Founding a Family of Fiddles

Home , Bow stroke, Marin Mersenne, Savart, Semitone, Vertical viola, Violino piccolo

The four members of the violin family have changed very little In hundreds of years. Recently, a group of musicians and scientists have constructed a "new" string family.

16 Founding a Family of Fiddles

Carleen M. Hutchins

An article from Physics Today, 1967.

New measmement techniques combined with recent acoustics research enable us to make vioUn-type instruments in all frequency ranges with the properties built into the vioHn itself by the masters of three centuries ago. Thus for the first time we have a whole family of instruments made according to a consistent acoustical theory. Beyond a doubt they are musically successful

by Carleen Maley Hutchins

For three or folti centuries string stacles have stood in the way of practi- quartets as well as orchestras both cal accomplishment. That we can large and small, ha\e used violins, now routinely make fine violins in a

violas, cellos and contrabasses of clas- variety of frequency ranges is the re- sical design. These wooden instru- siJt of a fortuitous combination: ments were brought to near perfec- violin acoustics research—showing a tion by violin makers of the 17th and resurgence after a lapse of 100 years— 18th centuries. Only recendy, though, and the new testing equipment capa- has testing equipment been good ble of responding to the sensitivities of enough to find out just how they work, wooden instruments. and only recently have scientific meth- As is shown in figure 1, oiu new in- ods of manufactiu-e been good enough struments are tuned in alternate inter- to produce consistently instruments vals of a musical fourth and fifth over with the qualities one wants to design the range of the piano keyboard. into them. Now, for the first time, Moreover each one has its two main we have eight instruments of the \ iolih resonances within a semitone of the family constructed on principles of tuning of its middle strings. The re- proper resonance for desired tone sult seems beyond a doubt successful quality. They represent the first suc- musically. Over and over again we cessful application of a consistent hear the comment, "One must hear the acoustical theorv- to a whole family of new instruments to believe such musical instruments. sounds are possible from strings." The idea for such a gamut of violins

is not new. It can be found in Mi- chael Praetorius's Syntagma Musicum Catgut Acoustical Society published in 1619. But incomplete Groundwork in the scientific investiga- understanding and technological ob- tion of the violin was laid bv such men

233 as Marin Mersenne (1636), Ernst the pressure of heavy teaching and and violin makers, coordination of Chladni (1802), Felix Savart (1819) concert schedules. Nevertheless some much technical information from and Hemiann L. F. Helmholtz (1860). were able to find time for the testing, widely separated sources, and design, Savart, who can rightly be considered designing and craftsmanship needed construction and testing of experimen- the grandfather of violin research, in the development of experimental in- tal instruments. In 1937 Saunders re- used many ingenious devices to ex- struments. In 1963 about 30 persons portedi in the Journal of the Acousti- plore the vibrational characteristics of associated with Saunders in this proj- cal Society of America what later the violin. But he was unable to gain ect labeled themselves the "Catgut proved to be basic to the development sufficient knowledge of its complicat- Acoustical Society." This infonnal so- of the new violin family, namely the ed resonances to apply his ideas suc- ciety now has more than 100 members position of the main body resonance cessfully to development and construc- (see box on page 26), publishes a as well as the main cavity resonance tion of new instruments. Recent re- semiannual newsletter and holds one in a series of excellent violins. (The search that has led to our new fiddle or two meetings each year. Among its main body resonance is the lowest family is largely the work of Hermann members are acousticians, physicists, fundamental resonance of the wood

Backhaus, Herman Meinel, Gioacchino chemists, engineers, instrument mak- structure; the cavity resonance is that Pasqualini, Ernst Rohloff, Werner Lot- ers, composers, performing musicians, of the air in the instrument cavity.) ternioser and Frieder Eggers in Eu- musicologists, patrons and others who But the necessary knowledge of liow rope and of the late Frederick A. believe that insufficient attention has to place these resonances with any de- Saunders, John C. Schelleng, William been paid to the inherent potentialities gree of predictability in instruments of Harvey Fletcher and myself in the of bowed string instruments. They good tone (jualit)' was not evolved and United States. are making a coordinated effort to dis- reported until 1960.2 The tonal effect Saunders, widely known for his cover and develop these potentialities of this placement of the two main work on Russell-Saunders coupling, pi- and are encouraged that many mem- resonances for each instrument and the oneered violin research on this side of bers of the violin fraternity share their necessar>' scaling theory was not re- the Atlantic. He was a former chair- aims. ported until 1962.3 man of the physics department of Har- Among other accomplishments of Between 1950 and 1958 Saunders

vaid Uni\ersity, a fellow of the Na- our Catgut Acoustical Society is a con- and I undertook a long series of exper- tional Academy of Sciences and presi- cert played at Harvard last summer iments to test various features of violin dent of the Acoustical Society of during the meeting of the Acoustical construction one at a time. We deter- America. In his work on violin acous- Society of America. It was dedicated mined effect of variations in length,

tics, Saunders gradually became as- to Saunders and the instruments were shape and placement of the f holes, sociated with colleagues who were our eight new fiddles, which are the position of the bass bar and sound

highly competent in various scientific outgrowth of research he began. I post, significance of the inlay of pur- and musical disciplines. These associ- write about the concert and about the fling around the edges of top and back ates greatly furthered the development instruments as a member of the society plates and frequency of the ca\ity res- of his work and contributed valuable and as one who worked with Saunders onance as a function of rib height and

technical knowledge, but they had lit- from 1948 until his death in 1963. f hole areas (see figure 2). Because tle time for experimentation. Some My activities include reconciliation of many of these experiments needed de- were skillful musicians living under the wisdom of experienced musicians finitive testing equipment not then

available, most of the results are still unpublished in Saunders's notebooks. One sobering conclusion we reached was that with many alterations in such

features as size and shape of f holes, position of the bass bar and sound post, the best tonal qualities resulted when conventional violin-making rules In addition to nur- W were followed. In other words, the turing her fiddle \ early violin makers, working empirical- family, the author ly b\' slow trial and error, had evoked shows interest in children. .After Krul- a s\stem that produced practically op- uatiiig from Come timal relationships in \iolin construc- she taiiKhl for IS tion. years in Now Yoik In 1958. during a long series of ex- schools, acquiring an periments to test the effect of moving M.\ from New York l'ni\crsity nican- \i()lin and viola resonances up and whilc. She also ,u- down scale, the composer in residence ^ ,#10^ i (piiii'il a clicmist hits- Ij ^''jT at Bennington College, Henry Brant, h.uul and two iliil- Ij ^^^M_ and the cellist. Sterling Hunkins, pro- (Iren, all of whom 1 '^HV^ posed development of eight violin- live MnnU'laiv. f^ ^^^u type instruments in a .scries of tunings I -Mm

