THE CATGUT ACOUSTICAL SOCIETY NEWSLETTER
Number 13, published semiannually May 1,1970
As these pages go to press (April 22), the Acoustical Society of America is meeting in Atlantic City, New Jersey. Papers by several of our members are on the agenda, two of them by John Schelleng and by Richard Menzel and Carleen Hutchins "being presented in this Newsletter. Various other recent events are as follows. During December the tenor violin and the contrabass violin were used by Frank Lewin in music which he composed for the motion picture "Angel Levine", produced by Belafonte Enterprises and which will be released shortly. Charles McCracken played the tenor and Alvin Brehm the contrabass. The tenor can be heard as a solo voice in many parts of the music with its clear carrying tone quality, while the contra- bass blends its full rich low tones with those of the bass clarinet throughout. Again Mr. Lewin has composed for these instruments with a sensitive awareness of their distinctive tone colors and capabilities. True Sackrison, who has played her vertical viola extensively in concert throughout the Washington (state) area, has now moved to Lynd, Minnesota, where she is working with a friend to start the string department at a new college. Her first eight weeks there were spent in getting acquainted, playing cello, vertical viola, conventional violin, and her experimental vertical violin to about 45,000 students. You may remember that in 1965 Mrs. Sackrison played the "Suite for Viola and Piano" with the composer Robert Whitcomb at the piano. This is probably the first piece of music composed with this particular instrument in mind. Since then Mrs. Sackrison, a graduate of the Curtis Institute of Music, and Mr. Whitcomb, a graduate of the Eastman School of Music, have concertized widely using this Suite as well as other music for vertical viola and piano. Patsy Rogers reports that her Concerto for Tenor and Symphony Orchestra is nearly finished and will be ready soon for trial perfor- mance. Hammond Ashley of Seattle, Washington has undertaken to produce some of the new instruments of the violin family. About a year ago, he and his wife visited Carleen Hutchins to get patterns, information, and test equipment for checking plate resonances. With help from Arthur Ross of Moscow, Idaho, two mezzos, four altos, one tenor, one baritone, and one 3/4 size bass (5 strings including a high C) have already been finished. Several of these have already been sold. In addition, work has started on a large and a small bass, although suitable material for backs is difficult to find. Louis Dunham of Maplewood,N. J. and Donald Mugridge of Mirror Lake, N.H. both continue to make parts for the new violin family instruments. Their skilled work will soon be augmented hy the addition of -.Thomas Knatt of West Concord, Mass, to the group working for the Society. Mr. Enatt will work on the testing and construction of the tenor and alto violins. Furtherance of this work is being made possible by the Martha Baird Rockefeller Fund for Music. 2
We are pleased to report that we have a new Executive Secretary, Mrs. Elizabeth CATGUT ACOUSTICAL SOCIETY McGilvray, of Montclair, N.J. who will take President over much of the detailed work of running Arthur Benade the Society at 112 Essex Avenue. 3126 Woodbury Road l UUI2O Since the last Newsletter, Carleen Hutchins Cleveland, Ohio has given lecture demonstrations on the Vice President physics of violins and the development of Virginia Apgar the new violin family to: 30 Engle Street U.S. Coast Guard Academy, New London, Conn. Tenafly,N.J. o767o Montclair Women's Club Secretary College Women's Club,Montclair State Coll. Carleen Hutchins Music Conservatory and Physics Department, 112 Essex Avenue Oberlin College,Oherlin, Ohio Montclair,N .J . orJok20 rJ0k2 Kalamazoo College,Kalamazoo, Michigan At the Montclair Women's Club, Louis Zerbe Treasurer with the help of his graduate assistants Warren Creel and Ferrara Street Carl Sala, John Furia, Lawrence 1+56 Hamilton gave an excellent and most interesting Albany ,N.Y.l22o3 demonstration of the new violin family. Editor So much interest was generated by the new Robert Fryxell at that a vertical viola Drake Road instruments Oberlin 7355 and a mezzo violin will stay there on an Cincinnati Ohio 1+52^3 experimental basis for the rest of the term. Arthur Montzka, formerly of West Orange, N.J. not only arranged for a group of students to play the new instruments in ensemble, but took some excellent photographs of them. This year the New Jersey Symphony "Annual Arts Award" made to a resident of the State of New Jersey who has made a significant contri- bution to the arts was given to Carleen Hutchins. The presentation was at the Annual Dinner-Ball at the Robert Treat Hotel in Newark, N, J. Dr.P.E.Pashler spoke on "The Secret of Stradivarius" on April 2 to the Hudson-Mohawk Section of the American Society of Mechanical Engineers in Schenectady,N.Y. He has spoken on violin physics on previous occasions and is our spokesman in the Schenectady area. Our President, Arthur Benade, has recently made great strides in under- standing and improving wind instruments, and he has presented his findings to a number of interested audiences during the past year. Hopefully, pertinent parts of this research will be reported in future issues of this Newsletter. It is with great regret that we report the death of Robert Wallace of Miami, Arizona, who for many years has been the Editor of the "International Violin, Guitar Makers and Musicians Journal", a prime force in the Violin and Guitar Makers Association of Arizona. Through the pages of the monthly journal, Bob Wallace has created an exchange of information that has served not only to increase understanding of the highest traditions of violin and guitar making throughout the world, but also to encourage many amateur violin makers to develop the skills of good craftsmanship into the art of fine violin making. Bob Wallace has truly devoted years of his life to encouraging and developing the art of violin making. On October 15,1969, the Finance Committee of the Catgut Acoustical Society held its first meeting. The following attended: Chairman Timothy Arbuckle, Warren Creel, Donald Engle, John Huber, Carleen Hutchins, Earle Kent. Winifred Flatt served as secretary. The principal topic under discussion was the idea of starting an institute for the study of violin acoustics. All present agreed to the desirability of such a program. The committee decided to seek a university affiliation for three reasons. First, such an association would make available equip- ment, facilities and brain power not otherwise available- Second it would facilitate the procurement of funds necessary to support the project. Third it could provide a formalized program of study for graduate students interested in this field. Robert Scanlan and Carleen Hutchins have volunteered to establish contact with friends at MIT and broach the idea to them. Timothy Arbuckle and Warren Creel offered to compose a memorandum describing the activities of the proposed institute and soliciting financial support for it. The administrative structure of the institute and its relationship to the Catgut Acoustical Society came under discussion, but the meeting did not resolve these questions. Someone suggested that we name the institute after Professor A majority of the committee concurred in this. The question of raising the membership dues from $s*oo to $10.00 per year arose. The committee, however, decided not to increase dues at present since voluntary contributions had brought In sufficient funds to cover expenses. The final order of business was a tasty meal prepared by Carleen Hutchins-
TREASURERS REPORT: Balance, October 1,1969 $2747*48 Income $1294.04 Dues $550,00 Contributions 653.50 Sales 43*00 Performance 200.00 Refund 67.54
Expenditures $3039.01 Insurance $24U00 Reprints 36.00 Postage 284.63 Printing & Stat. 122-32 Office secretary 272-87 Newsletter, publ, 145*33 Telephone 212-93 Labor 815.24 Performers 75*00 Materials 404.04 Equipment 12.75 Meeting expenses 273*25 Music & Composition 41*55 Executive, secy. 100.00 Bank charges 2.10 Balance, April 1,1970 $1002.51 Respectfully submitted, Warren Creel, Treasurer
3
Saunders, 4
Recent publications by members or about their activities are: (1) "Science and New Instruments for the String Family", Marjorie Bram, Amer. String Teacher, Winter, l97o (2) "Gary Karr - Genius with Bass Motives", Ishaq Arazi, Amer-String Teacher, Winter, l97o (3) "The Suzuki Method, Child Development and Transitional Tunes", Marjorie McDonald, Amer. String Teacher, Winter, l97o t (4) "The Tenor Violin - Past, Present, and Future", Hans Bender, Amer, String Teacher, Fa11,1969 (5) "A Comparison of Acoustical Measurements and Hologram Interferometry Measurements of the Vibrations of a Guitar Top Plate"', Erik Jansson, Speech Transmission Laboratory, Stockholm, Report No,STL- QPSR 2*5/1969 (6) "Importance of the Strings and Resonance Box for theTimber of the Violin", Erik Jansson, Slfljd och Ton* No. 1,1970. The first install- ment of a serial article- (7) "The Irondequoit Violin Sleuth", Margaret Converse, appearing in Upstate New York newspapers, Jan.25,1970. A story about Louis Condax. (8) "Shaping Sound in Wood", Bill Wingell, National Observer, Jan-5,1970- A story of the Martin Guitar Company and their Research Director, John Huber. * A bimonthly Swedish journal devoted to stringed instruments, in its 40th year of publication. Its editor, Ingvar Mflckle, is one of our members.
