Mathematics and music: composition, perception, and performance
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla.
Chapman & Hall/CRC
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes Internet access |
| Beschreibung: | 318 S. Ill., graph. Darst., Notenbeisp. |
| ISBN: | 9781439867099 1439867097 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematics and music |b composition, perception, and performance |c James S. Walker ; Gary W. Don |
| 264 | 1 | |a Boca Raton, Fla. |b Chapman & Hall/CRC |c 2013 | |
| 300 | |a 318 S. |b Ill., graph. Darst., Notenbeisp. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes Internet access | ||
| 650 | 4 | |a Music / Mathematics | |
| 650 | 4 | |a Musical notation | |
| 650 | 4 | |a Mathematik | |
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| 689 | 0 | 2 | |a Musiktheorie |0 (DE-588)4040876-0 |D s |
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Datensatz im Suchindex
| _version_ | 1804150392830820352 |
|---|---|
| adam_text | Contents
Preface
About the authors
1
Pitch, Frequency, and Musical Scales
1
1.1
Pitch and Frequency
.................................. 1
1.1.1
Instrumental Tones
............................... 2
1.1.2
Pure Tones Combining to Create an Instrumental Tone
............ 4
1.2
Overtones, Pitch Equivalence, and Musical Scales
................... 6
1.2.1
Pitch Equivalence
................................ 7
1.2.2
Musical Scales
................................. 8
1.3
The ^-Tone Equal-Tempered Scale
.......................... 12
1.4
Musical Scales within the Chromatic Scale
....................... 15
1.4.1
The
С
-Major
Scale
............................... 15
1.4.2
Other Major Scales
............................... 17
1.4.3
Scales and Clock Arithmetic
.......................... 18
1.4.4
Relation between Just and Equal-Tempered Tunings
............. 20
1.5
Logarithms
....................................... 23
1.5.1
Half Steps and Logarithms
........................... 23
1.5.2
Cents
...................................... 27
2
Basic Musical Notation
33
2.1
Staff Notation, Clefs, and Note Positions
........................ 33
2.1.1
Treble Clef Staff
................................ 33
2.1.2
Bass Clef Staff
................................. 34
2.1.3
Grand Staff
................................... 35
2.2
Time Signatures and Tempo
.............................. 37
2.2.1
Time Signatures
................................ 39
2.2.2
Tempo
..................................... 42
2.2.3
Rhythmic Emphasis
.............................. 42
2.3
Key Signatures and the Circle of Fifths
......................... 45
2.3.1
Circle of Fifths
................................. 46
2.3.2
Circle of Fifths for Natural Minor Scales
................... 48
3
Some Music Theory
51
3.1
Intervals and Chords
.................................. 51
3.1.1
Melodic and Harmonic Intervals
........................ 51
3.1.2
Chords
..................................... 53
3.2
Diatonic Music
..................................... 58
3.2.1
Levels of Importance of Notes and Chords
.................. 58
3.2.2
Major Keys
................................... 58
3.2.3
Chord Progressions
............................... 60
3.2.4
Relation of Melody to Chords
......................... 61
3.2.5
Minor Keys
................................... 62
3.2.6
Chromaticism
.................................. 64
3.3
Diatonic Transformations
—
Scale Shifts
....................... 68
3.4
Diatonic
Transformations
—
Inversions,Retrograde
.................. 76
3.4.1
Diatonic Scale Inversions
............................ 76
3.4.2
Retrograde
................................... 78
3.5
Chromatic Transformations
............................... 81
3.5.1
Transpositions
................................. 81
3.5.2
Chromatic Inversions and Retrograde
..................... 85
3.5.3
Chromatic Transformations and Chords
.................... 87
3.6
Web Resources
..................................... 90
4
Spectrograms and Musical Tones
93
4.1
Musical Gestures in Spectrograms
........................... 93
4.2
Mathematical Model for Musical Tones
........................ 97
4.2.1
Basic Trigonometry
............................... 98
4.2.2
Modeling Pure Tones
.............................. 99
4.3
Modeling Instrumental Tones
.............................. 103
4.3.1
Beating
..................................... 104
4.4
Beating and Dissonance
................................. 107
4.4.1
Some Uses of Dissonance in Music
...................... 108
4.5
Estimating Amplitude and Frequency
.........................