234 Founding a Family of Fiddles

D 293.7- E 329.6 C 261.6 F 349.2 B 246.9 G 392 ! A A A A A A 27.5 55 110 220 440 880 1760 3520

FREQUENCY (cycles/sec)

iiiiiimmmiifniiimiiiniTff TREBLE (6-D-AE)

lllllll1!ITimil!!!lllltHI!ll! SOPRANO ((>G-D-A)

IIIIIIH!H!lllllt!lfllglTIIIIIT MEZZO (6-D-A-E)

IIHHIf!ll!filirilllllfflltf ALTO (C-G-D-A)

l!ll'll!!Hmi!l!IHIIHIiri[! TENOR (G-D-AE)

lllll!l!H!ltl!ll!!lllll!!ll!!l! BARITOFtf (C-G-D-A)

lllltltllfri!!ll!!lfflHII!lfim SMALL BASS (A-IW3-C) mMUMBM CONTRABASS (E-A-IVG)

NEW INSTRUMENT TUNING spans the piano range with eight fiddles that range in size from 210-cm contrabass to a 27-cm treble. The conventional violin is the mezzo of the new scries. Colored keys show tuning of new instruments and white dots that of conventional instruments. —FIG. 1

235 —

and sizes to cover substantially the sion Saunders and I agreed that a seri- contrast to the conventional viola, cello whole pitch range used in written ous attempt would be made to de- and string bass. music; these instruments would start velop the set. The main problem with an oversize contrabass and go to would be to produce an instrument in Research and new fiddles a tiny instrument tuned an octave each of the eight frequency ranges The problem of applying basic re- above the violin. Their request was having the dynamics, the expressive search results to actual design and so closely related to our experimental qualities and overall power that are construction of new instruments now work that after half an hour's discus- characteristic of the violin itself, in faced us. From the previous ten

Who's Who in Catgut Acoustics

Without cross fertilization of vibrations, elasticity, shear W. Hinckley, Ellis Kellert, Schradieck Aue, Virginia ideas from experts in many and damping in the instru- Henry Allen Moe, Ethel and Apgar, Emil Bloch, Harold related disciplines our new ments and their parts: Ar- William R. Scott. Coletta, Helene Dautrich, fiddle family could not have thur H. Benade, Frieder Eg- Secretaries. Lorraine El John D'Janni, Lillian Fuchs, evolved in the short period of gers, Roger Kerlin, Max V. liott. Belle Magram. Raphael Hillyer, Henry nine or ten years. No listing Mathews, Bernard W. Robin- Violin experts and makers James, Boris Kroyt, Eugene of names and activities can son, Robert H. Scanlan, John Karl A. Berger, Rene Morel Lehner, Rustin Mcintosh, do justice to each one whose C. Schelleng, Eugen J. Simone F. Sacconi, Rembert John Montgomery, Elizabeth thinking and skills have been Skudrzyk, Thomas W. W. Wurlitzer, myself—and Vir Payne, Werner Rose, David challenged and who has Stewart, Sam Zaslavski. ginia Apgar, Armand Bartos Schwartz, Emanuel Vardi, given time, energy and Chemists. Effects of var- William W. Bishop, Donald L Eunice Wheeler, Bernard Zas- money. Their only reward nish and humidity on the in- Blatter, William Carboni lav, Sam Zaslavski, myself. is sharing in the project. struments; varnish research: Louis M. Condax, Fred Dau Cellists. Robert Fryxell, The spirit of the group has Robert E. Fryxell, Morton A. trich, Jean L. Dautrich, Louis John C. Schelleng, India been likened to the informal Hutchins, Louis M. Condax. Dunham, Jay C. Freeman Zerbe—and Charles F. Aue, cooperation tha; flourished Architect. Basic design Louis Grand, Jerry Juzek Joan Brockway, Roy B. and development of patterns Chamberlin, Frank Church, among scientists in the 18th Otto Kaplan, Gordon McDon for the violin family, Elwood Culbreath, Oliver century. In addition many new and aid, William E. Slaby. Edel, Maurice Eisenberg, of the active experimenters maker of bows for them: Violinists. Charles F. Aue are themselves enthusiastic Maxwell Kimball. Broadus Erie, William Kroll George Finckel, Marie Gold- man, Barbara Hendrian, string players so that a tech- Electronic engineers. Sonya Monosoff, Helen Rice Ar- Norman Dooley, Francis L. nold Kvam, Russell B. King- nical session is likely to end Louis E. Zerbe—and Sam man, Charles with chamber-music playing. Fielding, Sterling W. Gor- uel Applebaum, Catherine McCracken, rill, A. Stuart Hegeman, Alvin Stephen McGee, George In the following list I try to Drinker Bowen, Marjorie Hopping. Ricci, Peter Rosenfeid, Mary include all those who have S. Bram, Ernestine Briemeis Lou Rylands, True Sackrison, helped along the way, listing Translators. Mildred Al- ter, Alan Branigan, Nicos Mischa Schneider, Sanford those who have been most len, Edith L. R. Corliss, Don- Cambourakis, Roy B. Cham Schwartz, Joseph Stein, Mis- active first even though they ald Fletcher. berlin Jr., Frank Clough cha Slatkin, Joseph Tekula. are not all members of CAS. Editors. Harriet M. Bart- Louis M. Condax, Yoko Mat Some of the numerous lett, Dennis Flanagan, Rob- suda Erie, Sterling Gorrill Bassists. Julius Levine, musicians are not actually ert E. Fryxell, Mary L. Har- Walter Grueninger, Ann Ha Alan Moore, Ronald Naspo, Alvin familiar with the new instru- bold, Martha Taylor, Alice worth, H. T. E. Hertzberg David Walter—and ments, but their comments Torrey, Howard Van Sickle. Carol Lieberman, Max Man Brehm, John Castronovo, on earlier experimental mod- Photographers. Louis M. del. Max V. Mathews, David Garry Karr, Stuart Sankey, Traeger, els of conventional violins, Condax, Russell B. Kingman, Montagu, Max Pollikoff, Ber Charel Howard Van violas and cellos have provid- Douglas Ogawa, Peter N. nard W. Robinson, Booker Sickle, Ellery Lewis Wilson. ed musical insights and in- Pruyn, J. Kellum Smith. Rowe, Frances Rowell, Rob Composers and conduc- formation necessary to the Artist. Irving Geis. ert Rudie, Florence DuVal tors. Henry Brant and new instruments. Lawyers. Harvey W. Mor- Smith, Jay C. Rosenfeid. Marjorie Bram, Justin Con- Physicists. Basic re- timer, J. Kellum Smith, Rob- Violists. Robert Courte, nolly, Herbert Haslam, Frank search and scaling for the ert M. Vorsanger. Lilla Kalman, Maxwell Kim- Lewin, Marc Mostovoy, Har- new instruments: Frederick General consultants. ball, David Mankovitz, Louise old Oliver, Quincy Porter, A. Saunders, John C. Schel- Alice T. Baker, Donald Engle, Rood, Frederick A. Saunders Cornelia P. Rogers, Leopold leng and myself. Theory of Cushman Haagensen, Mary —and John A. Abbott, Alice Stokcwski, Arnold M. Walter.