**********#*********■****** TENOR DRAWING TO BE AVAILABLE In response to the many requests for a set of drawings and directions for making the tenor violin we are presently working to make these available strange - The lack of a true tenor instrument in the present day violin family has been lamented by many musicians and scholars. In his encyclopedic work, "Ancient European Musical Instruments", Nicholas Bessaraboff says: "There is no true tenor voice in the present violin family, although at one time there was one in existence and parts were written for it. This is a strange deficiency, since the true tenor tone color cannot be adquately replaced by either the violas or violoncellos- The tenor parts are too low for the violas and too high for the violoncellos. Classical and modern composers learned how to overcome this difficulty by a clever disposition of voices, but the tone color which only the tenor could supply Is absent now in the most important and basic group of instruments of our contemporary music-" This failure to perpetuate a true tenor voice in the violin family seems to have had two causes: First, the successful development of the present small sized cello (small as compared to the earlier larger ones, many of which have been cut down) with its full rich tone quality; second, the undersized dimensions on which violin makers have constructed their tenors. Both Stradivari and the Amati family made tenors with a body length of about 20 inches- Records show that other violin makers have followed suit- Appar- ently this body length was, assumed to be proper because of the 20 inch body length of the tenor viol, a highly successful member of the viol family of instruments.
In scaling for the new violin family of eight instruments (The Physics of Violins, SCIENTIFIC AMERICAN, November 1962) it is obvious that both the tenor viol and the 20 inch tenor violin are entirely too small to give tone power and clarity comparable to the violin itself an octave higher. Since the musical- scale is logarithmic, an instrument an octave below the violin should be nearly twice as large- The standard violin body length is 5
very close to 14 inches; so the tenor violin an octave lower should be nearly 28 inches in body length- The wood does not need to be twice as thick so the instrument does not need to be quite twice as large- In accordance with the scaling theory developed for the new violin family by John Schelleng, the new tenor is 1.82 times the violin, or about 25"i inches in body length. At this dimension it is possible to adjust the wood of the top and back as well as the air volume inside the instrument to give the same relative placement of main wood and cavity resonances as are found in the violin, thus producing violin tone quality an octave down. In the AMERICAN STRING TEACHER (Fall 1969), Hans Bender has written an interesting and informative article "The Tenor Violin, Past, Present, and Future' Mr. Bender explains many of the variations and efforts to develop this instru- ment over the years, and indicates the resurgence of interest currently growing around the tenor violin. The full scale drawings with instructions suitable for a trained violin maker will be ready by September 1970. The price will be $20.00 per set. ft-"**.-**-**-***** -K *#-.-*"***-#- * ■*.* * * * -* ■* * * An interesting notice has been received from the MUSEUM OF FINE ARTS in Bostonx The surge of interest in early music has brought the viola da gamba once again into prominence. This instrument of clear and resonant tone has a large solo litera- ture, an even larger role as a continuo instrument in Baroque music and a wealth of consort music rivalling and indeed surpassing, in the estimation of many musicians, the music for string ensemble. Yet it is still very difficult to buy a properly designed and fitted viola da gamba on the American market, while orders from European makers are often long delayed. Furthermore, the viols of English, German and Swiss makers cannot be tested by the purchaser beforehand, nor conveniently adjusted and repaired in their shops. In increasing numbers, players in this country, including many who have learned on rented viols, are faced with an acute shortage of instruments they may own. And demand, already far exceeding the supply, continues to grow. It can only be met by American luthiers. To stimulate the production of viola da gambas in the United States, the Museum of Fine Arts in Boston has had prepared a set of construction drawings by J.Donald Warnock, noted American maker whose lutes and viols are used by the Nev York Pro Musica, the Universities of California, Michigan State, Rochester and Chicago, and by many performing artists. The plans are blue line -on-white, full scale and include drawings of detail. They come with a manual of instructions that assumes a basic knowledge of violin making as set forth in Heron-Allen's book, and concentrates principally on procedures and structural characteristics peculiar to the viol. A discussion of woods and varnishes is included. Plans for the bass viola da gamba, in the popular division size, are now available; those for tenor and treble are under preparation. Drawings and manual may be procured by writing to the Musical Instruments Collection, Museum of Fine Arts, Boston,Mass., 02115, enclosing a check for $25.00 which includes mailing cost.
ERRATUM: The last sentence of the third paragraph on page 19 of Newsletter No. 12 is incorrect. The need for the tempered scale is not based on the inharmonicity of plucked or struck strings, but on the possibility of playing music that sounds well in a series of different keys on an instrument where the tuning is fixed and the player cannot alter the frequency of a given note. If there were not some sort of compromise tuning, or temperament, many more than the present twelve notes would be required in each octave on the piano, for example, to play even moderately complicated music in perfect tune. String players, on the other hand, are well aware that the intona- tion for an F sharp is not the same as for G flat; yet when playing with a keyboard instrument or organ they must adjust to the even tempered scale of these instruments. In a good ensemble of strings alone the players will invariably use the inherent pitch flexibilityof their instruments to play with practically ideal temperament. The inharmonicity of piano strings does, however, add complications for the piano tuner especially in the higher octaves. If in tuning two strings an octave apart he adjusts them to "zero beat" when played softly, the result does not give a true octave relation. In doing this he is tuning the second vibrational mode of the lower string in unison with the first mode of the upper string which does not give a true octave relation since stiffness in the strings makes all the higher modes a little sharper than the whole number ratios would indicate. Thus tuning a succession of octaves in this way up the piano keyboard tends to sharpen all the notes at the top. It is possible with the use of a Stroboconn which gives an accurate determina- tion of frequency to one cent (one one-hundredth of a tempered semitone) to tune a y piano with so-called unstretched octaves". There will, however, be additional roughness in the tone due to string stiffness no matter which way it is tuned. For a detailed discussion of musical scales, temperament, and inharmonicity of strings, see: Benade, A.H., "Horns,Strings, and Harmony", Doubleday Anchor Books, i960 Science Study Series #S 11, Chapter VI. Wood, Alexander, "The Physics of Music", University Paperbacks UP ks, 1962 (available from Dover) originally published in 19^. Carleen M.Hutchins
The following letter should be of interest to all of us, and the attachment is of considerable value. Sir C.V.Raman was a devoted and prolific researcher in the acoustics of stringed instruments in his earlier years. His moving into another branch of physics was even more successful, but a loss to the fiddle. Raman Research Institute Hebbal Post, Bangalore 6. Dear Professor Benade: In the first place, let me acknowledge with pleasure the greetings from your father which you have been so good to pass on. I have much pleasure in sending you today separately by registered? book post a copy of my incomplete monograph entitled "Bulletin N0. 15 - On the Mechanical Theory of the Vibrations of Bowed Strings and of Musical Instruments of the Violin Family, with Experimental Verification of theßesults:Part I* which was published half a century ago. The VIII Volume—of the Handbuch der Physik published by Julius Springer In the year 1927 contains an article by me on Musical Instruments covering some seventy pages in that book. Twenty pages from 369 to 388 contains a summary of my work on Bowed String Instruments. That gives a fair idea of what I did. I am enclosing herewith a complete list of all my publications in this field. I doubt very much whether I should be able to lay my hands on the reprints of the same. I write this, in haste to catch you befo. 3 you leave for Delhi. With kind regards, Yours sincerely,
(signed) C.V.Raman Prof .A, H. Benade Dept,of Physics Summer Consultant Physics Institute University of Allahabad
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Ci CO TAPE RECORDER TRANSPOSITION OF STANDARD VIOLIN TO SIMULATE THE HIGHEST SEVEN MEMBERS OP CM HUTCHINS 1 FAMILY OF TRUE VIOLINS Arthur Benade and Edith Roberts In the spring of 1964 it seemed to us worthwhile to attempt a direct comparison of the tone of the Hutchins family of large and small violins with the tone of a single good conventional violin. The new family was designed with the intention of keeping the characteristic voice of the. violin intact, while transposing its pitch over the complete orchestral range. Technicallyr this goal requires the design of a family of instruments whose characteristic wood and air resonances lie above and below the four open string resonances of each of these fiddles, in a manner which is similar to the pattern observed on the conventional violin. Because of this we. thought of recording a musical passage from a violin, and then transposing its pitch by playing back at a speed different from that used in recording. In this way the tonal characteristics could be displaced to the pitch location of any of the new instruments, and the two types of sound compared. Because the successive members of the Hutchins family of violins are tuned successively lower by intervals of a musical fourth or fifth, it is not possible to simulate all of the instruments simply by use of the octave transpositions which are obtainable via the two-to-one speed changes provided on a tape recorder. The intermediate transpositions are made possible by the fact that a recorder driven by a hysteresis synchronous motor will run faster or slower than normal when the frequency of its AC electrical power supply Is varied from the standard value of 60 Hz. When, for example, the recorder is set for normal 5.75 inches/second but supplied with 90 Hz elec- trical power, it will drive the tape at 5*75 x (90/60) = 5.625 inches/second. A normal violin recording made at the 3.75 inches/second speed and played back using a 90 Hz power supply will come out transposed a fifth higher. There are several musical implications to such a transposition: The tempo is drastically altered, along with the pitch change, as is the rate of vibrato. To make an acceptable imitation of the "tenor" (octave down) instrument, it is necessary to play at a very fast tempo (approximately double) so that on playback the music comes out at a reasonable pace. It seems that a musically acceptable absolute tempo for a given musical passage tends to be slightly slower on large instruments than on small ones, so that allowance for this needs to be made in making a recording. A recording was made by us in 1964 which represented a first attempt to make a workable set of compromises in the transposition process. A single: tape was made, intended to be played at 3-75 ips, to simulate the family of violins from treble down to the cello. This recording was made in a labora- tory room rather than in an auditorium and no great care was taken with micro- phone placement, so that the normal tone of .he violin was not rendered with complete fidelity. In this preliminary effort, no correction was made for the alteration produced in the tape recorder frequency response curve when it is played back at a different speed than that for recording. Even so the resulting tape gave sounds which matched the voices of the "Hutchins family" quite surpris- ingly well. This encouraged us to seek ways of making a more sophisticated effort at synthesis.
