I PHYSICISTS and FIPPLE FLUTES I at APL

S. A. Elder I •

Amateur chamber music groups instrument, used in the time of easiest instruments to learn to play, are springing up throughout the land Johann Sebastian Bach and George which perhaps accounts in part for as a result of the twentieth century Frederick Handel, has in its literature its growing popularity. revival of the recorder, or English some of the greatest music of the ages. Pictured in the accompanying illus­ fipple flute. This wooden end-blown I t is, at the same time, one of the tration (Fig. 1) are members of the occasional-Friday-l unch time chamber music group of the Applied Physics Laboratory. The APL Altkammer­ musikgesellschaft (the old chamber music society), or AKMG as it is familiarly known, has been function­ ing for about four years under the able and imaginative leadership of Martin Davidson. * There have been other recorder players at APL even before the formation of AKMG; for example, Dr. R. Herman, who publish­ ed an article on recorders in the Ameri­ can Journal of Physics. 1 Only within the last four years, however, has re­ corder playing become an organized activity at the Laboratory. The re­ corder group that meets in Parsons Auditorium has been augmented from time to time by other musicians,

Dr. Samuel A. Elder, a physicist on the Rocket Tunnel Project staff of the Fluid Me­ chanics Group, is responsible for development of a new recording pyrometer, discussed in "Transistorized Pyrometer With and Without Feedback," APL T echnical Digest, 2 , May­ June 1963, 17- 18. * Assistant Supervisor, Radar Communica­ tions Project.

Fig. I-Members of the Altkammermusikgesellschaft enjoy a 17th century quartet by Fresco­ 1 R. Herman, "Observations on the Acous­ baldi in Parsons Auditorium. Left to right, they are: R. P. Rich, soprano recorder; A. H. Dell, tical Characteristics of the English Flute," bass recorder; the author, alto recorder; and M. Davidson, teno recorder. Am. ]. Phys. , 27, 1959, 22-29.

IfI11'll(lr), - F eb r u{I/")' J 9 6-1 15 including a summer bassoonist, a Baroque vocalist, and a chemist accompanist. t The latter has so far confined his art to the piano since the auditorium is not equipped with a WIN DWAY ~ CYLINDR I CAL harpsichord. I BOR E --;------TA PERED BOR E------/ Actually, the brief Friday noon get­ togethers represent only a small frac­ THUM B HOLE tion of the musical activities of the AKMG members. Martin Davidson has been heavily involved in the work of the Washington Chapter of the American Recorder Society (ARS ). Fig. 3-Recorders are usually made in three parts, the upper, or head, portion being cylindrical in bore, and the mid and foot sections being tapered. Early recorders of the Renaissance period Last year he undertook the task of had straight cylindrical bores. publishing a complete directory of the approximately 200 players in the greater loudness and dynamic range should use in designing larger instru­ Washington area. He also teaches of the former. This was the period ments." At the time, he was just the recorder. A number of Washing­ in which the piano replaced the beginning work on a Great Bass in F, ton ARS members are his former clavichord,2 the violin family won out the largest of the recorder family. pupils. over the soft-toned viols,3 and the This six-foot giant cannot be de­ Al Dell's home-workshop hobby, at modern orchestra was born. signed according to the same rules the moment, is making recorders and