PHOTO BY J. KELLUM SMITH

REHEARSAL for a concert with Henry Brant conducting an octet of fiddles.

236 Founding a Family of Fiddles

BRIDGE

INSTRUMENT PARTS, except for scaling, have remained the same since master years' experimentation, the following resonance of a completed violin or makers brought the violin to near perfection about three centuries four working guides were at hand: viola is approximately seven semitones ago. —FIG. 2 1. location of the main body and above the average of the main free- main cavity resonances of several plate resonances, usually one in the hundred conventional violins, violas top and one in the back plate of and cellos tested by Saunders and oth- a given instrument.'- This obsen'a- ers.i. 4-« tion came from electronic plate test-

2. the desirable relation between ing of free top and back plates of violins violas main resonances of free top and back 45 and under construc- itself that would set it apart from its plates of a given instrument, devel- tion. It should not be inferred that cousins, the viola, cello and contra- oped from 400 tests on 35 violins and the relation implies a shift of free-plate bass. The search for this controlling 2,10,11 violas during their construction, resonances to those of the finished in- characteristic, unique to the violin, 3. knowledge of how to change strument. The change from two free led us through several hundred re- frequencies of main body and cavity plates to a pair of plates coupled at sponse and loudness curves of violins, resonances within certain limits their edges through intricately con- violas and cellos. The picture was at (learned not only from many experi- structed ribs and through an off-center first confusing because many varia- ments of altering plate thicknesses, rel- soundpost, the whole \mder varying tions were found in the placement of ative plate tunings and enclosed air stresses and loading from fittings and the two main resonances. However, volume but also from constru'^tion of string tension, is far too complicated to Saunders's tests on Jasha Heifetz's experimental instruments with varying test directly or calculate." Guamerius violin^^ showed the main- body lengths, plate archings and rib body resonance was near the fre- What is good? heights) and of resultant resonance quency of the unstopped A 440-cycles- placements and effects on tone quality In developing the new instnmients our per-second string and the main cavity in the finished instruments,**-^^ main problem was finding a measura- resonance at the unstopped D 294 4. observation that the main body ble physical characteristic of the violin string. Thus the two main resonances

237 I of this instrument were near the fre- small violas, showed enormous varia- violin, this shallow, heavy-wooded in- quencies of its two unstopped middle tion in the placement of these two res- strument had amazing power and clar- strings. onances. We hoped to find some in- ity of tone throughout its range. It Ten violins, selected on the basis strument in which even one of these sounded like a violin although the that their two main resonances were resonances would approximate what quality on the two lower strings was within a whole tone of their two open we wanted for the new instruments. somewhat deeper and more viola-like middle strings, were found to be some In one quarter-size cello the body that the normal violin. of the most musically desirable instru- resonance was right for viola tuning, D The next good fortune was discov- ments—Amatis, Stradivaris, Guar- 294, but the cavity resonance was too ery and acquisition of a set of three in- neris and several modem ones. In low at D 147. We bought this struments made by the late Fred L. marked contrast to these were all vi- chubby Uttle cello and reduced the Dautrich of Torrington, Conn., during olas and cellos tested, which charac- rib height nearly 4 in. (10 cm), the 1920's and '30's. He had de- teristically had their main body and thereby raising the frequency of the scribed them in a booklet caUed Bridg- cavity resonances three to four semi- cavity resonance to the desired G 196. ing the Gaps in the Violin Family.^ tones above the frequencies of their When it was put back together, it His vilonia, with a body length of two open middle strings although they looked very thin and strange with ribs 20 in. (51 cm) was tuned as a viola still had the same separation, approxi- only 1.5 in. (3.8 cm) high and a body and played cello-fashion on a peg. mately a musical fifth, between these length of over 20 in. (51 cm), but The vilon, or tenor, which looked like two main resonances. strung as a viola it had tone quality a half-size cello, was tuned an octave We reasoned that the clue to our satisfactory beyond expectations! below the violin, G-D-A-E. His vi- problem might be this placement of An experimental small viola that I lone, or small bass, with strings tuned the two main resonances relative to had made for Saunders proved to have two octaves below the violin, filled the the tuning of the two open middle its two main resonances just a semi- gap between the cello and the con- strings. A search through many small tone below the desired frequency for trabass. These represented three of violins and cellos, as well as large and violin tone range. When strung as a the tone ranges we had projected for the new violin family. Tests showed that their resonances lay within working range of our theory. A year of work, adjusting top and back plate wood thicknesses for desired resonance frequencies and rib heights for proper cavity resonances in each of the three instruments gave excellent results. The vilono proved to have ex- actly the resonance frequencies projected for the enlarged cello, or bari-

tone. So it was moved up a notch in the series and tuned as a cello with extra long strings. Dautrich's pioneering work had saved years of cut and try. We now had four of the new instruments in playing condition; mezzo, alto (verti-

