THE CATGUT ACOUSTICAL SOCIETY NEWSLETTER
* Number 24 > published semiannually November 1,1975 Margaret Tucker Saunders, widow of Frederick A. Saunders, the founder of the Catgut Acoustical Society, died last May. Those of us who were privileged to know Professor and Mrs. Saunders and visit with them in the big house overlooking the valley of the Connecticut River or later on Silverwood Terrace in South Hadley, Massachusetts, will remember many good times evenings of music, early morning bird watching, discussions about violins -- and testing, as well as wide-ranging interests in community and world af- fairs. After Professor Saunders died in 1963, Mrs. Saunders continued to extend her warm hospitality to her many friends to carry on her work in local politics, conserva- tion and school affairs, based on her deep conviction that citizens should take an active interest in the democratic process. She founded the "Know Your Town"- group in South Hadley and last year received the annual Lions Club Citizen of the Year Award at a spec- ial town meeting in her honor. A great lady has gone and we shall miss her. C.M. Hutchins ****,***#************.*.**.*
We note also the death on June 10 of Professor W.H.Van Zoest of Eindhoven, who contri- buted to our last Newsletter an English translation of "Paul Gerhard Schmidt's Violoncello Ingrandito" (by W.C.deJong).
We are**************pleased to announce that an index to articles*********from our Newsletters is in preparation. This edition will be comprehensive for all issues through No. 24 and will be mailed out with Newsletter No. 25 in May 1976 to all members in good standing. The Board of Trustees held its annual business meeting at Society head- quarters on May 31 , 1975- Attending were Warren Creel, Frank~~3Clough , Joseph- Domaleski, Carleen Hutchins, Morton Hutchins, Dugald McGilvray, and Richard Menzel. The nominating committee of Loraine P. Elliott, Ethel H. Piggins, and Barbara Hendrian had presented the following slate which was unanimously accepted. A. SteVart Hegeman President (re-elect) Robert Fryxell Trustee (re-elect) Jurgen Meyer Vice President Francis Clough Trustee (re-elect) Warren Creel Vice President Joseph Domaleski Trustee (re-elect) Dugald McGilvray Treasurer (re-elect) George Bissinger Trustee Irving/Hoffman Trustee Ronald Naspo Trustee In addition to various other matters of business, the occasion included a delightful musical demonstration by William Berman of the "big. viola" as well as- four standard- violas recently completed by Carleen Hutchins. RECENT PUBLICATIONS
Elizabeth Cowling, The Scribners (1975) 224 pages $15.00 (reviewed in THE STRAD September 1975, page 325) Carleen M. Hutchins, (Editor), Musical Acoustics, Part I: The Violin Family. Dowden, Hutchinson & Ross, Inc. (1975), 478 pages (reviewed in this issue) Harry S. Wake, Violin Bow Rehair and Repair, (1975) 93 pages $8.50 (reviewed in this issue) Ake Ekwall, Mera om Fiolhorn" Slojdochton, V. 44, No. 2 (1974) Ake Ekwall, Fiolhorn, Proportionering Slojdochton, V. 45, No. 3-4 (1975) Warren Creel, Paul C. Boomsliter, REythm Patterns in Language: Connecting the Links of Human Thoughts, Albany Medical College of Union University, Northeast Regional Learning Center Empire State College,State Univ. of N.Y. .Albany,N.Y. (1975) 156 pages J. Meyer, Akustische Untersuchungen zur Klangqualitat yon Geigen. Instrumentenbau, Heft 2 Februar(l97s; 29 Jahrgang o pages — E. Jansson and J. Sundberg, Long-Time-Average Spectra... Part I, Acustica, (1975) E.V. Jansson and A.H.Benade, On Plane and Spherical Waves in Horns with Non-Uniform Flare Acustica N0. 4, V01. 31, 1974 F.Fransson, Johan Sundberg, Per Tjernlund, The Scale in Played Music. Svensk tidskrift for musikforskning Vol. 56:1, 1974 D. Kimball, Constructing the Mountain Dulcimer. David McKay Company (1975) 111 pages $8.95 " COPYRIGHT (cont. page 3) Catgut Acoustical Society, Inc. 1975
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CATGUT ACOUSTICAL SOCIETY, INC. President Stewart Hegeman 176 Linden Avenue Glen Ridge, N.J. 07028 Vice-President Warren Creel 456 Hamilton Street Albany, N.Y. 12203 Vice-3President Jurgen Meyer 33 Braunschweig Bundesallee 100 PTB West Germany
Secretary Carleen Hutchins 112 Essex Avenue Montclair, N.J. 07042 Dr. and Mrs. F.A.Saunders with Carleen Hutchins (center) Treasurer visiting at the Saunders home in South Hadley, Mass. (1957) Dugald McGilvray 12 Clairidge Court Montclair, N.J. 07042 Editor Robert Fryxell 8430 Old Hickory Drive Cinci Tmat-L ,_ohio„ A5243
William Berman of Oberlin Conservatory Copy of letter received from pupil of Professor Dear Ms. Hutchins: August 8, 1975 " having with the I lust wanted to write before school begins to tell you the success I've been Things were going quite well with it at school after having it only a few weeks (as Vertical Viola mstrument I'm sure Mr. Berman told you) in the Spring, but having had time to really work with the the Sunnier nonths, I've made tremendous progress. It is possible to play the most ditticult during s viola literature with it - if one has the proper physique to handle it, and if one executes Mr. Berman principles of freedom and relaxation. No doubt if one were not to approach such a large instrument with to seriously per- an acute awareness of means for eliminating tension and strain, it would be impossible form on. Yet, as Mr. Berman so emphatically argues, this is true on an£ size instrument. ideas and Inmy case, the combination of Mr. Berman's excellent principles and your revolutionary e_xpertise on instrument construction are allowing me to produce a geniunely unique sound. I hope I don't sound vain, for I give others credit for making it all possible. I it Further discussing the immense size of the instrument, I'm sure Mr. Berman told you that found at Oberl_m easier to play than a normal sized viola. One of the reasons I changed from violin to viola cramped when playing. After playing a 16% inch viola for three years I began exper- was because I felt away from iencing same frustration. With the Vertical Viola, my left arm is. extended very^comfortably the enabling me to the my body (as it should be) , and my bow arm is able to move from the shoulder some; get more kind of "suspended" arm weight that cellists are experiencing. In short, I've never been comfortable with playing. Ihe larger intervals do present a challenge, but diligent work with 3 octave scales and arpeggios are gradually eliminating this. stick, permit I was also fortunate to find a very fine extra heavy viola bow. With such a I m able to the bow's naturalwei^it catch the string, eliminating the need to force. Without forcing, lam able to pull a round, open sound from the instrument. Adding a little vibrato, sound literally pours from the instru- ment - powerful - penetrating. Anyway, just wanted to express mp happiness with the instrument, as well as my thanks. Sincerely, Randall Vemer
Note: Effective immediately, the Editor's address is changed to 8430 Old Hickory Drive, Cincinnati Ohio 45243. 3
The hairing procedure as presented by Mr. Wake is conventional in BEHAIR S, REPAIR ■oat respects. He is the "tip First" but doesn't why no- By H. Wake body else has explained his individual preference either. I suppose, -as 93pp * 2 Full Drawings one the "Catgut mentality", I am most perturbed by "how to"*books that 8i x 11" never tell "why". Mr. Wake is probably better than most in this respect, 18.50 the author: k33h Voltaire Diego, 9210? but he still leaves me wondering why, he soaks the hair in Reviewed by R. E. Menzel hot water, while el6e seems to use luke warm water; or why he aeals the hair ends with hide glue, when the traditional method This is the third violin book by H. hia previous titles melted rosin. Why does he insert the hair end into the tip mortise in a b«lngittA Luthier's Scrapbook" and "The Technique Violin Making". Like "0" when others tell us to use an "L" (Of course I am aware Its predicessors, it is privately published and completely the work the allegations by some, that Catgutters are constantly presenting reasons including photographs and illustrations. As it is not a "why", without knowing "how"). There is little that could be added to the polished example the bookbinding and printing arts, but it is never section on hairing, but I would like to have seen, in a detailed cleanly done within the obvious budget constraints of publishing- cross section the wedged hair to illustrate the wedge locking principle, which surely will never make the Beet List. The which la essential to an understanding the bow hairing process. wonder such books is not in their individual but that they are done at all. Each is a labor and authors such as Mr. Wake are to The remaining portion the book is devoted to bow repairs, a sub- be commended theit contributions to the art. ject that is almost completely lacking in the literature. Although, by the most comprehensive material on bow repair anywhere, I let down This book is not the "Heron Allen" the bow it is too in- going this Mr. Wake did not all the and really complete, and the prose less amusing; nor is it an -elegant (and expensive) detail all bow repairs there really aren't that more. The failing collector's item 6uch as the forthcoming Vatelot bow Lea Archets here, I is one - organization; not developing an overview FrancalB. it is the most complete book on bow repair yet all repair problems, and then addressing them. Mr. it seems, is published. Previously published pamphlets: How to Rehair a by Melvin fully capable of doing so, but he chooses to simply discuss the repairs and Rehairing Bows by Moeller and Lohberg leave much to be at random. There is an extensive alphabetical index at the end the desired in the clarity of the as well as ln the presenta- but it does not serve to organize the contents. tion the little details involved in bow hairing. The The not section on bows in the book: How to Repair Violins is so repair section is as such in the it simply simplistic as to be almost dangerous. good line drawings the the rehairing a bow and proceeds on repair to anoth- er. Here is a listing those presented: Salvaging Used Installing anatomy the bow are to be in: Re-Hairing and Repairing Bows For a Plastic Stringed Instruments by Peter Spicer. Its title notwithstanding, the Tip, Installing an Ivory Tip, Restoring a Worn Frog Repairing a Split Replacing a Tip, Removing a Tip,R- book contains scarcely a word about bow repairs. A more recent book: How epairing to Rehair Bows (I an by now, beginning to sense a certain lack origin- a Split Bow Tip, Recambering a Applying a Leather Wind- ing and Whalebone Gripe, and Various Methods of Splicing. As exten- ality in titles in these books) by J. P. McKinney is well illustrated and sive as this list into considerable but it is greatly overblown in so appear, consider the following common repairs which much so that I have lost because it could not be This book were not discussed: Fitting a New Frog, Fitting New Fyes, and Bow Tips; Replacement of Loose or Worn Eyelets, Rebushing a could easily be reduced to one its present and still present torn its etory very well. and Restorative Frog Work. Those repairs that discussed Fully a third Mr. Wake's book is devoted to the rehairing process, are are well presented, and his ■ethods are completely plausible. Mr. Wake is quite current in his think- and it is the most complete and rational treatment the subject that I ing ac to the use presently available have yet seen. It is heavily illustrated with photographs by the materials and and he which are generally helpful, them thoughtfully in his repair work. Epoxy and other modern ad- quite but they could have been greatly en- Sppliesesives are as well as the conventional hot glue. The drill press hanced by Judicoua retuching to bring out pertinent especially or milling machine is employed in in close views text an extensive section on bow grafting. up the tying technique. The is poorly coordinated To those who have wondered about the winding Mr. Wake re- with the - which jump figure 1 to figure 15 at the veals hie method. I have never seen it printed elsewhere. opening the book. The figures then proceed in the following order: 10,5|2,8,3» 13|4,9» 1 ,and become more ordered. Needles6to I would that with the inclusion the previously mentioned a great deal ' flipping is required to the instructions. and possibly a more which might come to this book could well merit the designation: "Encyclopedia Bow Repair". It is easily the best book on the subject to date.
