## Dissertation Index

Author: Scotto, Ciro, G.
Title: Can Non-Tonal Systems Support Music as Richly as Tonal Systems?
Institution: University of Washington
Begun: September 1991
Completed: December 1995
Abstract: Can non-tonal systems support music as richly as the tonal system? The question has many possible interpretations, and each interpretation requires a different type of answer. Moreover and more important, each interpretation of the proposition and its corresponding answer directs the investigation down a different path. A proposition's context often determines its sense, and determining a proposition's sense is one method of specifying its interpretation. Chapter one begins by examining the role context plays in establishing the proposition's sense and the role context plays in determining the sense of a musical expression in music. The sense of a musical expression in music leads to a discussion about expressed and unexpressed music theories which lays the groundwork for establishing the context and sense for proposition P . This essay examines proposition P in the comparative context. The goal of the investigation in this context is to build bridges between domains by integrating tonal structures, such as prolongation and structural levels, and non-tonal structures, such as trichords and uniform trichordal arrays, into a single system called the hybrid system. However, since a recent argument has suggested that the design of compositional systems may be limited by certain cognitive constraints, the author addresses this question in depth in chapter one before constructing the hybrid system. Since uniform trichordal arrays form the hybrid system's rear end, and since uniform trichordal arrays are a subclass of the class of self-deriving rows, chapter two constructs a detailed model of all self-deriving rows. Using the model of self-deriving rows as a foundation, chapter three constructs a model of the subclass of uniform trichordal arrays, while chapter four compares the subclass of self-deriving rows capable of generating uniform trichordal arrays to other self-deriving rows capable of generating other array types and twelve-tone arrays in general. Chapter five begins the transformation of a uniform trichordal array's structure into the foundations of the hybrid system. Chapter six integrates uniform trichordal arrays and tonal theory to produce the engine that drives the hybrid system. Chapter seven demonstrates how intra-set-type relations translate into inter-set-type relations, and finally, chapter eight briefly reexamines proposition P. Keywords: non-tonal system, tonal system, cognitive constraints, self-deriving rows, structural levels, hybrid system
TOC: Chapter 1: Philosopheme 1 Review of Meaning and Truth 2 Meaning in Music 14 Context, Meaning, and Theory 23 Expressed and Unexpressed Theories 28 Context 38 Lerdahl's Cognitive Constraints 41 Universals 62 Representations 70 Linguistics, Psychology, and Generative Music Theory 81 The Terms of Proposition P 121 Outline of the Hybrid System 139 Chapter 2: Ampliation--A Model of Self-Deriving Arrays 2.1 Towards a Model of Self-Deriving Arrays 145 Set Properties and Folding Sub-Category 3 Type 2 Arrays 164 Partitioning Type 1 and Type 2 Arrays into Subclasses 171 Pruning Table 2.4 by Means of Algorithms for Type 1 and Type 2 Self-Deriving Arrays 193 2.2 Type 1 Combinations 195 Subclass 1a--General 195 Algorithm for Type 1 Subclass 1a Arrays 201 Preliminaries 201 Procedure 208 Procedural Changes 216 Multiple Orderings, Cycle Length, and Hidden Cycles 221 Merging Schemata 234 Subclass 1c--General 240 Algorithms for Type 1 Subclass 1c Arrays T0-TnIR/TnI-TnR Special Case 243 T0-TnIR/Tn-TnIR 248 Procedural Changes 253 T0-TnIR/TnM-TnIMR 268 Subclass 1b--General 277 Algorithm for Type Subclass 1b Arrays T0-TnR/TnM-TnMR 280 T0-TnR/TnIM-TnIMR 286 Subclasses 1d and 1e--General 292 Algorithms for Type 1 Subclasses 1d and 1e Arrays T0-TnMR/Tn-TnMR, T0-TnMR/TnIM-TnIR, and T0-TnIMR/TnM- TnIR 294 T0-TnMR/TnM-TnR, T0-TnIMR/Tn-TnIMR, T0-TnIMR/TnIM-TnR 300 2.3 Type 2 Combinations Preliminaries 306 Subclass 2a: Hexachords 325 Algorithm: Partition Identity Arrays 326 Commentary 328 Subclass 2a: Tetrachords 329 T0-Tn/TnR 334 T0-Tn/TnM 335 T0-Tn/TnMR 337 Commentary and Summary 338 Subclass 2b: Hexachords 339 Algorithm: Partition Identity Arrays 340 Commentary 346 Algorithm: Intersecting Partition Arrays, Subclass 2b, Schema 3-3, T0-TnI/TnR Combination 347 Algorithm: Intersecting Partition Arrays, Subclass 2b, Schema 3-3, T0-TnI/TnIR Combination 352 Commentary 355 Algorithm: Intersecting Partition Arrays, Subclass 2b, Schema 4-2 358 Subclass 2b: Tetrachords 359 Algorithm: Partition Identity Arrays 360 Summary 362 Subclass 2c: Hexachords 363 Algorithm: Partition Identity Arrays 363 Commentary 366 Subclass 2c: Tetrachords 367 Algorithm: Partition Identity Arrays 367 Summary 370 Subclass 2d: Hexachords 371 Algorithm: Partition Identity Arrays 371 Commentary 374 Algorithm: Intersecting Partition Arrays, Subclass 2d, Schema 3-3, T0-TnIM/TnMR Combination 375 Subclass 2d: Tetrachords 381 Algorithm: Partition Identity Arrays 381 2.4 Summary 383 Chapter 3: Cosmogony--Uniform Trichordal Arrays Preliminaries 385 Algorithm for Generating a Uniform Trichord Array from a Seed Array 399 Structural Model of Uniform Trichordal Arrays 419 Chapter 4: Alternative Worlds--Semi-Uniform Trichordal Arrays and Non-Self-Deriving Arrays Prelininaries 473 Generating a Semi-Uniform Trichordal Seed-Array from an Alternative-Merging Schemata 481 Three-Lyne Self-Deriving Arrays 487 Non-Self-Deriving Arrays 494 Chapter 5: The Hybrid System--from Array to Schema Uniform Trichordal Arrays: Definition of Function 500 Array as Schema: From Pitch-Class to Pitch 512 2'Schematic Structure as Compositional Determinant From Order to Content 519 Chapter 6: The Schema of Causality 537 Exposition and Translation 538 Trichord Progressions: Part I 580 Trichord Progressions: Part II 614 Translevel Connections 653 Chapter 7: Second Plane Tertiary Structures 673 Chapter 8: Epilogue 703 Bibliography 716 Appendix i: Common-Tone Vectors for Hexachords Under M5 and M7 728 Appendix ii: Hexachordal Information for the Generation of Uniform Trichordal Arrays and the Arrays They Generate 733 Appendix iii: Trichord Partitioning Patterns for Uniform Trichordal Arrays 845 Appendix iv: Detailed Trichord Vectors for Tn/TnI Type Hexachords 858 Appendix v: Episodes for Guitar 871 Appendix vi: Tetralogy 886 Contact: 5009 40th Ave NE, Seattle, WA 98105 Voice: (206) 525-8190 |