Dr. Robert Rich, director of the as can normal-sized recorders and wooden cross flutes (Fig. 2 ) . His University Computing Center of The still be playable by normal-sized peo­ one-key flutes, made after the style Johns Hopkins University and super­ ple. The large, widely spread finger of those used in Mozart's day, have visor of APL's Computing Center, is holes require an elaborate system of been played by experts and declared another member of AKMG who has keys and pads to extend the capa­ to be of high quality. The one-key instrument-making as a hobby. He bilities of the human hand. flute was historically the immediate has invented a new chamber music An even greater problem is the successor to the Baroque recorder as instrument that he calls the trecorda. breath volume required. Human a concert instrument. Composers of This is essentially a keyed version of vital capacity, or total exhalable air the Classical period that followed the the guitar, with a soft tone that volume, is about 4500 cc. A Great age of Bach favored the cross flute blends well with recorders. In out­ Bass designed according to the scal­ over the recorder because of the ward appearance it is easily mistaken ing laws of small instruments would for some obscure court instrument of demand some 500 cc/sec on its lowest the Renaissance period. As a matter note and as much as 1300 cc/sec in of fact, the trecorda could have been its upper range. Apart from the pro­ invented in Shakespeare's time! duction of occasional oom-pahs, it My own interest in the recorder is would be relatively useless as a musi­ both musical and scientific. Two cal instrument. What Mr. von summers ago I played with a trio of Huene wanted to know was how to strolling musicians at the Sylvan make it loud and still playable. Theater production of "The Taming Although I did a little thinking about of the Shrew." In spite of my cos­ the problem through the winter, the tume, I was recognized by a few of real impetus to research came last the APL personnel who were among spring. At that time Dr. Paul E. some 70 thousand visitors taking Clark, managing edit!Jr of the Digest, advantage of the free Shakespeare asked me to write an article on performances. "recorder playing as a physicist's During last year's vacation I visited hobby;" I immediately began a sur­ the New England workshop of vey of books and scientific papers re­ Friedrich von Huene, who is one of lated to the subject. Before long, I the foremost of modern recorder began to realize that the time was makers. When he learned that I am ripe fO.r the first fundamental treat­ a physicist, Mr. von Huene said: ment of recorder acoustics. Only Fig. 2-A. H. Dell poses with reproductions of an 18th century cross flute and several "Good, I have a problem for you. within the last decade has the basic 17th century recorders. Other "one-key" Tell me what scaling laws one knowledge become available to make flutes made by Mr. Dell are on loan to area musicians. such a task possible. 2 C. Welch, Six Lectures on the Recorder, Oxford University Press, London, 1911, There is still much to be done, but 128. t Respectively, D . Klausner, a summer assist­ since the beginning of the summer I ant in the Research Center in 1961, Miss 3 Carleen M. Hutchins, "The Physics of have made enough progress to be able Kathryn Froelich, associate engineer, and Violins," Sci. American, 207, Nov. 1962, Dr. E. J. Blau, senior chemist. 79- 93. to present a technical paper at the