REVIEW to learn that both CV. Raman and Felix Savart made—significant-j:ontxibutions,_in_._this_ ieldj!8 Musical Acoustics, Part Violin Family Raman on the bowed string early in his career, Components and Savart on the soundpost. Savart's paper is the earliest (1840) which appears in the book. Edited by Carleen M. Hutchins The papers heavily emphasize experiments rather Benchmark Papers in Acoustics, Volume 5 than theory, notable exceptions to this are found in some of the work of Cremer, Raman and Dowden, Hutchinson and Ross Schelleng. The sophistication of the experi- Stroiidsburg, Pennsylvania, 1975 mental apparatus ranges from 19th century de- 478 pages, vices to the instruments required for holo- gram interferometry which display the modes of This is the first in a two-part series on plate and bridge vibration. Brief comments on violin acoustics edited by Carleen Hutchins. each paper by the editor provide biographical Part 11, Violin Family Functions will follow. information and continuity. Space limitations Scanning the contents of this book, one is im- required the omission of important papers from mediately struck by the significant develop- the volume. Many of these are listed at appro- ments in violin acoustics contributed from all priate locations. parts of the world. Nine countries are repre- sented in the total of twenty-nine papers se- A few misprints were noted. page 352, lected. Twenty papers are in English; the other it is stated that, "Recent work indicates that nine are in French, German, and Italian with the logarithmic decrement for good violin spruce abstracts and in some cases full translations is around 0.002". The figure should be 0.020. in English provided for each. More than half page 444, the summary by I.P. Beldie of his of the papers have been published since 1960, paper discusses shear moduli and on the sixth indicating the intensity of activity in recent line, the equality GyZ Zy appears. This inequality, years. should be an i.e., GyZ^G 2y. The papers are grouped into six sections: This book obviously fills a great need for I. General Papers in Violin Acoustics, 11. The a compilation of important works which have Bowed String, 111. The Bridge, IV. The Sound- been heretofore widely scattered and little post, V. Wood for the Violin Family, VI. Varnish. known. But the editor's contribution far The editor's own 1962 Scientific American arti- beyond that. Her own efforts have directly in- cle provides a highly appropriate opening paper. spired a significant amount of the research and The work of John Schelleng is found in four of the writing represented in this volume. the six sections which justly reflects the Daniel ¥" Haines scope of his research. Readers may be surprised RECENT PUBLICATIONS************ * ************ J. Sundberg, Formant Technique in a Professional Female Singer, Acustica N0. 2,V01.32 (1975) J. Gauffin and J. Sundberg, An Attempt to Predict the Masking Effects of Vowel Spectra, 4/1974 A.H. Benade, On Plane and Spherical Waves in Horns with Nonuniform flareFlare, Acustica No. 2, Vol. 31, 1973 Free Reed, The magazine of the Concertina Revival, has compiled a list of music and records available. For information Free Reed, Duf Derby.England or Andy's Front Hall, RDI Wormer Rd. ,Voorheesville ,N.Y.-l2lB6 or Box 385, Dickson, Act 2602, Australia
VIOLIN BOW of school, say S. Scale of Softbound fro* St., San California for instance, everyone call* for S. Wake, of bend, bend? of of author, many such, of addition, theleae, of "fiddle books", Seller of of merit, of love, of for far, felt of far that, after far, go way many book, think, of of of Nevertheless, Wake, Bow, Schneider, of book, illustrations, of of fine many identified Alfred Common follows book, Some of after of from of found of Hair, S. Mortise, Stick, Screw Screw Bow, of Silver Grin, goes detail, size, may my copy filed. Ferrules, Slides, half Silver size, Screw Hole,
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THOUGHTS ABOUT THE VTOLEN Ernest D. Hodges It seems that in this day of scientific advancement in acoustical research inportant steps can be achieved in the study of violin construction. I believe that much has been learned, with more to come, through science. However, scientists and sincere makers have copied, measured and experimented these long years to discover the principles involved in this art. I say "principles" because unless there were principles the maker would not be consistent. From the oldest .makers.* through trial and error, based en experiences of themselves and others , the masterpieces appeared. These people were not scientists; many could hardly read and write. Yet their finest works have excited the interest of professionals and laymen alike. By the same token, violirmakingmust be considered art by its construction, beauty and acoustical effects. Having made instruments for thirty-five years, I have experimentedwith many theories, woods, varnishes, etc. I have repaired thousands of instruments from the masters to the cheapest, learning something from all. My little knowledge has cone from my experience and that of others . Since lam a musician and have made my living for years in music, this has been a great help to me as a violinmaker and repairman. However, I welcome any help science can give me. Scientific instruments can tell us what we already know, that is, that the instruments of the masters are best. What we want to know is how to achieve this. It seems to me that there are so many considerations to deal with that it must mainly rely on the sensitive hands of the maker. Yet modern science can help in many ways and lam highly pleased that it is taking the violin seriously. The work of Ms. Hutchins and associates is to be highly praised. In the 40's an associate violinmaker of mine, at the re- quest of sent an instrument to Dr. Saunders for testing. I have made many experiments from the stage and under many physical conditions with varying degrees of humidity and tenperature. Therefore the work of Saunders and Hutchins is of great interest to me, t±ough I do no know hew to analyze the results obtainedby them. From the standpoint of ny experience I will share a few points for the consideration of those interested. If we assume that the maker is capable and know what he or she is about, the first essential is tonal wood. cannot expect more than the potentialof the wood. I consider the top more important than the back, as it is more complicated. Many masters have spliced rather than try new material and they have treasured known good vrood. It would be interesting to analyze acoustically the woods the old makers used, especially that in the rough if any could be found. I have found that evenness of graduation is found in the best instruments. Even a string does not vibrateper- fectly if it is uneven. String length, angle of neck, pressure of the bridge and other parts can be measured and are of utmost impostance. 3Lupot stated that all parts should be without strain. I have seen tops so badly fitted that danping them to the ribs glued in torsional strain. How could it vibrate evenly? Some repairmen "spring" in the bassbar! I have opened old violins whose fibers were yet struggling to be free. If the instrument is evenly made, I believe that tuning the plates is the safest way. This takes care of the variance in wood. But we must be careful! One can take two tops from the same wood, graduate it the same way, and tune to the same pitch, yet one top can be thinner than the other. If one leaves a high bead edge on one and thin- ner edges on the other, the pitch of the plate will vary. Of course, other things will affect the tuning also. Tenperature affects the tuning as the plate expands or contracts or absorbs moisture. I have seen one-half step variance What notes to tune the plates to? Savart stated that Strad plates were C and D for the top and back. But let us again be careful. Was not the standard pitch of that time one-half step lower than A440? And what* have aging and former repairs done to the pitch? I read lately that in some judging of violins (new ones) that cabinet work and skill stands first while tone is placed several steps lower. The Italiansput tone first and I agree completely. If one can produce a fine tone, it should be the highest aim. Everything else is secondary. However, the greatest makers achieved fine tone and beauty. It is a pity that the masters did not write down some guidelines for us to follow, some "do's and don'ts". They were violinmakers, not writers. Artists seem never to be able to pass on their knowledge, leaving that for others to guess at. We can measure the physical, but what about timbre? Timbre—that quality we drink of aidcan never fill our souls sufficiently; that something that can never be measured but only experienced. How could a computer tell us who is the greatestartist, for art touches our emotions, even if we experience it in a different manner. Surely, in many ways modern science can help us, though it would have to be physically. If the old masters could have had our technical "know how" they would have left us thousands more of their work. I hope science can tell us, not only what we alreadyknow about violins, but also how to maJke superior instruments consistently. It's a large request, but think of all the fun we could have! * I have known of Felix Savart' s experiments since I first read them as a boy in an English translation which appeared in The Violin and How to Make it by a 'master of the instrument" (actually William C. Honeyman, 1845-1919, a Scottish violinist and prolific writer) . These writings were from L'lnstitut, and have appeared in English translation in several other publications including Newsletters No. 5 and No. 21.
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It is quite ture content of wood and Krech possible that the fundamental resonance frequency of stiffness and density to moisture content) . Moisture Kollmann 's and Krech' s original strip was just below content of wood, of course, is related to the humidity this threshold. (The threshold is indeterminate in of the environment. Our plan to store and test our this case as trot enough data was given, however, based woods under controlled conditions will eliminate this on our tests we can say that it most probably was variable fran our data. slightly above their resonance frequency) . Calcula- d) Varnishes, fillers, and _Lacquers: The supposed tion shows that shear deformation would then remain effects of the varnish on the quality of violins has negligible up to 7000 Hz as reported, therefore their a rich history. The Hills (15) ranked varnish above report of constant danping is plausible. Schelleng the quality of the wood and the skill of construction in his test reported a somewhat higher fundamental in importance. Modem research most notably by frequency, possibly his was above the threshold, uhich Schelleng (16) has relegatedvarnish to a substantially would cause his danping observations to be frequency lesser role, but nonetheless it is not denied that var- dependent. In our proposed research, we intend to in- nish must be seriously considered. Schelleng was con- vestigate this line of thought by performing our own cerned with the properties of the varnish alone and did tests. Of course, if we find shear not to play the not consider the additional effects of the filler ap- assumed role in danping we will have to look elsewhere plied to the wood before the varnish. Working with for a resolution of this point. specimens prepared by Morton Hutchins, we have found the effects of the filler to be nearly as great as the Another observation of considerable interest with varnish. Crossgrain danping of typical spruce strips regard to damping was apparently first reported by was found to be doubled with the applicationof typi- Skudrzyk (13). He found that tests of danping at cal violin filler and varnish. Areal density is raised successively higher modes of flexural resonance showed nearly 20% when applied to plain spruce the thickness the previously discussed rise in danping, but if the of violin tops . Crossgrain stiffness is predictably frequency was raised by shortening the strip instead, increased, but stiffness along the grain is affected the rise was not nearly so pronounced. In our pilot less. These are results obtained with one type of var- tests we have observed the same phenomenon. We have nish and filler, but the orders of magnitude should be not yet performed tests under conditions suitable for meaningful. analysis, but when we do I would expect that differ- ences in shear deformationmay again be the source of Meinel (17) is the only other investigator known by the apparent discrepancy. When a strip is excited at me to have sought quantitative information on violin one of the higher modes of flexural resonance, the mode varnish. He measured the effect of varnish on the over- shape is composed of four branches of the dispersion all acoustical radiation of a violin. Meinel also not- curves, two real (propagatingwaves) and two imaginary ed the increase in danping of wood strips when tested (non-propagating waves) . The real and imaginary along the grain. It does not appear that he