Acoustical and physical dynamics of the diatonic harmonica JASA 1998.pdftongue, causing the air to...

Acoustical and physical dynamics of the diatonic harmonicaHenry T. Bahnson and James F. AntakiDepartment of Surgery, University of Pittsburgh, School of Medicine, 3550 Terrace Street, Pittsburgh,Pennsylvania 15261

Quinter C. BeeryDepartment of Otolaryngology, University of Pittsburgh, School of Medicine, 3550 Terrace Street,Pittsburgh, Pennsylvania 15261

~Received 18 February 1997; revised 24 December 1997; accepted 5 January 1998!

The harmonica is arguably the most widely played instrument in the world, yet there is a surprisingpaucity of published studies of its acoustics or physical dynamics. The typical diatonic harmonicaand the physical forces involved in its natural function are described, and simple observations of theharp’s functions are reported. The speaking of the reeds, naturally, when producing a bend, andwhen speaking as an overblow or overdraw is discussed and investigated by simple stopping of thereeds, by videostroboscopic analysis, and by recording vibration of the reeds with displacementgauges. The reeds of the ten hole harmonica can be made to vibrate at varying frequenciesdepending on the size and shape of the player’s vocal tract. Three different modes of speaking fromeach hole and its pair of reeds are revealed and studied: first, naturally in a closing mode, eitherblown or drawn; second, as a bend, either blown or drawn, with pitch in the interval between the twonotes in the hole; and third, as an overblow or overdraw in an opening mode with a pitch outsidethe interval between the two natural notes of the hole. This dynamic interaction allows the player tospeak with the instrument perhaps as with no other. ©1998 Acoustical Society of America.@S0001-4966~98!02404-7#

PACS numbers: 43.75.Pq@WJS#

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INTRODUCTION

The name,Harmonica, has been used to designate mainstruments over the years, some being reed instrumentlated to the instrument under discussion, and others seingly unrelated, such as the glass harmonica attributedBenjamin Franklin, which consisted of a set of glassesvarying size, tuned by varying the amount of water withThe modern harmonica—a.k.a. harp, mouth organ, Freharp, Mundharmonica~in Germany!, pocket piano, and Mis-sissippi saxophone—is a descendant of instruments firsported and patented in the 1820’s.1 The principle embodiedin the harmonica can be traced to the Orient where variatof the Chinese sheng existed for several millennia. Allthese instruments use a vibrating free reed.

Structure and function of the harmonica

The active element of the harmonica is a metal reed wone end fastened to the surface of a thin metal plate;other end is free to vibrate. All but the fastened end ofreed overlies a slot in the reed plate that is just large enoto allow the reed to vibrate freely in the slot@Fig. 1~a!, ~b!#.The reed is activated by the flow of air across it. It vibratesa frequency which is near its natural~i.e., plucked! fre-quency. This frequency is determined by the mass and sness of the reed in cooperation with its associated acoussystem. The throttling action of the reed on the flow ofcauses a periodic fluctuation of the otherwise steady air psure provided through the mouth, thus creating sound.

The body of the harmonica is a comb, made of woplastic, or metal, with prongs separating a row of ten or mchambers. One plate of reeds, theblow reeds, which are

2134 J. Acoust. Soc. Am. 103 (4), April 1998 0001-4966/98/103(

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activated by positive pressure in the comb~i.e., blowing!, isfastened to the top side of the comb with the reeds insidesecond plate of reeds, thedraw reeds, which are activated bynegative pressure, is fastened to the bottom side of the cwith the reeds outside. The reed slots on the blow- and drreed plates are arranged to coincide with each other onposite sides of the chambers of the comb. Thin metal covover the reed plates provide small resonating chambwhich further modify the generated sound. The reeds canarranged in various sequences of tones that encompasseral octaves. Reeds of the popular ten hole, diatonic hmonica, tuned in the Richter model in a major key, areranged as shown in Fig. 2. With this arrangement, oneproduce the major chord of the key of the harp by blowion any three adjacent holes. Drawing on the first four hoproduces the dominant chord of the key. In order to accoplish this harmony, certain tones are omitted in the scalethe lowest and highest octaves, as can be seen in Fig. 2.10-hole diatonic harmonica has a range encompassing 3octaves, 22 diatonic tones, but since there are only 20 rein the 10 holes and 1 tone is repeated, there are 3 ‘‘missinnatural tones in the 3 octaves of the diatonic scale.