Ill
4.5.1
How the Estimating Is Done
.......................... 112
4.6
Windowing the Waveform: Spectrograms
....................... 118
4.7
A Deeper Study of Amplitude Estimation
....................... 122
4.7.1
More on Rectangular Windowing
....................... 126
4.7.2
More on
Blackman
Windowing
........................ 128
5
Spectrograms and Music
131
5.1
Singing
......................................... 131
5.1.1
An Operatic Performance by
Renée
Fleming
................. 131
5.1.2
An Operatic Performance by Luciano
Pavarotti................ 135
5.1.3
A Blues Performance by Alicia Keys
..................... 135
5.1.4
A Choral Performance by Sweet Honex in the Rock
.............. 136
5.1.5
Summary
.................................... 137
5.2 Instrumentals...................................... 140
5.2.1
Jazz Trumpet: Louis Armstrong
........................ 141
5.2.2
Beethoven,Goodman,and Hendrix
...................... 143
5.2.3
Harmonics in Stringed Instruments
...................... 145
5.3
Compositions
...................................... 153
5.3.1
Roy Hargrove s Strasbourg/St. Denis
..................... 153
5.3.2
The Beatles Tomorrow Never Knows
..................... 154
5.3.3
A Portion of Morton Feldman s The Rothko Chapel
.............. 155
5.3.4
A Portion of a Ravi Shankar Composition
................... 156
5.3.5
Musical Illusions: Little Boy and The Devil s Staircase
............ 157
5.3.6
The Finale of Stravinsky s Firebird Suite
................... 161
5.3.7
Duke Ellington s Jack the Bear
........................ 162
5.3.8
Concluding Remarks
.............................. 165
6
Analyzing Pitch and Rhythm
167
6.1
Geometry of Pitch Organization and Transpositions
.................. 167
6.1.1
Pitch Classes, Intervals, Chords, and Scales
.................. 167
6.1.2
Transpositions
................................. 169
6.1.3
Clock Arithmetic Formally Defined
...................... 170
6.2
Geometry of Chromatic Inversions
........................... 173
6.3
Cyclic Rhythms
..................................... 177
6.3.1
Cyclic Rhythm in Down in the Valley
..................... 177
6.3.2
Cyclic Rhythm in Drumming
.......................... 178
6.3.3
Time Transpositions of Cyclic Rhythms
.................... 178
6.3.4
Afro-Latin Clave Rhythms
........................... 179
6.3.5
Phasing
..................................... 182
6.4
Rhythmic Inversion
................................... 188
6.4.1
Inversionof Cyclic Rhythms
.......................... 188
6.4.2
Rhythmic and Pitch Transformation Groups
.................. 189
6.5
Construction of Scales and Cyclic Rhythms
...................... 192
6.5.1
The Euclidean Algorithm
............................ 192
6.5.2
Constructing Musical Scales
.......................... 193
6.5.3
Constructing Cyclic Rhythms
......................... 195
6.6
Comparing Musical Scales and Cyclic Rhythms
.................... 198
6.6.1
Interval Frequencies and Musical Scales
.................... 198
6.6.2
Measuring Dissonance for a Scale
....................... 201
6.6.3
Interval Frequencies for Cyclic Rhythms
................... 202
6.7
Serialism
........................................ 206
6.7.1
Pitch Serialism
................................. 206
6.7.2
Musical Matrices
................................ 208
6.7.3
Total Serialism
................................. 212
7
A Geometry of Harmony
217
7.1
Riemann s Chromatic Inversions
............................ 217
7.2
A Network of Triadic Chords
.............................. 223
7.2.1
Musical Examples
............................... 225
7.3
Embedding Pitch Classes within the Tonne
t
z.
