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The Acoustics of the Steel String Guitar

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The Acoustics of the Steel String Guitar THE ACOUSTICS OF THE STEEL STRING GUITAR By Ra Inta SUBMITTED IN TOTAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY SCHOOL OF PHYSICS THE UNIVERSITY OF NEW SOUTH WALES SYDNEY, AUSTRALIA September 6, 2007 To the memory of Tamzin Sherwood (1977-2000) Sic Transit Gloria Astra ii Table of Contents Table of Contents iii Abstract vii Acknowledgements viii Why study the acoustics of the guitar? (An overview) 1 0.1Introduction................................ 1 0.2Outstandingproblemsofinterest.................... 4 0.3 The approach in this thesis . 4 0.4Overview.................................. 6 1 Previous work 9 1.1Abriefhistoryoftheguitar....................... 9 1.2Earlyworkinacoustics.......................... 14 1.3 Previous work on stringed musical instruments and related systems . 15 2 How the guitar produces sound 29 2.1Thebasicanatomyoftheguitar..................... 29 2.2 Specialised anatomical features . 34 2.3Excitationmethods............................ 38 2.4TheHelmholtzresonator......................... 43 2.5 Soundboard-air cavity coupling: the two-mass oscillator model . 46 2.6 Three-mass oscillator model . 56 2.7Theimportanceofbracing........................ 58 2.8 General behaviour in various frequency regimes . 62 2.9Resonantmodesoftheguitar...................... 65 2.10Interpretationofresponsecurves.................... 74 2.11Acousticradiativityoftheguitar.................... 77 iii 2.12Conclusion................................. 80 3 The Construction of the Guitar 82 3.1Introduction................................ 83 3.2Materialusedinconstruction...................... 84 3.3Damping.................................. 93 3.4Traditionaltechniquesofconstruction.................. 99 3.5 Recent innovations . 121 3.6 Phases of construction examined in this thesis . 122 4 Applications of the Finite Element Method to instrument construc- tion 124 4.1 Methods and motives for using finite element calculations . 125 4.2 Inputs for the model . 129 4.3Bracescalloping..............................131 4.4Gluebonds................................141 4.5 The free guitar soundboard . 142 4.6Guitarbody................................148 4.7 Conclusion: Applications of finite element simulations to instrument construction................................150 5 Experimental: Selection of Materials 152 5.1Timberusedintheguitarsstudied...................153 5.2Measurementtechniques.........................155 5.3 Measuring and controlling the moisture content of wood . 162 5.4 Selection criteria . 168 5.5Bracingmaterial.............................169 5.6 Soundboard material . 176 5.7Bridgematerial..............................180 5.8Neckmaterial...............................181 5.9Fingerboardmaterial...........................183 5.10Back,sides,bindingandothermaterials................188 5.11Dampingmeasurements.........................188 5.12Results...................................188 5.13Conclusion.................................192 iv 6 Experimental: Plates, bodies and the guitar 193 6.1Experimentalmeasurementtechniques.................194 6.2Simpleplates...............................196 6.3 Free guitar soundboards . 205 6.4Guitarbodies...............................210 6.5 The thinned soundboard . 217 6.6 Binding the soundboard . 222 6.7 Discussion . 225 7 Experimental: Completed instruments and parameter evolution 231 7.1Effectsfromtheadditionoftheneck..................231 7.2Additionofthebridge..........................240 7.3 The polished instruments . 246 7.4Effectsoflacquercuring.........................250 7.5Shorttermageingandplayingin....................254 7.6Theeffectsofbracescalloping......................266 7.7Parameterevolution...........................280 7.8Results/Comments............................290 8 A lexicon and a preliminary study of subjective responses to guitar sounds 296 8.1Introduction................................296 8.2 Study I—establishing a guitar timbre lexicon . 298 8.3 Study II—evaluation of guitar sounds . 308 8.4 Discussion . 328 9 Conclusion and Further Work 330 A Some derivations and measurements 335 A.1TheHelmholtzresonator.........................335 A.2 Soundboard-air cavity coupling parameters . 339 A.3 Two mass model for a cantilever beam driven at the base . 342 A.3.1 Change in frequency of bending mode of a profiled beam . 343 A.4 Measurements of dimensions of the guitar soundboards . 350 B Vibratory data acquisition system (ACUZ) 351 B.1Background................................351 B.2 Design and operation . 352 v B.3Impedancespectroscopy.........................355 C Alternative methods of measuring mechanical properties of wood 356 D Soundboard thickness measurement device 361 D.1 Outline of soundboard thickness problem . 