175-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804176738034384896 |
|---|---|
| adam_text | Contents
1 Discrete Fourier Transform of Distributions.......................... 1
1.1 Mathematical definitions and preliminary results................ 1
1.1.1 From pc-sets to an algebra of distributions ................ 1
1.1.2 Introducing the Fourier transform........................... 4
1.1.3 Basic notions............................................. 5
1.2 DFT of subsets................................................... 9
1.2.1 What stems from the general definition...................... 9
1.2.2 Application to intervallic structure...................... 14
1.2.3 Circulant matrixes ........................................ 18
1.2.4 Polynomials ............................................... 22
2 Homometry and the Phase Retrieval Problem............................ 27
2.1 Spectral units.................................................. 29
2.1.1 Moving between two homometric distributions................ 30
2.1.2 Chosen spectral units.................................... 31
2.1.3 Rational spectral units with finite order.................. 32
2.1.4 Orbits for homometric sets................................. 40
2.2 Extensions and generalisations.................................. 41
2.2.1 Hexachordal theorems....................................... 41
2.2.2 Phase retrieval even for some singular cases............... 44
2.2.3 Higher order homometry..................................... 45
3 Nil Fourier Coefficients and Tilings................................. 51
3.1 The Fourier nil set of a subset of Zrt.......................... 52
3.1.1 The original caveat........................................ 52
3.1.2 Singular circulating matrixes ............................. 55
3.1.3 Structure of the zero set of the DFT of a pc-set........... 58
3.2 Tilings of Z* by translation...................................... 61
3.2.1 Rhythmic canons in general............................... 61
3.2.2 Characterisation of tiling sets............................ 63
3.2.3 The Coven-Meyerowitz conditions............................ 65
XIV Contents
3.2.4 Inner periodicities....................................... 67
3.2.5 Transformations......................................... 69
3.2.6 Some conjectures and routes to solve them................. 77
3.3 Algorithms....................................................... 80
3.3.1 Computing a DFT........................................... 80
3.3.2 Phase retrieval........................................... 82
3.3.3 Linear programming ....................................... 82
3.3.4 Searching for Vuza canons................................. 83
4 Saliency............................................................... 91
4.1 Generated scales .............................................. 92
4.1.1 Saturation in one interval................................ 93
4.1.2 DFT of a generated scale.................................. 94
4.1.3 Alternative generators.................................... 96
4.2 Maximal evenness................................................ 99
4.2.1 Some regularity features................................. 100
4.2.2 Three types of ME sets................................... 101
4.2.3 DFT definition of ME sets.............................. 104
4.3 Pc-sets with large Fourier coefficients......................... 108
4.3.1 Maximal values......................................... 108
4.3.2 Musical meaning ........................................ 113
4.3.3 Flat distributions....................................... 123
5 Continuous Spaces, Continuous FT...................................... 135
5.1 Getting continuous.............................................. 135
5.2 A DFT for ordered collections of pcs on the continuous circle.. 140
5.3 ‘Diatonicity’ of temperaments in archeo-musicology............. 142
5.4 Fourier vs. voice leading distances............................ 145
5.5 Playing in Fourier space........................................ 149
5.5.1 Fourier scratching....................................... 149
5.5.2 Creation in Fourier space................................ 151
5.5.3 Psycho-acoustic experimentation.......................... 153
6 Phases of Fourier Coefficients........................................ 157
6.1 Moving one Fourier coefficient.................................. 157
6.2 Focusing on phases.............................................. 159
6.2.1 Defining the torus of phases............................. 160
6.2.2 Phases between tonal or atonal music..................... 166
6.3 Central symmetry in the torus of phases......................... 170
6.3.1 Linear embedding of the T/I group........................ 170
6.3.2 Topological implications................................. 173
6.3.3 Explanation of the quasi-alignment of major and minor triads 177
7 Conclusion
179
Contents
XV