8 In May 1968 a second, more careful attempt was made. The violin was played in a large living-room music-room area of the Benade household, which is acoustically live and pleasant for music making. It is also large enough that the density of room resonances is sufficient to have several hundred of them within one room-resonance bandwidth of any note played on a violin. Under these conditions it was possible to exploit the statistical properties Of the room in a manner reported by one of us (AHB) at the CAS symposium during the Philadelphia meeting of the Acoustical Society of America in April 1969 (see Newsletter No. ll for further details). The basic recording technique requires the player to stand well away'from the wall of the room, with the micropnone within an inch of one corner- of the room. We got an excellent recording of the normal playing of the violin, using a l/2" B and K microphone and an Ampex tape recorder. As a check of the method, a trial recording was also made with the microphone pulled out about a foot into the room. This produced a fairly good sound from the tape, but there was an edginess to the tone that came from the aggravated peaks and dips in the coupling of the microphone to the room modes. A one-foot spacing of the microphone from the corner (l kHz sounds have a wavelength of about a causes strong fluctuations foots in the coupling at roughly 500 Hz and its harmonics » The main recording was done with the microphone pushed right into the corner. The table shows the program followed in making the recording: The column marked Recording Tempo gives the metronome setting used by the player. The next column gives the speed setting of the tape recorder. The raw tape pro- duced during the recording session was then played back at the speed indicated in the fourth column in the table, and rerecorded on a second machine which was set with a tape speed indicated in the fifth column, headed Re-recording Speed. For tape segments 4, 5, and 7 the playback speed is indicated as 7.5 x (90/60) or as 3.75 x (90/60). This means that on playback the recorder was run at a speed setting of 7.5 or 3.75 ips, but with the motor supplied with 90 Hz AC power rather than with normal 60 Hz power from the wall socket. In practice the nominal 90 Hz frequency was set to raise the pitch of the played back tape exactly a musical fifth above the pitch it has when playing on normal commercial power. The pitch adjustments were made with the help of a stroboconn. The recorded tape generated by the program outlined in the preceding para- graph constitutes a good approximation to the synthesis of the various new violin tones. However there is a certain amount of extraneous noise apparent In the tape (such as hum that is made more audible when it is transposed to higher pitches). Also the normal equalizations of the tape recorders are not correct when speed changes are made between recording and playback. The tape was therefore recorded once more, through a General Radio 30-channel 1/5 octave multifilter, that was set up along with some locally built high and low pass filters to correct the various equalizations, and to eliminate noise that is outside the spectral range of the instrument being synthesized. For instance on the treble violin, everything below about 350 Hz was attenuated at least 40 db. This eliminated low frequency noise but left the violin tone unaffected, since the G string on this instrument vibrated at 392 Hz. There was no trouble with roll-off in operating this close to the cutoff frequency, since the multifilter uses 6-th order Butterworth filters which give an extremely flat response close to cutoff. Similarly, the filters were used to cut out high frequency hiss and room noise above about 5000 Hz when recording the Basses. The final filtered and compensated tape gives a very satisfactory sound from a purely musical point of view, and each synthesized instrument gives a good subjective match to its real life prototype. We hope that opportunity will arise for someone to make acoustically dependable recordings of the
9 actual instruments playing the same music, at the same tempos. A comparison tape could then be put together for closer and more detailed study of the relations between the transposed tone of a violin and the tone of a family of instruments that were designed to have resonances placed violin-fashion relative to their own strings. Written-out parts with tempos etc are available for the various instruments, and help with the acoustical details required in making a meaningful recording will be gladly given.
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> O cfl ri «H > O O > X! ri r ® Q) cd ri P P -P +3 X) > +3 rH A > fl fl fl fl ri «H r*| fl Cd o B O o O O > r Cd O O 0 XI XJ XI A A rH A w U 0 -P p p 4-3 >» Pi +> O rH ri ri ri ri "H cd <-n *H o r r > r rH O J* ri Ph rH +» 0) s s s s ri r>» cd rH ri ri ri & cd O ed B ri ri ri rri rH O iri 0 e ft ft ft Ph Pn rri Pi u CD O 0) 10 O rQ CD O CD O "> O CD O O CD CO O CD O ' ON & CD 11 REBEC RESURRECTION or APPRECIATION OF AN ANCIENT ANCESTOR Carl Hugo Sgren Introduction: Opinions seem to be very divided among historians as to which were the ancestors of the violin as we know it. One of the most interesting no doubt Is the rebec, that very handy fiddle, shaped like half a pear and tuned in fifths, which was common over all of Europe and North Africa during all the Middle Ages. It seems to be still in use in North Africa- We do not know the rebec from examples but only from pictures, which as is usually the case with old instrument pictures, vary quite a good deal depending on the opinion of the artist of how the fiddle looked that he was painting or sculpturing. However, both Praetorius (Syntagma Musicum) and Mersenne (Harmonie Universelle) have drawings of rebecs, in the case of Praetorius even with a scale. These two worthies are known for the exactness of their drawings, so that we may say that we have a fair idea of how this ancestor looked. Apparently it had very nearly the same length as a modern violin; it possessed a tailpiece, bridge and fingerboard and was tuned in fifths, sometimes with three, sometimes with four strings. The author has built a rebec, possibly the first electronically tuned rebec in musical history, and since this little fiddle has shown some very interesting properties, the story of its birth will be related here. Design Considerations: The rebec built is shown in Figure 1. Its total length is 550 mm, its string length nut to bridge is 325 mm (the standard violin value) In order to make it easily playable by the author's violinist wife, who owns the fiddle- The size closely agrees with Praetorius and Mersenne. While engaged in the study of some different flat viol backs, the author was struck by the extremely low frequencies these backs resonated at. For example, a rosewood back intended for the Magnum treble viol (see Newsletters No.lo,ll)with the thickness of 2.5 mm had, with cross bars and all, a frequency for the fundamental of 220 Hz. Unbraced it came down to 160 Hz.. This observation led to the idea of trying out a rebec since the very small size of its soundboard might at first lead one to suppose that its fundamental frequency would be impossibly high for violin tuning, which the present rebec has. This turned out a success, and as will be shown this very antique design, can actually be made to fit the Saunders-Hutchins criterion, that is to say the air fundamental comes at the frequency of the open D string and the main wood resonance at the frequency of the open A!. Body volume and soundhole size could without any difficulty be adjusted for an intended air resonance frequency of 300 Hz, which was very nearly achieved. The present example has a rear side of the lute type with five rosewood strips bent by heat and glued edge to edge, which incidentally is a formidable carpentry exercise. Plate Measurements: The soundboard is shown in Figure 2. Since the medieval bracing was not known (it is supposed by some to have been in the form of transverse braces) a design was chosen with one brace under each bridge foot, somewhat resembling radial guitar bracing, which has been successful. As for the author f s viols, a tuning jig was made, consisting of a heavy 12 o u Ort o ® ■rt am ■rt T3 U oas io OJ a> x CQ wood bloc£, with a cutout corresponding to the inside of the finished rebec. The plate was clipped to this with clips around its outline and was electromagnetically excited by means of a moving coil electromagnetic driver and a sinewave generator. Sensing of the response of the soundboard was by piezoelectric contact pickup. Unfortunately there are no holograms, since our laser chose this very moment to collapse and the rebec had to be ready for Christmas, since it was intended as a Christmas present for the author's wife. The very small size of the plate made measurement a bit problematical, since even the small weight of the pickup (2 grams) had a considerable influence on the peak frequencies. A method was therefore chosen whereby the five lowest peaks of the plate were first located by pickup, after which the pickup was taken away and the peaks located again by ear. The driver was placed to the left in the lower bout and the sensor in the upper part, which by experiment had been found to excite the greatest number of readable peaks. The result is given in Table 1. As can be seen, the fundamental does not change much because the sensor sits far away from the vibration maximum of the fundamental, but it does influ- ence the higher peaks quite a good deal. Relocating the peaks by ear gave the results in Table 2, The soundboard was then mounted onto the rest of the rebec and the measurements repeated with the rebec in the white. In this measurement the air fundamental was also checked. The most important peak frequencies and Q's of the finished rebec are given in Table 3- able I:Peak frequencies ofi Table 2: Same peaks as n Ta oundboard, pickup reading relocated by ear freq.Hz Q freq .Hz 410 15 410 650 16 750 690 820 750 1100 1300 1500 Table JiVeak frequencies and Q's of complete rebec peak type freq-Hz Q Air peak 290 Wood fund. 465 2"3 11 11 765 25 it « 820 " " 850 28 " " 1200 30 « " 1450 29 Playing Qualities: One might well ask how a fiddle as small as all this can give off any sound worth mentioning. This in fact has puzzled builders of rebec copies for a Ions: time. The fact is that its volume is surprising considering the plate area, no doubt due to the excellent peak spacing it has- It has a certain spicey tang to its tone which is very appealing, but which Is very far from the ethereal sound of viols. It is about the same difference as between Oxford English and genuine Cockney* The spicey tang comes out especially well when using open strings as drones. Holding the fiddle is a problem, but it can be held under the player's chin if anchored with a strap going from the tailpiece gut around the player's right armpit and up 13 14 across the chest back to the tailpiece gut- The strings are standard violin strings which the frail fiddle carries with ease due to the very slight string angle. It speaks with an ease which at first is slightly disconcerting to standard violinists, but one soon gets used to this. The rebec described will be used together with recorders, cornets, viols etc. in broken consorts which will play medieval dances and the like, A composer such as Guillaume de Machault should have much material for a fiddle