Composition with pitch-classes: a theory of compositional design
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New Haven u.a.
Yale Univ. Press
1987
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000489844&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XX, 359 S. |
| ISBN: | 0300036841 |
Internformat
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| 245 | 1 | 0 | |a Composition with pitch-classes |b a theory of compositional design |
| 264 | 1 | |a New Haven u.a. |b Yale Univ. Press |c 1987 | |
| 300 | |a XX, 359 S. | ||
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| 650 | 4 | |a Atonalité | |
| 650 | 4 | |a Composition (Musique) | |
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| 650 | 4 | |a Atonality | |
| 650 | 4 | |a Composition (Music) | |
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Datensatz im Suchindex
| _version_ | 1819281466653147136 |
|---|---|
| adam_text | Contents
Preface xi
Acknowledgments xv
Abbreviations and Functions xvii
Mathematical Symbols xx
Chapter One: l
Pitch and Post-Tonal Composition 1
A Theory of Compositional Design 2
Introduction to Compositional Designs 3
Chapter Two: 23
Pitch-Spaces 23
C-Spaces 26
Unordered Sets of C-Pitches 27
Contours 27
Comparison Functions and Matrices 28
Contour-Classes 28
Operations on Contours 29
C-Space Segment-Classes 32
P-Spaces 33
Pitches 36
P-Space Intervals 37
Psets, Psegs, and Pcycs 37
The Interval Content of a Pset 38
The Interval Succession of a Pseg 40
Interval Succession in Pcycs 40
Operations in P-Space 41
Composite Operations 42
vii
viü ¦ Contents
Inversion in P-Space 44
Contour-Classes and Psegs 45
Order Operations on Psegs and Pcycs 47
Intersection between Psets 47
Pseg and Pcyc Intersection 51
Set-Classes in P-Space 52
Segment-Classes in P-Space 56
Set-Theoretic Aspects of P-Space 57
Chapter Three: 59
Pitch-Classes and Pc-Spaces 59
Intervals in Pc-Space 62
Pcsets, Pcsegs, and Pccycs 64
TTOs 65
The Interval-Class Content of a Pcset 67
The Intervals between Two Pcsets 69
Set-Theoretic Aspects of Pcsets 70
Intersection between Pcsets 70
Pcset Invariance 73
Pcset Complementation 74
Invariance Vectors 77
Set-Classes in Pc-Space 78
Tn/I Set-Classes 81
Abstract Pcset Relations 85
Chains of SCs 90
K- and Kh-Complexes 98
Pcset Similarity 103
Ordered Sets in Pc-Space 107
Order Operations in Pc-Space 108
TTO Relations among Segments and Pccycs 109
Segment Classes 114
Similarity among Segments 116
Chapter Four: 123
TTOs 123
The TTO Group 124
TTO Commutivity 125
TTO Periodicity 126
TTO Inverses 127
The Cyclic Representation of TTOs 128
i
Contents ¦ ix
General Property Preservation with TTOs 135
Sets and Strings of Operations 137
Operator Invariance Matrices 139
Aspects of Specific TTOs: Tn 141
The TnI Operators 142
The TnM and TnMI TTOs 148
The Subgroups of /U/ 150
Simple Compositional Designs with TTO Groups 154
Aggregate Completion via TTO Groups 159
Cosets and Automorphisms of Subgroups of AJ/ 162
Non-TTO Pc Operations 170
Permutation Operators 178
Order Operations and Permutation 182
Chapter Five: 184
Two-Dimensional Arrays of Pitch-Classes 184
Array Classes 186
The Content of Arrays 190
Binary Relations and Posets 198
Binary Relations and Arrays 202
Poset Matrices 210
Transformations within Arrays 216
Repetitions in Arrays 216
Array Insertions and Extractions 218
Swapping in Arrays 220
Expanding Array Positions 223
Merging Arrays 225
Chapter Six: 233
Eight Compositional Designs 233
Aspects of Compositional Designs 233
Structural Hierarchies 235
Design I 237
Design II 241
Design III 246
Design IV 251
Design V 257
Design VI 265
Design VII 270
Design VIII 274
x ¦ Contents
Chapter Seven: 281
Sequential Ordering and C-Pitches 281
Sequencing Pitches and Pcs 285
Interpreting Arrays of Pcs 289
Issues in Array Interpretation 291
Time and Pitch-Space Isomorphisms 299
Toward a Unity of Musical Time and Space 306
Ordering Pitch and Time in Pitch and Time 307
Arrays of Time-Points 309
Appendix One: Set-Class Table 313
Appendix Two: The Cycles of the TTOs 320
Appendix Three: Automorphism Classes of Subgroups of IVI 322
Notes 324
Glossary 339
References 349
Index 355
|
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| id | DE-604.BV000782263 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:26:37Z |
| institution | BVB |
| isbn | 0300036841 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000489844 |
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| owner_facet | DE-12 DE-83 |
| physical | XX, 359 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Yale Univ. Press |
| record_format | marc |
| spellingShingle | Morris, Robert 1943- Composition with pitch-classes a theory of compositional design Atonalité Composition (Musique) Ensembles, Théorie des (Musique) Atonality Composition (Music) Atonale Musik (DE-588)4143343-9 gnd |
| subject_GND | (DE-588)4143343-9 |
| title | Composition with pitch-classes a theory of compositional design |
| title_auth | Composition with pitch-classes a theory of compositional design |
| title_exact_search | Composition with pitch-classes a theory of compositional design |
| title_full | Composition with pitch-classes a theory of compositional design |
| title_fullStr | Composition with pitch-classes a theory of compositional design |
| title_full_unstemmed | Composition with pitch-classes a theory of compositional design |
| title_short | Composition with pitch-classes |
| title_sort | composition with pitch classes a theory of compositional design |
| title_sub | a theory of compositional design |
| topic | Atonalité Composition (Musique) Ensembles, Théorie des (Musique) Atonality Composition (Music) Atonale Musik (DE-588)4143343-9 gnd |
| topic_facet | Atonalité Composition (Musique) Ensembles, Théorie des (Musique) Atonality Composition (Music) Atonale Musik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000489844&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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