8 Annexes and Tables..................................................... 183
8.1 Solutions to some exercises .................................... 183
8.2 Lewin’s ‘special cases’......................................... 188
8.3 Some pc-sets profiles ........................................... 189
8.4 Phases of major/minor triads..................................... 196
8.5 Very symmetrically decomposable hexachords....................... 197
8.6 Major Scales Similarity ......................................... 197
References................................................................. 199
Index
205
|
| any_adam_object | 1 |
| author | Amiot, Emmanuel 1961- |
| author_GND | (DE-588)1119480930 |
| author_facet | Amiot, Emmanuel 1961- |
| author_role | aut |
| author_sort | Amiot, Emmanuel 1961- |
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| dewey-ones | 004 - Computer science |
| dewey-raw | 004 |
| dewey-search | 004 |
| dewey-sort | 14 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Musikwissenschaft |
| format | Book |
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| id | DE-604.BV043859071 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:36:57Z |
| institution | BVB |
| isbn | 9783319455808 9783319833231 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029269235 |
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| owner_facet | DE-12 DE-11 DE-20 |
| physical | XV, 206 Seiten Illustrationen, Diagramme, Notenbeispiele (teilweise farbig) |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer |
| record_format | marc |
| series2 | Computational music science |
| spelling | Amiot, Emmanuel 1961- Verfasser (DE-588)1119480930 aut Music through Fourier space discrete Fourier transform in music theory Emmanuel Amiot Cham Springer [2016] ©2016 XV, 206 Seiten Illustrationen, Diagramme, Notenbeispiele (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Computational music science Hier auch später erschienene, unveränderte Nachdrucke Computer science Music Computer science / Mathematics User interfaces (Computer systems) Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing User Interfaces and Human Computer Interaction Signal, Image and Speech Processing Informatik Mathematik Musik Musiktheorie (DE-588)4040876-0 gnd rswk-swf Diskrete Fourier-Transformation (DE-588)4150175-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Musiktheorie (DE-588)4040876-0 s Informatik (DE-588)4026894-9 s Diskrete Fourier-Transformation (DE-588)4150175-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-45581-5 Digitalisierung BSB Muenchen - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029269235&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Amiot, Emmanuel 1961- Music through Fourier space discrete Fourier transform in music theory Computer science Music Computer science / Mathematics User interfaces (Computer systems) Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing User Interfaces and Human Computer Interaction Signal, Image and Speech Processing Informatik Mathematik Musik Musiktheorie (DE-588)4040876-0 gnd Diskrete Fourier-Transformation (DE-588)4150175-5 gnd Informatik (DE-588)4026894-9 gnd |
| subject_GND | (DE-588)4040876-0 (DE-588)4150175-5 (DE-588)4026894-9 |
| title | Music through Fourier space discrete Fourier transform in music theory |
| title_auth | Music through Fourier space discrete Fourier transform in music theory |
| title_exact_search | Music through Fourier space discrete Fourier transform in music theory |
| title_full | Music through Fourier space discrete Fourier transform in music theory Emmanuel Amiot |
| title_fullStr | Music through Fourier space discrete Fourier transform in music theory Emmanuel Amiot |
| title_full_unstemmed | Music through Fourier space discrete Fourier transform in music theory Emmanuel Amiot |
| title_short | Music through Fourier space |
| title_sort | music through fourier space discrete fourier transform in music theory |
| title_sub | discrete Fourier transform in music theory |
| topic | Computer science Music Computer science / Mathematics User interfaces (Computer systems) Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing User Interfaces and Human Computer Interaction Signal, Image and Speech Processing Informatik Mathematik Musik Musiktheorie (DE-588)4040876-0 gnd Diskrete Fourier-Transformation (DE-588)4150175-5 gnd Informatik (DE-588)4026894-9 gnd |
| topic_facet | Computer science Music Computer science / Mathematics User interfaces (Computer systems) Application software Mathematics Computer Science Computer Appl. in Arts and Humanities Mathematics in Music Mathematics of Computing User Interfaces and Human Computer Interaction Signal, Image and Speech Processing Informatik Mathematik Musik Musiktheorie Diskrete Fourier-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029269235&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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