'«S 1/ '^

2 3 4 S BODY LENGTHS for new instniments w«re determined by plotting lengths WAVELENGTH (relativ»—log scale) of known instruments against wavelength, then extending data in a smooth curve to include treble at one end and contrabass at the other. Identified points show where old and new instruments fall. —FIG. 3

238 Founding a Family of Fiddles

cal viola), tenor and baritone. I was struments, and the musicians gave the moval of its low E 41 string and the able to add a fifth by making a so- new family of fiddles its first workout. addition of a high C 131 string to prano, using information gained from The consensus was that our hypothesis bring the tuning to A-D-G-C (basses many tests on three-quarter- and half- was working even better than we had are tuned in musical fourths for ease of size violins. dared to hope! Apparently the violin- fingering) it fitted quite well into the With five of the new instruments type placement of the two main reso- series as the small bass. But as yet no developed experimentally and in play- nances on the two open middle strings prototype for the contrabass could be ing condition, we decided to explore of each instmment was enabling us to located. This final addition to the se- their musical possibilities and evaluate project the desirable qualities of the ries was to come later. the overaU results of our hypothesis of violin into higher and lower tone resonance placement. In October ranges. First musical success 1961 the working group gathered at The next step was to explore the By January 1962 we were ready for a the home of Helen Rice in Stock- resonances of various size basses to real test in which experts could hear bridge, Mass., where Saunders and his help in developing the small bass and our six new instruments and compare associates had, for some years, met fre- the contrabass. A small three-quarter- them with good conventional violins, quently to discuss violin acoustics and size bass with arched top and back violas and cellos. Composers ar- play chamber music. Short pieces of proved to have just about proper reso- ranged special music, and professional music were composed for the five in- nances for the small bass. With re- players had a chance to practice on the new instruments.

Ensemble results exceeded all our expectations. We had violin-like quality and brilliance through the en- tire range of tones. Our soprano produced a high clear quality that carried

well over the other instruments al- iliiliiiliiliiiliili lilijli III iiliiiliili III I ilill A though the high positions on its two 440 lower strings were weak. The mezzo tone was powerful and clear although somewhat viola-like on the two lower strings. The alto (vertical viola) was STRAOIVARIUS VIOLIN 1713 m rf^r judged a fine instrument even with in- adequate strings. The unique tone of HUTCHINS VIOLIN tioM the tenor excited all who heard it. OPEN STRINGS 6 D A E The baritone produced such powerful and clear tones throughout its range

that the cellist playing it in a Brahms

sonata commented, 'This is the first HUTCHINS 42.5-CM time I have been able to hold VIOLA No.34 my own with the piano!" The small bass was HUTCHINS 44<:M adequate VIOLA No.42 but needed more work. General comments told us that the c e D A new instr\iments were ready to stand on their own, musically, although much more work was to be done on

CARLOS BERGONZI III adjustments, strings and proper bows. CELL0-l«17 End-of-scale problems HUTCHINS CEaONo.38 With the helpful criticisms and suggestions that came from the C G D A first musical test we were encouraged to

p::: TESTORE BASS LOUDNESS CURVES are useful GERMAN BASS instrument character- RESONANCES evaluations of istics. Each is made by bowing an W = WOOD PRIME instrument to maximal loudness at 14 semitones on each string and plotting C =: CAVriY the resulting loudness ceiling against B = BODY (wood) frequency of sound. — FIG. 4

239 k tackle the problems of the largest and quency at the low end and the treble tone, and the cavity resonance is a smallest instruments. No existing in- frequency at the upper end, an octave fourth above that. (Wood prime is struments could be adapted experi- above the normal violin. This proce- the strengthened frequency one oc- mentally. We had to design and build dure gave a projected body length of tave below the main body—"wood" them. 51 in. ( 130 cm) for the contrabass and —resonance.) These conditions are The largest bass available for testing 10.5 in. (26.5 cm) for the treble. Of exemplified in Heifetz's Guamerius was a huge Abraham Prescott, with a course rib height and enclosed air vol- violin and many other good ones, but 48-in. (122-cm) body length, made in ume were separately determined by they are not found in all good violins. Concord, N.H., in the early 1800's but other considerations. The loudness curve developed by even that was not big enoughl A tiny Saunders is one of our most useful pochette, or pocket fiddle, from the Current design practice measures for evaluating overall instru- Wurlitzer collection, with a body From all of this experience we have ment characteristics. We make such a length of 7 in. (18 cm) had the right developed what we might call a "de- curve by bowing an instrument as cavity resonance, but its body reso- sign philosophy." It depends mainly loudly as possible at 14 semitones on nance was much too low. on resonance placement and loudness each string and plotting maximal loud- The body length of each of the new curves. ness against frequency. Despite una- instruments has been one of the con- Our resonance principle, according voidable variations in any test that re- trolling factors in all of our experi- to which each member of the new quires a musician to bow an instruments. Thus it was decided that the violin family has been made, can be ment, the loudness curve is significant best way to arrive at the dimensions stated as follows: The main body res- because there is a fairly definite limit for the largest and smallest would be onance of each of the instruments to the momentary volume an experi- to plot a curve of body lengths of tuned in fifths is placed at the fre- enced player can produce with a short known instruments, to check against quency of the open third string, and rapid bow stroke. their resonance placement and string the main cavity resonance at the fre- As you will see in figure 4, the loud- tuning. This tvorking chart is shown quency of the open second string. ness ceiling varies for each semitone in figiure 3 in which linear body length Another way of stating the principle, on a given instniment. The curves of is plotted against the logarithm of and one that includes the instruments this figure were made by bowing each wavelength. The curve for the new tuned in fourths as well as those timed instrviment without vibrato at a con- instnmients was extended in a smooth in fifths, is this: Wood prime is stant distance from a sound meter. arc to include the contrabass fre- placed two semitones above the lowest From them you can see the placement of main body and cavity resonances in eight conventional instnmients—two violins, two violas, two cellos and two basses. You can see that in the violins the wood prime adds power to the low range of the G string. In the vi- \^THEOnmeAL LENQTH olas, cellos and basses the two main resonances, which are higher in fre- '\ ^mw wwTnuMcms quency relative to string timing, create

CONVENTIONAL

2 1.5

1.17 •MAN VIOUN

HORIZONTAL INSTRU ae7

CONTRABASS MRrTONE 0.75 VKMJN TREBLE TENOR VIOU SOfRANO

0.1C7 OJS aS3 0.5 0.67 1 1.33 FREQUENCY (relative—4oc seal*) SCALING FACTORS for old and new instruments are a useful reference guide for designers. —FIG. 5