The arrangement of reeds in the typical diatonic hmonica is such that each of the three octaves is playedferently. For the first six holes, comprising most of two otaves, the draw note is higher in pitch than the correspondblow note. For these six holes, it is the draw note that canbentdown or flatted through air pressure and manipulationthe vocal tract by the player. For the remaining four holthe blow reed is higher in pitch; here it is the blow note thcan be bent. In each case, it is the higher note of the hole

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FIG. 1. ~a! Exploded view of the ten hole diatonic harmonica showing tupper, blow reed plate, the lower, draw reed plate and the separating coUpper and lower covers of the reed plates are not shown. Reeds are moon the inside surface of the blow reed plate and the outside of the drawplate. Thus blowing closes the blow reed into the blow reed plate and opthe draw reed out of the draw reed plate. The reverse occurs on drawinis the closing reed that speaks on natural playing.~b! Schematic, crosssectional view of reeds and plates of a hole of a diatonic harmonica. Revibrate in slots cut out of the reed plate. Blowing into the hole closesblow reed and opens the draw reed. Drawing closes the draw reed and othe blow reed.

FIG. 2. Notes and approximate frequencies of a ten hole, diatonic hmonica, key of C. The upward arrow indicates blow; the downward arrodraw. Blow and draw bends are indicated by bent shafts, up and dorespectively; number of semitones bent is indicated by number of arheads. Overblow and overdraw are indicated by slashed arrows.

2135 J. Acoust. Soc. Am., Vol. 103, No. 4, April 1998 B

appears to be bendable, whether blown or drawn. The ostated rule is that one can bend the pitch of the higher nota hole down to a semitone above the lower note of thespective hole. It should be pointed out that bending produvirtually continuous pitch control within the interval betweethe blow and draw notes of the hole, in contrast to overbloing, to be discussed later.

In order to play the basic, natural tones of the key of tharp, no special configuration of the vocal tract is typicarequired. The player simply blows or draws through the apropriate hole. Vibration of the reeds occurs as a result ofinteraction of aerodynamic forces acting on the reed andmechanical properties of the reed itself. It is well known tha plucked reed will oscillate at a natural frequency detmined by its mass distribution and stiffness. In order to caself-sustaining oscillations, air must flow past the reed inmanner which reinforces this vibration. St. Hilaireet al.2

have shown that such pressure instabilities could result wair flow is sufficient to cause boundary layer separation atedge of the reed surface. When this occurs, the aerodynadrag force on the reed increases as the gap decreases, areed moves against the air flow. Conversely, the drag fodecreases when the gap increases, and the reed movesthe flow. This will thus inject energy into the reed motiogiving it a ‘‘kick.’’ This phenomenon can also be describein terms of acoustical impedance, as outlined by Johnst3

The resulting frequency of oscillation will differ from thplucked frequency because of the coupling with the acoucal inertance and compliance of the air flow and airwaythe player.

A reed vibrating in this fashion with the reed attachedthe high pressure side of the reed plate and being forprimarily into the reed plate is said to function as aclosingreed. Simultaneously the companion reed, overlying tsame cavity but attached to the outer, low pressure side oreed plate, is blown open. It vibrates only minimally whethe natural note is played and functions as anopening reed.Consequently, the frequency of vibration of the opening reis determined primarily by the closing reed. When the plablows through a hole, the blow reed is a closing reed, anddraw reed is an opening reed. When the player draws onhole, these actions are reversed. Alternatively, one can dethe blow reed as the reed which speaks primarily whenplayer blows through a given hole. The reverse occursdrawing. The primary speaking reed is the closing reedeach case of simple blow and draw.~It is worth pointing outthat despite the names,openingandclosing, both reeds do infact open and close their respective reed slots in the courstheir vibration. Accordingly, this nomenclature conventiounfortunately introduces some confusion. However, inmuch as this designation is well established, we will adthis terminology to designate the mode of operation oparticular reed.!