tested branches have different contributions of shear, A crossgrain strips. There is no data known to me on the short strip excited at fundamental resonance can have effects of the lacquer typically applied to guitars. the same frequency as a much longer strip excited at We intend to explore this also. one~ofTt^""overtonesT—Smce-~they~are-excitetl^atr±te same frequency, the two types of vibration are com- It is now evident that the effects of any be posed of the same modes, obtained from the dispersion it varnish or lacquer must be included in the criteria curve, but there is a different "mix" of these modes, for matching the properties by means of a substitute yielding different contributions of shear-hence dif- material. Fortunately, this consideration is benefi- ferent danping if our hypothesis of the dependence of cial, for matching spruce exactly as we have attempted danping on shear is shown to be correct. Skudrzyk's with the graphite-epoxy plate is probably impossible, partial qualitative explanationcan be shown to be but with a varnish applied to the spruce, the match is equivalent to this reasoning. Fukada (8,9) reported brought much closer. a decrease in danping at very high frequencies. Wheth- er this drop was due to shortening the strips is not Short and long term aging of varnished wood is known known; he did not indicate any shortening of his strips to be of some significance. Consequently, testing of though he may have done so. varnished and filled specimens will be initiated as soon as possible and the tests repeated periodically. Fukada also reported danping values to be slightly higher at low frequencies, and by tests in a partial vacuum, he determined that this effect was due to the REFERENCES presence of air. Most investigators, if they dis- l. J.C.Schelleng, "The Violin as a J. Acoust. Aner. , pp. 326-338. Schelleng, "Wbod unpublishedmanuscript, 1965. cussed air danping at all, e.g., Barducci and 3; R.F.S.Heanron, "The Significance Coupling Between and Extension In the Elastic Behavior danping to Wbod and Plywood,"Proc. Soc. (London), 55, pp. 67-80. Pasqualini, have only considered due acous- R.F.S.fleaimDn, "The Fundajrental Frequency Vibration Rectangular Wood and PlywxxJ tical radiation and discounted its influence. We have Proc. Phys. Soc. (London), 1946. pp. 78-92. s- J.T.Drow and R.S.tfcßumey, "The Elastic Properties Wood,: Report No. USD*. Forest found that by considering the danping due to air fric- Products Laboratory , Madison, Wisconsin. tion, 's experiments can be explained. This is 6. E.R.Bell, Peck, and N.T.Krueger, "Modulus Elasticity Wood Determined by Dynamic Fukada Report No. Forect Products Laboratory, Madison, Wisconsin. part of a recently initiated theoretical investigation 7 I. Barducci and G. Pasqualini, "lteasurement the Internal Friction and the Elastic Constants up the threshold frequency of shear which Wood," Translation from Nuovo 5, pp. 416-445. of danping to E. "The Vibrational Properties Wood" J. Physc. Soc. Japan, 5, pp. 321-327. offers some promise. We have not yet gone beyond the 9! E.FUkada, "The Vibrational Properties Wood J. Physc. Japan, pp. 417-421. 10 F. Kallmann and H. "Dynamic Measuranent of the Damping Capacity and" Elastic Properties ' threshold to incorporate shear. Fukada also presented Wbod (Dynamische h-fessung der elastischen Holzeigenschaften und D-mpfung), English Translation a the results of a theory danping which indicated close report the Institute Wood Research and Wood Technology the University of Translated by the Research 40 E. 23rd New the Forest agreement of theory and experiment, unfortunately, his Products Laboratory. presentation was very sketchy although he did indicate v and the Resonance Spruce Newsletter N0. Catgut flcoustical Society, 1972, pp. 10-16. the considerationof non-linear viscosity. I doubt this 12 F. Kruger and E. Rohloff, "Über die innere Reibing yon Holz (Ch the Internal Friction Vfood)", Fur Physik, pp. 58-68. is necessary and his omission of shear makes me more in- v V. and E. Skudrzyk, Properties J .Acoust. ,46,1969,p.124 (Abstract), clined to question the result. w R.C.Tang and N.N.Hsu, "Dynamic Young's Maduli Wbod Related to Maisture Wood 5, pp. 7-14. 15 and Antonio Stradivari, Hia and Work. Dover Pi&licaticns.lnc.New dependence of danping on temper- 1963 (First publishedin 1902 by W.E.Hill and Sons), pp7Ts9^lsd. We have observed the Schelleng, ''Acoustical Violin J. Acoust. Amer., pp. 1175-UB3. ature and humidity. Tang and Hsu, testing poplar and 17 H. "Regarding the Quality Violins and a Scientific Basis Violin oak (14) , and Kollmann and Krech reported experimentally J. Acoust. pp. 817-822. determined relationships between danping and the mois- Support for this work was provided by the National Science Foundation under Grant No. ENGR74-19873. finish, Circuit," Soc. 35, 3, 1963, J.C. for Violins," of Shear of 1943, of of Plates," 58, of 1528-A, E.C. of of Methods," 1977,USDA of of Cimento, 1948, Fukada, of I," 1950, of II," Soc. 6", 1951, of Krech, of from for of of Munich,1960, Infomntion Service, St.,tlewYork, York, for GheluEziu Beldie, "Cn Characteristicsof Wood," 17, of Zeitschrift 110,1938, Sakurai "Scoustic of Wood," Soc.Atrier. of Content," Science, 1, 1972, W.H.Hill, A.F.Hill, A.E.Hill, Ufe York, J.C. Effects of Varnish," Soc. 44, 1968, Meinel, Sound of for Construction, Soc.Amer.,29, 1957, 11 A VIOLA WITH ELECTRONICALLY SYNTHESIZED RESONANCES was made as inconspicious as possible, and bat- tery operation eliminates the need for a power Sterling Gorrill cord. Physics Dept. Hofstra University Hempstead, New York The instrument started as a viola with 15# inch body. A hole was cut in the back to This is a progress report for a program mount the 5" speaker (fig. 1). The speaker is started in 1972 with the principal objective of mounted off-center so that its weight is ..mostly finding a useful definition for "fine tone" or over the player*s left shoulder. The top and "quality" in a viola or violin. We talk about back plates were brace extensively to suppress "fine tone" or "quality", and we recognize (more both the normal acoustic radiation and the or less!) when we hear it, or play on an instru- possible feedback from the speaker to the strings. ment that has it. But at present we cannot really The bracing reduces the output (with amplifier describe it. Our judgement is effected by the off) to roughly 20 DB below normal volume. The environment in which we hear the instrument, and body of the viola thus serves essentially as only a speaker upon our past training and experience" " enclosure. Part of our judgement of "fine tone" is A special fibre-glass shoulder-rest (fig. 1) certainly based upon past experience. But another was molded to serve a dual functioni to keep part may have a solid physical basis as is the the shoulder from blocking the speaker opening, case with "just" musical intervals. As an ex- and to reduce the sound power radiated to the ample, it is neither a value judgement nor a player's left ear. This ear is very close to matter of experience that two notes spaedd an the speaker. The first attempt to play string octave apart sound "the same, but different". quartets proved the needi ~ the violist thought It is due to the physics of our perceptual he was playing much too loud, and the other mechanism in its response to tones with a freq- players couldn't hear him at all. The shoulder uency ratio of exactly 2il. Again, a perfect rest is completely closed around the back edge of sth from a string instrument sounds smoother the viola, and it does interfere somewhat with than a tempered sth because of the lack of beats. the frequency response of the speaker. The broad peak shown in fig. 5 between 1.5 and 2 KH* At present our subjective feeling as listener provides equalization for this loss of response. or player is the only basis for the final judge- ment of tone. If, however, we do succeed in finding a detailed physical description that gives good reproducable agreement with the sub- jective judgements of fine tone, then we may proceed to determine which aspects are learned and which are inherent. We will certainly have a tool of great value in the whole field of instrument research and development. This project really goes back to John Schelleng's paper (l) of 19&3 in which he suggests number of parallel, narrow band pass, electrical filters might be made to behave dynamically like the many body resonances of a violin. It was quite impractical to build such circuitry in 1963. However, with the availability of IC operational amplifiers, Max Mathews (2; recognized the possibility of building the filter circuits and constructed several success- ful violins. More recently he has built a viola and a cello. The present work is similar in 1, AND concept to Mathews' but different in ultimate objectives and design details. The writer (an amateur violinist and violist) was particularly intrigued with the thought of building a viola. It not only should be suit- able for use in the search for the definition of "quality", but it suggested the practicality of an easily played 15" viola having the tone of a fine 17" instrument. The work to date has resulted in an elec- tronic viola which has been used for solos, son- atas with piano, in recital with a singer, and frequently in string quartets and other chamber groups. When properly adjusted and played with other instruments,it is normaly not recognized as electronic by either fellow players or aud- iences. And it has been complimented for its "quality". If,on the other hand.it is demon- strated by itself as an "electronic viola", then many people feel that it sounds a little "elec- tronic". And the writer tends to agree. The current instrument is the result of many mod- FIG. W7IC7. TRANSDUCERS ifications and was built essentially in its present form in the of spring 1974. Fig. 2 shows the four string motion trans- ducers mounted on the bridge. These produce DESCRIPTION signal voltages proportional to the instan- taneous velocities of the strings relative to It was felt that the instrument should be designed minimize the bridge. Fig. 3 is a functional schematic. to as much as possible any The pole pieces, coils, and permanent magnets prejudice in the subjective judgement of its are this rigidly attached to the bridge. The magnetic tone quality. To end it was designed flux lines are transfered from one pole piece to be as much as possible like a normal viola by in appearance, in to the other the vibration of the steel-core playing characteristics, and strings. This results in a signal voltage from in its sound radiation pattern. The electronics the two series coils horizontal package, carried with a strap due to string over the shoulder. vibration, but zero net voltage from any vert- ical string motion. $35 FIG. VIOLA BACKSHOWINGSPEAKERMOUNTING SHOULDERREST £. S'PRIKO 12 A micropower pre-amplifier in the viola body allows equalization of the signals from VIOLA AND the four strings before mixing and low imped- ance transmission out on a single pair of leadsa Fig. 5 shows a typical frequency response curve The electronics package, 9i" by 8" by 2£". of the viola's electronics including the is shown in fig. k. It includes the driver string transducer but not the speaker system. band pass filters, attenuators, The test signal comes from an audio oscillator, amplifiers, inductance, a summing amplifiers, noise reduction circuits, a series and flux generating coil power Ni-Cad batteries. Tone placed just above one of the string transducers. amplifiers, and the rate-of-change quality can be modified by variable Q adjustments The of flux is held constant each of the and over the test frequency range so that the volt- and attenuators on 26 age output by 6 "master" attenuators each of which control of the transducer should be constant. output are The signal to the recorder is the voltage at the summed of four filters. There the terminals. thus a total of 58 tone controls! A socket speaker accepts a second plug-in set of "master" atten- . , _. uators (either pre-set or adjustable), and an r EjEiE :t|-i^i-.L-ir{^L-...r:i:. -. t.[_ |.:j- jr-pf-j :^£t.T_Ld—i~ | A-B switch allows quick transfer between the plug- . . !IT_EIB E3ClElBi33i.BLp;BCE.'B.E~'. j 8'" "I J . J3"T8'83~.88. 3 -L in set and the wired-in set. -E;.EE|p£pp Ejpp- -pJ£|EEpp: EX JE.-" (- -_| .-j P"|jfe p)'-: E.-ji3-__- ; The batteries provide about four hours play- E i"EE!~-|E.iE3E/\:'-- ; : yPiEFEIEJr EjB.--j-" i" ..;E3iElE' ■ A "- EE3JE j-jEiir.-EEj ing time between recharges, and the power amp- r— t 1 83 j A*: l:;-:\ >_ 1. -:;:.! _.! I; ; A* -E.l-zi: i ■-"[ ..:-. lifier give about 15 watts peak into the 8-ohra I\~f\ ! ::j '""''■ 'ELijwnk-ELJ (\J \ I /U\A ' M A/VY ' speaker. This power rating is required because [~*°3r* I: T j£j\i./i-.:"' ■■■■ \ 'i'-' 1 -i-' j /j' "■'-'■'■ r B '': : ~ \/J. j: \-\~ t tfre-T^raTdrex-^ave^orm^^^^ ~ !""T v—"!^'^"' — high peak relative to RMS voltages. Much less :~;.;r"!ZJLXIX^—^II / I._;1 ._; | !rt_T\\ : i-j-'EJ-f \f\ \f\ yY 3 v!>l'l power would give adequate volume level for most _-..'" I j ! b : : Lp—E>>-' :-1/ \ j : j ~ |—Jl^^wl-—~.—I— /^/\''" playing but would not handle double stops or - |_: j "\j\ j '\'-''< -j j -EtE-i E .