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Acoustics of Bar Percussion Instruments

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Acoustics of Bar Percussion Instruments 71-7522 MOORE, James Loyal, 1934- ACOUSTICS OF BAR PERCUSSION INSTRUMENTS. The Ohio State University, Ph.D., 1970 Music University Microfilms, A XEROX Company, Ann Arbor, Michigan Copyright by James Loyal Moore 1971 THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED ACOUSTICS OP BAR PERCUSSION INSTRUMENTS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By James Loyal Moore, 3. Mus., K.Mus ****** The Ohio State University 1970 Approved by i Adviser School of Music PLEASE NOTE; Some pages have small and indistinct type. Filmed as received. University Microfilms ACKNOWLEDGMENTS I would like to express my appreciation to the members of my dissertation committee. Professor Norman F. Phelps of the School of Music, Professor Wave H. Shaffer of the Department of Physics, and my adviser Professor William Poland for their encouragement and guidance. The interest shown by Dr. Donald E. McGinnis, Head of the Instrumental Music Area of the School of Music is appreciated, as is the cooperation of Professor Karl F. Graff of the Department of Engineering Mechanics and the technical assistance of Louis J. Kiraly which made possible the experimental por­ tion of this investigation. Appreciation is also extended to Mr. Richard J. Richardson, President of Musser-Kitching Division of Ludwig Industries, who provided the bsir material for testing and willingly shared the problems and concerns of the industry. A special thanks is due Pro­ fessor James D. Salmon, of the University of Michigan, my teacher some years ago, who first inspired my curiosity about the bar percussion instruments. Finally, the en­ couragement and concern shown by my wife, Lyn, helped greatly to bring this dissertation to completion. VITA May 2, 1934 Born— Jackson, Michigan 1956 . • B.M. Mus. Ed., University of Michigan, Ann Arbor, Michigan 1957 . • M.M. Mus. Ed., University of Michigan, Ann Arbor, Michigan 1957-1960 • Percussion Instructor, Army Element U.S. Naval School of Music, Washington, D.C. 1960-1964 • Percussionist,Indianapolis Symphony Orchestra 1961-1962 • Percussion Instructor, School of Music, DePauw University, Greencastle, Indiana 1962-1964 • Percussion Instructor, School of Music, Butler University, Indianapolis, Indiana 1964-1967 • Teaching Associate, School of Music, The Ohio State University, Columbus, Ohio 1967- . • Percussion Instructor, School of Music, The Ohio State University, Columbus, Ohio 1964- . • Principal Percussionist, Columbus Symphony Orchestra FIELDS OF STUDY Music Theory: Professors William Poland and Norman F. Phelps Music History: Professor Keith Mixter Musical Acoustics: Professor Wave H. Shaffer iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS ........................................ il VITA ........................................................ ill LIST OF FIGURES ........................................ vi Chapter I. INTRODUCTION . ................................. 1 Purposes op the Investigation ................ 1 Outline or the Investigation .................. 4 II. NOMENCLATURE OF THE BAR PERCUSSION INSTRUMENTS . 6 Bar Percussion Instruments .................... S Modes of Vibration of the B a r s ................ 9 Cross Sect.r ................................. 13 Bar Materials ................................. 15 R e s o n a t o r s .......................... 20 M a l l e t s ........................................ 28 Ranges of the Instruments .................... 31 Other Terminology Factors .................... 3^ Summary . 35 III. LITERATURE REVIEW ............................... 38 B a c k g r o u n d ...................................... 38 C h l a d n i ...................................... 38 H e l m h o l t z .................................... 39 Twentieth Century Musical Acoustics Texts . 40 R i c h a r d s o n .................................... 4l Bartholomew ................................. 43 C u l v e r ........................................ 44 Taylor . .................................... 45 O l s o n ........................................ 48 J o s e p h s ...................................... 50 Le varie and L e v y ............................. 51 S u m m a r y ........................................ 53 Literature on Experimental Research and T u n i n g ........................................ 54 S u m m a r y ........................................ 63 iv TABLE OF CONTENTS— Continued Chapter Page IV. BAR TUNING .............................. 66 Tuning Standards ............................... 