The discovery that missing notes of the diatonic scand some notes of the chromatic scale can be fashionebending is attributed to the African-Americans of the souern United States in the last half of the nineteenth centuModern instructions on this technique have been descrias: ‘‘...draw in sharply, drop the jaw a bit, along with th

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tongue, causing the air to dart downward to the floor of tmouth;’’4 ‘‘...suck the air through the harp towards the tip@the# tongue;’’5 ‘‘ @inhale# with more force and@cause# the airstream to move to the bottom of the mouth and throat;’’6 or,most descriptively, ‘‘@take# in air from your shoe.’’7 Glover8

instructs that if one visualizes drawing a column of air, likestraw, over the tongue and throat, then bending consist‘‘bending that column of air down to the front part of@the#lower jaw.’’ Palmer9 relates that Sonny Terry’s techniquwas: ‘‘If you constrict the flow at any point along its passafrom reeds to lungs, you change the resultant pitch ofreeds. Most harpmenchokethe harp to achieve this effecThey narrow the opening in their throats to constrict theflow....there is a simultaneous increase in pressure fromlungs.’’ Most practical is the advice of Baker,10 ‘‘...thetongue and throat movements when bending notes is~analo-gous to! different vowel sounds,... like forming AAH toOOH,... or EEE to OOO for the high notes.’’ We interprthese instructions as attempts to describe alterations ofvolume and configuration of the vocal tract—here useddescribe the lips, cheeks, mouth, pharynx, and trachea~Fig.3!. Unfortunately for the novice, the oropharyngeal configrations required in bending are not identical to any of thoof normal speech.

There is an unfortunate dearth of reports in the scientliterature about the acoustics of the harmonica, or the phology involved in playing it. Perhaps this is due to its humbnature, for there are many reports, and indeed volumesmore ‘‘noble’’ instruments. In the nearly unique article cocerning physics of the harmonica by Johnston,3 all of thereferences cited are to observations on other instrumemostly woodwind and reed instruments. He cites no refences to previous studies of the harmonica. SubsequenJohnston’s article, in the second edition ofHarp Handbook,1991,10 Steve Baker described his experience basedsimple observations and logical deductions, but his desction lacks the benefit of vigorous scientific procedure. O

FIG. 3. Cross section of the vocal tract.


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studies elaborate on Baker’s observations and couple twith Johnston’s theoretical examination of the physical dnamics of harmonica reeds.

I. FUNCTION OF HARMONICA REEDS

A. Preliminary observations

Key to most of the expression on the harmonica isability of the musician to play a single note. Pursing the lito the size of a single hole is the commonly used techniqTongue blocking is another technique in which the lips coseveral holes but the tongue blocks one or more of thholes. The player forces air through a hole on one or bsides of the tongue. Another method, curling the tip of ttongue into a tube that surrounds the hole, limits use oftongue for other purposes, such as tongue blocking fortaves. However, curling the tongue permits playing with tcovers of the harmonica removed. Consequently, the cutongue technique was used in several of our studies. By splaying with the covers off and alternately stopping onethe other reed with a finger, one learns that stopping the dreed while blowing has no effect on pitch and only a sligincrease in loudness of the blown tone. This is most notiable with more vigorous playing. The findings are reverson drawing and stopping the blow reed. This suggestsstopping the reed that is not primarily speaking decreasesleak of air from the chamber, and that the natural blow adraw tones come predominantly from the blow and drreeds, respectively. The other reed of the hole contribuminimally if at all.

As mentioned above, the technique of bending noteperceived as a lowering of pitch as the player appropriaalters the vocal tract. Draw bends are obtained in the loholes 1 through 6 where the higher pitched tone is draand blow bends are obtained in holes 7 through 10 wherehigher pitched tone is blown. Alterations of the vocal trainvolved in bending tones principally consists of archiand/or thickening the tongue at various places alonglength ~anterior or posterior!. This has the effect of alteringthe volume and shape of the resonant cavity.