--ifj8 L ..; .i -1 i i kpi-!. j-| \> percussive transients. —y/—f! .V4 l | 3 j"" 1: tTT—-~r?*j ' j 'L-Ci-.j j ; . IV- aJLjLIJjLLjL : ! L'; : j : ! TESTS AND RESULTS i- 1 li ' IJ» ' < L i '^J"f'"'. 1 . I J The adjustment of 58 tone controls presents even so because the goal is As with normal violas, different makes of a problem more different tone poorly defined— and based upon subjective judge- steel core strings gave qualities tested). Room ment. One starts by setting the filter (band (7 types of C-strings were acous- widths), the center frequencies, and the indiv- tics affected tonal judgements, and listeners produce an overall fre- did not always agree with players. The final idual attenuators to be quency response curve similar to some previously and most critical test has always proved to a normal instrument. However the playing with a string quartet. Frequently measured curve from satisfactory no two of the many methods of measuring frequency tonal adjustments which seemed quite response on normal instruments give identical relative to the test instrument proved entirely results, and all will differ somewhat from the unsatisfactory with the quartet. However in method necessarily used with the electronic these cases the trouble was always corrected there is no point in attempting any with minor readjustment. In contrast, playing viola. Thus very precise match of our frequency curve to that of viola by itself or with piano proved some exceptionally fine normal viola. After the tolerant of a wide variety of tonal adjustment. must be largely The main volume control setting also showed initial setting the proceedure very trial and error toward optimizing the tone. this tolerance for solo playing, but was "optimum" tone is unknown,we started critical for quartets. If the volume is set But since violist to by simply trying to match our tone to a stan- too high the automatically tries particular 16 inch instrument, play softer. He finds himself using pian- dard a 3/^f technique produce well known— and liked by a number of violists. issimo bowing to a mezzo forte he becomes very unhappy! The volume The adjusting process proved almost will be—corrected to mezzo fort, but the sound impossible until an A-B circuit was installed, will be wrong because of the light bowing. This circuitry provided two separate sets of master controls with a switch to allow rapid The electronic viola has been played comparison of the two corresponding tone mostly with its own internal speaker, but qualities. Thus tonal judgements were re- larger external speaker systems have been duced to the simple question of "which tone used for some test and demonstrations. The A, or tone B". In practice small internal speaker has a limited range is better tone from a fairly good— tone adjustment, A, was left and a response curve which is far flat. many B tones until one The lack of flat response is easily equalized, fixed and comparedto but of the B tones seemed definitely superior. by use of the filter attenuators, is Then that B tone was transfered to become the bothersome because of the increased demand new fixed A standard for comparison to a for peak power at some frequencies. The newer series of B tones. With this test pro- limited range, was satisfactory ceedure it has been quite easy to closely simply because normal violas have similar approach the quality of the test instrument, ranges. But both ends of the range proved but never, with the equipment built to date, interesting. to make the tones indistinguishable. FIG. ELECTRONICS BATTERIES filters, ■ ■._ " ■ ;.-■; '' ■ ; ' " ' ■ ■ Q's however, 13 It appears that the radiation pattern One entertaining feature of the electronic in the high frequency region is much more cri- viola is that it allows the violist to play tical for a violin or viola than for normal duets with himself! Recordings can of course reproduction of music. Listeners in the be made with a direct wire from the elec- on-axis beam of a typical external speaker tronics package to a tape recorder. This were apt to find the viola sound very "edgy" eliminates the distortions inherent from and "electronic", but natural and satisfying studio acoustics and the use of a microphone. at 60° off axis. For almost any playing For a duet, one part is recorded and then played environment it appears that the high fre- on the floor, quency pattern back not through the big speaker radiation should be fairly but instead through the amplifier uniform for at least the frontal viola's own 270°. and internal speaker. At the same time the part through viola is apt to have air violist can play the second the A normal 17" its speaker all right under at about Hz and will typically same amplifier and resonance 215 his own chin! Balance of tone— can be essen- have three wood resonances spaced at still "togetherness" lowest very close tially perfect, and the sense of lower frequencies, the being is unique it far exceeds the to Hz. These lower resonances radiate rel- for the player 145 excitement of any of the —duet schemes recently little acoustic power but do prove atively to in "Strad". be very important. The electronic viola was discussed the originally set up without them in the erroneous CONCLUSIONS belief that the "air resonance" was the lowest of real importance. It had an unconvincing It has been shown that a practical small C-string until the three lower resonances were size viola can be built with essentially the added. tone of a fine large viola by substituting battery operated electronic circuits and a The small speaker in the viola gives loudspeaker for the wood structure of a normal reasonably flat response down to 180 Hz. viola. When played in chamber music groups Though it then falls off at 12 DB per octave the tone quality is not recognized as diff- its low frequency response is probably more erent from that of normal fine violas. When than adequate for simulation of a 17" viola. played as a solo instrument the tolerance to It is easy to set too much gain into the lower increased volume level and bass response filter channels resulting in a big deep sound, suggests use for recitals or for viola concert!. but not a true viola tone. Nearly all violists become excited at the possibility of having The difficulties of performing useful tests a much bigger C-string. But they really dont with such a large number of variable tone con- want it when they hear it particularly when trols have suggested modifications to the in- played with a string quartet.— strument and its electronics. The modified equipment, nowunder construction, should bring When an external speaker system with good us much closer to the definition of "fine tone" response down to 70 Hz is substituted, the change or "quality". In the revised equipment, design is dramatic. It is not only that the fundamental compromises in the original amplifiers and can be heard for the first time with full power speaker system will be eliminated, the provision on the C-string, but there is also a marked for A-B testing will be greatly expanded, ___ change in apparent quality of the upper strings - ~ and tRe reproducebili.ty of~-tests should b&— where 110 steady state frequencies can be effected much improved. by the bass response. The effect seem due to the change in the transient response. The (1) J. C. Schelleng, "The Violin as a Circuit" starting and stopping of high frequency sounds (1963) can excite the low frequency resonances. J.A.S.A. 2s, 326 cello-like sound but The instrument has a J. Kohut, retains the fast response of the small viola. (2) M. V. Mathews and "Electronic of Violin It is marvelous fun for violists to play! Simulation Resonances". J.A.S.A. 1620 (1973) FINITE ELEMENT ANALYSIS OF A GUITAR SOUNDBOARD The equations defining the modes of vibration of a plate can be written, but H. L. Schwab the exact solutions exist only for a few simple geometric cases. However, if the structure (soundboard) is represented by a The primary concern of the Catgut Acous- collection of "elements" of finite size, tical Society is that of studying and developing the equations have an approximate solution. musical instruments. Most of this work has The set of linear second-order differential been accomplished using semiemperical techniques equations defining the vibration of a finite during an instrument' s construction its compon- element model can be written in matrix form ents must be tested several times to ensure as: that the finished instrument's response is correct. The ultimate goal is to be able to [ra] lx> + W fourth - 574 hz (Figure 5) and fifth - 623 hz (Figure 6) . These five modes agree very closely with those obtained by K. A. Stetson for another Torres-braced guitar soundboard using laser holographic inter- ferometry, even though the geometrical dimensions and wood properties were not identical. Further work is now being conducted in the adaptation of existing computer programs to guitar soundboard vibrations. This work will be published in the next issue of the Catgut Acoustical Society Newsletter. Ultimately it will be possible to theoretically create an instrument with the desired response. . .and then build it. *Hurty, W. C. and Rubenstein, M. F., Dynamics of Structures, Englewood New Jersey: Prentice-Hall, Inc., 1964. The author would like to thank Dr. K. Chen for his invaluable help in the prepara- tion of the computer program used for this work. Figure 6. Fifth Mode Vibration ; Cliffs, C, of 16 ANALYSIS CF TONES FUCtI AUTOMATICALLY BCKvED VIOLINS — S.J.R.Higgs, L.J. Parsons and P.D.Townsend Scliool of Mathematical and Physical University of Sussex, Brighton, BNI England INTRODUCTION RESULTT Quantitative attenpts to characterize the performance our pcwer we been made In early measurements of the total emitted of a violin in terms of the many variables have the familiar of resonances, as shown pro- found spectra major in a variety of ways (1-5) although in essence the in figure 2, These three examples are for a pleasant toned blem is irerely to play a violin in a reproducible fashion violin by (1779) , a very modern instru- spec- Beretta inexpensive and analyze the intensity of the emitted frequency ment and for contrast, a quarter size violin made by Hill. tra. Value judgements as to "good" or "bad" tone can then As expected the full size instruments show resonances near be compared with these spectra and desirable features iden- the open string frequencies with the high quality instru- tified. Previous work indicates that "good" violins have ment producing stronger resonances. An interesting feature two principal resonances at approximately the frequencies of the Beretta spectrum is an unexpectedly strong resonance of the A and D strings. An additional resonance, which is near the B flat on the G string. (We do not know if this possibly a subharmonic of the A, is also noted for many in- is a fundamental or a subharmonic of a higher note, but struments. However, the method of determining these res- from the relative intensity of B flat resonances we suspect onances has varied. Alternative methods range frommanual it is a fundamental). In normal playing a "buzzing" sound bowing to mechanical or electrical excitation at a single had appeared at this note and since it was previously ab- frequency. Subsequent measurements then record the total sent, and is still sensitive to humidity, one suspects that power or the power at each frequency. it is a crack. The analysis chanfoer has not yet been used to localize the fault although this is clearly a potential Whilst the response of the violin is essentially linear use for it. with the applied driving force under normal playing condi- tions there can be problems of non-linearity from the bow The modem violin tested here had the usual resonances to the string. The response of the instrument may there- near the D and A string frequencies but their relative am- fore be influenced by the method of excitation. (This is a plitudes differ from those in better violins. If one es- pessimistic view and one generally expects such artifacts timates the position of the air resonance for the k size to be fairly minor) . In order to simulate normal playing violin by assuming the box is a Helnholtz resonator, then conditions as closely as possible we decided to reproduce the stick-slip action of the normal violin bow. Manual bowing at constant speed, pressure and position is re- markably difficult and impractical for prolonged experi- ments. We have therefore devised an automatic bowing sys- tem and having achieved reproducible control bowing pres- sure, speed and position and are able to analyze the sounds which are produced. For a particular selection of the variables we can then construct a three dimensional display of total emitted power and emission spectra for each note played on the instrunent. The result offers a characterization of a particular violin as is obvious from the previous published data. (1-5) . EKKKIMIMtAL MKIHUt) A sketch of our experimental apparatus is shown in fig- ure 1. The chamber is a 4 ft. cube of \rood lined with waffle foam to minimize sound reflections. A bow is held G A B 0" F A B C« D" F 6 A B D« F G A B C" 0" F Fig. 1. Apparatus used for tone analysis Fig 2. Total intensity curves for three violins, a Beretta and a quarter size track and is of 1779, a poor modem instrument in a counterbalanced frame running on a Hill violin driven by a variable speed reversible motor. The bowing velocity is controllablebut for the data reported here only a single bowing rate was used (approximately 50 cm/ , distance from the bridge and the the frequency is increased as the resonant frequency is sec) Bowing pressure this the rise would "finger". select a note are all set manually before proportional to (/olume) - .