...................... 228
7.3.1
Geometry of Acoustic Consonance and Dissonance
.............. 229
7.3.2
Analyzing Scales
................................ 230
7.4
Other Chordal Transformations
............................. 233
7.4.1
Using the Tonnetz. to Define More Transformations
.............. 233
7.4.2
Modeling Chord Progressions in Diatonic Music
............... 235
7.4.3
Explaining the Qualitative Difference in Modes
................ 237
8
Audio Synthesis in Music
241
8.1
Creating New Music from Spectrograms
........................ 241
8.2
Phase Vocoding
..................................... 245
8.2.1
A Basic Example
................................ 245
8.2.2
Imogen Heap s Hide and Seek
......................... 247
8.3
Time Stretching and Time Shrinking
.......................... 249
8.4
MIDI Synthesis
..................................... 253
A Exercise Solutions
257
В
Music Software
295
B.I Audacity
....................................... 295
B.I
.1
Configuring Audacity
............................ 295
B.I.
2
Loading and Displaying a Music File
..................... 295
B.1.3 Music Files from CDs
............................. 296
B.2 MuseScore
...................................... 296
B.2.1 Different
Soundfonts
for MuseScore
.................... 296
С
Amplitude
and Frequency Results
299
C.I Proof of Theorem
4.7.1.................................299
C.2 Proof of Exact Amplitude and Frequency Estimates
..................300
D
Glossary
303
E
Permissions
305
Bibliography
307
Index
309
|
| any_adam_object | 1 |
| author | Walker, James S. 1950- Don, Gary W. |
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| discipline | Kunst Mathematik Musikwissenschaft |
| format | Book |
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| id | DE-604.BV041032489 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:38:12Z |
| institution | BVB |
| isbn | 9781439867099 1439867097 |
| language | English |
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| physical | 318 S. Ill., graph. Darst., Notenbeisp. |
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| spelling | Walker, James S. 1950- Verfasser (DE-588)1038633192 aut Mathematics and music composition, perception, and performance James S. Walker ; Gary W. Don Boca Raton, Fla. Chapman & Hall/CRC 2013 318 S. Ill., graph. Darst., Notenbeisp. txt rdacontent n rdamedia nc rdacarrier Includes Internet access Music / Mathematics Musical notation Mathematik Musik Musiktheorie (DE-588)4040876-0 gnd rswk-swf Komposition Musik (DE-588)4133320-2 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Komposition Musik (DE-588)4133320-2 s Mathematik (DE-588)4037944-9 s Musiktheorie (DE-588)4040876-0 s DE-604 Don, Gary W. Verfasser (DE-588)1038633257 aut Digitalisierung BSB Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026010007&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walker, James S. 1950- Don, Gary W. Mathematics and music composition, perception, and performance Music / Mathematics Musical notation Mathematik Musik Musiktheorie (DE-588)4040876-0 gnd Komposition Musik (DE-588)4133320-2 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4040876-0 (DE-588)4133320-2 (DE-588)4037944-9 |
| title | Mathematics and music composition, perception, and performance |
| title_auth | Mathematics and music composition, perception, and performance |
| title_exact_search | Mathematics and music composition, perception, and performance |
| title_full | Mathematics and music composition, perception, and performance James S. Walker ; Gary W. Don |
| title_fullStr | Mathematics and music composition, perception, and performance James S. Walker ; Gary W. Don |
| title_full_unstemmed | Mathematics and music composition, perception, and performance James S. Walker ; Gary W. Don |
| title_short | Mathematics and music |
| title_sort | mathematics and music composition perception and performance |
| title_sub | composition, perception, and performance |
| topic | Music / Mathematics Musical notation Mathematik Musik Musiktheorie (DE-588)4040876-0 gnd Komposition Musik (DE-588)4133320-2 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Music / Mathematics Musical notation Mathematik Musik Musiktheorie Komposition Musik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026010007&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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