So-calledoverblowandoverdrawtones are a relativelyrecent addition to playing. Such tones can be elicited fromholes of the diatonically tuned harmonica~cf. Fig. 2!, butthey are used for holes 1, 4, 5, and 6 blow and 7, 9, anddraw to produce notes that are otherwise missing on thetonic harmonica~a flatted third—holes 1 and 4 blow;sharped fourth and a flatted seventh—holes 5 and 6 blowflatted second—holes, 7 and 10 draw; and a flatted sixthole 9 draw!. Stringent control of breath and positioning othe player’s vocal tract are required in order to play overbland overdraw tones. The novice attempting to play overbtones can be very rapidly frustrated, for the consequencan incorrect posture of the vocal tract is either silence, orinharmonious sound. The first recording of such a tonecredited to Blues Birdhead~James Simons! in 1929,11 butfull use and perfection of the tones awaited the skill apersistence of Howard Levy who plays them with as mufacility as he plays the bends. Consequently he is able tothe naturally diatonic harmonica as a fully chromatic inst


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The preliminary qualitative observations of reed motiowith the covers off prompted a more rigorous investigatioof reed and function. This was accomplished by three tecniques: analysis of pitch production, videostroboscopic oservation, and precision, noncontacting measurement ofdisplacement of the reeds.

B. Pitch production and reed primacy

Figure 4 illustrates the range of pitch that can be otained from each hole of the diatonic harmonica as it is usally played, i.e., draw bending holes 1 to 6 and blow bendiholes 7 to 10. The pitch was determined with a digital tun~Korg, DT-2, Tokyo! and is expressed as cents abovebelow the targeted pitch. It is convenient to refer to hamonica reeds as functioningprimarily and secondarily, be-cause although actions of the blow and draw reeds are

FIG. 4. Tones that can be modulated from blow and draw reeds togetheralone on a Golden Melody Harmonica~Hohner! key of C, observed byblocking reeds with a finger.~1! and~2! indicate cents above or below thenotes indicated along the abscissa.s is blow note,d is draw note. Symbolsotherwise are as in Fig. 2. Bars indicate range of frequency obtainedbending: black, straight with both reeds free; light gray, blow and drabends with draw reed alone with blow reed blocked; dark gray~lowermostof the 3 bars!, draw reed alone with blow reed blocked. Bars on holes 1–indicate draw bends, and on 7–10 blow bends. A more skillful player migincrease the ranges with more precise configuration of the vocal tract. Nthat both reeds are usually active with bends. Pure overblow and overdtones are obtained from a single reed~see overblows and overdraws forholes 1, 4, 5, 6, 7, and 9!. Note that in holes 1 to 6 the draw note is highepitched than the blow note, and bends are drawn. In notes 7 to 10 the revis true, i.e. the blow note is higher pitched than the draw note, and bendsblown rather than drawn.


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lated, one reed usually dominates and is thespeakingreed.Some simple initial studies were conducted to identify reprimacy by alternate blocking of one or the other of the twreeds of the hole while playing various notes—straight, beand overblown. Figure 4 also illustrates the range of pithat can be obtained from each reed when the opposingof the hole is blocked. Within certain limits both reeds ofgiven hole can be induced to vibrate over a range of frequcies between the natural frequencies of the two reedsgiven hole.

When the blow and draw notes in the hole are two setones apart, for example hole 4, the bent tone can be obtafrom either reed with the proper configuration of the voctract. This suggests that the bent tone normally comes feither or both reeds, and that the reeds can be made to sprimacy in producing the bent tones. When the tones inhole are four semitones apart as in hole 3, the higher pitcreed~whether blow or draw! is primary for the first portionof the bend and lowering of pitch one semitone. Whenfull, three-semitone bend is obtained, however, the sounproduced entirely from the lower pitched reed which bcomes primary. More specifically, the first semitone, drbend of hole 3~B flat on a C harp! is produced primarilyfrom the draw reed. The second semitone, A, can be pduced from either reed alone and is most easily producedboth together. The third semitone bend, A flat, comes frthe lower pitched blow reed. Similar reed function is fouin holes two and ten where the notes are three semitoapart.~In hole 10 the bend is a blow bend.!

