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ZEEB ROAD, ANN ARBOR, Ml 48106 IB BEDFORD ROW. LONDON WC1R 4EJ, ENGLAND 7922527 HCNEAL, HORACE PITMAN * JR. A METHOD OF ANALYSIS BASED ON CONCEPTS AND PROCEDURES DEVELOPED BY ALLEN FORTE AND APPLIED TO SELECTED CANADIAN STRING QUARTETS, 1 9 5 3 — 1962 . THE OHIO STATE UNIVERSITY, PH.D., 1979 University Microfilms In ternational 300 N ZEEB ROAD, ANN ARBOR, Ml 48106 A METHOD OF ANALYSIS BASED ON CONCEPTS AND PROCEDURES DEVELOPED BY ALLEN FORTE AND APPLIED TO SELECTED CANADIAN STRING QUARTETS, 1953-1962 DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Horace Pitman McNeal, Jr., B.M., M.A. * * * * * The Ohio State University 1979 Reading Committee Approved By Burdette L. Green Norman Phelps William Poland - Adviser School of Music ACKNOWLEDGMENTS I wish to express my appreciation to Dr. Burdette Green for his thoughtful attention to this project. His interest and consistent encouragement have contributed immeasurably to the success of this in vestigation. The many painstaking hours he has contributed are deeply appreciated. Invaluable literary evaluation has been received from Dr. Norman Phelps. His attention to clarity and conciseness has sped the progress of this study. Astute observations relative to semantics have been contributed by Dr. William Poland, and the text communicates more clear ly than would have been possible without his probing comments. Dr. George Pollcello has given his statistical expertise frequently during the course of the project and is thanked in particular for his interest. Special thanks are due to The Canadian Music Centre for its gracious cooperation in supplying scores and cassettes for study. The friendliness and helpfulness of the people in this agency assisted Immensely in my research. I wish to thank my wife, Jennie, who has supported me in many ways, helping me to complete this study. Her kind help has given me the encouragement to stay with and finish this dissertation. ii VITA February 28, 1949................. Born - Cedartown, Georgia 1971 ........ ................. B.M., Furman University, Greenville, South Carolina 1972-1974..........................Teaching Assistant, Department of Music, The University of Georgia, Athens, Georgla 1974 ..............................M.A., The University of Georgia, Athens, Georgia 1974-1976. .................. Teaching Associate, School of Music, The Ohio State University, Columbu s, Ohio 1976-1977........ ............... .. University Fellow, The Ohio State University, Columbus, Ohio FIELDS OF STUDY Major Field: Music Theory Studies in Contemporary Music Theory. Professor Burdette L. Green Studies In History of Music Theory. Professor Norman F. Phelps Studies in Stylistic Analysis. Professor B. William Poland ill TABLE OF CONTENTS Page ACKNOWLEDGMENTS.............................................. i± VITA ....................................................... iii LIST OF T A B L E S .............................................. vi LIST OF FIGURES.............................................. iac LIST OF E X A M P L E S ............................................ xi INTRODUCTION ............................................... 1 Chapter I. THE COMPOSERS AND THEIR QUARTETS...................... 16 Canadian Compositional Activities, 1920-1960 .... 16 Jean Coulthard ........... 23 Claude C h a m p a g n e ........ ,........... 29 Harry S o m e r s ...................................... 35 John W e i n z w e l g .................................... 46 II. CLARIFICATION OF THE ANALYTIC M ETHO D.................. 55 Relevant Concepts and Terms ............... 55 Pitch Class .......................... 55 Interval Class .................................. 58 Pitch Class Set .............................. 63 Prime F o r m ...................................... 64 Interval Vector . ' ............................ 72 Similarity Relations............. 77 Supplemental Procedures Employed In This Study . 85 Hypothesis Testing .......................... 85 Distributions ............. 87 Improved Procedure for Prime Form Identification..................... 89 Statistical Comparisons ........................ 92 Prime Form Comparison in the Quartets ......... 94 iv TABLE OF CONTENTS (Continued) Chapter Page III. COMPARISON OF HORIZONTAL PRIME FORM S E T S ............. 98 Four Hypotheses................. 98 Procedures for Linear Segmentation .......... 101 Tabulation of Results............................ 107 Interpretation of Results........................ 117 IV. COMPARISON OF VERTICAL PRIME FORM SETS AND SUMMARY OF SIMILARITY R E L A T I O N S .......................... 132 Four Hypotheses.................................. 132 Procedures for Vertical Segmentation ••••••.•• 133 Tabulation of Results ................................ 138 Interpretation of Results 146 Similarity Relations Between the Two Planes ...... 163 V. EVALUATION AND CONCLUSIONS.......................... 177 APPENDIXES A. Prime Forms and Inversions Notated Conventionally and in Integer Notation: 3-Sets and 4-Sets .............. 184 B. 3—Sets and 4-Sets in Integer Notation with Interval Vectors ........................................ 190 C. All Prime Forms Identified by Their Integer Intervals . • 192 SELECT BIBLIOGRAPHY ............................................ 203 v LIST OF TABLES Table Page 1. Numerical Representation of Pitch Classes ......... 57 2. Subtraction of Each Integer Interval From a Constant of Twelve ........... .......... 62 3. Numbers of Prime Forms for Pitch Class S e t s .............. 70 4. Numerical Relationships Between Pitch Class Sets and Interval Vectors ......... 74 5. The Format for Entries in Appendix B . .......... 75 6. Basic Descriptions of Similarity Relations .......... 78 7. Rp— Maximum Similarity of TWO Pitch Class S e t s ............ 79 8. The Rp Relation Not Evident in Prime F o r m s................ 79 9. Rp Relation Revealed Through Transposition................ 80 10. Ri““Maximum Similarity of Interval Class Content with Interchange Feature ............. 81 11. R«— Maximum Similarity of Interval Class Content Without Interchange F e a t u r e ......... 82 12. Rq—Minimum Similarity of Interval Class Content ...... 83 13. The R^, Rp R e l a t i o n ...................................... 84 14. The R2, Rp Relation .......... 84 15. The Rg, Rp Relation 85 16. Successive Reorderings and Differences .............. 90 17. Horizontal Plane - Prime Form Counts, 3-Sets ........ 107 18. Horizontal Plane - Prime Form Counts, 4-Sets 108 vi LIST OF TABLES (Continued) Table Page 19. Horizontal Plane - Prime Form Percentages, 3-Sets......... 109 20. Horizontal Plane - Prime Form Percentages, 4-Sets ..... 110 21. Prime Form Totals: 3-, 4-, 5-, 6 - S e t s .................. 112 22. Frequent Horizontal 3-Set Forms, Coulthard .............. 113 23. Frequent Horizontal 4-Set Forms, Coulthard ........ 119 24. Frequent Horizontal 3-Set Forms, Ch a m p a g n e............... 119 25. Frequent Horizontal 4-Set Forms, Champagne ........ 120 26. Frequent Horizontal 3-Set Forms, Somers 121 27. Frequent Horizontal 4-Set Forms, Somers .......... 122 28. Frequent Horizontal 3-Set Forms, We i n z w e i g ............ 123 29. Frequent Horizontal 4-Set Forms, Weinzwelg ........ 124 30. Horizontal T-Square Data for Musically Significant Differences....... ............ ................. .. 129 31. Degree of Confirmation for Hypotheses Relative to Horizontal Plane ........................................ 130 32. Vertical Prime Form Counts, 3-Set F o r m s .................. 138 33. Vertical Prime