of this sort. #:■#**■#**#**#■****#*#■******** VIOLIN STRUCTURE Gordon R. McDonald An instrument of the violin family with its esthetic arches and curves has strength and durability quite amazing for a structure mainly made up with thin wood parts held together with old fashioned glue. The general designs and even details of construction established by the great luthiers remain practically unchanged after hundreds of years of experience and experimentation. Undoubtedly they had logical reasons for their practices which are still followed faithfully. The reasons, however, although probably known by some people, are seldom, if ever, acknowledged in the voluminous literature. This discussion, although it does not actually contain new information, does assign reasons for the accepted Orientations of the grain of the wood of various parts of the instruments. Many of the points considered are of a minor nature but are offered in an attempt to give full coverage of the subject and also with the realization that "trifles make perfection". These instruments are sensitive to changes in ambient conditions which affect them both musically and mechanically. Temperature changes modify wood dimensions by varying amounts in different directions but the changes are small and negligible as compared with those caused by humidity, V/e are principally interested herewith in considering the effect of humidity changes on glued joints particularly where different wood grain orientations and different kinds of woods are involved. Humidity may change through wide limits and cause sizable changes in wood weights and dimensions. Both types of change have considerable influence on the musical properties of the instrument. We are not discussing these herewith except to state that if it is desirable to maintain fixed conditions, some method of minimizing humidity changes would be in order. A penetrating wood filler, used before varnishing, goes far in this direction. The amount of water absorbed by wood depends mainly on the relative humidity and through the range from 32 F to 100 F is almost independent of temperature, in fact, if constant humidity is maintained through this range the wood will take up slightly moire water at the low temperatures than at the high tempera- tures. On the other hand, the amount of water in the air at 100 F is some ten times the amount at 32 F with the same relative humidity at both tempera- tures* If constant humidity is maintained for a sufficient time, the moisture content of wood in contact with the air adjusts to "equilibrium" conditions of water content affecting weights and dimensions as shown by Figure #1. The dimension changes are different* for the radial, tangential, and longitudinal directions in the wood defined as follows. The radial change "R" is in the dimension from the center to the outside of a log across or perpendicular to the annual rings. The tangential change "T" is in at It should be noted that these comments are limited to the equilibrium changes which take place. In addition, there are differences in rates of equilibration which are also important. a direction perpendicular to the length of the log and tangential or parallel to the annual rings. This is usually the largest change and accounts for the seasoning checks fl or cracks which take place radially. The longitudinal change "L which takes place along the length of the log is usually quite minor. Other definitions which should be established are those for quartersawed and slab- sawed: Figure 2 A and B. Quartersawed wood is cut so that the annual rings are perpendicular to the main surface. Slabsawed wood is cut so that the main surface is parallel or tangential to the annual rings. The curves of Figure I** are for three kinds of wood that are commonly used in violins These are domestic species but the data probably apply to similar European species. Growing conditions vary so it must be recognized that the curves represent average conditions for the particular species. The curves are based on holding a fixed tempera- ture and varying the humidity. Bellies or Tops - Spruce Bellies are usually made of two pieces joined along the center line. The pieces are always from adjacent positions in the log and the grain orientation is the same for each. Both pieces have the same changes with varying conditions so there are no forces tending to break the joint. Bellies are always made with the annual rings, as closely as possible, perpendicular to the large surfaces (quartersawed). With changing moisture content the greatest percentage change is in the plate thickness, T type change, but as the thickness dimensions are small, the effect is negligible. The change across the width of the instrument, R direction, is about half of the T change, providing the least possible change in width and arching. This is also the best arrangement of the grain of the wood to resist splitting. The dimensional change of spruce in the L direction, length- wise, is practically zero. Backs - Maple Backs are made with either quarter- or slabsawed maple and may be one piece or two pieces joined along the center line. The comments above for two piece bellies apply also to two piece backs. With quartersawed wood the R change in instrument width is the minimum possible and as it is almost identical with the belly, the ribs should maintain parallel align- ment. With slabsawed backs the change in width is about double that of the belly in- troducing a twist on the corner blocks. Slab back instruments probably have larger back to belly changes, as affecting the sound-post length, than instruments with quartersawed backs. In the longitudinal L direction the change in maple is only about one third of its R direction. Backs do, however, change in length somewhat more than bellies. Ribs - Maple Changes in rib widths modify the air volume of an instrument but more importantly they change the required length of the sound post. The usual quartersawed R direction change ribs have half the magnitude of change of slabsawed ribs- Quartersawed are also more resistant to cracking. The small instruments have very little sound post trouble. The rib width is small so that the percentage change caused by moisture is only a small amount and even this is nullified by the penetration of the finish into the very thin ribs. Sound Post - Sjpruce Sound posts made of spruce have practically no change in length with humidity changes. The dimension between the back and the belly at the sound-post location varies with rib, back and belly changes. These are enough with large instruments to necessitate seasonal changes of the posts. A material having L changes at least equal to the R changes of the ribs would be desirable. Agriculture **From "Wood Handbook," Forest Products Laboratory, U.S. Dept. of Agriculture, Handbook #-72. 15 oo -l* -I? j a ;- k (Si A I l\ \* n v .■j t *": gll „'„,^ ,~ I 3£ -..;. -^ 8, I g 16 17 Scroll and Peg Box - Maple The grain of the maple used for the neck, peg box and scroll should have the plane of -the annual rings parallel to the surface of the finger board. This assures minimum change in the shape of the peg holes, Figure 2C. The R change is three times the L change tending to make the holes elliptical. The same thing happens to the peg so it is not hard to account for pegs loosening and tightening depending on their position in the hole and the direction of the humidity change. Pegs must on occasion develop quite high pressures against the sides of the peg holes tending to cause splits. The wood is most easily split perpendicular to the annual rings; consequently, the orientation of the wood of the peg box is best from this standpoint , also. Shoulder: Neck - Maple, Back= - Maple The shoulder joint between the neck and the back involves L type changes for both in the longitudinal direction. In the transverse direction the neck part has T type changes which would exactly match a slabsawed back or be twice as large as the R type changes of a quartersawed back. In this latter case, there is a slight advantage in having a long lengthwise and a short crosswise joint between the parts. Finger Board, Neck - Ebony, Maple Our source gives no data on ebony. The general statement is made, however, that "the heavier species of wood shrink more across the grain than the lighter ones". The glue joint between the neck and the finger board has T type changes for the maple side and may be the best orientation if the above rule applies to ebony. Bridge - Maple The hard maple of the bridge is quartersawed making for minimum up and down or R dimension changes and minimum tendency to warp. Bass Bar - Spruce Since the grain of the bar is in effect an extension of the grain of the belly, Figure 2D, changes in moisture content should not affect the joint. The bass bar supports the pressure from one leg of the bridge and so requires con- siderable strength. Considering the natural bending of a tree, it might be thought that greater strength would be obtained with a 90 change in the orientation of the bar, that is, annual rings parallel to the belly surface. Actual bending tests made by the writer, with loading on a spruce bar parallel to the grain and across the grain, show identical deflections. This is confirmed by Handbook #72. As a parenthetical comment on the relative strengths of wood with the two directions of loading, the Handbook states that for "hardwoods" the proportional limit stress and modulus of elasticity is higher by one-third with loading perpendicular to the grain This is the orientation used for bows. Neck Blocks - Willow Spruce and willow are commonly used for the end and corner blocks of instruments. This discussion will be confined to willow- Handbook #72 gives data for Black and Pacific willow. These two have almost identical characteristics and it is to be hoped that other kinds of willow, commonly used, have the same extraordinarily good features very - change Willow is a soft wood which probably would without damage dimensions to match the changes of a stronger wood glued to it. It Is,however, to be expected that the more nearly the two or more woods of a joint follow the same dimensional changes, with varying moisture content, the better and more durable the joint. The grain orientation of the neck block E, Figure 2, should be perpendicular to the ribs and the L dimension connects between the back and the belly. I Joints between the block and back, belly, ribs and neck are to be considered- j Two directions of change are to be considered for the joint between the block and the ribs. In the direction parallel to the rplane of the back the R change of the willow block is small and is matched with the L change of the maple ribs which is practically zero. In the other direction, perpendicular to the back, The L change of the block Is practically identical with the R change of the ribs. Where this joint is long as in cellos and double basses, 3 the use of willow would appear to be particularly advantageous- The back and belly joints with the block are much longer in the direction across the instrument than in the longitudinal direction. The long dimension involves the R dimensions of willow, spruce and quartersawed maple. The R of the willow is somewhat less than of the other two. If a slabsawed back is considered, its change is about three times as much as the willow- In the other direction, longitudinal, the small L of the back and belly is matched with the large T of the block. This is