69 Shaping the B a r ............................... 74 S u m m a r y ........................................ 84 V. IDENTIFICATION OF STEADY STATE AND TRANSIENT RESPONSES ........................... 86 Description of Experimental Work ............. 8? Steady State Testing ........................... 91 Transient Testing ............................. 94 S u m m a r y ........................................ 96 VI. RESULTS OF EXPERIMENTAL W O R K .................... 97 Steady State Measurements .................... 97 Transient Measurements ........................ 125 Resume of Steady State and Transient R e s u l t s ..................................... 131 VII. SUMMARY AND RECOMMENDATIONS .................... 135 Summary of the Investigation .................... 135 Recommendations for Further Work ............. 147 APPENDIX A ..................................................162 REFERENCES ..................................................175 LIST OP FIGURES Figure Page 1. Distinguishing Factors of Bar Percussion Instruments ...................................... 8 2. Harmonic Series and Ideal First Three Modes of Vibration of Uniform Theoretical Bar, Marimba Bar, Xylophone Bar, Vibe Bar, and Orchestra Bell Bar Expressed in Musical Notations and as Frequency Ratios of the Fundamental ...................................... 10 3. Resonator with One-quarter Wavelength C o n t a i n e d ........................................ 23 4. Length of Resonator for Bar of Ag = 220 Hz C o m p u t e d ........................................ 24 5. Sounded Scale Ranges Musser Mallet [Bar] Percussion Instruments ........................ 32 6. Mode of Vibration of Supported Bar According to R i c h a r d s o n ...................................... 42 7. Mode of Vibration of Fundamental of B a r ......... 67 8. Ideal Ratios of Modes of Vibration and Musical Note Representation for Percussion Instrument B a r s ............................................. 68 9. Fundamental and Second Partial of Marimba and Vibe Bars Represented on Stroboconn ........... 72 10. Cross Section View of Basic Tuning Arch of Percussion Instrument Bar ...................... 76 11. Effect of Material Removed from Bar in Various A r e a s ............................................. 7 8 12. Cross Section View of Second Partial Tuning Arch ....... .................. ..... 80 13. Cross Section Views of Typical Marimba and Xylophone B a r s ................................. 82 vi LIST OF FIGURES— Continued Figure Page 1^. Testing Apparatus for Percussion Instrument B a r s ............................................. 88 15. The Mechanical Striker ........................... 88 16. Bars Used In Acoustics of Percussion Bar Experiment (No. EM6X, I969) .................... 90 17. Equipment Used In Steady State Testing ......... 92 18. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 110 Hz ( A g ) .................... 105 19. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 220 Hz ( A g ) .....................IO6 20. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 440 Hz ( A % ) .....................107 21. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 880 Hz (A5 ) .....................IO8 22. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of a Rose­ wood Xylophone Bar 440 Hz ( A % ) .................. Ill 23. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of a Rose­ wood Xylophone Bar 880 Hz ( A ^ ) .................. 112 24. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of an Aluminum Vibe Bar 220 Hz ( A ^ ) .................... 115 25. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of an Aluminum Vibe Bar 440 Hz ( A % ) .....................II6 26. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of an Aluminum Vibe Bar 88O Hz ( A g ) .....................117 vll LIST OP FIGURES— Continued Figure Page 27. Modes of Vibration and Musical Note Representa­ tions of Partial Tone Structure of a Steel Orchestra Bell Bar 880 Hz (A5 ) .................. 120 28. Modes of Vibration and Musical Note Representa­ tions of Partial Tone Structure of a Steel Orchestra Bell Bar 1760 Hz ( A g ) ................... 121 29. Modes of Vibration and Musical Note Representa­ tions of Partial Tone Structure of a Steel Orchestra Bell Bar 3520 Hz ( A y ) ................... 122 30. Summary of Frequencies of Modes of Vibration of Marimba, Xylophone, Vibe, and Orchestra Bell B a r s ........................................... 123 31. Comparison of the Frequencies of the Modes of Vibration of Marimba, Xylophone, Vibe, and Orchestra Bell Bars Tuned to Nominal 880 Hz (A5 ) .........................................124
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