16 APL Technical Digest November meeting of the Acoustical the orifice, that eventually becomes Society of America, in Ann Arbor, on large enough to shift the entire jet the subject of recorder voicing. My across the edge. The modulated flow wife Sylvia, an equally enthusiastic of air in the mouth of the pipe is advocate of recorder playing and a equivalent to a spherical radiator of former technical illustrator, did the sound, since the wavelength is much ink drawings for my slides. larger than any mouth dimension. "Voicing" is the name given to the This type of sound generator will fine adjustments of mouth geometry work with or without the presence and bore profile that make the differ­ of a resonator pipe, and is called an ence between a good recorder and a "edgetone." In 1961 Dr. Alan bad one. I t is, as the Englishman Powell, 5 a former British scientist Carl Dolmetsch told me, "a subtle who is now an American citizen, art." Mr. Dolmetsch, whom I met showed that the edgetone oscillator after one of his concerts in the U.S., is similar to an electronic-feed back­ is noted both as a virtuoso and as a amplifier circuit. In his model of the maker of some of the finest avail­ Fig. 4-Dr. W. M. Oler, internal medicine edgetone, amplifier gain corresponds able recorders. His father, Arnold specialist and owner of nearly 100 recor­ to the growth of the jet disturbance ders, helped take the data on which this ar­ Dolmetsch, is generally considered to ticle is based. Shown here are some Baroque resulting from hydrodynamic insta­ be responsible for the renascence of recorders from his collection. bility. Even when there is no reso­ the recorder. nator present, the resultant "dipole" Figure 3 shows the profile of the Friedrich von Huene. I was surprised source caused by the sloshing of the to discover that all well-voiced re­ alto recorder, an instrument about 42 jet triggers a new disturbance back em long. Very-low-pressure air is corders produce nearly the same at the orifice and thus provides posi­ blown through the narrow windway sound power, except for the extremely tive feedback to make the oscillations at the left, at a rate of about 100 to large types, which are slightly weaker. regenerative. Frequency of a free 200 cc/sec. This excites the hollow On its lowest note, a recorder puts edgetone is determined by the speed pipe at a resonant frequency deter­ out, according to my measurements, at which the growing undulation mined by the pattern of open and approximately 30 microwatts of moves from orifice to edge. Dr. closed finger holes in the mid-section. acoustic power. Near the middle of Powell had long been convinced that its scale where it has maximum Recorders are usually made in three the "gain" of the edgetone system 4 sections, of which the upper, head strength, the output is about 2.5 must come from the tendency of milliwatts. These figures are, to a fair portion is cylindrical in bore, while high-Reynolds-number jets to break approximation, independent of not the mid and foot sections are tapered. up into turbulence. H e and one of only the instrument size, but also the G The acoustic function of the taper his graduate students were able manufacturer and the player. This seems to be to match the large upper finally to prove this by studying the uniformity may be the result of a bore, required for good sound volume, fundamental gain-bandwidth-product to the narrow foot bore required for limitation, analogous to that of an wide-scale range. Early recorders of electronic amplifier. the R enaissance period had straight The recorder belongs to a class of cylindrical bores and th us could not musical instruments in which the encompass as wide a scale as the sound is generated by the action of a Baroque model shown here. sloshing air jet, without the help of The family of Baroque recorders any moving solid surfaces such as are is shown in Fig. 4. The instruments found in the clarinet and oboe. pictured here are part of a large and Physicists classify the recorder, along excellent collection belonging to Dr. with the flue organ pipe and trans­ Wesley M. Oler, an internal medicine verse flute, as a jet-edge resonator. specialist of Washington, who is In the recorder the jet-edge driver shown holding a small gamba. Dr. is located in the "head" portion of Oler, who is also an expert recorder the instrument at the top of the bore. player, has worked closely with me in Figure 5 is a schematic representa­ making the acoustic measurements. tion of the mouth of the recorder, Fig. 5-Physicists classify the recorder The recorder family comprises six along with the flue organ pipe and trans­ showing the oscillation of the jet verse (or Boehm) flute, as a jet-edge resona­ (or seven ) sizes of instruments, rang­ tor type of instrument. This schematic about the fixed edge. Switching of shows the basic driving mechanism, which ing from great basses, such as that the jet from one side of the edge to contains no moving parts. shown on the extreme left in Fig. 4, another is caused by the growth of a to the diminutive sopranino shown 5 A. Powell, " On the Edgetone," J. Acoust. transverse undulation, triggered at Soc. Am., 33, 1961 , 395-409, at the extreme right. The seventh 6 R. C. Chanaud and A. Powell, "Experi­ size is the extremely rare Great Bass 4 A. von Lupke, "Untersuchungen an Block­ ments Concerning the Sound-Sensitive floten," Akustische Z eitschrift (Zurich), V, Jet," J. Acoust. Soc. Am., 34, 1962, 907- in F of the size now being made by 1940, 39- 46. 915.