The rule that one can bend the tone of a reed downsemitone above the lower note in the hole is a convenone for the player since that is what appears to happen. Tmore accurate, however, one should recognize that primshifts to the lower pitched reed which is modulated up. Thbends more properly must also be considered as involvingupward as well as downward modulation of pitch. Furthmore, when the higher pitched reed is blocked, it is possto bend the lower pitched reed down. When the highpitched reed is unblocked during one of these bends, thenote is rapidly squelched.

Greater skill in bending allows wider range of controlall modes of reed action. A more skillful player might extenthe range of bending beyond those shown in Fig. 4, as wmight one do with a differently configured or tuned harNonetheless, it appears that whether bending a tone udown with both reeds free, the pitch can be bent most eain the direction of the other note in the hole and is mumore difficult ~if not impossible! when the lower pitchedreed is blocked.

In summary of these observations of reed functionappears that both draw and blow bends involve both reedproduce pitches in the interval between the natural pitchethe two reeds. The higher pitched reed bends down andlower pitched reed bends up. The bent tone seems to cprimarily from the reed with the natural pitch closest to ttone being played. There is more overlapping function oflower pitched reeds, as in hole 3, than in the higher onesin hole 9. These conclusions require more quantitative vdation. Accordingly, the speculation and subjectivity asso

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C. Stroboscopic evaluation of reed primacy

The above observations, obtained by blocking reewere confirmed by direct observation and by video recordthe reed motion through a magnifying fiberoptic videoendscope having a 70° angled tip~Nagashima! under strobo-scopic illumination~Bruel and Kjaer, Rhinolarynx stroboscope, 4914!. When the frequency of the strobe was offsslightly from the frequency of the tone being played, reactivity could be observed as a slow motion portrayal ofmovement.12 Analysis of the video tape recordings of sustudies, summarized in Table I, shows that with simple bland draw, the designated blow or draw reed vibrates frewhile the secondary reed barely moves or vibrates mmally, the displacement being estimated at a twentieth orthat of the primary reed. At the beginning of a draw benthe draw reed was observed to vibrate primarily, but astone dropped a whole tone or more, the blow reed begavibrate and to become primary, even though the air flcontinued to be drawn. In this mode, the blow reed futioned as an opening reed. Comparable observations wmade with the blow bends. These shifts in reed primacy wmost clearly seen in holes where the pitches of the blowdraw tones are more widely separated, as in holes 2 and

TABLE I. Stroboscopic examination of blow and draw reeds with variomodes of playing.~111! indicates vigorous action;~11! is moderateaction, and~1! is minimal action. D Bend, DD Bend, and TD Bend indicaa draw bend, double draw bend, and triple draw bend respectively.

Hole ActionAppx.note Blow reed Draw reed

1 Blow C 111 0Draw D 11 111

D Bend C# 11 11Overblow D# 1 11

2 Blow E 111 0Draw G 0 111

D Bend F# 11 111DD Bend F 11 11

3 Blow G 11 0Draw B 0 111

D Bend A# 1 111DD Bend A 11 11TD Bend G# 11 1 to 11Overblow C 0 11

4 Blow C 11 1Draw D 1 111

D Bend C# 11 11Overblow D# 0 111

5 Blow E 11 1Draw F 1 11

Overblow F# 1 11

6 Blow G 111 0Draw A 0 111

D Bend G# 111 0Overblow A# 0 111


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10. Somewhat similar observations were reported indepdently by Thaden,13 Baker,10 and other observant players.14