240 Founding a Family of Fiddles

a condition of somewhat weaker re- We developed a series of scaling with basic traits in common. But they sponse on the lowest four or five semi- factors^ based on relative body length, also have their own personalities. tones. relative resonance placement and rela- Treble ( G-D-A-E ) . The main prob- tive string tuning that could be used as lem with our treble has been to get the to players Fitting fiddles a reference guide in actual instrument frequencies of body and cavity reso- After you decide what kind of acous- construction. Figure 5 shows set the nances high enough and still keep the tics you want, you still have another which has proved most useful in mak- mensure long enough for a player to problem: You have to make fiddles ing the eight new instruments as well finger consecutive semitones without that people can play. For years we as those of conventional instruments. having to slide his fingers around. worked toward design of an acousti- We had a problem in measuring re- We projected a theoretical body cally good instrument with genuine sponses of plates of sizes— all many the length of 10.5 in. (26.7 cm) and a viola tone. Meanwhile we had to way from the 10.5-in. (26-cm) one of string length of 10 in. (25.4 cm), but keep in mind such conflicting require- the treble violin to the 51-in. (130- to have the proper cavity resonance in ments as large radiating areas in the cm ) one of the contrabass. We solved this size body, the ribs would be only plates adequate clearance in it by redesigning and bow our transducer from 3 mm high-a potentially dangerous (figure Relation of a magnet-armature the C bouts 2). to a moving-coil structural condition! Besides we string length to other dimensions that type. Then the wooden fiddle plate, knew of no string material that could define tone spacing on the fingerboard suspended at its comers by elastic be tuned to E 1320 at a length of 25.4 —the viohn maker's "mensure"— is an- bands, was made to vibrate as the cm without breaking. At one point other consideration important to the cone of a loudspeaker (figure 6). we thought we might have to resort to player. With our acoustic pattern as a Using the know-how developed in a three-stringed instrument in this enlarging, making and testing model we undertook scahng several hundred range as was indicated by Michael and redesigning all our new instru- violin, viola and cello plates, I could Praetorius in 1619.1^ tune ments, always keeping violin place- the plates of new instruments so The cavity-resonance problem was ment of resonances in tone range. that not only did each pair each of top and solved by making six appropriately From our set of experimentally back plates have the desired frequency sized holes in the ribs to raise its fre- adapted instruments, which represent relation, 2 but it also had its wood quency to the desired D 587. A string a variety of styles and designs in violin thicknesses adjusted to give a reason- material of requisite tensile strength to making, things. able approach to what we had learned many would be an reach the high E 1320 was finally optimal response. ^^ The vertical viola was about right in found in carbon rocket wire, made by As a starting body dimensions, but its strings were guide in adjusting plate National Standard Company. This frequencies I used too long for viola fingering and too the finding that a proved suitable not only for the high E seven-semitone short for cello fingering. The tenor interval should sepa- string but for a number of others on was too small, and the cellists were rate the main body resonance of the the new instruments. As a temporary asking for it strings as finished violin from to have as long the average of the measure the ribs were made of soft two possible. The baritone was right for frequencies of the free plates. It aluminum to prevent the holes from body size, but it had much too long was soon obvious, however, that this unduly weakening the structure. Re- relationship strings. The bass players were asking was not going to hold as design should eliminate the nasal for the instnmients a long neck on the small bass and a increased in size. As quality found on the lower strings and short the the instrument gets larger the one on large bass with string interval improve the upper ones. Despite this lengths as close as possible to conven- becomes smaller, but we do not have nasal quaHty many musicians are tional. enough data yet to make a precise pleased with the degree in which the From such comments we realized statement about it. upper strings surpass the normal violin that there were two basic designs for We used scaling theory and the in the same high range. ease of playing in relation to string three basic acoustical tools of scientific Plans are to redesign this instrument lengths violin making: and overall mensure of each (a) frequency rela- in several different ways in an effort to instrument. ControlHng factor in the tionship between free top and back discover the best method of achieving instrument is plates, (b) optimal response in mensure placement of each desired tone quality throughout its en- the notches of the f holes because a plate and (c) interval between body tire range. line drawn between these two points resonance and average of free-plate Soprano (C-G-D-A). The soprano dictates the position of the bridge and frequencies. We are able not only to was designed to have as large a plate the highest part of the arch of the top create new instruments of the violin area as possible, with resulting shallow plate. Mensure for the tenor and family but also to improve the present ribs and fairly large f holes to raise the small bass would need to be as great members. But we have to combine cavity resonance to the desired G 392. as possible and for the vertical viola the acoustical tools with the highest The overall tone has been judged good and baritone it would need to be as art of violin making. and is most satisfactory on the three small as possible. Since the relative upper strings. The instrument needs Traits of family members areas of the upper and lower bouts are redesign, however, for a better quality critical factors in plate tuning, adjust- Any family has its resemblances and on the lower strings. The mensure is ment of these mensures posed quite a its differences. So it is with our vio- as long as possible for playing con- set of problems. lins. They make a family (figure 7) venience. J. S. Bach wrote for an in-

241 TESTING FIDDLES. New tech PHOTOS BY PETER PRUYN niques enable today's makers to achieve results their predecessors that even an excellent concert violin floor. Even with an unusual body could not produce. Redesigned transducer measures response of plate that did not have the power of the other length of 20 in., its mensure has been is made to vibrate like a loudspeaker members of the group. According adjusted to that of a normal 17.5-in. cone in operation. —FIG. 6 to scaling theory^^ this instrument, (44.5-cm) viola, and some violists

which is 1.14 times as long as the with large enough physique have been strument in this tuning, which Sir violin, has somewhat more power than able to play it under the chin. Cello George Grove describes in Grove's dic- necessary to match that of the others. teachers have been impressed by its tionary:^'^ "The violino piccolo is a So a second instrument has been de- usefulness in starting young children small violin, with strings of a length veloped that is 1.07 times as long as on an instrument that they can handle suitable to be tuned a fourth above the the violin. It has violin placement of readily as well as one they can con- ordinary violin. It existed in its own resonances yet is adjusted to have con- tinue to follow for a career. The right for playing notes in a high ventional violin mensure for the play- greatest advantage is the increase in '^ compass. . . .It survives as the 'three- er. It has more power than the nor- power and overall tone quality.^o quarter violin' for children. Tuned mal violin and seems most satisfactory. Leopold Stokowski said when he like a violin, it sounds wretched, but In fact several musicians have indicat- heard this instrument in concert, "That in its proper pitch it has a pure tone ed that it may be the violin of the fu- is the sound I have always wanted color of its own, for which the high ture. from the violas in my orchestra. No positions on the ordinary violin gave Alto (vertical viola) (C-G-D-A). viola has ever sounded like that be- no substitute." The greatest difficulty with the alto fore. It fills the whole hall."