the worst combination but it is for the shortest dimension. The joint between the neck and the block involves mainly the dimensions perpendicular to the back where the L of the willow and the R of the maple provide a good match. In the direction parallel to the back along the sides of the neck the Lof the maple is quite small and is matched with the of the willow which is quite large, the worst combination but the dimension is small. Across the end of the neck the maple T is matched with the willow R, not a very good combination, but gluing to the end grain of the maple is not considered very effective. Tail Block - Willow Comments for the neck block apply. See F, Figure 2. Corner Blocks - Willow The L type of the willow closely matches the R type changes of the ribs. See G Figure 2. The top and bottom contacts with the belly and back, also the contact along length of the ribs all involve R type expansion of the block with L type for the other parts, quite a good match. The T type change of the block does not match the R type of the back and belly, but the dimension is small. L changes of the ribs are small, but when there is shrinkage tending The tending to open the corners, it is opposed by the R type change of the blocks to keep the corners closed - Another interesting consideration in connection with these corners is that from in the corner there is very little block change involved. As the distance the is increased on each side of the corner, there is more and more R corner joints type change of the block. If the parts were not restrained by the glue at with the plates, the ribs would act like radii of a circle with its center the corner. Moisture changes would then affect the angle between these radii. The joint with the plates prevents this kind of movement - Linings - Willow appear to be From the relative dimension change standpoint, there does not a for willow linings used with maple ribs. The willow strips good orientation this, used are, however, so small in section that from a practical standpoint application is satisfactory. A better match from a relative change standpoint of \ could be made with spruce, but we think willow is to be preferred because its excellent gluing characteristics- 18 Flat Back Instruments Considerable trouble is often experienced with large flat back instruments such as bass viols. These have cross bracing glued to the inside of the quartersawed maple backs. Humidity changes cause warping. and splitting of the backs. and the cross bracing has a tendency to break loose- A solution to this problem might be the use of willow bracing members with L type changes about equal to the R type of the maple. These braces should be oriented to have R type changes of the willow in the instrument longitudinal direction giving an acceptable match of characteristics in this direction also. WOOD TESTS Subsequent to assembling the above information, the writer made some confirming tests of the effect of moisture on dimensions and weights of wood glass jars samples o The methofl involved placing the samples in closed which contained solutions of various chemicals to control the relative humidity. One to three samples of each kind of wood were used. In some cases they were probably from the same tree. After a suitable period of time, the samples were removed for weighing and measuring. In some instances, we suspect equilibrium was not entirely achieved, and In fact there may have been humidity variations within the jars although we had no means of monitoring. Thus, although the results should not be considered quantitative, they serve for making comparisons between species. Results are given in the accompanying table. WOOD CHARACTERISTICS Relative Percent changes from Wood bpecies. humidityJ dry wood conditions a* Density * R T L V Weight gm/cccc Weeping Willow 25 100.4 100.9 100.2 101.5 103.0 0.43 50 101.0 102.2 100.3 103.5 108.0 0.44 75 101.8 103.9 100.5 106.3 115.0 0.45 Black Willow 25 100.3 100.7 100.1 101.1 103.0 0.37 50 100.6 101.6 100.2 102.4 107.7 0.58 75 101.6 103.5 100.6 105.8 114.7 0.59 European Spruce 25 100.4 101.0 100.0 101.4 102.7 0.40 50 101.3 102.6 100.1 104.0 107.4 0.41 75 102.3 104.8 100.2 107.3 114.0 M3 Sitka Spruce 25 100.8 101.3 100.0 102.6 103.5 0.46 50 101.8 103.1 100.1 105.1 107.0 0.47 75 103.1 105.4 100.2 108.9 114.0 0.48 European Maple 25 100.4 100.9 100.1 101.4 104.0 0.64 50 101.1 102.5 100.2 103.8 110.5 0.66 75 103.1 105.1 100.3 108.7 119.0 o*6B Sugar Maple 25 100.6 101.3 100.1 102.0 103.5 0.73 50 101.5 103.0 100.2 104.7 107.5 0.74 75 102.8 105.4 100.3 108.7 115.5 0.76 Ebony 25 100.8 101.0 100.0 101.8 103.1 1.11 50 101.9 102.3 100.0 104.2. 106.2 1.12 75 10Z.7 103.9 100.0 106.7 109.3 1.13 Rosewood 25 100.5 101.0 100.0 101.5 102.33 0.89 50 101.5 102.0 100.1 103.6 105.2 0.89 75 101.7 103.5 100.2 105.3 108.3 0.90 R - radial direction, across annual rings T - tangential direction with respect to annual rings L Lengthwise, direction of log V - volume 19 Willow - Weeping and black willows were compared. Weeping has an interlocking type of grain whereas black is of a more layered type of growth. Weeping is somewhat heavier but in the amounts used this should not be a factor. Both types showed measurable changes in length but not nearly as much as Wood Handbook #2 indicates.* Heron-Allen in "Violin Making" mentions, that Stradivarius nearly always blocks for the sake of lightness. Referring to the table it will used willoV spruce- be noted that there is very little difference between willow and Willow carves nicely, takes glue well and was probably readily available- What kind of willow did Stradivarius use? Did it have large L changes as in the shown in Figure 1 or changes typical of other willow as indicated tahle? Spruce An interesting observation with European spruce, was that one sample - having having 5 annual rings pe* centimeter weighed 0.39 gm/cc- Another sample 18 rings per cm weighed 0.46 gm/cc, both measured at 70°F and 25% RH. This difference illustrates the variability of wood characteristics. Sitka spruce is generally somewhat heavier than European spruce- The annual rings seem to be thicker and harder making it more difficult to work. For equivalent tap tones the section must be thinner than that of a European spruce belly so the weight used in an instrument is about the same. The changes with humidity are slightly more than with the European type and are almost identical with those of maple Maple - European maple,- obtained from supply houses, is much softer, lighter and easier to work than sugar maple with which it is compared in the table. The dimension changes are about the same for either type. A back made from sugar maple is thinner so the instrument weight is about the same for either type. If. sugar maple were used for the neck, peg box and scroll, the weight would be greater than if European maple were used. However due to greater, strength, smaller sections would serve, a point worth considering when necessary to accommodate the small hand. Domestic red maple was not tested. From Handbook data it would appear to have many features about the same as; European maple and might warrant consider- able attention. Ebony/Rosewood - Handbook #72 indicates the weight of rosewood to be 2/3 of the weight of ebony, hence desirable from a weight standpoint for pegs, tail piece, and end pin. The present tests indicate a rather smaller difference- The amount that peg bearing surfaces change from round with humidity changes will depend on the ratio between R and T changes and themagnltudes of these factors- It was hoped to obtain data in favor of the use of rosewood for pegs in order to support a personal bias- The data however do not cooperate except for the factor of weight - Fingerboards The maple neck surface to which the fingerboard is glued has T type changes- It would be desirable to match this, with T type changes of the ebony which are greater than its R changes but less.. than the neck T changes. A difficulty In in doing this is the fact that it is very difficult to see the annual rings ebony. Fortunately there does not appear to be as much difference between R and T as with most woods. A point that does seem to be important is that the board be made of ebony cut or split parallel to the center of the log. This woulJ. tend to prevent 20 21 a tendency of the board to hump or dish along its length, changing the spacing between, the strings and the board. This action would be due to the unequal effects of R and T changes. It is of course appreciated that the board must bend the neck in making these changes- The converse is also true. The neck block must be cut or split parallel to the log center- The writer has encoun- tered this change in string spacing- The fingerboard was first removed and replaced with a new one using meticulous care but no improvement resulted. A new neck was then put in the instrument, fully correcting the trouble ; Wood Handbook #72 defines five types or warping - bow, crook, twist, cup,- and, diamond - all of which could influence changes in the fingerboard and neck Some of the string spacing changes caused by humidity have been described in the literature with emphasis on the direction of the change- It Is quite evident that the type change described above could result in either increasing or decreasing the spacing with Increasing moisture depending on the orienta- tion df the wood grain. Wood Preparation Seasoning of a whole log should never be attempted. Consider a log 10"' in diameter when saturated with moisture. If in drying it sustained yfo R and 6$ T changes and all shrinkage forces were fully relieved, a radial crack or series of cracks totaling approximately 1'" in width would be necessary. V/e have checked this figure with willow logs which split easily- On the other hand, pieces of this wood split radially season without cracking- We do not have the R and T figures for Pernambuco wood, used for bows. We have however seen and purchased sections of logs some JB" long sold for bow making. These pieces were full of seasoning cracks making it difficult to obtain crack free pieces for bow stick blanks. These logs when freshly cut should have been halved, quartered, or better still split into bow blanks- It seems impottant enough to repeat that It would be very desirable to obtain wood split lengthwise to sizes suitable for various fiddle making purposes rather than sawed pieces- This must have been the practice of the old makers before the days of power saws. Conclusions The above thoughts have proven interesting to the writer and have assisted in solving some problems that were attributed to "unstable" or "not fully seasoned" wood- There is full realization that individual pieces of wood vary considerably. Also the waterproofing provided by filler and varnish treatment modify the effects of humidity. There is some argument for the use of willow for various functions but other materials or arrangements probably could be successfully used. It is to be hoped that the comments will emphasize the excellence of the accepted design features. The handbook information serves to introduce a quantitative aspect, of the subject and should promote critical thinking on even minor points- "Trifles make perfection and perfection is no trifle". The cited data (see Figure 1) do in fact appear suspect, i-e -longitudinal * changes greater than radial. *******-**"**'**"****'*.