%. In case to a strong analysis of a particular note. A microphone is positioned be from the usual C#4 to fy and indeed there is in the box and the signal is fed to either a tuned arrpli- resonance at this frequency. fier, a total power meter or an oscilloscope with facility and In our later experiments the automatic bowing system for frequency analysis. A loudspeaker, oscillator is now for tuning and the amplifier provided reproducible conditions so it possible to frequency counter are used analyze the emitted frequency spectrum in detail. For gain was always tested at a single frequency. The chamber the spectra changed these exploratory experiments we have studied the poor is not anechoic and because observed modern instrunent, and as exanples the emission curves cf as one moved the relative orientation of the violin and The bowed string (6) used a constant position with the the open strings are shown in figure 3. the microphone we should (7,8) a series of harmonics which de- microphone 60 cms above the bridge. The violin was sup- generate the chin iest crease in intensity so that the anplitude of the nth is ported on cushioned clanps placed to simulate observed spectrum is the the on a second cushioned pad. only 1 the fundamental. The and support, scroll rested produßt of this series and the frequency response of the S.R.Coates, Sciences, 9QH, C" G C" t CO z LU z UJ > -J cr FREQUENCY KHz Fig." 3. The spectra of the open strings from tie modem violin bowed at 30 qms at 3 cms from the bridge assembled instrument ( figure 2) . "Since the hi^i fre- quency response of this violin is essentially featureless the spectrum generated by bowing the E string resembles the overall response. This string pattern is less obvi- ous for the A and D strings. However the G string re- sponse needs special conment as we see that the final spectrum of notes scarcely included any power at the fundamental. Psychologically this was a surprise as wtei playing the instrunent one assumed the presence of the G. Praur^lyJ^cause^j^ differences generated by the ear fran the harmonic series provide a fundamental for the brain. Indeed in the hind- sight of the recorded spectrum we became more conscious of the higher harmonics generated by this string! This ex- anple clearly demonstrates the difficulties in making aural judgments of violin tone. The result also indicates the need to take into account the method of analysis when conparing the response of dif- ferent instruments. The advantage of this particular meth- od is that it produces a response curve of a violin which is being excited by normal bowing. In our studies of the effect of bowing pressure and bow position we also found that the ratio of harmonics to a fundamental can vary considerably. Figure 4 shows exanples of changes produced on the G and E strings for bowing pres- sures of 40 or 100 qms at 1 or 6 cms from the bridge. The 100 gm pressure is near the upper limit for a musical tone from the E string at the 6 an position. The general trend of our results is in agreement with Schelleng, for example, the total emitted power decreases with distance from the bridge for a chosen bowing pressure. However, our observations showed that the relative inten- sities of the higher harmonics is conplex and they do not necessarily decrease with distance from the bridge. Con- sidering the nunber of variables involved differences be- tweenresults frcm different instrunents are inevitable. CONCLUSION FREQUENCY RELATIVE TO THE FUNDAMENTAL r. v v our experiments show that violin tones generated by a Fig. 4. Variations in emission spectra produced by changes in simple automatic bowing system can give reproducible data bow pressure and position at a constant bowing speed f" «» used to separate the effects of different var- iables. Further data from such simple apparatus might lead to diagnostic skill in violin repairs or manufacture References or be the basis for quantitative assessments of tone quality 1. "Recent Work on Violins" J. Acoust J.Meyer, An Acoustical Method of Violin Testing" Soc. Amer. 25, 491, 1953. ' CAS Newsletter 23, 2, 1975. 2. 6> 8 - 1 Im ilne Avera e H.M.Meinel, "Regarding the Sound Quality of Violins i"} *? * " 8-T g sPectra *» Critical and a Scientific Basis for Violin Construction* Bands for Analysis of Conplex- Sound Sources in J. Acous. Soc. , Reverberant Roans" C.A.S. Newsletter 22,9,1974. Amer. 29, 817, 1957. C. 3. C.M. Hutchins, "The Physics of Violins" Scientific Schelleng, "The Physics of the Bowed String" Amer. 78, 1962. Scientific Anrer. 230, 87, 1974. 207, Cremer, 4. "Instrunentation and hfethods for Violin "The Influence of Bow Pressure on the Testing" Journ. Audio Movement of a Bowed String" C.A.S. Newsletter Eng. Soc. 21, 563-570,1973 18, 13, 1972. ruiNu^mciNiflL 8° F.A.Saunders, " C.M.Hutchins, 18 A NEW TYPE OF VIOLIN DRAWING — Ake Ekwall In addition to the instrurients which were looked in that article I have now worked out a series of chil- In an earlier article (1) I gave a brief account of drens1 violins (six in all) with principal dimensions my discoveries concerning the principles governing the according to the recormendations of Konrad Leonhardt(2) . design of the instruments of the violin family during The proportions of these mstruments differ a great deal the classical period. My theories about violin design from those previously considered normal for childrens meant that the leading violin-makers a hundred years instrunents . It is no longer a question of simply re-' before Descartes, in the 16th century and even earlier ducing in scale a full size violin but we are now con- had carried out similar mental feats as Descartes , and cerned with a set of instruments initially intended to then embodied them in sounding wood - a geometric sys- be. optimum for the use of children of differing ages. tem which it is nowadays possible to computerize. Table 1 X « the distance of the cross section from the lower end of plate H « the height of the section R » the sections convex radius Following figures give the distance from the centre line to the contours (Z » 5.0, 7.0, 9.0 etc) of the section concerned. V J 1/16 269 158/53 85/137 129/213 H= 12.9 (Type A) 3= 5.0 , 7.0 , 9.0 ,etc MDULD TEMPLRTE « FORMBRETTSCHRBLDNE « measurements arching. FORHBRRDEnRLL Masse Gewclbung. valimingsnidtt. X= 40.0 H= 6.4 R= 447.1 35.0 X= 50.0 H= 7.7 R= 388.8 45.6 23.0 X= 53.0 H= 8.0 R= 372.4 47.5 27.9 X= 60.0 H= 8.8 R- 335.0 507F 35T1 = X= 70.0 H= 9.9 R= 281.5 52.1 40.1 22.1 X- 80.0 H= 10.7 R= 224.6 50.4 40.8 27.9 X= 90.0 H= 11.5 R» 161.0 45.1 37.6 28.0 12.1 X«= 100.0 H= 12.0 R- 116.6 39.9 33.9 26.4 15.5 X= 110.0 H= 12.5 R- 91.7 36.2 31.2 25.0 16.3 X=. 120.0 H- 12.7 R=- 77.8 33.9 29.4 23.9 16.4 X*= 130.0 H= 12.9 R- 71.2 32.6 28.4 23.2 16.3 X«= 137.0 H- 12.9 R« 70.0 32.3 28.1 23.0 16.2 X= 140.0 H= 12.9 R» 70.3 32.3 28.2 23.0 16.1 X» 150.0 H= 12.7 R- 75.1 33.2 .28.8 23.4 16.0 X= 160.0 H= 12.4 R= 86.9 35.2 30.2 24.2 15.7 X= 170.0 H= 12.0 R= 109.1 38.4 32.6 25.3 14.6 X= 180.0 H= 11.4 R= 139.6 41.8 34.7 25.7 10.4 X* 190.0 H* 10.7 R« 169.0 43.3 35.0 23.6 X- 200.0 H= 9.8 R* 197.9 43.2 33.0 17.4 X- 210.0 H= 8.7 R= 227.5 41.1 28.1 X= 213.0 He 8.4 ft- 236.7 40.0 25.7 l/IB VIOLIN Z6S ISS/53 BE/ 1 37 129/213 CORNERS « ECKEN HORN VARIANT S Ii X* 220.0 H- 7.6 R* 258.4 " 36.3 17.0 X- 230.0 H- 6.2 R* 289.5 26.6 Copyright by the author and printed with his permission. $t VIOLIN g Back, of Boden, fur Botten, ■ 19 l/IS VIOLIN " 289 ISB/S3 BS/137 123/213 " VRRIRNT L I The tables of measurements for countersink templates to- gether with the radii and heights from the arching tables can be used to draw up section templates of the traditional sort if required. They can however also be used for counter- sink templates according to figs 8& 9. In which case separate , relatively short radius templates for convex arching is used. In type A, back, the longitudinal curve, fig. 6, con- sists of the part circumference of a single circle, and in type D, belly, it consists of two part circumferences of circles with radii R and r with a joining straight line, fig 7. Sizes I and J indicate how long from the plate's The countersink system above is valid also lower edge the straight line begins and ends . (Table 3 & 6) . at lower and upper ends. 20 1/16 1/16 269 153/53 85/137 129/213 158/53 85/137 129/213 H= 13.4 D)Z= 5.0 7.0 B= 12.9 (Type A) KU 1.25 E2- 2.0 (Type , , 9.0 ,etc Belly, measurements arching measurements countersink templates, __asse Gewolbung. Masse fiir Hohlkchle-schablonen. vslvningsntitt. X Q T H X= 20.0 H* 5.1 R= 400. 1 9.3 Alt. 1 53.0 64.4 69.4 8.0 9.6 3.0 0.5 2.5 3.3 X= 30.0 H« 7.4 R- 345.2 90.0 17.4 55.3 11.5 ■ 3.4 40.6 16.6 137.0 5.8 38.3 12.9 4.2 " " " 3.3 170.0 lola 46.7 1210 "» " " 3.4 x= 40.0 H= 9.3 R- 308.4 213.0 38.6 56.7 8.4 7.8 » " "3.33.3 51.4 37.7 13.8 E 66.6 12.9 9.7 """ "n 3.4 c 66.6 12.9 9.7 n n n 3.4 X= 50.0 H= 10.8 R= 278.1 " " 56.7 46.1 32.0 Alt. 2 53-0 86.4 67.9 8.0 11.1 3.5 0.5 3.0 4.0 90.0 22.2 55.0 11.5 n "4.0 X= 53.0 H- 11.2 269.4 137.0 7.1 37.8 12.9 4.7 ■" 3.9 57.6 47.6 34.6 11.3 170.0 13.6 12.0 « ""4.0 213.0 51.1 55.5 8.4 9.0 " "4.0 X= 60.0 H= 12.0 R=- 249.3 E 86.6 12.9 11.1 " " "4.1 58.8 49.8 38.7 22.5 86.6 12.9 11.1 " " "4.1 " " X= 70.0 H= 12.8 R« 219.0 Alt. 3 53.0 44.0 67.7 8.0 11.3 3.5 1.0 2.5 3.1 58.0 50.2 40.8 28.3 90.0 11.5 54.9 11.5 n "3.1 137.0 3.5 37.7 12.9 4.8 Bn" 3.0 X= 80.0 H= 13.3 183.7 170.0 6.9 45.9 12.0 n n "3.1" 54.6 47.7 39.5 28.9 10.3 213.0 26.0 55.4 8.4 9.1 " " "3.1 E 46.0 12.9 11.5 " " "3.2 X= 90.0 H= 13.4 R= 139.5 " " 47.7 41.8 34.8 46.0 12.9 11.5 " " * 3.2 25.8 10.6 Alt. 4 53.0 60.2 65.9 8.0 13.1 4.0 1.0 3.0 3.7 X= 100.0 H= 13.4 106.0 90.0 15.0 53.9 11.5 ■ "3.7 41.4 36.3 30.2 22.4 9.2 137.0 4.4 37.1 12.9 5.4 " 3.6 170.0 8.9 45.1 12.0 . " "» ""3.7 X= 110.0 H= 13.4 86.2 213.0 35.3 53.9 8.4 10.6 « "3.7 37.1 32.6 27.2 20.2 8.3 E 61.2 12.9 13.2 » " "3.8 61.2 12.9 13.2 " 3.8 X« 120.0 13.4 74.7 " " " 34.4 30.2 25.3 18.8 7.7 Alt. 5 53.0 33.1 66.8 8.0 12.2 4.0 1.5 2.5 3.0 90.0 8.2 54.3 11.5 n n "2.9 X= 130.0 H= 13.4 R- 69.0 137.0 2.1 37.3 12.9 5.2 "n "n n 2.8 33.0 29.0 24.2 18.0 7.4 170.0 4.7 45.5 12.0 "2.9 213.0 19.3 54.6 8.4 9.9 " "2.9 X= 137.0 H= 13.4 67.9 E 34.9 12.9 12.4 " " "3.0 32.7 28.8 24.0 17.9 7.4 12.9 12.4 " . " "3.0 34.9 " " X= 140. H= 13.4 R- 68.1 32.8 28.8 24.1 17.9 7.4 X the distance the cross section from the lower end plate. X- At E and c however values are for the longitudinalsection. 150.0 H= 13.4 R= 72.0 E m lower end, c ■ upper end. For the meaning Q, E, 33.3 29.7 24.3 18.4 7.6 jS-j-X^-Kiy-I-and-ze-Trae-fiBS-e—~Mi X= 160.0 H= 13.4 R= 31.6 36.1 31.7 26.4 19.6 8.1 X= 170.0 H= 13.4 R= 98.9 39.9 35.0 29.2 21.7 5.9 X= 180.0 H= 13.3 121.4 1/16 LIU 44.1 38.6 32.0 23.5 8.3 269 158/53 85/137 129/213 H= 13.4 (Type J» KU 1.25 K2-= 2.0 X= 1?0.0 H= 12.9 R= 141.7 46.6 40.4 33.0 23.1 Belly, measurements countersink templates. liasse Hohlkehle-schablonen. X- H= 12.2 R« 160.7 mitt 47.6 40.6 31.9 19.6 X= 210.0 H= 11.2 R_- 179.2 X Q T E PE3K4TZC 46.6 38.7 28.2 9.0 X= 213.0 H= 10.9 185.0 Alt. 1 53.0 30.5 71.9 11.2 7.1 3.0 0.5 2.5 3.4 46.3 37.7 26.3 90.0 12.3 56.5 13.4 n 3.4 137.0 5.3 33.4 13.4 4.1 "« "n "n 3.3 X- 220.0 H= 10.0 R= 198.1 170.0 8.4 47.1 13.4 . » « 3.3 44.1 34.1 19.5 213.0 21.5 53.2 10.9- 6.3 " 3.4 E 25.8 13.4 6.7 " "b "n 3.4 X- 230.0 H= 8.4 216.5 32.3 13.4 7.3 "» n « 38.2 24.6 Alt. 2 53.0 39.4 70.9 11.2 8.1 3.5 0.5 3.0 4.1 X- 240.0 H= 6.5 236.0 90.0 15.4 55.8 13.4 27.0 137.0 6.5 37.9 13.4 4.6 "n "n 3#c 170.0 10.3 46.5 13.4 "n 4.0 213.0 27.7 57.3 10.9 7.2 " " " 4.0 1/16 E 32.9 13.4 7.6 ■"" "» «" 4.1 269 158/53 85/137 129/213 41.4 13.4 8.3 "" " 4.1 H= 13.4 (Type D) -t. 3 53.0 20.6 70.6 11.2 8.4 3.5 1.0. 2.5 3.1 Belly, longitudinal curve 90.0 7.9 55.6 13.4 IJ n n 3.1 Decke, Langskurve. 137.0 3.1 37.8 13.4 4.7 ti n 3.0 Lock, lSngdkurva. 