Mezzo (G-D-A-E). The present is that it puts the trained viola player Tenor ( G-D-A-E ) . The body length mezzo with a body length of 16 in. at a distinct disadvantage by taking of the tenor was redeveloped from the (40.5 cm) was added to the new the viola from under his chin and set- Dautrich vilon which had a length violin family when musicians found ting it on a peg, cello fashion on the ratio of 1.72 to the violin. The pres-

242 Founding a Family of Fiddles

PHOTOS BY J. KELLUM SMITH

THE WHOLE FAMILY poses for pictures with performers trying them out. —FIG. 7

MAX POLLIKOFF ERNESTINE BREIMEISTER LILLA KALMAN treble soprano mezzo

ent tenor has a ratio of 1.82 with onance of our baritone is nearly three trabass^i is 7 ft (210 cm) high overall; other factors adjusted accordingly, and semitones lower than projected, and yet it has been possible to get the the strings as long as possible for con- this departure probably accounts for string length well within conventional venience in cello fingering. Many the somewhat bass-like quality on the bass mensure at 43 in. (110 cm) so musicians have been impressed with low C 65.4 string. Its strings are 0.73 that a player of moderate height has its potential in ensemble as well as solo in. (1.8 cm) longer than those of the no trouble playing it except when he work. They are amazed to find that it average cello. One concert cellist said reaches into the higher positions near is not a small cello, musically, but a after playing it for half an hour, "You the bridge. For sheer size and weight large octave violin. have solved all the problems of the it is hard to hold through a 10-hr re- The main problem for this instru- cello at once. But I would like a con- cording session as one bassist did. ment is that there is little or no music ventional cello string length." Thus a When it was first strung up, the player for it as yet. Early polyphonic music, redesign of this instrument is desirable felt that only part of its potential was where the tenor's counterpart in the by shortening the body length a little. being realized. The one construction- viol family had a voice, has been rear- This redesign would raise the fre- al feature that had not gone according ranged for either cello or viola. It has quency of the body resonance and at to plan was rib thickness. Ribs were 3 no part in classical string or orches- the same time make possible a shorter mm thick, whereas violin making indi- tral literature, and only a few con- string. cated they needed to be only 2 mm temporary compositions include it. Small bass (A-D-G-C). Our first thick. So the big fiddle was opened; Grove'" has this to say: "The gradual newly constructed instrument in the the lining stripes cut out, and the ribs suppression of the tenor instrument in bass range is shaped like a bass viol planed down on the inside to an even the 18th century was a disaster; with sloping shoulders, but has both 2 mm all over— a job that took 10 days. neither the lower register of the viola top and back plates arched and other But when the contrabass was put to- nor the upper register of the violon- features comparable to viobn construc- gether and strung up, its ease of play- cello can give its effect. It is as tion. This form was adopted partly to ing and depth of tone delighted all though all vocal part music were sung discover the effect of the sloping who played or heard it. Henry Brant without any tenors, whose parts were shoulders of the viol and partly be- commented, "I have waited all my life distributed between the basses and cause a set of half-finished bass plates to hear such sounds from a bass." contraltos! It is essential for 17th was available. The next small bass is century concerted music for violins being made on violin shape with other How good are they really? and also for some works by Handel features as nearly like the first one as All who have worked on the new in- and Bach and even later part-writing. possible. Bass players have found the struments are aware of the present In Purcell's Fantasy on One Note the present instrument has a most desira- lack of objective tests on them—aside true tenor holds the sustained C. . . ble singing quality and extreme play- from musician and audience com- The need for a real tenor voice in the ing ease. They particularly like the ments. In the near future we plan to

19th century is evidenced by the many bass-viol shape. It has proved most compare comments with adequate abortive attempts to create a substi- satisfactory in both concert and re- tonal analyses and response curves of tute." cording sessions. these present instruments as well as

Baritone ( C-G-D-A ) . The body res- Contrabass (E-A-D-G). Our con- new ones when they are made. The

243 STERLING HUNKINS PETER ROSENFELD JOSEPH TEKULA DAVID WALTER STUART SANKEY alto tenor baritone small bass contrabass

only objective evaluation so far comes with high-pitch playing, but the mu- free plate as compared to those in the from A. H. Benade at Case Institute: sician was up to it and we managed to assembled instrument; the reasons for "I used my 100-W amplifier to run a guess reasonably well. The playing the effect of moisture and various fin- tape recorder alternately at 60 and 90 was done without vibrato. It is a ishes on the tone of a vioUn and the cps while recording a good violin with tribute to everyone involved in the de- possibility of some day being able to the machine's gearshift set at the three sign of those fiddles that they really do write adequate specifications for a nominal 1-, 3.5- and 7.5-in/sec speeds. sound like their scientifically trans- fabricated material that will equal the This was done in such a way as to posed cousin violin." tone qualities of wood! make a tape which, when played back But as yet we know only part of e o • give forth sounds why this theory of resonance place- at 3.5 in/sec, would This work has received support from the • at the pitches of the six smaller instrument is working so well. Probing John Simon Guggenheim Memorial Foun- dation, the ments in the new violin family (small deeper into this "why" is one of the Martha Baird Rockefeller Fund for Music, the Alice M. Ditson bass and contrabass excluded). There challenges that lie ahead. Still un- Fund of Columbia University, the Catgut interesting problems about solved are the problems of the intri- were some Acoustical Society and private contribu- the subjective speed of low- compared cate vibrational patterns within each tions.