361 D.2TheHalleffect..............................364 D.3 Measurements of soundboard thinning . 368 D.4Thedevice.................................369 D.5Methodologyandusage..........................370 E Excitation and coupling apparatus 374 E.1Magneticcouplingapparatus.......................374 E.2Cup-hooksupportmechanism......................378 E.3Magneticsupportmechanism......................379 E.4Materialsusedinexcitationstand....................380 E.5 Design of excitation stand . 380 E.6 Specific operating techniques . 382 F Lists of terms in describing the timbre of guitar sounds 383 F.1 .......................................383 Bibliography 386 vi Abstract To improve the replication of acoustic guitars, measurements of three Martin OOO style steel-string guitars were made at various stages of their construction. The guitars were constructed in parallel, as similar to each other as possible, with the exception of the soundboard material—which were made of Sitka spruce, Engelmann spruce and Western Red cedar. To improve the similarity of the instruments, methods were developed to measure and control the material properties of key components before their incorporation into the instruments, including a device to measure the thickness of a guitar soundboard attached to the back and sides of the instrument. Some of these measurements were compared to numerical models of the instrument and, after the establishment of a lexicon to describe guitar sounds, some physical factors contributing towards the timbre of guitar sounds were determined. The results of these investigations may be developed to improve the consistency in the manufacture of stringed musical instruments. vii Acknowledgements TM Thankfully, this is not an Academy Awards speech, so I am able to properly thank the following, without whom this project would have been impossible. These truly are debts I will not ever be able to repay. First, I would like to thank my supervisor, Prof. Joe Wolfe, who was supportive and generous well above and beyond the usual obligatory demands placed on super- visors. Joe has not only been a mentor in my scientific life, but also contributed much to my broader existence, both in the day-to-day, and the philosophical sense. A true captain of men as well as sailing ships. Gerard Gilet, my industrial supervisor: I am indebted to his extraordinary fore- sight in recognising the importance of research on improving the construction of the guitar—especially in an industry with such ‘slim overheads’. This is evident not only in his support of this project, but in his history of supporting research in a collegial and intelligent manner. I hope I have helped in some small way. Dr John Smith, my co-supervisor: I am grateful for his continuous suggestions and expertise offered, as well as his broad knowledge, which helped me solve innu- merable problems with his many great ideas. One day I hope I will visit Mileto, too. (The) John Tann: No amount of muffins would equal the accumulated help I have received from this man. From my very first day on this project (helping him make an anechoic chamber) until the very(!) last minute, help support and inspiration was ungrudgingly, nay, willingly, offered. An acknowledgement of foresight and support rightly belongs to the Australian viii ix Research Council. This is not offered as a platitude: I really am grateful for support to what may have looked like a high-risk venture! I would also like to thank: Emery Schubert: For help with the psychoacoustical aspects of this project. It would have been a right SASS-P without him. David Vernet, Matthieu Maziere and Davy Laille: It was a pleasure working with you all. I hope you remember your brief stay in Australia fondly and wish you well for the future. The people in the Music Acoustics Lab, including Paul Dickens, Attila Stopic, Jane Cavanagh, Manfred Yew, Alex Tarnopolsky, Claudia Fritz, David Bowman, Ben Lange, Romano Crivici, Michael Lea, Harry Vatiliotis, Ryan France, Pierre- Yves Pla¸cais, Olivier Marnette and the many others who passed through in the time I was there. You have all helped make my PhD life richer and more enjoyable in innumerable ways. The people at the Gilet Guitars workshop: Darrell ‘Deathride’ Wheeler, Michael Prendergast and Charles Cilia, plus Arjuna, Charles Milne, Pete, and Frank. I would have had a lot of expensive firewood without your help. I would also like to thank the good people of the UNSW School of Physics, in- cluding Jules, Tony Travolta, Cormac, Sue Hagon, Bosco, Steve ‘Yaarrgh’ Curran, Dr Matty, Vincent, Gary Keenan, Tammy Reztsova and so many others for provid- ing such a stimulating environment. So many good people. So many good times. Of course, any acknowledgements would not be complete without especially thanking Aunt Elly, Doug
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