January -Februa'ry 196-1 17 conditions under which free jets be­ nolds number approaches the edge­ orifice separation to the fundamental come unstable and by plotting tone threshold, corresponding to the pipe frequency, h ~ V 72//0 cm. We their data in special non dimensional excitation of both free edgetones have plotted on the universal mode coordinates- Strouhal number (S) (horizonfal lines ) and pipe reso­ diagram in Fig. 7 the entire two­ as the ordinate and Reynolds number nances (diagonal lines ) . This effect octave scale of an alto recorder. Each (Re ) as the abscissa. When the sta­ is known as "chiff" in an organ pipe note was blown in tune at its opti­ ble regions of edgetone oscillators and lends a certain charm to the tone mum point. Notice that four pipe were plotted in the same coordinates, quality of old organs. modes are required to cover the scale they fell neatly within the unstable The diagonal lines are fixed fre­ range. By overblowing to modes in region of the free jet as predicted. quencies corresponding to the first the upper octave, it is possible to It has long been known that the few resonant modes of the pipe, due encompass more notes with fewer empirical frequency formula 7 for free to standing waves of sound. The finger holes. edgetones does not work when dominance of the pipe feedback is All scale notes of the recorder are applied to pipes. The pipe resonance shown by the way in which the state driven by the first edgetone mode. modes are dominant over the natural of the system tends to approach the Higher modes seem to be important edgetone modes just as a quartz crys­ pipe resonant frequency as the Rey­ only during the starting transient of tal can be made to control an elec­ nolds number is increased. The cross­ a note. tronic oscillator. Dr. Powell sug­ ing point "0" in Fig. 6 is the place The degree of fluctuation of the gested that this is because the sound at which the pipe is normally driven driving point from one note to field in the pipe provides a stronger in sounding its lowest note. At a another is a measure of the accuracy feedback from edge to orifice. 5 slightly greater R eynolds number, of the instrument's intonation. The Figure 6 shows a Strouhal­ "overblowing" occurs and a sudden alto recorder used for these measure­ Reynolds plot similar to that used by jump brings the system to the second ments is an unusually fine one made Dr. Powell. I have employed slightly pipe mode (or octave). Still harder by my friend, Friedrich von Huene, different definitions of the coordi­ wind pressure causes a succession of and it can be blown in tune on every nates, using the edge-orifice distance overblows to higher modes. note very easily. In taking the data h where Powell used the jet thick­ I have called this plot a universal for this plot, the velocity U o was ness 8. In this representation mode diagram because it represents m easured by means of a home-made Powell's stable edgetone regimes the coupling of edgetone and pipe pitot probe and water manometer. appear as horizontal and parallel line modes in a scale-invariant way. Ex­ Another type of measurement we segments, arranged in order of their perimental data for recorders indicate have made utilized a Va-inch diame­ mode number. The lowest mode, M', that the fundamental pipe mode line ter probe tube mounted on a cali­ corresponds to the simple to-and-fro always crosses the first edgetone mode brated condenser microphone bor­ motion pictured in Fig. 5. Higher line near its beginning. Physically, rowed from the Laboratory. With this modes correspond to more compli­ this is due to the practical necessity equipment Dr. Oler and I plotted cated undulations of the jet. of fitting all the desirable pipe modes the axial sound pressure fields for Strouhal number in this plot is de­ within the stable regime of the first each note on a number of recorders. fined as the frequency times the edgetone mode. This fact leads to a Data of this type have led to an orifice-edge separation, divided by simple scaling law, relating the edge- understanding of the radiating source the mean orifice velocity U o• It is thus a nondimensional measure of 2.0 oscillation frequency, though for a ~ "- -- ~ .... ·::,...... --MIII fixed frequency the Strouhal number ~ p decreases with increasing U o. The 1.0 ~ ~ J"o. MII J utility of this type of representation .. , ..., ~ is due to the fact that edgetone modes c><: 0.8 ~ / ~ "" " "" .. ) EDGETONE MODES are lines of constant Strouhal num­ ~ 0.6 \. z MI ber. R eynolds number-the product ~ -0< V ""'" ~ ~ Uoh divided by the kinematic vis­ <0.4 - I "" cosity- corresponds in a rough way o:J c><: '" " to blowing pressure. Both scales are ... tn logarithmic. The broken line shows ~ . ~ \. ~ 0.2 ~ ~ the actual path by which the state of 0 '\ • h = 10 } an edgetone-resonator is changed as • h = 7.5 m m 0 h = 5 fI '" the blowing pressure is continually fII 0.1 I ~ ~ , 0.2 0.4 0.6 0.8 1.0 2.0 4.0 6.0 8.0'" 10.0 increased from zero. A number of "" 20.0 40.0 60.0 transient sounds occur as the Rey- REYNOLDS NUMBER (THOU""SAN DS) 7 G. B. Brown gives the following empirical Fig. 6-When pipe resonance modes and edgetone modes are plotted simultaneously on an formula for edgetone frequencies : f = SeRe graph, the universal mode diagram that results helps to explain many of the mysteries of 0.466j (Vo = 4D ) (l/h-O.07) where j = recorder acoustics. Strouhal number is here defined as sound frequency times orifice-edge 1, 2.3, 3.8, and 5.4; from " The Vortex separation, divided by the mean jet velocity at the orifice. Reynolds number is the product Motion Causing Edge Tones," Proc. Phys. Voh divided by the kinematic viscosity of air (= 0.15 cgs). (Edgetone data are from: A. Powell, Soc. (London), 49, 1937, 493. op. cit.)

18 APL Technical Digest