**-**** THE SEARCH FOR THE PERFECT BOW Otto Reder The basic physical properties of bows have been very clearly explained by Maxwell Kimball in his article "On Making a Violin Bow". (Newsletter No. 11), So far very little has been investigated about the relation between measurable physical characteristics of bows and their playing qualities. Every violinist will change during his lifetime from one bow to another until he has found what he thinks is the "perfect" bow- Many a student, depending on advice 22 from often unqualified bow experts or teachers, will put away bow after bow as his skill increases. Could all these disappointments not be avoided if some easy measurable data could be obtained to assure that a bow will be correct for good all-round performance or at least for certain styles of music, such as Bach polyphony or Paganini fireworks? It would be very instructive if we only knew the main physical data of the bows used by some of the famous artists and their preferences for certain programs or violins. The basic physical data of bows can be obtained with simple equipment (shown in Fig. l-3) which can be transported for taking measurements, if necessary, at the violinist*s home under his suspicious eyes. Additional tools are a small pair of calipers and an accurate letter balance (zero to 250 gram range). Fig.l shows how to measure length, maximum camber and its position by means of a 2.5 foot long T-square and a flexible metal rule ending correctly at zero. Fig. 2 shows how to balance the bow over the edge of a triangular rule for finding the position of the center of gravity. The bow should be in playing condition with a hair distance of a ■ 8 mm (approximately equal to the maximum bow diameter). This distance can be set by clamping a small rubber eraser of 8 mm thickness between stick and hair and tensioning the hair until the eraser drops out. A plush-padded wooden block for sliding the stick will help to damp the stick at the point of balance. The radius rof the center of gravity from the center of rotation (i.e. the point on the curved part of the frog) will be required later for comparison with the radius of gyration i- Fig.3 shows at the right an alternative of Kimball !s arrangement for find- ing the center of percussion or the radius of gyration i, by synchronizing the swinging bow with a pendulum. A small disc at one side of the frog will prevent torsional motions of the stick- A wooden peg or a violin peg serves for adjusting the thread length of the pendulum- Fig. 3 shows at the left the rig for measuring the central deflection f of the stick when supported as a beam hinged at the ends and loaded centrally by a weight L varying in steps from 200, 400, to 600 grams. The hook-wire should be plastic covered (fence wire) to prevent scraping the stick. Accurate measurements are obtained by projecting a sharp shadow of the stick with a strong lamp onto a sliding rule which is set at a zero line when the stick is unloaded. A magnifying lens will help to concentrate the light and to enlarge the scale lines for better reading. As an example for a bow data sheet the table shows the sequence of measure- ments obtained from my 3 violin bows and one viola bow. Fig. 4 gives the deflection curves of the bows. Violin bow No.l is my preferred bow, followed by N0.2 and N0. 3. The No.l bow is the best for thrown "saltato" playing (see third movement of Ist Paganini Concerto) as well as for all-round playing. The camber lines and the deflection curves of No.l and N0.2 are nearly identical, the main difference between them lies in the heavier weight and in the higher ratio i/r of No.l, The viola- bow N0. 4 has an old stick of the 19th century and received a new part at the frog mortice and a small addition at the head some 70 years ago. In spite of that I was greatly satisfied with it since I acquired it together with an excellent Paolo Vimercati viola of 1663. In order to draw some worthy conclusions It would be necessary to obtain considerable data from bows used by famous artists. These results would be extremely beneficial to the bow makers and th all other violinists. Si 0r» § r 5 I S I? 1 u t<4> 1 i «J Ml Vr> t> 00 00 1« NT u-." c> ccT « u V V* tn "£ ft: u 1 \s> CM cvi X $ S > «0 8 0) !© I «p I o \> cm ms K V Q i e © Ci is irT °c>T 4^"° OS v cC CM Co Vj oJ ty *w* © c "I c V 8 0 o "5 V c N o (Q U» o "o "0 «0 V *> «o *0* Uf I « «M Of ! M 0* 4 > © <" 8 * I a 4. Ifi X N t S "5 -A k o "» or»*" sIT <\T fV kT "o N « C\J "i V SJ "* V CU O «0 o «<5 © 3: <" t c tt o v» I tt * . f c fa* U cj 'S "x **o» I *a -*j o 1 ii "S b ""»4 %j Vj k. "» o O "S 1 cs § * a. o * ?*^ ? -^ ft: Ci ft: <§3 ->i>* Vi * in O) luuig f E K (OS -j %1 to I I \ \ V* \SS v.l \ \ \ -J 23 OCXS Co © ft CO *J» CJ> Ob <\l fro Ci CM OS V"ft CU "fa, O OJ **< CJ © CO ' \ 24 PRESSURE ON THE BOWED STRING — John C. Schelleng In playing an instrument one is not necessarily aware of exactly what it Is that he is doing, even though he may be doing it exceedingly well- On the other hand, most players are able to benefit by an understanding of thescience that underlies their art, A case in point is the relationship between bow pressure, bow velocity and bow position, which together form so important a part In the mechanics of playing the fiddle- Changing bow position is something like shifting gears in a car; the further the bow is from the bridge the less is the vibration of the bridge for a given speed of bow and the less is the force that needs to be applied to the bow: the mechanism is in low gear. Place the bow near the bridge on the other hand and our mechanism goes into "high"; the bridge vibrates with its greatest speed relative to that of the bow and large driving force is needed at the bow, where instead of gear teeth we are depending on friction. In order to provide sufficient friction we now need relatively great bow pressure* As players we can be thankful that there is a considerable range of pressure within which the sticking and slipping of the string will carry on In a reliable manner. As players however we know that the range does have limits. It is the present purpose to establish as accurately as we can what these limits are, and why. There are two problems concerning the force applied to the string, commonly called "bow pressure", that are of importance, to the musician.. When is this force so small that the fundamental vibration fails, and when is it so large, that the wave on the string is unable to trigger a clean repetition of similar pulses? The result of the first is a falsetto or a squeak, of the second a raucous scratching. The mechanical requirements for avoiding failure are that (1) throughout the period in which the bow clings to the string, and particularly toward tha middle of that period, bow pressure must exceed a certain minimum value, and that (2) at the end of the period, pressure must not be so large as to inter- fere with release of the string. The force that the bow exerts on the string may be thought of as comprising three components: one that provides the power that vibrates the bridge, one associated with release and capture of the string by the bow, and a steady unvarying component in the direction of the bow's motion. In the phase when slipping occurs the one that vibrates the bridge has its greatest backward value, and this in combination with the third or average component gives the forward resultant that we associate with sliding friction, namelyyu^p. In. considering minimum pressure we are concerned with the first component of force at the bow, which depends on the resistance of the bridge- At the bow impedance falls off rapidly as the order of harmonic increases so that in an order-of-magnitude estimate not many harmonics need to be considered Raman pointed out that the peak-to-peak force necessary for the delivery" of useful power must be equal to or less than the bow pressure times the differ- ence between coefficients of static and dynamic friction, and that if this fails the long period in which the bow should engage the string will be interrupted by the spurious pulses that Helmholtz was the first to notice- Failure occurs at that point because it is there that the force has its greatest value. On this basis I arrive at the following approximation: If we take the difference of coefficients to be 0-5, the bow position (i to be 0.1 of string length, the characteristic impedance of a cello A string second), the bridge C gs as Z Q ■ 50 cgs units (grams per resistance 4*lo^ units (a figure more or less in keeping with measurements of Frieder Eggera) grams, and bow velocity as 40 cm/sec, the minimum pressure turns out to be 18 which is about 1/3 the weight of a cello bow. Maximum pressure depends on all these quantities except, r, the bridge resistance (it would probably be better to refer to this as the reciprocal of the bridge conductance). The reason for the exception is that the string detaches itself from the bow so suddenly that the event is complete before any echo of it can return from the bridge. Normally detachment takes place at the beginning of the. slip region at a time when the force occasioned by the bridge load is actually near its greatest negative value and when its resultant with the average component has the lowest positive value that it ever attains. According to a plausible concep- tion, the string is detached at a certain moment because its displacement is then greatest. But the essential fact is that at this moment an irresistible negative acceleration arrives from the far end of the string,, namely the Helmholtz velocity discontinuity or timing wave. The force associated with the bridge load therefore has nothing to do with detachment. Combined with the average force, it equals the frictional force of slipping, and /l^tthe string has to be augmented to the force of static friction,^ gP* before ** can be freed. The greatest addition that the discontinuity can make without suffering considerable reflection is ZqV-^. This leads immediately to an expression for the maximum permissible bow pressure: PMax.-' ZoV?CV/%) the same numerical assumptions used for P we obtain ?_,_„ « grams, With nun.. mM.x 3^o several times the weight of a cello bow. — We also find that the ratio of maximum to minimum pressure equals 2^-t; Using these relations we can construct a diagram of significance to players. The accompanying diagram assumes constant bow velocity throughout and plots logarithmically the two limiting conditions for sustained tones against relative bow location^ , A second set of coordinate scales gives data for the cello A string previously assumed, in which the intersection A lies so close to the bridge (about 4 nun) as to be within the width of a bow- Far other strings, formulas on the figure locate point A in a simple manner. Normal playing employs the cross-hatched area. With the bow well away from the bridge there is a large range of pressures that can be ased for long- sustained tones without the tone breaking, though of course the actual require- ments of music are more stringent than this suggests. To play louder or softer one changes the speed of the bow or its position or both. To keep within safe limits pressure also must change, but change of pressure alone will not suffice. Far from thebridge but still within the cross-hatched area one plays sul tasto, the soft quality when one bows properly "over the fingerboard". Closer to the bridge the tone tends toward increased brilliance and power. Exceed maximum pressure and the result is unmusical. Fall short of the minimum and the fundamental mode of vibration is lost. The closer the bow 25 BOW PRESSURE vs. BOW POSITION used in playing i "UDOf TO tOW, ANY INSTIUMINT RIIATIVI DIITiHCI, * too is to the bridge the less generous is the ratio of maximum to minimum pressure and the greater is the skill needed to preserve acceptable tone. The experienced player prizes this domain for its nobility of tone; the beginner finds it prudent to play nearer to the fingerboard. Closer still to the bridge the gap between maximum and minimum all but disappears and with it goes the solid fundamental. When such effects are intended the term "sul ponticello" is used, which means playing on or rather near the "little bridge". 