170.0 5.2 46.4 13.4 n 3.0 213.0 14.3 57.2 10.9 7.3 n fl tl 3.1 E 17.3 13.4 7.8 n n n 3.1 c 21.9 13.4 8.5 n ■ 3.1 B> 13.4 1= 87.8 J= 171.1 R= 281.6 t= 350.1 .t. 4 53.0 27.2 69.4 11.2 9.6 4.0 1.0 3.0 90.0 10.2 54.8 13.4 it n 3.7 Z X 1 X 2 137.0 3.9 37.2 13.4 5.3 n tl A 3.6 170.0 6.6 13.4 « n It 45.7 n 3.7 5.0 19.6 247.3 213.0 18.8 56.1 10.9 8.4 * 3.7 7.0 28.1 237.7 22.7 13.4 9.0 3.8 c n n n 9.0 38.2 226.4 28.7 13.4 9.8 3.8 11.0 51.1 212.0 Alt. 5 53.0 15.2 70.0 11.2 9.0 4.0 1.5 2.5 3.0 13.0 72.8 187.8 90.0 5.5 55.1 13.4 "2.9 137.0 1.9 37.4 13.4 5.1 " " 2.8 170.0 3.4 46.0 13.4 ""n " 2.9 The longitudinal curve cuts each contour-line, at two 10.4 56.6 "n " " points with as Die Langskurve 213.0 10.9 7.9 n 2.9 X-values above. * schneidet E 12.7 13.4 8.5 " " 3.0 Jede Hohelinie, in zwei Punkten nit X-'erten wie oben " n " 16.2 13.4 9.2 " 3.0 angegeben ist. * LUngdkurvan sk ir: varje nivAlinje, 3, i " tvi punkter :aed X-vSrden enligt ovan. VIOLIN VIOLIB 26° of Back, of 3ec>:e, fur Boden, Lock, Botten, mS.tt for h&lkSlsißallar. PK3E4TZC ■ ft- 46,1 7. ft- ft" ■ ft« t%= ft- ■ ft- C m of of fdven of I, P, Xl, ft- VIO of Decke, fur 2C0.0 Lock, for hilkSlsaallar. ft- ft- 3,4 ft- ■ ■ 4.C VIOLET 3.S S ■ ■ ■ Z, Z, 21 THE WOLF TONE ON VIOLIN FAMILY INSTRUMENTS * - A. H. BENADE There has been great interest in recent years among players of wind instruments in a type of sound which has acquired the name of multiphonics. These are sounds which arise under conditions which are abnormal to conventional music as a result of small perturba- tions in the construction of the instrument and intentional introduction of non-linearity into the source of vibrations such as the mouthpiece of the clarinet. The result is that the overtones depart in frequency from the customary harmonic series. The wolf tone, though I trust it can never be used with musical intent, exhibits in the fundamental prin- ciples of its product a close analogy to multiphonics, as Professor Benade points out in the following article. John C. Schelleng P3layers of bowed string instrunents, particularly influence of the detuned first mode so as to give a cellists, are troubled by spots In the playingrange slightly shifted playing frequency of the sort that of their instruments in which it is more or less im- is familiar in the playing regimes of ordinary wind possible to produce a steady tone of good quality. A instruments (whose resonances are almost never in bowed note may suddenly leap upward an octave or give perfect alignment). a rough, pulsating sound whose pitch is close to that of the desired note but which contains strong hints of Raman's studies led him to describe the wolf note the octave, as though it were thinking of jumping into as an alternation of a fundamental frequency tone and what a woodwind player would call the second register. of its octave, this alternation taking place several It is this latter, pulsating sound that is commonly times a second at what we shall call the pulsation known as a wolf note. String players and craftsmen frequency. In 1963 Schelleng provided us with a some- have given a lot of attention to the wolf note because what more illuminating way of describing Raman's ob- of the practical inportance of suppressing or weaken- servation, a way that allows him to demonstrate that ing it, or at least of moving it to a place where notes the phenomenon is consistent with the basic stick-slip ordinarilyused in playing do not provoke it into ac- physics discussed by He_Lnholtz and Raman. Schelleng tion. The wolf note has also received a fair amount points out that the even harmonic components of the of scientific attention, with Raman and Schelleng be- string oscillation run fairly steadily during the en- ing the major contributors to our present knowledge of tire pulsation cycle, whereas the odd harmonics (in- its behavior. cluding the fundamental) appear to grow and shrink mote or less en bloc at the pulsation rate. The perceived Let us begin our examination of the wolf-note phe- switching of octaves is easily understandable in these nomenon with a brief description of the conditions un- terms , since it coincides exactly with the physical der whicti it occurs and of the effect of changes in changes that are taking place. At instants when the bowing pressure on its behavior. The wolf is usually odd partials are of appreciable amplitude, our ears are encountered at places in the scale where the first- presente^withntl^ cci^^ mode frequency of the bowed string is in the general the string modes, and we assign the pitch accordingly. neighborhood of some strong resonance frequency of the At those moments on the other hand when the odd com- body. The so-called main body resonance frequency de- ponents are insignificant, we perceive the even partials termines the region in which the wolf takes place. If in their own right as a tone having its pitch an oc- one uses very light bow pressure to play a chromatic tave higher. scale, the tone is likely to jump up an octave as one gets into the wolf region. Heavier bow pressure gives rise to the characteristic rough sound of the wolf taie; in certain mild cases of the disease, increasing the bowing pressure yet more may suppress the wolfing and produce a more or less normal tone. We have had numerous occasions in this book to rec- ognize that a strong resonance in one part of a two- part system can lead to shifts in the resonance fre- quencies of the other part, the shift being relatively small if the two parts have widely different wave im- pedances, as is the case of a string coupled to the body of a cello. We conclude here that under wolf-tone conditions the instrument's body resonance is able to shift the string's first-mode frequency away from its normal position as the lowest member of a harmonically related set of string resonance frequencies. The oc- tave change arising from the wolf-note displacement of the first-node frequency produces a change analogous to the loud-playing type of woodwind register change. Let us glance briefly at the reason vihy it is some- Figure 1 . times possible to stabilize the oscillation and prevent a wolf by use of heavy bow pressure. At any sliding The top three lines of figure 1 illustrate Schelleng's speed, increasing the bow pressure makes the bow-plus- explanationof how the idealized sawtooth motion at the string interaction more nonlinear, so that the various bowing point of a normally operating string (top line) heterodyne effects become more pronounced. Assuming, can be separated into the parts contributed by the evai- for example, that a dozen of the string resonances are nuribered conponents (second line) and by the odd-nun- available for participation in a regime of oscillation, bered ones (third line) . It is clear from a conparison it may become possible with heavy bow pressure for the of lines 1 and 2 that abolition of the odd conponents upper eleven resonances to jointly control the disruptive leaves us with a double-frequency oscillation that is to be included in the forthcoming book Fundamentals of Musical Acoustics, Oxford Univer- * sity Press, March 1976. 22 otherwise of a normal appearance. The bottom line of tone are all harmonically related and are thereby ad- figure 1 shows the appearanceof the bowing-point mo- mirably set up to generate a set of conponents whose tion during the course of a wolf tone. At some instaits frequencies are even multiples of the string's normal (marked A) when the odd components are of normal playing frequency. If we confine our attention to strength, we find the sawtooth wave belonging to ordi- these even-numbered peaks by themselves and to the com- nary operation of the string. At other times (marked B) ponents that they generate directly, it is clear that the odd components have disappeared, leaving a sawtooth no matter what sort of nonlinearity is present at the whose repetition rate is double that of the normal os- contact point between bow and string, all the hetero- cillation. In between these we have intervals dyne frequencies that are generated among the even- (marked C) during which small amounts of odd harmonics numbered peaks will be themselves menfcers of this same are present, producing a jaggedwaveform which never- collection of even-numbered harmonics.* In other theless is of the stick-slip type discussed by words, these components will be very strongly gener- Hehriholtz and Raman. ated in a stable kind of sub-regime. So far we have provided ourselves with a description of one type of wolf-note motion for a bowed string and have verified that it is consistent with the stick-slip behavior expected of such a system. We have also recog- nized that the presence of a body resonance near the wolf-note frequency is required and that it will alter the first-mode vibrational properties of the string (but not those of the higher modes) . We will now consider the ways in which the complete dynamical system comes to choose the wolf tone as its preferred type of oscillation. Schelleng in his discussion of the wolf note points out that the presence of a body resonance converts the ordinary first-mode string resonance peak (measured at the bowing point) into a pair of peaks. The upper part' of figure 2 shows the nature of the bowing-point reso- nance curve that is found when the body resonance lies below the first-mode string frequency. For simplicity, the string is assumed to be tuned to 100 Hz. Notice that the body resonance has caused the original 100-Hz first-mode peak (shown dotted) to be displacedupward in frequency, while the other peak lies below the natu- ral frequency of the body itself. Notice also that the -dip-between the^air-^fB-peaks-i^^nc4:-as-^ep^-as-the--dips- that lie between the normally spaced resonances of the string. The lower part of figure 2 shows similarly that when the body resonance lies above that of the isolated 200 300 string, the string resonance is displaced slightly be- IHz) low its original 100-Hz position, while the newly added FREQUENCY peak lies somewhat above the natural frequency of the Figure 2. body itself. Let us now ask what happens to the oscillatory con- The essential feature for the production of a wolf tribution of a first-mode peak that is displaced to run note on a bowed string is that there be a strong reso- a little sharp, generating a conponent at 102 Hz.The nance inmediately above or below the ideal position of simplest heterodyne offspring of this conponent and the lowest string resonance relative to the higher modes. the strongly maintained even harmonics turn out to be (3ln woodwinds there is an exactly analogous type of os- of the following type: cillation to which I have given considerable study since it provides a valuable diagnostic tool for the adjustment 102 t 200 = 98, 302 Hz of the conical woodwinds). The presence of the second 102 ir 400 298, 502 Hz member of the 102 + 600 -= 498, 702 Hz pair of peaks is not required for the pro- duction of the wolf, although it can aggravate the wolf- tone tendency if it is placed symmetrically opposite its etc . etc . mate, so that the unmodified (100-Hz) first-mode frequency of the string lies exactly halfway between the two peaks. Notice that each of these heterodyne components lies close to the frequency of one of the odd-numbered res- The physicist lan Firth of the University of St. onance pealcs and so has a reasonable chance of gaining Andrews in Scotland has made a roriber of experimental support from it. Pay particular attention to the 98-Hz studies of the wolf-tone behavior of cellos, some of heterodyne conponent; although it lies in the dip between which he carried out during the sunner of 1974 at the the pair of first-mode resonance peaks, this dip is rel- Speech Transmission Laboratory in Stockholm. Firth's atively shallow, so the is able to confirm that component gain data the general correctness of Schelleng's considerable oscillatory support in its own right. Be- analysis and contain a wealth of additional informa- cause of this help, the conponent can have an amplitude tion. Despite certain apparent inconsistencies in the is quite comparable to those of and Firth's that its higher-frequency data in interpretation of them, his re- odd-numbered heterodyne brothers, which sit on the shoul- sults underlie a considerable portion of my explana- ders of their respective resonance peaks. tions in the remaining part of this section. Here is the first place where we can make a direct mind its of the Keeping figure 2 in with pattern comparison with experience: in the neighborhoodof first resonance peak slightly misplaced and everything 100 else neatly lined up, we can By now make ah analysis of heterodyne frequencies" is meant the new fre- the oscillationpossibilities. Notice particularly quencies that can be produced in a non-linear device that the even-numbered resonance peaks of the string tor example, mp T nq, where p and q are the frequencies or applied tones and m and n are position integers two/, 23 we have a pair Hz found of conponents 98 and 102 Hz In every case we find the of appreciable (but not necessarily equal)— anplitude,— same low-frequency (4-Hz) component and an exact even-harmonic conponent that cm which can beat together. This is exactly what one ob- cooperatewith in a typical tone. its corresponding peak to aid the net os- serves wolf Their joint appearance cillation in a vigorous way. The is roughly that of a pulsating of low-frequency conpo- fundamental conponent nent is low to by player's the sort recognized by Raman and by Schelleng, although enou^i be felt the hands as a pulsation or stuttering of tie bow and perhaps of (contrary to a conmon inpression) it is not correct to the instrument itself. say that the pair of conponents at 98 and 102 Hz is e- quivalent to a single 100-Hz component of fluctuating am- plitude When we combine each odd-numbered conponent with one except in the unusual case in which the two ac- from another pair, the following frequencies tual conponents have precisely equal anplitude. result: 98 298 » 200, 396 Hz We can continue our examination of the descendants of J 302 204, the two noticing that 98 = 400 Hz fundamental components by pairs of 298 