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An Investigation of Periodicity in Music

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An Investigation of Periodicity in Music AN INVESTIGATION OF PERIODICITY IN MUSIC, with reference to three twentieth-century compositions: BARTOK's Music for Strings, Percussion, & Celesta LUTOSLAWSKI's Concerto for Orchestra LIGETI's Chamber Concerto by Rosemary Mountain B. Mus., University of Western Ontario, 1980 M.Mus., University of Victoria, 1986 A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY in the School of Music Supervisor: Prof. M. Longton ABSTRACT An investigation into the nature and functions of periodicity is presented through analysis and discussion. Periodicity is established by the repetition of any musical event at regular intervals in time. The three works analyzed exhibit periodic elements in a variety of contexts and on different structural levels, thereby illustrating typical functions of periodicities in complex twentieth-century music. These functions include stratum delineation, textural definition, and metric-style organization. In some cases, the regularity of the periodicities is crucial to their function, while in others the periodicity of the elements simply provides a convenient model for study. Reference is made to perceptual tendencies and thresholds including Gestalt principles of grouping, the phenomena of auditory streaming and fusion, and the temporal limits of the perceptual present. As our response to periodicities is affected by the specific rate of recurrence, a classification is made according to the rate of recurrence. The links between rate and function are discussed. Boundaries are suggested for three main divisions: very fast rates (less than 0.10"), medium (between 0.10" and 10"), and long (greater than 10"). An additional tripartite division of the medium range is proposed, incorporating the levels of pulse, sub-pulse, and super-pulse. The term "super-pulse" is introduced to emphasize the potency of the pulse-grouping level. ii Relationships between levels of periodic events are described in terms of rhythmic consonance and dissonance. The analyses show that a contrast in the degree of rhythmic consonance is a typical means of indicating structural boundaries. They also suggest a link between the levels which produce a dissonance and the degree of harshness felt. Consonance on several levels adds significant coherence to a stratum, enhancing its recognition in complex textures or on later appearances. Keywords: PERIODICITY, RHYTHM, TEXTURE, POLYRHYTHM, AUDITORY STREAMING iii TABLE OF CONTENTS TITLE PAGE i ABSTRACT ii TABLE of CONTENTS iv LIST of EXAMPLES and FIGURES v ACKNOWLEDGEMENTS vii INTRODUCTION 1 PART ONE -- BACKGROUND I. A CLARIFICATION of TEMPORAL ISSUES 13 II. A SUMMARY of PERCEPTUAL INFLUENCES 28 III. PERIODICITIES in MUSIC 45 PART TWO -- ANALYSES IV. TEXTURES and TEXTURAL STRANDS 87 V. CANONS 116 VI. ENHANCER of THEMATIC STRUCTURE 133 VII. DELINEATION of STRATA 146 VIII. PULSE and SUB-PULSE 167 IX. DELINEATION of STRUCTURE 182 X. CONCLUSIONS 208 EXAMPLES 227 ENDNOTES 288 BIBLIOGRAPHY 312 APPENDICES A. Glossary of terms 324 B. Estimates of perceptual boundaries 333 C. Reasons for choice of works 335 D. Converting metronome mark to clock time 337 E. Examples of meter overrides 339 iv LIST OF EXAMPLES Ex. 4.1 Bartok II:199-239 228 Ex. 4.2a Lutoslawski III: 598-599 229 Ex. 4.2b Lutoslawski III: 600-601 230 Ex. 4.2c Lutoslawski III: 659-665 231 Ex. 4.3 Lutoslawski III: 593-595 232 Ex. 4.4a Lutoslawski I: 41-45 232 Ex. 4.4b Lutoslawski I: 64-66 233 Ex. 4.4c Lutoslawski I: 103-108 234 Ex. 4.5 Lutoslawski III: 715-717 235 Ex. 4.6 Lutoslawski III: 802-807/822-829 236 Ex. 4.7 Bartok I: 78 237 Ex. 4.8 Bartok III: 36 237 Ex. 4.9 Bartok III: 65 238 Ex. 4.10 Ligeti III: all (1-66) 239 Ex. 4.11a Ligeti III: texture "A" - pitch 240 Ex. 4.11b Ligeti III: 4-5 240 Ex. 4.11c Ligeti III: 9-11 240 Ex. 4.12 Ligeti III: 23-27 241 Ex. 4.13a Ligeti III: 32-39 242 Ex. 4.13b Ligeti III: 36-38 242 Ex. 4.14 Ligeti III: 46-48 243 Ex. 4.15 Ligeti I: 17-25 243 Ex. 4.16 Ligeti I: 22-23 244 Ex. 4.17 Ligeti I: 30-34 245 Ex. 5.1 Bartok I: 16-22 246 Ex. 5.2 Bartok I: 29-33 246 Ex. 5.3 Bartok II: 310-338 247 Ex. 5.4 Bartok I: 65-69 248 Ex. 5.5 Bartok II: 94-112 249 Ex. 5.6 Bartok II: 287-300 250 Ex. 5.7 Bartok II: 40-55 251 Ex. 5.8 Bartok III: 6-12 252 Ex. 5.9 Bartok III: 50-63 253 Ex. 5.10 Bartok IV: 121-129 254 Ex. 5.11a Lutoslawski I: 1-43 255 