Overblows and overdraws are examples of thingsbeing exactly what they seem on the harmonica. It wouldlogical to think, and was commonly believed, that the ovblow notes come from the blow reed on which the playerblowing and that the pitch jumps up two or three semitonas one continues to blow. In actual fact, our simple, initstudies of reed blocking with a finger showed that the ovblow tone actually comes from the draw reed of the hwhich abruptly begins to vibrate as an opening reed, witpitch that is only a semitone higher than the draw reenatural frequency. Conversely, an overdraw tone wasserved to come from the blow reed of the hole. In additiostroboscopic analysis of the reeds during overblows shothat the blow reed becomes almost still, in spite of intensifivibration of the draw reed. Stopping the blow reed whplaying an overblow tone also makes the tone purer, louand easier to hit. This observation led to the developmena modification of the typical diatonic harp that makes it eily fully chromatic.14,15The pitch of both overblow and overdraw tones is outside the interval between natural pitchethe blow and draw notes of the hole, in contrast to benwhich are almost completely within these intervals. Henthere appear to be three modes of useful function of ereed: closing as in the natural modes of simple blow or draopening as in bending with the pitch within the intervalthe two tones, and an overblow or overdraw as an openreed with a pitch above that interval.

D. Reed primacy by dynamic vibration measurements

Dynamic measurements of reed vibration were pformed to better quantify the observations obtained fromabove stroboscopic evaluation. These experiments wereducted with a Hohner Golden Melody harmonica with coveremoved, key of C, upon which were mounted two precisinoncontacting, proximity sensors~KD-2400, Kaman Instru-ments Corp., Colorado Springs!, one over the blow reed anone over the draw reed. A specially constructed fixturelowed these sensors to be positioned to measure simneously the motion~displacement! of both the blow anddraw reeds of any hole@see Fig. 5~a!#. The frequency re-sponse of the system was flat from DC to 10 kHz~63 dB!.The output of the reed displacement transducers wascorded digitally at 10 000 Hz by a computer workstati~Apollo 3500, Apollo Computer Inc., Chelmsford, MA!which implemented high-speed data acquisition softw~Significat, Hudson, MA!. These signals were further processed in real time by a custom built circuit which measuthe frequency and peak-to-peak amplitude of both signalreed displacement. The latter data were recorded on a386 with commercial acquisition software~LabTech Note-book, Laboratory Technologies, Inc., Wilmington, MA!.

In addition to observations with simple oral playing,resonating volume chamber was placed in the air streamjacent to the harp@see Fig. 5~b!#. This device acted as arudimentary equivalent of the vocal passage, similar tosystem described by Johnston.3 With the simple plunger thevolume of the resonating chamber was easily altered, and


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reeds were made to vibrate in any of the three differmodes of speaking~blow and draw; blow and draw bendand overblow and overdraw! using regulated air pressuravailable in the laboratory.

Raw displacement data were displayed in compresform in order to reveal the relative displacement envelopethe two reeds during various maneuvers~for example, seeFigs. 7 and 12!. The uncompressed display of the same dallowed detailed analysis of the shape of the trajectory ofindividual reed displacement. The relationship between rtive amplitudes and frequencies of the two reeds couldobserved during bends and overtones from the real timeplay of the signal processor circuit.

Measurement and display of reed vibration providseveral qualitative observations as well as quantitativesults. Although all 10 holes were studied, we present bedetailed results for hole 3, which were taken to representgeneral behavior observed for the remaining holes. It shobe noted, however, that the two reeds of hole 3 providwider interval of tones than any other hole~six semitonesfrom G, a straight note, to C, an overblow!. Although unique,the hole appears to encompass all modes of action.

When a natural note was obtained by either blowing

FIG. 5. ~a! Schematic of experimental apparatus for measuring and recing reed displacement.~b! Sketch of variable resonating volume chamb~60-cc syringe! used to crudely simulate vocal tract, modified from devidescribed by Johnston~Ref. 10!.


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drawing, only the primarily speaking blow or draw reed wasignificantly active. There was only a minimal amount of thsecondary reed vibration@Fig. 6~a!,~b!#. This confirmed theobservations made with the strobe light listed in Table I.addition to the peak-to-peak amplitude of vibration, it waalso informative to consider the relative displacement of tnominal position of the vibrating reed.