t 502 = 204, 800 Hz components are found centered about all the odd harmonics * 100 of Hz—e.g. , 298 and 302 Hz, 498 and 502 Hz, etc. As etc. etc. has been remarked earlier, these pairs will feed them- selves from odd-nuaxtbered the resonance peaks, and in gen- Onceagain we find that exact even are eral one or the other member of the pair will particu- harmonics pro- be duced by each ccmbination, along with something we have larly strongly supported in consequence of the small up- not seen a set of weak ward and downward frequency displacements before— satellites that are 4Hz of these peaks away from the strong even in tone, that are an inevitable consequence of various harmonics the the kinds of fact that even the paired, pulsating, odd partials them- string inharmonicity. These paired components will beat selves give rise to even-harmonic conponents at exactly the same in all 4-Hz rate as does the fundamental pair. their dealings serves to stabilize them by This beating rate is in further with the binding than agreement obser- ever more closely to the more normal oscillatory be vation of Raman, as reformulated by Schelleng and confirmed havior of the even partials. Adding weak - by Firth, that the paired odd partials all satellites to give rise to a these even partials does not make them pulsate very pulsation at exactly the same frequency, regardless of the much, is of since there little chance for a few weak com- accidents placement of string tuning and body resonance. ponents of differing The fact that we do not expect the frequency to gang up simultaneous- members of each pair to ly on the strong central conponent to be of equal anplitude is also in accord with experiment. cancel it out. During the course, of a wolf-tone pulsation, one does not In the preceding paragraphs we have learned how the generally find a total extinction of the odd partials, nor displacement of the first-mode peak in the response does one find the degree of extinction to be the same for curve of a string can give to wolf all of them. bowed rise the tone: an oscillation in which the even partials run fairly steadily (i.e. with weak satellite conponents) while When one looks more closely at the details of the vi- the odd partials pulsate strongly, which is a simple bration spectrum of-a wolf-tone tiiere -are-many com|x»ients way of saying that -they are in fact cons^gueted-oat of present besides the ones that we have listed so far. These two or more conponents of roughly equal anplitude. Since other conponents tend to be somewhat weaker, and more the first-mode displacement (and splitting into two res- particularly their presence does very little to alter onances) depends on the mutual influence of the string the basic behavior that has been outlined—i.e..rea- and the cello body, it is clear that the presence or ab- sonably strong and steady even partials and synchron- sence of the wolf phenomenon depends on the relationship ously beating odd partials. Let us exanine a few ex- between the wave impedances of the string and of the body amples of these less inportant additional conponents, Schelleng studied this relationship and has suggested chiefly with an eye to seeing why they play a minor not only a means for predicting whether or not a given role in the behavior of the string. Here are some of instrument will have a wolf but also the ability to de- the heterodyne conponents that are generated by the vise changes in the design that can minimize its ef- odd-partial pairs themselves: fects. Schelleng's own experimental observations plus more recent ones by many other people confirm the cor- 98*102 = 4, 200 Hz rectness of Schelleng's analysis. 298*302 4, 600 Hz 498i: 502 - 4, 1000 Hz etc. - etc. # ************* **********Height adjustment the cutter is accomplished by ro- tating the hand wheel on the top of the assembly. The Bruce M. Robertson height stop screw and its locking screw are to the right of the hand wheel. (See Figure 3.) 1. Located on the side The machine is comprised two round is the spring loaded screw 1.1 of the which profile reduction head tail holds down the end of the hinged piece, and permits up and down movements drive screw, cutter carriage, limit and drive the assembly ,see figure 2.) motor. Located on the stand under the machine is a con- 1.3 Profile bar: The profile located between the tactor when actuated by the limit shuts front bar and the drive screw, provides means to con- power to the drive and cutter motors. the front trol shape the bow stick being machined. This is ac- the stand are two switches for manually starting or complished by unlocking the seven alien screws and ro- stopping the drive and cutter motors individually. (See tating the seven height adjustment wheels below the bar. Figure 1.) The adjustment wheels are engraved 0 thru 11 clockwise. (See Figure 3.) 1.2 carriage: The cutter carriage consists the motor, cutter counter guard, assembly, cutter 2 the hollow square support guide, the lever engaging . the carriage with the drive screw, and the limit actuator. 2.1 Preliminary setup; (See Figure 2.) 2.1.1 First place the two manual switches on the stand 1.2.1 counter shaft assembly: The counter shaft to position, next disengage the carriage from the assembly is hinged to the right end the carriage so drive screw. the cutter can raise or lower according to the setting 2.1.1 bar: the profile to the the profile bar. This is accomplished by the roller on Adjust bar shape dusired for the as the hinged piece below the carriage, which travels on the bow stick follows: Slide the carriage profile bar. Felt wipers on either side the roller to the rif;ht for access to the first several adjustments. wipe chips from the profile bar. Use an alien wrench and unscrew the seven alien screws in OPERATINGINSTRUCTIONSFORMILLING MACHINE of FOR VIOLIN BOWS DESCRIPTION left bars, way free flat bar, gear stock, stock, of switch, bar, which, switch, way off On of of Cutter of shaft for OPERATION Cutter OFF of of Profile of 24 Figure 3. carriage? X,.1. view the bar approximately one-quarter turn, to unlock the ad- 2.2 TRIAL justment wheels. Rotate the wheels counter clockwise to 2.2.1 Trial Sample: Obtain a straight stick approximate- raise the bar. When adjusting the wheels also loosen ly 3/8 in. square and h in. longer than a violin bow stick. the locking screws. Adjustment settings shown in Table 1 (Soft such as spruce or port orford cedar is prefer- will give the approximate shape as determined from Fetis' able). Carefully using scriber, the exact center book Anthony Stradivari pp 121-124 (Robert and each end with a small punch mark. London 1864). Start on the left hand set the adjust- 2.2.2 Setup: Adjust the tail stock such that when the ac- ment wheel and lock the screw. in sequence, to tuating lever is in mid-travel position, the cup center is set and lock all adjustments. approximately h in. from the end of the sample stick when the other end is touching the head center. Lock the tail 2.1.2 Limit Switch: Adjust the limit switch (microswitch) stock in position with the knurled screw located in the located on the right rear of the by dismounting base. Slide the carriage to the left until the square it the plastic mounting place,right hand and middle guide slides over the tail stock and exposes 3/4 in. of the holes in the plate, and re-mounting the left hand and mid- cup center portion. dle holes in the mounting plate. Then loosen the two screws holding the mounting plate and slide the plate as To set the approximate retract tail stock and far to the left as the slotted holes will allow, then measure the space between the point of the cup center and tighten the screws. The switch position adjustments are a cutter edge. Raise or lower the cutter, by adjusting the essential for stopping the the cutter con- hand wheel and height stop until the desired radius ( h tacts the tip of the bow stick. diameter) is attained. Cutfc&r OPERATIONS. ' CCW, wood, mark, of Cocks Co., end, Proceed, machine, from diameter, machine, before 25 To set the exact proceed as follows: Operate 3. the machine as described in 2.2.3, and turn about two 1. operating, oil all oil cups and pulley shafts. inches of the then stop the drive and cutter During operation, oil the two bars. motors, disengage the drive screw and slide the carriage 2. It be in making bow sticks to remove to the guide clears Measure left until the the stick. the aluminum chip the cutter guard to pre- the diameter with a micrometer and determine the nec- vent interference with the bow tip. change. 3. Since bow sticks are hard wood, It is advisable, To increase diameter, select the appropriate of as a minimum, to remove the corners to make octagonal a thickness gauge, then using the height adjust wheel, cross-section. Make two small saw cuts at right angles raise the cutter until the thickness just slides across the center mark on the tip end to engage the spur under the end of the height stop screw. (See Figure 3.) drivecenter. Also, taper the frog end the stick so Remove the and adjust the height stop screw to the hollow square guide can open and slide easily over contact the base. the stick. To decrease use the thickness gauge, and ad- 4. If the hollow square guide becomes mis-adjusted or just the height stop until the gauge just slides under the to change guides, proceed as follows: Remove the two end. Lock the screw in position, remove the and ro- alien screws holding the guide to the carriage. Slide the tate the height adjust wheel until the height stop screw guide on the tail piece. Move the carriage until the screw contacts the base. holes are aligned, then carefully replace the screws. (See Figure 4.) 5. Keep the machine clean, remove chips from under the MACHINE WITHOUT IN carriage and in the drive screw threads and 2.2.3 Operation: Carefully center the sample stick on the spur center, and with hand pressure sink the spur ap- TABLE I proximately 1/16 in. into the wood. Then slide the cup center into contact with center the pressing it slightly into the wood. I 2 3 4 5 6 7 In sequence, place the cutter switch to the drive 26 29 29 19 I the carriage engagement A 129 25 13 0 switch to then move lever in- A 01 2+12+2+1 2*2)!2)(12+t2*5)!(12M2+5)'12+12*5) 12+12+5)(12+12+1)(l 2-*12+1) (12+7) (12+1)(12+f) to drive position, engaging the drive screw. Hold the 1 tail stock in contact with the stick until the hollow square guide has cleared the tail stock. B IIIi IIS I .11-11- -1212 II-11- II11 7 The machine will stop when the actuator on the car- riage depresses the limit switch. When this occurs, first place both manual switches in the position, then move - the lever on the carriage to disengage the drive screw. A FOR Carefully slide the carriage back to the tail stock while B - POSTS hoidin "the~bow~stickv - * ****** ************* A Violin and a Guitar With Graphite-epoxy Composite Soundboards Daniel W. Haines Carleen and Morton Hutchins Donald A. Thompson INTRODUCTION The use of graphite composites in the construction of stringed instruments was dis- cussed in a previous article fl] . it was shown that the mechanical properties of a composite sandwich plate with graphite-epoxy facings and a low density core successfully matched those of a conventional spruce plate . Figure 1 shows a guitar and violin constructed using the new material for the top plates. Al- so shown are a roll of the graphite fibers and a rectangular plate with the graphite- epoxy facing partially removed to expose the cardboard core. The guitar was a CP. Martin D-28 model. During the construction of this instrument, another guitar, identical with the first ex- cept for its conventional spruce top, was built to serve as a control instrument. We present a comparison of these instruments in this arti- cle. 1. Violin and guitar with top plates of the new composite material. Also shown are the graphite as they By means of tap tone frequency analysis fibers appear before be- and ing bonded with the epoxy resin and a resonance mode shapes, the composite violin rectangular plate compared with panel of the composite with a was its spruce counterpart portion of before and during stages of its the graphite-epoxy facing re- installation in moved to expose the cardboard core. the violin body. This not only gave us confi- dence that a successful instrument could result, but the information was also essential to enable diameter, NOTES Before stick, way may necessary deflector from essary leaf gauge of gauge, diameter, gauge CAUTION DO NOT OPERATE CUTTERGUARD PLACE groove. of stick, ON, ON, OFF FORBOWS FOR SOUNDPOSTS g 26 the new top plate to be acoustically matched with the back and sides of the resonating en- closure. Frequency response and loudness curves of the completed violin were obtained. For both guitar and violin, we relate the subjective o- pinion of musicians and listeners. PLATE DESIGN A composite top plate of constant thick- ness was employed in both the guitar and violin. A wood thickness of 2.5 mm was assumed as a typical value for the guitar top and also a suitable mean value for the traditionally vari- able thickness violin top. The principles of design and fabrication of the composite plate replacement to match a 2.5 mm spruce plate are given in Ref. 