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On Chords Generating Scales; Three Compositions for Orchestra INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1. The sign or “target” for pages apparently lacking from the document photographed is “Missing Page(s)”. If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of “sectioning” the material has been followed. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete. 4. For illustrations that cannot be satisfactorily reproduced by xerographic means, photographic prints can be purchased at additional cost and inserted into your xerographic copy. These prints are available upon request from the Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases the best available copy has been filmed. University Microfilms International 300 N. Zeeb Road Ann Arbor, Ml 48106 8518911 Roush, Dean K. ON CHORDS GENERATING SCALES AND "THREE COMPOSITIONS FOR ORCHESTRA." (ORIGINAL WORKS) The Ohio Siate University D.M.A. 1985 University Microfilms International300 N. Zeeb Road, Ann Arbor, Ml 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1. Glossy photographs or pages______ 2. Colored illustrations, paper or print_______ 3. Photographs with dark background_____ 4. Illustrations are poor copy_______ 5. Pages with black marks, not original co p_______ y 6. Print shows through as there is text on both sides of page________ 7. Indistinct, broken or small print on several pages 8. Print exceeds margin requirem ents______ 9. Tightly bound copy with print lost in sp in________ e 10. Computer printout pages with indistinct print_______ 11. Page(s)_____________ lacking when material received, and not available from school or author. 12. Page(s)_____________ seem to be missing in numbering only as text follows. 13. Two pages numbered . Text follows. 14. Curling and wrinkled p a g e______ s 15. Dissertation contains pages with print at a slant, filmed as received__________ 16. Other _______________________________________________________ University Microfilms International On Chords Generating Scales D.M.A. Document Presented in Partial Fulfillment of the Requirements For the Degree Doctor of Musical Arts in the Graduate School of The Ohio State University By Dean K. Roush, B.F.A., M.M. The Ohio State University 1985 Reading Committee: Approved by Professor Thomas Wells Professor Gregory Proctor Advisor Professor David Butler School of Music Copyright by Dean K. Roush © 1985 V ita January 26, 1952 ' Born: Richmond, Virginia 1973 B.F.A., Music Composition: Ohio University, Athens, Ohio 1973-1975 ............................................................................................ Graduate Teaching Assistant: Bowling Green State University, Bowling Green, Ohio 1975 M.M., Music Composition: Bowling Green State University 1975-1981 ..............................................Instructor: College of Musical Arts, Bowling Green State University 1981-1984 ............................................................................................Graduate Teaching Associate: School of Music, The Ohio State University, Columbus, Ohio 1984-1985 ............................................................................................Graduate Research Associate: Department of Computer Science, The Ohio State University Publications Sonatina and Suite for harp. Published by Salvi International. Recorded on Orion Master Recordings, ORS 83458. Fields of Study Composition Tonal and Atonal Theory Digital Sound Synthesis Music History Performance: Harp, Organ, Piano ii Table of Contents Page V i t a ............................................................................. ............................................................................. ii List of Tables .................................................................................... ........................................... iv List of F igures ......................................................................................................................... v Introduction ................................................................. ................................................................ 1 Chapter I. Definition of Basic Concepts, Operations, and Equivalence Systems . 3 II. Pitch-CIaes Set Relations Inclusion R elations ......................................................................................... 13 Similarity Relations ............................................................................................. 19 Common-Tone Relations ............................................................................................................21 III. The Generation of Scales by Configurations of Chords Scale Types in Pair-Generation ............................................................................................... 25 Multiple-Generation ....................................................................................................30 Exceptional Chord Configurations ...........................................................................................37 Voice-Leading Considerations ................................................................................................... 42 IV. Examples of Set-Complexes for Composition ........................................ 45 List of References ..................................................................................................................................59 iii List of Tables Table Page 1. SG(2) Set-Classes...........................................................................................................................11 2. Self-partition vectors for trichords . ................................................................................... 24 3. Numbera of distinct self-partition vectors for classes of size 3-9 ...................... 24 4. Self-partition vectors for trichords, modified .........................................................26 5. Numbers of distinct scale classes generated by SG(2) pair-configurations .... 27 6. Ratios of distinct pair-generating classes to distinct subset classes ............................... 29 7. Scales successively generated by T„-configurations of 3 - 1 1 ............................................34 8. Exceptional Tn-configurations where Ml and M2 are of the same class ...................... 37 9. Exceptional Tn-configurations where CT, Ml, and M2 are of the same class . 39 10. Configurations of 3-5 for which CT and MU are of the same class ............................... 40 11. Other trichords with the same pro p erty ..........................................................................40 12. Hexachords with this p r o p e r t y ....................................... 41 13. Self-configurations for which MU=2-1 ........................................................ 43 14. Self-configurations with possible semitonal connections in contrary motion . 44 15. Sizes of scale-complexes for 3-11 45 16. Self-configurations where MU is an all-interval tetrach o rd ............................................51 17. Tetrachordal groups of Example E ........................................................................................55 18. Prime forms of hexachords of Example F ............................................................................... 56 19. Vector complex of Example F ............................................... 57 iv List of Figures Figure Page 1. CTF matrices for 7-35 and two forms of 3-11 . 21 2. Tn-configurations of pairs of 3-I I P ........................................................................................33 3. Symmetrical trichords formed by complementary transpositions ................................... 33 4. Generalized model of a closed cycle of configurations .....................................................35 5. A closed cycle of configurations of 3 - 4 ........................................................................ 35 6. A closed cycle of 4-Z15 . .....................................................................................................35 7. A corresponding closed cycle of 4 -Z 2 9 .......................................................................
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