26 27 The line for maximum pressure, according to this formulation, depends on the string but not on the body of the instrument. On the other hand the horizontal line through point A depends on the instrument and not on the string,. The intersection of these lines would therefore locate point A in a very simple manner and make it easy to construct the entire diagram if only we had reliable data for body resistance r. It will be realized that ris too variable from note to note to permit a single quantitative representation of minimum pressure for an instrument. I believe however that players will agree that at least in a qualitative sense the picture is confirmed by experience. We have been talking about sustained tones. But how do sustained tones Start? There are two forms of beginning that we might call the hard and the soft attack. In the first, one sneaks up on the note by initially using less than the maximum pressure indicated for sustained tones that employ the same speed of bow, perhaps even using less than the minimum. The bow is in motion before making a "soft landing" on the string. The tone probably takes many vibrations to reach an equilibrium, A hard attack on the other hand begins with a quasi-pizzicato and with pressure that for a sustained note would fall in the region labelled "raucous", unpleasantness being avoided either by use of an initially low speed of bow or by a prompt decrease in pressure. The hard attack is easier than the soft and is the one most used by uncritical players- I leave it to the teachers to say what Is musically desirable. The diagram of course applies to sustained tones, in particular those of relatively long duration. Another influence in determining bow position is the fact that in eliciting the extreme in loud sounds, pressures demanded near the bridge are excessive and that velocity times frictional force can as a practical matter be made greatest away from the bridge - Finally, experience and theory agree that a bow having acceleration in addition to velocity requires either greater pressure or greater distance from the bridge than one with velocity alone. In a steady tone the total energy stored in the string remains unchanged: that is why we say "stored" energy supplied merely "re-stores" that which is lost to dissipation- At the beginning of a note however the reservoir must be so quickly filled that the initial power needed may be increased by a considerable factor- Suppose that the decaying velocity of free vibration In a string contains the exponential factor e" , where** Q, Is positive. Suppose that we now force this string into a growing oscillation with velocity proportional to eo^*, where 0 is found to be 2-6. Minimum pressure will therefore be similarly raised, perhaps above the pressure being used. If so it will be necessary either to increase pressure, or to bow further away from the bridge in order to preserve a healthy tone. WOOP TRANSLUCENCE AND VIOLIN MAKING — John CSchelleng Holding a wood plate to the light to help judge the approach to. proper thinness is nothing new in violin making. Probably all luthiers have used the criterion to some extent. But there is something new in making trans- lucence a keystone in a method of violin making. A book in which this method is described by the Director of the Staatliche Fachschule ftlr Geigenbau In Mittenwald, Konrad Leonhardt, has recently appeared*- Other matters are discussed and many conclusions reached, several highly debatable, but if his conclusions concerning the "Lichtdurchlassigkeitmethode" can be by others the method should prove to be of considerable importance in making fiddles. $ confirmee, There- is a school of thought that believes it good to have variations from place to place in the wood because this increases the number of resonances in the instrument. Perhaps the analogy behind the belief is the fact that the acoustics of an irregular room are better than those.of one having impor- tant regularities such as the parallel walls of a parallelopiped, though irregularity does not give more resonances but a better distribution of them- In a fiddle however it is hard to see how irregularities in the wood can contribute more than confusion. Without them there are no mathematical regu- larities In form to suggest the degenerate modes of a parallelopiped. It seems more likely that In the long process of evolution ;in the contours of the instrument, natural selection led to a geometric form that in itself gives a musica'lly desirable distribution of resonances with statistically optimum coupling to the strings and that these properties can only be harmed by the introduction of random variables. The method starts with the assumption that the more homogeneous the wood the Detter, and aims at providing the means for securing flexural homogeneity over' the surface in spite of such variations as do occur in the wood. Leonhardt repeatedly speaks of variations in density, but the variations are more complex than that. However, he insists that the method Is a practice, not a theory, and this in any case is a good attitude with which to set out. If you hold a 3 mm plate of spruce to a strong source of light, you find that some light pass'es through, giving a soft rosy glow- The wood is excep- tional however If different areas are equally translucent. Instead, across the grain one finds inequalities that are stretched out along the grain and obviously are related to the effect of climatic change on rate of growth. Perhaps a wood specialist could as readily read the same story from the surface, but this seems doubtful. The author says "The wood speaks only to the violin maker" (not to the calculating scientist) but apparently not even the violin maker understood the message until he used translucence, and the author marvels at the way the old masters succeeded without the method. The method, in the. words of the author, is based on the principle that the vibration of a wood plate follows the distribution of mass, which Is indicated by various degrees in which the light penetrates. (He does not mention variations in elasticity)- The plates of instruments used to demonstrate the method best were first fashioned symmetrically in regard to thickness patterns as one would do if material were homogeneous. The final trimming operation was the further thinning as needed so as to remove excesses of light absorp- tion as indicated by translucence. The final light pattern was thus made symmetrical as it would be with homogeneous material, darker in the thick center and brightest, in the scoop, while the thickness pattern became asymmetric. As a result there were variations in thickness from those for homogeneous material up to plus or minus 3/10 millimeter, corresponding to difference in light absorption. Further checks were made by tapping the plates and observing pitch and decay of the tone, great emphasis being placed on the duration of response. Pitch however he believes to play a subordinate role (more about that later), but the flexibility as tested by hand he regards as an important criterion for determining optimum thickness. It is not clear however how he uses the tests except for equalizing flexibility over the plate since he gives one table for violin, viola, and cello in which thickness at breast, cheek and scoop are specified for the condition just before illuminating, and another plus or minus 3/10 mm after final trimming, all these probably being average values rather than extremes. In view of the considerable variety in available tone woods, how can thickness be thus specified in millimeters? 28 \ The results with two cellos are described as in every respect good; both instruments, among other advantages, being free of wolf tone- In this case however no test of the assembled Instruments was made before the translucence treatment. Two violas, of length 39 cm (15 3/8") were first made with symmetrical thickness (right and left), tested in the white and found good but with certain undesirable characteristics such as A string having a sharp character, C string hoarse. They: were then given the translucence treatment and the results in every case showed the defects to be no longer noticable* The same general conclusion applies to the several violins made by the method- These are broad claims and call for duplication of the experiments by others with the hope, of course, of confirming them. If true one may reasonably exnect a new era in German violin making, led by the legion of graduates from the Staatliche Fachschule. It is appropriate at this point to think in more detail about causes of variations and their effect on the bending waves that produce radiation of sound. First consider a linear bending wave on an infinite sheet of homo- geneous isotropic material of uniform thickness. Its velocity is proportional to (cHf )"2 f where c is the parameter (E/p)z having the dimensions of a velocity, E being Young's modulus and p volume density, H the thickness of the plate and f the frequency of the wave, (it appears permissable in wood to ignore Poisson' s ratio). If we now allow variations in^> and c, the bending wave will be unaffected if they occur in such a way that by giving corresponding variations to H we are able to keep both cH and^oH invariable over the surface, f remaining unchanged. Dividing constant cH by constant/O H, we find that o/p must be everywhere the same, and that H must vary inversely withj!) thing immediately irregularity - completely One obvious is that the cannot be compensated unless c and p vary in such a way as to keep their ratio constant. Replacing parameter c by its more meaningful equivalent (E/p )i we find that (E/p*)« must remain invariable- Thus if the density in going from one point to another increases one percent the elastic modulus must increase three percent to permit perfect correction by reducing thickness one percent. What we should probably hope is that along the grain En/P^, and across it will remain unchanged- This is a large order and it is unlikely that Mother Nature will accommodate- Because of difficulties in analysis even assuming precise knowledge of the wood, approach to final adjustment must remain empirical, as Leonhardt is well aware. The difficult question is how far to go, should it be to the point of equal translucence, or within or beyond it? On pages 23 and 85 Leonhardt dismisses the importance of the frequencies of tap-tones by the remark that their significance is subordinate to that of hand-measured flexibility. This is unfortunate. When two wheels are geared together, we do not regard the speed of one as more informative than the other Likewise, since flexibility, and frequency are connected by the laws of nature, - we do not wisely attempt to legislate relative importance- The rule connecting these two significant data is expressed by the following equation**: Stiffness S 5 jL4 - K»(f/c)fb where K is a constant, p/c is the parameter used above, f-u is the frequency and f, is the length of the instrument assumed to have a standard shape. If wood were reliably the same regardless of source, we could ignore the quantity in parentheses and stiffness and frequency could be regarded interchangeably- But suppose that in the instrument now under construction p/c of the wood is lower than that of the preceding one, do we still make the stiffness the same as it was? This will make f^ higher (violin length %, remaining the same), and if, as we should, we make a proportionate change In the/°/e of the back, the body of the resulting instrument will be pitched higher than the 29 preceding one, in spite of the fact that we shall still tune the A string to 440 Hz. The tuning of the body in the musical scale Is certainly not a matter of indifference. Frequency has the additional advantage that it can be measured with accuracy, whereas stiffness, useful as it has been in the past, ill traditional methods depends on a psycho-physical judgment that la Incapable of objective standardization. Fortunately the efficacy of the method of translucence is not at stake in this question- "Geigenbau und Klangfrage" , Verlag Das Musikinstrument, Frankfurt am Main, * Review by J.C.Schelleng in press, Journal of the Acoustical Society of America ** "The Violin as a Circuit", John. C. Schelleng, JASA, V01. 