1. layer of Hercules Magna- mite high-modulus graphite-epoxy tape, 0.15 mm thick, was bonded to each side of a cardboard core, originally 1.25 mm thick of density 0.594 g/cm^, to produce the composite plate in- 100 200 4-00 ZOO stalled in both instruments . FREUVBHCY ~ H* GUITAR CONSTRUCTION AND TEST Since the purpose of this experiment was to evaluate the new composite as soundboard material, spruce bracing was employed. Braces of similarly unconventional material could al- so have been used but this would have intro- duced more variables than we could effectively evaluate. The only serious difficulty encountered in the guitar construction was the choice of glue to attach the braces to the plate and the plate itself to the body of the instrument. The poly- vinyl glue typically used in guitar construction would not bond the epoxy to the wood, so it was necessary to use epoxy glue for this purpose. To compare this guitar objectively with the control instrument having the conventional spruce top, the frequency response of each to was obtained sinusoidal mechanical excitation 100 too 400 800 as shown in Figure 2. The test procedure was basically as described in Ref. 2 under "Forced FRetoetitY "* tf« Vibration Test" with the microphone placed just only modifica- outside the soundhole. The test Frequency response to sine wave input: a Spec- 2. tion of substance was the addition of a) graphite-epoxy top plate, tracking guitar with tral Dynamics 1018 filter to ensure b) control guitar with spruce top plate. that only the response to the test signal was measured. Comparison of the two curves in Figure 2 indicates extremely close agreement Further evidence of the similarity of the below 300 Hz. This range includes the two im- composite and spruce plates is given in Fig. 4 portant body resonances: the air resonance where the mode shapes, obtained by holographic above 100 Hz and the wood resonance just just Hz interferometry, are shown for the first five below 200 Hz. A strong resonance at 373 in shapes comparatively weak resonances. Both mode and corresponding the control instrument was frequencies are in close agreement. Mode 5 is in the instrument with the new composite top. been the "ring mode" which corresponds to the strong The reason for this difference has not resonance of the tap tone. These interfero- determined. grams were obtained by Dr. Karl Stetson. F-holes were cut in the composite plate VIOLIN CONSTRUCTION AND TESTS and a conventional spruce bass bar was attached with epoxy glue and tuned with modern tech- The composite violin plate was formed to restore the ring mode [4] A conven- had a rather niques . over an available rigid mold which tional maple back was prepared with a purposely low arch. A higher arch would have been pre- compos- low arch to be compatible with the top. Its ferred, so in this sense the resulting tap tone frequency was 298 Hz, lower than that ite violin plate was less than optimum.. How- top (337 Hz) [3], for the after installation of bass ever, it did possess a clear tap tone bar and f-holes. Normal construction practice indicating its strong potential as an accept- of the violin was observed except for the omis- able violin top plate. Further verification sion of purfling at the edges of the plates of the plate's suitability is offered by epoxy glue to analy- and the use of attach the com- noting the similarity of the frequency posite top plate to the maple ribs. sis of this tap tone (Fig. 3a) with its counterpart in a well- tuned spruce plate The frequency response to sinusoidal ex- (Fig. 3b) . This analysis was obtained as citation of the unvarnished violin is shown in described in Ref. 2 under "Impulse Test" with Fig. sa. Shown for comparison is the frequency the microphone placed one plate length from response of a highly valued 18th century Italian the center of the plate. The plate, suspended violin (Fig. Sb) . The test apparatus employed within a frame by means of four stretched electromechanical excitation at the bridge with rubber hands, was tapped at its geometric cen- the sound field detected by a microphone placed ter. The strong resonances at 328 Hz in the one body length from the top [ s] . In each composite and 340 Hz in the spruce determined curve, the strong peak close to 270 Hz indi- the pitch of the tap tone. cates the air resonance; the wood resonance is indicated by the peak near 400 Hz. One 27 3Z6 \ is shownsi in Fig. 6. The other loudness curve in Fig.F: 6 was obtained from a conventional high-high-quality violin (SUS 29) . It is evident that the new violin with the composite top plate (SUS 184) has a loudness curve very simi- I a W J[ lar in: shape but with lower overall amplitude. 0 1000 4000 1000 10000 10000 20000 3. Frequency response of violin top plates to FREQVEUCyfHi impulse input (tap tone) : a) graphite-epoxy composite, 5 Frequency response of violins to sine wave b) unvarnished spruce, well-tuned. input: a) Violin with graphite-epoxy top plate, SUS 184, ARCHEDVIOLIN PLATE MODES b) High quality old Italian violin. GRAPHITE-EPOXY SANDWICH SUBJECTIVE 80 142 237 260 327 Both the guitar and violin have been re- ceived veryfavorably by musicians and listen- ers. Numerous judgements established their sound to be indistinguishable from that of fine instruments made with conventional materials. Most agree especially for the violin that these are dark-toned instruments indicating a dominance of lower partials for a given tone. This has been confirmed for the violin by com- paring the frequency spectrum of bowed tones on SUS 184 (composite top) and SUS 29 (convention- al construction) . The analysis was performed on a Spectral Dynamics 330 A real time analyzer. it< iti m This dark quality of the sound may be due to II % the fairly high along-the-grain damping in the composite above 2000 Hz [13. Just after construction, the new guitar was compared with the control instrument. The 80 140 253 . 257 334 two were judged equal for scales, but chords were superior when played on the control guitar. SPRUCE This might be attributed to the stronger reso- nance noted at 373 Hz in the control instrument. 4. Mode shapes obtained by hologram interferom- etry. In addition to its pleasing tone, the vio- lin is judged to have very uniform response throughout its range and to speak well. It a a obtained by does not appear to have the power desired in Finally, loudness curve hand instrument (see 6) Perhaps this bowing [ 3] verified the air and wood resonance concert Fig. . new violin be located the open D is due to the higher along-the-grain damping of the to near graphite-epoxy composite (294 Hz) A (44 Hz) strings, respectively, of the or the lower and 0 typical which is consistent with the findings for many than arch in this violin. high-quality violins [ 3] . This loudness curve l.oeoO TESTS 28 ACKNOWLEDGEMENTS The skills of Donald Dech and Frank Kern, who constructed the guitars at the CF. Martin Factory, were crucial for the success of this work. Thanks are due to John Schelleng and Nagyoung Chang for helpful discussions, and Karl Stetson for the holographic interferograms. The composite plates were fabricated by Hercules Inc. under the supervision of Stan Cross. Grants GK35913 and ENGR74-19873 from the Na- tional Science Foundation partially supported this work. 1. Haines, D.W. and Chang, N. , "Application of Graphite Composites in Musical Instru- ments", ASME Paper No. 75-DE-27, also 6. Violin loudness curves with resonances mdi Catgut Acoustical Society (W) prime Newsletter, No. cated: air (A) , wood , and wood 23, May 1975, pp. 13-15. (W ) . Haines, CONCLUSIONS 2. Haltiwanger, M.A. and D.W. , "A Study of Body Resonances and Their Influ- Two stringed instruments, a violin and a ence on the Performance of a Folk Guitar" , constructed with graphite- Catgut Acoustical Society Newsletter, this guitar, have been issue. epoxy composite top plates instead of the usual Tests indicate that these instruments spruce. 3. Hutchins, C.M. , "The Physics of Violins", are very successful. Unlike wood, the new reproducible and stable Since * Scientific American, Vol. 207, No. 5, Nov. composite is . 1962, 78-93. the replacement of spruce soundboards has been pp. regarded as perhaps the most challenging prob- instruments, 4. Hutchins, CM., "A Note on Top Plate Tun- lem in the development of non-wood Catgut Acoustical Newsletter, an step ing", Society we feel this work represents important No. 21, May 1974, p. 11. toward the ultimate goal. It now appears possi- ble that fine instruments for student use can be Hutchins, materi- 5. CM. and Fielding, F.L. , "Acousti- constructed entirely of this and similar cal Measurement of Violins", Physics Today, als. Vol. 21, No. 7, July 1968, pp. 34-40. _ *..__* _*_.._____*_ j»_ _ _ _ _ *_ *_l_*__# *__jfc__Jt-.--Jt__jf_-ji JL. » . J * ».. * * m- — —*— .». — - - The discussion of the wolf tone which appears elsewhere in this issue will be included in the forthcoming book MUSICAL ACOUSTICS by Arthur H. Benade. This book is addressed to readers having some knowledge of music who wish to learn something of how music is related to our current understanding vibrating objects, auditory perception, and the instrument maker's craft. A secondary purpose of the book is to show how a practicing scientist actually about chopping his through the underbrush toward a new and how he develops his under- standing uy intuitive leaps, alternating with careful returns to solid ground. The organization of the book is dominated by the need to resynthesize musical acoustics in the light of recent data and their interpretation. The author's experience in perfecting musical instru- ments for performers and manufacturers gives the book a practical flavor which is enhanced by the fact that almost all it has benefitted John Schelleng and Virginia Apgar rehearsal in both written and lecture before October 14* 1973 at and scientists. Douglass College- Campus Topics are generally introduced through examples from the everyday whence the discussion progresses nonmathematically, making use of the reader's physical insight, which is carefully As we to press, we have just learned the cultivated throughout the book. No more than death on October 21 of Jay C. Eosenfeld of ordinary arithmetic is used in the Pittsfield, Mr. Rosenfeld was a but the mathematically sophisticated reader will Massachusetts. leading deeper follower and supporter of the activities recognize clues him to the impli- Dr. and Mrs. Hutchins since long cations the text. the Catgat Acoustical Society was formed. He was also a fine violinist and it was the Editor's good fortune to play quartets with him regularly a decade beginning in 1950. His home in the Among other activities, Professor Benade Berkshires was a focal point for many traveling has been asked to organize a set of papers on soloists who appeared at Tanglewood and for "The Social, Cultural, and Technological members of the Boston Symphony. He will be Connections of Acoustics" on of to remembered as a reviewer of Tanglewood concerts be presented at the annual meeting the AAAS since their beginning in the 'JOs and as a in Boston on Feb. 1976. columnist for the Berkshire Eagle. REFERENCES FUNDAMENTALSCP of of of goes way idea, of from form Concert musicians, craftsmen, world, go of discussion, of Saunders before of for many behalf ASA of 23, 29 "5 T| 1 a) i m fl -A v _k tK-S SJ 1 to 1 Ola) A - d) j* ttjS I M -U ffl ffl '"6 8 6ti^aS^ U OHUlfi d^-W^.CU'fflM'S-IJ-S -ffl-H Q Q 43 H "g Sy^g^fl;** MHH g STJ _ 1 ffl "d cv 1 1 fl jc a) XZ_ I 43 f^owqeu co fiJ3- >»r-j < 6fl S«;P£^ C rtCoCdCo4Jffl fO C CUO O OH O CU O O CJ DC ,cuh O HO CS OlvO OJ CH O. CLOJO OS C4J CU "i-, r-IWO CU ■ Ct.fiW O fflrt O O Crf Cd o,^J G O ffld -mo^voM O ffi.a r C O COHH G O Offl O OuO C O O. bO O O O MO O C O C "Ufl C j Ol fa C CO Cd O O ftt« O ,14 nt CQ OH QJ O C CT C C afi e,CH C » O CH O Offl ,* B£ ofl CHOrt tOfl C >, O-HM ofl O ft C O O C j O Hrtrtfl £ &.J-I-HO. .C QJ O fflrt flfflUC bO-H OH CH fflJ a.^-ffl CU oSra ; O Offl QJ O ufl 23'Q cfloiflH CP £ SZ n rtfl & CUflfl CU4J CM O >,tH HfflO CUH WO O -fICU-H O C H43rtO.^,2+J4JCOC.4J fflO HOfflbO COfflflffl C OH 30 0)io) i ra _ tJ _, tlo) i co JJ 0) co i T3 -d 'P 0) bpJJ -H g* 0 H H 0) -H co 0) .d. 0) OVC ,^ , 3 d OPMJr-4 MOM JJ g g-iJ-Pojd, t-i dt3 «H 5 'S-V4 otj g O3UP'Brt W 0) 0} -H Dffl QJOdO .O 0.-H W M B|£ 0) &E 3 3P 0) X X-H* fi CO QJ co fi £) 0) r-4 JJ CO S0) -H < i: a) r- cd 8 0) tl 8 H JJ rt S0) «j q 8 f Oj ij . rj i M 0) ? ra JJ 0) JJ +J %&%0) T3 JJ n Hi 6 "ra vo X TJ -J: fs HJJ d w > w 1 -d jj . >^» -a g " O ?> QJ CO x. gfi^ ft JJ M V «S cut) V4ttj H a ft ol 5J v -j! i> &§ « fl 0) o t- g to It. ** oH tN i-H I5 CJ O O.co O CM CT.O ft w-O OJ O Cd ,60 CC C/3NV4 !>, BrG r 4J43QJ *d COO C-3-H O OJJ *a r OS CM CU -HO d'-'OJtO-H OT3 OO OM-t &4J O COCOT3 CI O. +JCOJJJJ Ot3 Hum!*; C CT CUd OJ bOcN OJ C L, «-< « CJ "v 31 w o 2 fl ffl i ffl ffl ffl u_i ffl aj si fl -fi 1 P 1 copp-H^ipffli ffl.c._q*tip fl P .1 P P43M-I IfflHPCOflHfipg ffl£PpTJ°Q PCP-fflfflCt^COObO- fi §-fflP CfSP rt_firtCoH ffl cng&O ffl "Hffl -HO) ffl- flq-? 3_2 I *Q rt *p p59 S fi fflujtiP co P>M pCMOCO Tl gfi ffl d36fl fi9J> ffl Offlrtgfiß as^gffli-^pp|l^3fi.sj s M p ju hya. 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