When playing a low blow note@such as 3-hole blow,Fig. 6~a!#, the nominal, or ‘‘average,’’ position of the blowreed moved away from the comb. In other words, the bloreed appeared to travel farther upward, into the reed slot,of the comb, than downward. The draw reed, although neaidle during blowing, appeared to displace slightly upwarinto its respective reed slot and into the comb. The low dranotes@such as 3-hole draw, Fig. 6~b!# were characterized bya primarily closing draw reed, but the blow reed appearedvibrate, albeit slightly, either about the nominal position oslightly away from the comb. The high blow and draw note

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FIG. 6. ~a!, ~b! Reed displacement with time for straight blow~a! and draw~b! notes on hole 3. Reeds move in parallel. Displacement values are relaonly.


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behaved similarly, with roles reversed. These observationcontradicted the intuitive prediction that the nominal positionof both reeds of a hole should move outward on blowingwith positive pressure in the hole and inward on drawingwith negative pressure in the hole.

Intuition would likewise dictate that the relative phasebetween the two reeds would result in their contrary motionoutward with blowing and positive pressure in the hole aninward with drawing and negative pressure in the hole. However, this was observed to be the case only for the high blonotes. When any of the ten holes was drawn, the reeds weobserved to oscillate in parallel with one another. Since thdraw reed did not vibrate appreciably for the low blow notesit was difficult to distinguish the relative phase. Parallel motion of reeds can be interpreted as both reeds acting simulneously to close, or open, their respective reed slots. Thlevel of pressure also appeared to bear a slight influencethe phase relation for some of the holes. For example, whehigh pressure was applied on the 3-draw or 3-draw bend, tmotion of the closing reed was observed to lag slightly further behind the opening reed.

The displacement patterns of the blow and draw reeddisplayed disparate degrees of departure from simple hamonic motion. In most cases, the blow reed appeared to folow a sinusoidal trajectory, whereas the draw reed displayea notable amount of superimposed third harmonic~secondovertone; see Figs. 6~b! and 8, for example!. The degree ofdeparture of both displacement patterns from a sinusoidshape was more prominent for higher air pressure and flo~not shown in figures! than for lower pressure and flow.

Dynamic measurements of reed displacement were rcorded whileenteringand exiting a 3-draw-bend~3DB!. Acompressed view of the reed displacements upon entry to tbend is demonstrated in Fig. 7. As the bent note was estalished, the amplitude of vibration of the~higher pitched!draw reed gradually diminished in favor of increased vibra

FIG. 7. Relative displacement of blow and draw reeds entering a bendhole 2, from G to approximately F#. Note, the draw reed speaks initially anas a closing reed, but the blow reed takes over as an opening reed, asplayer continues to draw but with a different embouchure.


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tion of the blow reed. A detailed view of reed displacemeat the point of a two-semitone bend~low A on a C harp! isshown in Fig. 8. Comparison with the pure blow and drawaveforms demonstrates that the bent note results in anmost composite of the two. The wave shapes and relaposition of both the blow and draw reed displacements wobserved to resemble those occurring for their respecstraight notes.~This is worthy of recognition since the blowreed is no longer operating as a closing reed, but operatean opening reed.!

Figure 9 depicts data for hole 2 played by mouth adouble draw bend is entered. The amplitude of vibrationplotted as a function of frequency. With proper configurati

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FIG. 8. Relative displacement of blow and draw reeds during a twsemitone bend of hole 3. Note significant vibration of both reeds, andallel motion of the reeds.

FIG. 9. Amplitude of reed displacement versus frequency while enterindouble draw bend from a straight draw on hole 2 of a 10 hole diatoharmonica. As frequency decreases, the amplitude of vibration of the dreed decreases as the amplitude of the blow reed vibration increases.


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of the vocal tract, a wide range of pitch was possible, cfirming observations shown in Fig. 4. As the bend wastered and frequency dropped, the amplitude of vibrationthe draw reed diminished while the amplitude of the bloreed increased. Thus the act of bending appeared to divetransfer the reed activity from the draw~closing! reed to theblow ~opening! reed.