References Acustica 9, 453 (1959). printed 1964 by Internationale Gesell- schafl fiir Musikwissenschaft, Baren- 1. F. A. Saunders, "The mechanical ac- 9. W. Lottermoser, W. Linhart, "Beit- rag zur akustichen Prufung von Gei- reiter Kassel, Basel, London, New tion of violins," J. Acoust. Soc. Am. 9, York, page 26. 81 (1937). gen und Bratschen," Acustica 7, 281 2. C. M. Hutchins, A. S. Hopping, F. A. (1957). 17. G. Grove, Grove's Dictionary of Musks Saunders, "Subharmonics and plate 10. C. M. Hutchins, A. S. Hopping, F. A. and Musicians, 5th ed., St. Martins

tap tones in violin acoustics," J. Saunders, "A study of tap tones," The Press, New York (1954). vol. 8,

Acoust. Soc. Am. 32, 1443 (1960). Strand, August, September ( 1958). page 809. 3. C. Schelleng, "The violin as a cir- 11. C. M. Hutchins, "The physics of vio- J. 18. J. C. Schelleng, "Power relations in cuit," J. Acoust. Soc. Am. 35, 326 lins," Scientific American 207, no. 5, the violin family," paper presented at (1963). 78 (1962). 71st meeting. Acoustical Society of 4. F. A. Saunders, "Recent work on vio- 12. R. H. Scanlan, "Vibration modes of America, Boston (3 June 1966).

lins," Acoust. Soc. Am. 25, 491 coupled plates," J. Acoust. Soc. Am. J. 19. C. M. Hutchins, C. Schelleng, "A (1953). 35,1291 (1963). J. new concert violin," paper presented 5. F. A. Saunders, "The mechanical ac- 13. F. A. Saunders, C. M. Hutchins, "On to the Audio Engineering Society, 12 tion of instruments of the violin improving violins," Violins and Vio- Oct. 1966 ( to be published ). family," J. Acoust. Soc. Am. 17, 169 linists 13, nos. 7, 8 (1952). 20. Hutchins, "Comparison of the (1946). 14. F. L. Dautrich, H. Dautrich, "A chap- C. M. acoustical and constructional para- 6. F. A. Saunders, unpublished note- ter in the history of the violin family," the con\entional 16 to books. The Catgut Acoustical Society News- meters of 17-in. viola and the new 20-in. verti- 7. H. Meinel, "Regarding the sound letter No. 4 (1 Nov. 1965). cal viola," Acoust. Soc. Am. 36, quality of violins and a scientific basis 15. C. M. Hutchins, The Catgut Acousti- J. 1025 (1964) (abstract only). for violin construction," J. Acoust. cal Society Newsletter No. 5 ( 1 May

Soc. Am. 29, 817 (1957). 1966) and No. 6 ( 1 Nov. 1966). 21. C. M. Hutchins, "The new contrabass 8. F. Eggers, "Untersuchung von Corp- 16. M. Praelorius, Syntagma Musicum violin," .•\merican String Teacher, us-Schwingungen am Violoncello," II: de Organographia (1619); re- Spring 1966.

244 Some nonscientlsts hold odd views of the nature of science. This article catalogs and analyses the most common fallacies.

17 The Seven Images of Science

Gerald Helton

An article from Science, 1960.

Pure Thought and Practical Power

Each person's image of the role of brace each of the three functions. zeal along a dimension where no ulti- science may differ in detail from that However, usually only one of the three mate—that is, religious—concerns pre- of the next, but all public images are is recognized. For example, folklore vail. It is evident that these views fail in the main based on one or more of often depicts the life of the scientist to recognize the multitude of divergent

seven positions. The first of these goes either as isolated from life and from influences that shape a culture, or a back to Plato and portrays science as beneficent action or, at the other person. And on the other hand there an activity with double benefits: Science extreme, as dedicated to technological is, of course, a group of scientists, as pure thought helps the mind find improvements. though not a large one, which really truth, and science as power provides does regard science as largely an icono- tools for effective action. In book 7 of Iconoclasm clastic activity. Ideologically they are, of the Republic. Socrates tells Glaucon course, descendants of Lucretius, who the rulers wrote on the first pages of De renim why young in the Ideal State A second image of long standing is naiiira, "The terror and darkness of should study mathematics: "This, then, that of the scientist as iconoclast. In- is knowledge of the kind we are seek- deed, almost every major scientific ad- mind must be dispelled not by the rays ing, having a double use, military and vance has been interpreted —either tri- of the sun and glittering shafts of day. philosophical; for the man of war must umphantly or with apprehension—as but by the aspect and the law of na- learn the art of number, or he will not a blow against religion. To some ex- ture: whose first principle we shall be- know how to array his troops; and the tent science was pushed into this posi- gin by thus stating, nothing is ever got- philosopher also, because he has to rise tion by the ancient tendency to prove ten out of nothing by divine power." out of the sea of change and lay hold the existence of God by pointing to In our day this ancient trend h;is as-

. . significance owing to of true being. . This will be the eas- problems which science could not solve sumed political iest way for the soul to pass from be- at the time. Newton thought that the the fact that in Soviet literature scien- coming to truth and being." regularities and stability of the solar tific teaching and atheistic propaganda

The main flaw in this image is that system proved it "could only proceed are sometimes equated. it omits a third vital aspect. Science from the counsel and dominion of an has always had also a mythopoeic func- intelligent and powerful Being." and Ethical Perversion tion—that is, it generates an impor- the same attitude governed thought tant part of our symbolic vocabulary concerning the earth's formation before The third image of science is that and provides some of the metaphysical the theory of geological evolution, con- of a force which can invade, possess, bases and philosophical orientations of cerning the descent of man before the pervert, and destroy man. The current our ideology. As a consequence the theory of biological evolution, and con- stereotype of the soulless, evil scientist methods of argument of science, its cerning the origin of our galaxy before is the psychopathic investigator of conceptions and its models, have per- modern cosmology. The advance of science fiction or the nuclear destroyer meated first the intellectual life of the knowledge therefore made inevitable —immoral if he develops the weap- time, then the tenets and usages of an apparent conflict between science ons he is asked to produce, traitorous everyday life. All philosophies share and religion. It is now clear how large if he refuses. According to this view, with science the need to work with a price had to be paid for a misunder- scientific morality is inherently nega- concepts such as space, time, quantity, standing of both science and religion: tive. It causes the arts to languish, it matter, order, law, causality, verifica- to base religious beliefs on an estimate blights culture, and when applied to hu- tion, reality. Our language of ideas, of what science cannot do is as fool- man affairs, it leads to regimentation for example, owes a great debt to hardy as it is blasphemous. and to the impoverishment of life. statics, hydraulics, and the model of The iconoclastic image of science Science is the serpent seducing us into the solar system. These have furnished has, however, other components not as- eating the fruits of the tree of knowl- jjowerful analogies in many fields of cribable to a misconception of its func- edge—thereby dooming us. study. Guiding ideas—such as conditions. For example, Arnold Toynbee The fear behind this attitude is genu-