35* N0, 5, 526-338, March 1963$ Equation 25* # * "* * * * * ■* * * * * * * * * * * * * *:'*-* * THE OPTICAL PROXIMITY DETECTOR IN VIOLIN TESTING Richard E. Menzel and Carleen M- Hutchina The optical proximity detector offers a method of measuring physical displacement at a precise point of a vibrating object without concern for the complications involved In close field acoustical measurements, or distortions introduced with a contact pickup on the surface of the violin. This method was first proposed for use on violins by Warren. Creel.. The detector* consists of a 0.109" diameter sensing probe containing 600 randomly distributed strands of glass fiber-optics encased in a flexible steel monocoil jacket approximately 36 inches long. Half of the fibers transmit light to the observed object, while the other half receive the reflected light, the amplitude of which is dependent upon the distance from the object. The system is so sensitive that it is capable of discriminating a displacement of only ten millionths of an Inch- A simplified diagram of a single pair of transmission and receiving fibers Is shown in Fig-1 ,. Each fiber is coated to prevent light leakage or crosstalk between fibers. Fig. l - Simplified Diagram of the Optical Probe 30 It is obvious that with such extreme sensitivity, the probe must be maintained in perfect relationship to the target area and that it be isolated adequately from ambient vibration to preclude measurement errors. If the probe is to be used in the testing of violin plates it is also necessary that the probe be capable of being precisely oriented to achieve a direction normal to the tangent of the curved surface - a necessity for optimum reflec- tance. With these requirements in mind the test apparatus shown in Fig. 2 was designed. It consists of a 300 lb, reinforced cast concrete base mounted on two 18" diameter pillars. Cast in the base is the input column which carries adjustable arms for supporting the neck of the instrument under test as well as the input transducer. The output column shown on the left is cast into a concrete "U" shaped base which can be moved along a channel cast into the main base. This allows the fixture to be used on all instrument sizes up to the small bass. The illustration shows arms and columns adjusted for a standard cello- The bottom of the channel is lined with -J-" of oil clay to isolate partly the input and output columns from each other. Mounted on the output column is the sensor arm assembly which provides all of the necessary adjustments for optimum sensor probe positioning. Fig, 3 shows a violin mounted with two sensors in position for simultaneous top-back measurement. The end pin has been pressed into a block of oil clay on the main base, while the neck is held in position by the adjustable arm and clay-lined "hand". Fig. 4 shows a top view with two sensors in position for simultaneous measurement of two points on the belly of a violin. The gap of the optical probe (5) is coarse adjusted by moving it through the turret (3) until it nearly touches the violin. It is then secured in position with the locking screw (4)* A very small target of adhesive backed aluminum foil is usually placed on dark surfaces in order to provide greater light reflectivity. The turret and the entire support arm are so designed that they may be adjusted to virtually any angle in order to achieve correct orientation between the probe and the violin plate. The probe distance may then be fine adjusted using the micrometer adjusting knob (.2). If the probe face is brought into direct contact with the surface of the violin, no light will be reflected to the receiving fibers, indicating zero displacement and zero voltage. As the probe is retracted the voltage will continue to rise until the diameter of the reflected cone of light exceeds the diameter of the probe, at which time the instrument becomes virtually insensitive to gap distance. Maximum voltage is achieved at a dis- tance of approximately 0.020". After aligning the associated detector elec- tronics at the minimum and maximum voltages, the probe is brought to a distance of approximately 0.004" from the test surface so that subsequent measurements will be taken in the most linear and sensitive portion of the system response curve. Excitation of the violin is accomplished in the same manner as in acous- tical testing shown in the block diagram, Fig. s. A constant amplitude sine wave from the audio generator sweeping from 20 to 20,000 Hz activates the transducer coil which is clipped to the bridge of the violin- A 5 Hz bandwidth tracking filter is used to eliminate ambient vibrations. 51 "p u o ft ? to M o to« 1 i t a0) 9 a)V h H H O »1 Ma i V) "rt 52 « CQ rt, Fig, 4 - Top View Showing Details of the Apparatus The results obtained with the optical probe adjusted to a point over the soundpost on the back of a viola in playing condition are shown by the dotted curve of the upper chart in Fig. 6- The lower chart shows the displacement recorded from a point near the lower right corner of the back of the same viola. In each chart the solid line is the curve obtained with a probe microphone close to the same spot. The chart shows good corre- lation in the frequencies at which the response peaks occur. The obvious difference in the two curves is the general trend of level as a function of frequency. This can be explained by the difference between the measured charac- teristics. The optical method (dotted lines) measures DISPLACEMENT of the surface Fig. s - Block Diagram of Test Equipment from its mean position and hence is concerned simply with the dimension of length. On the other hand, the acoustical method measures SOUND PRESSURE as from a simple source such as a small piston. 33 Sound pressure is the product of velocity times frequency. Since velocity is proportional to displacement time frequency, it follows that sound pressure is proportional to displacement times the square of frequency. One can see from dimensional considerations that this must be so, since force equals mass times: "" acceleration, and acceleration contains the square of time inversely, or the square of frequency directly, whereas displacement contains it not at all. * For a given displacement we therefore expect, in simple cases, that the slope > of the acoustical measurements will rise faster than that of the optical by twelve decibels per octave. In complicated radiators such as the violin other factors will of course modify the result. r' OPTICAL PROXIMITY DETECTOR Back at db soundpost VIOLA sus 51 Back near db lower right corner DISPLACEMENT SOUND PRESSURE (microphone close) Fig. 6 - Chart Illustrating Comparison Between Optical and Acoustical Methods. This relationship between sound pressure and displacement is shown thus: where P = sound pressure f = frequency v velocity D -= displacement and P ex-vf v «Df 2 whence P 34 55 In the two charts of Fig, 6, the 6 db per octave decrease is indicated by the slanted line. Note that the sound pressure curve (solid line) rises with increased frequency at about the same rate that the displacement curve (dotted line) decreases, approximating the theoretical difference of 12. db per octave. This difference in level has been observed by several researchers, including the late F, A, Saunders when using a stereo pickup actually in contact with a given point on the surface of a violin- Saunders had made, a dozen or more such pickups In an effort to measure the displacement of various points on the vibrating violin body. It must be remembered when working with point by point tests on the violin body that, whenever the nodal line of a given vibrational mode happens to coincide with the point under test, no displacement will be registered even though adjacent areas are vibrating vigorously ., Although the uses of the optical proximity probe in the testing of string instruments are still being explored, certain advantages as well as difficulties are already obvious. An optical pickup eliminates unwanted distortion and crosstalk present in close-field measurements when using both an electromag- netic driver and pickup. Displacement measurements are precise and not subject to the distortions of close-field acoustical pickup. The optical probe does not inhibit or distort the vibrations of the violin body, whereas even the lightest contact measurement system will do so- The wideband noise level of about one millivolt P-P of the present equipment is objectionable and causes some degree of signal loss particularly at the higher frequencies. Hopefully this condition will be remedied. With time and patience such a probe can be used to construct the same information that is beginning to come from the use of interferometric holography on vibrating plates. This involves vibrating the violin constantly at each resonant frequency while measuring the relative displacements with the optical probe at a number of points of the top and back of the instrument. With such information the pattern of nodes, and antinodes in the top and back of a given violin can be plotted for each resonant frequency, (see Newsletter #9: On Vibrational Patterns in Fiddle Plates - John C.Schelleng). The optical proximity detector, when used with an understanding of its essential characteristics, would seem to offer the investigator an extremely useful and relatively inexpensive method for exploring the vibration not only of the violin and other musical instruments, but also of variously shaped plates, shells, bars and strips in a wide variety of materials without the problems involved in acoustical measurement. In the final analysis, however, the airborne sound waves reaching our ears are of paramount importance so that optical methods of studying vibrations, while highly informative, are not likely to replace acoustical methods for measuring the output of musical instruments- *The detector described is the Model KDSB Fotonic Sensor manufactured by M.T^.I. Instruments Division, Latham, N.Y. Price: $259-00