Ex. 5.11b Lutoslawski I: 36-40 255 Ex. 5.11c Lutoslawski I: 160-172 256 Ex. 5.12a Lutoslawski III: 614-617 257 Ex. 5.12b Lutoslawski III: 620-623 257 Ex. 5.13 Lutoslawski III: 885-888 257 Ex. 5.14 Lutoslawski III: 888-890 258 Ex. 5.15 Lutoslawski III: 698-700 258 Ex. 5.16 Lutoslawski III: 766-770 258 Ex. 6.1a Bartok II: 243-250 259 Ex. 6.1b Bartok II: 264-285 259 Ex. 6.2a Bartok II: 1-7 260 Ex. 6.2b Bartok II: 1-19 260 Ex. 6.3 Bartok II: 69-76 261 Ex. 6.4 Bartok II: 373-377 262 v Ex. 6.5 Bartok IV: 5-9 262 Ex. 6.6 Bartok IV: 15-16 262 Ex. 6.7 Bartok IV: 28-40 263 Ex. 6.8 Bartok IV: 74-83 264 Ex. 6.9a Lutoslawski III: 426-433 265 Ex. 6.9b Lutoslawski III: 570-578 265 Ex. 6.9c Lutoslawski III: 802-809 266 Ex. 6.9d Lutoslawski III: 852-857 266 Ex. 6.9e Lutoslawski III: 876-877 266 Ex. 6.10 Lutoslawski II: 173-189 267 Ex. 6.11 Lutoslawski I: 2-34 268 Ex. 7.1 Bartok I: 78-79 269 Ex. 7.2 Bartok III: 38 269 Ex. 7.3a Bartok II: 113-120 270 Ex. 7.3b Bartok II: 123-127 270 Ex. 7.3c Bartok II: 149-155 271 Ex. 7.4 Bartok II: 205-211 271 Ex. 7.5 Bartok IV: 25-43 272 Ex. 7.6 Bartok IV: 136-183 273 Ex. 7.7a Lutoslawski II: 311-324 274 Ex. 7.7b Lutoslawski II: 307-314 275 Ex. 7.7c Lutoslawski II: 323-327 275 Ex. 7.8a Lutoslawski III: 438-441 276 Ex. 7.8b Lutoslawski III: 447-451 276 Ex. 7.8c Lutoslawski III: 455-458 276 Ex. 7.8d Lutoslawski III: 463-467 276 Ex. 7.8e Lutoslawski III: 471-475 277 Ex. 7.8f Lutoslawski III: 479-481 277 Ex. 7.8g Lutoslawski III: 484-485 277 Ex. 7.8h Lutoslawski III: 498-500 278 Ex. 7.8i Lutoslawski III: 505-508 278 Ex. 7.8j Lutoslawski III: 524-528 278 Ex. 7.8k Lutoslawski III: 530-532 278 Ex. 7.9a Lutoslawski III: 434-479 279 Ex. 7.9b Lutoslawski III: 498-543 280 Ex. 7.10a Ligeti I: 8-16 281 Ex. 7.10b Ligeti I: 14-18 281 Ex. 7.11 Ligeti I: 19 282 Ex. 8.1 Bartok I:45-53 283 Ex. 8.2a Lutoslawski II: 189-210 284 Ex. 8.2b Lutoslawski II: 210-221 285 Ex. 8.3 Ligeti IV: 48-49 286 Ex. 9.1 Bartok IV: 136-138, 148-153 287 Ex. 9.2a Lutoslawski I: 40-43 287 Ex. 9.2b Lutoslawski III: 597-614 287 vi ACKNOWLEDGEMENTS Excerpts from Bartok’s MUSIC FOR STRING INSTRUMENTS, PERCUSSION AND CELESTA are copyright 1937 by Universal Edition. Copyright renewed. All Rights Reserved. Used in the territory of Canada by permission of European American Music Distributors Corporation, sole U. S. and Canadian agent for Universal Eidition. Excerpst from Ligeti’s CHAMBER CONCERTO are used by kind permission of Schott & Co., Ltd. Excerpts from Lutoslawski’s CONCERTO FOR ORCHESTRA are copyright © by G. Schirmer, Inc. (ASCAP). International Copyright Secured. All Rights Reserved. Used by Permission. Thanks also to Eulenberg Edition and Polskie Wydawnictwo Muzyczne. vii Rosemary Mountain – An Investigation of Periodicity INTRODUCTION The subject of rhythm has received a surge of interest in the last few decades. Speculations by theorists, composers, cognitive scientists, phenomenologists and others on our perception of rhythm have led to the formulation of various approaches to rhythmic analysis. However, many of the stimulating questions posed have not yet been investigated in much depth within musical contexts. Also, some of the proposed analytical models have been designed initially for tonal and/or monorhythmic structures.1 Therefore, they remain inadequate for revealing the atonal rhythmic complexities which characterize much twentieth-century music. My investigation was prompted by a search for a perspective which would ease the study of polyrhythmic works, and which would incorporate the latest relevant research on rhythmic perception. Most researchers agree that certain types of periodic elements such as pulse and meter can have a very strong influence on our perception of formal structure. There appear to be intrinsic properties of periodicities which make some of their functions unique, though they do 1 Rosemary Mountain – An Investigation of Periodicity complement other elements that contribute to accent and grouping.2 Also, models of rhythmic complexes can be designed from periodic components in a way analogous to the construction of complex tones from sine waves. These aspects, and the relative ease of extricating periodic elements from a musical score, suggested that an examination of periodicities would be a logical first step in the formulation of appropriate methods for rhythmic analysis. This dissertation therefore undertakes an exploration of the periodic aspects of rhythm.
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