tions of equilibrium, centrifugal and charges science and technology with ine but not confined to science: it is

centripetal forces, conservation laws, usurping the place of Christianity as directed against all thinkers and inno-

feedback, invariance, complementarity the main source of our new symbols. vators. Society has always found it —enrich the general arsenal of imagina- Neo-orthodox theologians call science hard to deal with creativity, innovation, tive tools of thought. the "self-estrangement" of man be- and new knowledge. And since science A sound image of science must em- cause it carries him with idolatrous assures a particularly rapid, and there-

245 fore particularly disturbing, turnover of fashionable to confess to a lack of ac- Pasteur would clarify this point. It

ideas, it remains a prime target of sus- quaintance with the latest ephemera in would be well if in his education each picion. literature or the arts, but one may even person were shown by example that

Factors peculiar to our time intensify exhibit a touch of pride in professing the driving power of creativity is as this suspicion. The discoveries of ignorance of the structure of the uni- strong and as sacred for the scientist "pure" science often lend themselves verse or one's own body, of the be- as for the artist. readily to widespread exploitation havior of matter or one's own mind. The second point can be put equally through technology. The products of briefly. In order to survive and to pro- technology—whether they are better gress, mankind surely cannot ever know vaccines or better weapons—have the The Sorcerer's Apprentice too much. Salvation can hardly be characteristics of frequently being very ihought of as the reward for ignorance. effective, easily made in large quanti- The last two views held that man is Man has been given his mind in order

ties, easily distributed, and very ap- inherently good and science evil. The that he may find out where he is. what

pealing. Thus we are in an inescapable next image is based on the opposite as- he is. who he is, and how he may as- dilemma—irresistibly tempted to reach sumption—that man cannot be trusted sume the responsibility for himself

for the fruits of science, yet, deep in- with scientific and technical knowledge. which is the only obligation incurred in side, aware that our metabolism may He has survived only because he lacked gaining knowledge.

not be able to cope with this ever-in- sufficiently destructive weapons: now Indeed, it may well turn out that the creasing appetite. he can immolate his world. Science, in- technological advances in warfare have Probably the dilemma can no longer directly responsible for this new power, brought us to the point where society

be resolved, and this increases the is here considered ethically neutral. is at last compelled to curb the aggres- anxiety and confusion concerning But man, like the sorcerer's apprentice, sions that in the past were condoned science. A current symptom is the pop- can neither understand this tool nor and even glorified. Organized warfare ular identification of science with the control it. Unavoidably he will bring and genocide have been practiced technology of superweapons. The bomb upon himself catastrophe, partly throughout recorded history, but never through his natural sinfulness, and until is taking the place of the micro>copc. now have even the war lords of Wernher von Bruun. the place of Ein- partly through his lust for power, openly expressed fear of war. In the is a stein, as svnibols for modern science which the pursuit of knowledge search for the causes and prevention that and scientists. The efforts to convince manifestation. It was in this mood of aggression among nations, we shall, the development of pro- people that science itself can give man Pliny deplored I am convinced, find scientific investi- war: only knowledge about himself and his jectiles of iron for purposes of gations to be a main source of under- criminal environment, and occasionally a choice "This last I regard as the most standing.

I of action, have been largely unavail- artifice that has been devised by the hu- ing. scientist as scieniisi can take man mind; for. as if to bring death The I Disaster little credit or responsibility either for upon man with still greater rapidity, Ecological facts he discovers— for he did not we have given wings to iron and taught create them—or for the uses others it to fiy. Let us, therefore, acquit Na- A change in the average temperature ! make of his discoveries, for he gen- ture of a charge that belongs to man of a pond or in the salinity of an ocean

erally is neither permitted nor specially himself." may shift the ecological balance and

fittcil to make these decisions. They When science is viewed in this plane cause the death of a large number of are controlled by considerations of —as a temptation for the mischievous plants and animals. The fifth prevalent

ethics, economics, or politics and savage— it becomes easy to suggest a image of science similarly holds that therefore arc shaped by the values and moratorium on science, a period of while neither science nor man may be historical circumstances of the whole abstinence during which humanity inherently evil, the rise of science hap- society. somehow will develop adequate spirit- pened, as if by accident, to initiate an There are other evidences of the ual or social resources for coping with ecological change that now corrodes widespread notion that science itself the possibilities of inhuman uses of the only conceivable basis for a stable

cannot contribute positively to culture. modern technical results. Here I need society, .n the words o Jacques Mari-

Toynbce, for example, gives a list of point out only the two main misun- tain, the "deadly disease" science set off "creative individuals," from Xenophon derstandings implied in this recurrent in society is "the denial of eternal truth to Hindenburg and from Dante to call for a moratorium. and absolute values."

Lenin, but docs not include a single First, science of course is not an oc- The mam events leading to this state

scientist. I cannot forego the remark cupation, such as working in a store or are usually presented as follows. The

that there is a significant equivalent on on an assembly line, that one may pur- abandonment of geocentric astronomy the level of casual conversation. For sue or abandon at will. For a creative implied the abandonment of the con-

when the man in the street —or many scientist, it is not a matter of free ception of the earth as the center of an intellectual — hears that you are a choice what he shall do. Indeed it is creation and of man as its ultimate pur- physicist or mathematician, he will erroneous to think of him as advancing pose. Then purposive creation gave

usually remark with a frank smile, "Oh. toward knowledge; it is, rather, knowl- way to blind evolution. Space, time,

I never could understand that subjec:""; edge which advances towards him, and certainty were shown to have no while intending this as a curious com- grasps him, and overwhelms him Even absolute meaning. All a priori axioms

pliment, he betravs his intellectual dis- the most superficial glance at the life were discovered to be merely arbitrary

sociation from scientific fields. It is not and work of a Kepler, a Dalton. or a conveniences. Modern psychology and

246