The nominal positions of the reeds during the low drbends~holes 1 to 6! were somewhat counter-intuitive. Thnominal position of both reeds was displacedaway from thecomb@see Fig. 6~a!, for example#. In other words, the maxi-mal outward excursion of the reeds was surpassed bymaximal inward excursion—counter the principal air floand against the primary pressure gradient. The high nblow bends~holes 7 to 10! did not evidence such anomaloubehavior. However, for both draw bends and blow bencounterintuitive parallel motion of the reeds was demostrated. Most intriguingly, this did not occur in holes 9 a10. As with the straight notes, the phase relation betweenreed motions was observed to depend on the magnitudair flow. Particularly, for the low draw bends, it was possibto achieve phase from 0 degrees~parallel motion! to 90 de-grees phase lag between the reeds, depending on the isity of the tone.

It was possible to obtain overblow tones with thvolume-chamber apparatus, in most instances with a svolume. The overtones achieved in this fashion wereserved to occur abruptly, as they do with normal playingoverblow notes. The transition from blow to overblow wou‘‘pop’’ into place as one changed the volume rather thslide smoothly, as is characteristic of the bent tones.apparatus allowed more pure and complete overblows toachieved than could be obtained with oral playing. Figureshows the detailed waveforms of reed displacement fosustained hole-3-overblow. The minimal activity of the bloreed noted here was not always easily obtained and sustawhen the harp was played by mouth. For all holes stud

FIG. 10. Relative displacement of reeds with overblow on hole 3. Almosaction is on draw reed.~Clipping of waveform at bottom is due to saturatioof the amplifier.!


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the nominal position of the reeds was observed to moveward with respect to the comb, concurrent with the air floThis was especially true for the vigorously vibrating drareed.

The relative phase of the reeds for the overblows stud~hole 3 to 6! was observed to depend upon the location ofdisplacement transducer. When placed near the roots otwo reeds of hole 5 and 6, the phase relation evidencedallel motion; whereas, when placed at the tips, the motwas in opposition. The opposite was true for hole 4. Holewas inconclusive due to the negligibly small amplitudevibration of the blow reed.

The distinguishing characteristics of the overblowcompared to the bend are further illustrated by comparingamplitude versus frequency plot of an overblow~Fig. 11!with that of a bend~Fig. 9!. Unlike the bend, which displaysa smooth and gradual transition of reed primacy as thequency changes, the overblow demonstrates a much shadrop in the amplitude of oscillation of the closing, blow reeand simultaneous rise in amplitude of oscillation of the oping, draw reed. The interval between natural frequenciesthe two reeds is far more devoid of activity in the overbloas compared to the bend.

The resulting overlap in frequency response of the treeds during bending allows the player not only to bemore easily, but to slide between bent and straight noConsequently, this provides more opportunity to introduexpression into the notes being played. An example of thidepicted in Fig. 12 which shows a tracing of the amplitudereed vibration compressed in time and recorded during adraw to 6-draw-bend, played by Howard Levy.

In some cases, it was possible to obtain, and maintaidissonant overblow. In this case, the vibration of the treeds remained synchronized but assumed different funmental frequencies. Figure 13~a! and~b! shows, respectively

llFIG. 11. Relative displacement of reeds during onset of overblow on hthree~not used in normal playing!. Note: blow reed, with pitch of G, speakinitially but abruptly becomes silent as the draw reed, with natural pitchB, speaks with~overblow! pitch of C.


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a consonant and dissonant overblow obtained in hole 3the case of the dissonant 3-overblow, the draw reed, witnatural pitch of B~494 Hz!, was induced to vibrate at 518Hz, but the blow reed with natural pitch of G~392 Hz! vi-brated at 358 Hz~approximately F! with an apparent 25%modulation in its period from cycle to cycle. In a consonaoverblow, the draw reed was observed to vibrate at 523(C5) and the blow reed vibrated at the same frequencywith diminished amplitude. In normal oral playing such disonance is common during overblows, and is produced emore frequently by less skillful players.

FIG. 12. Relative displacement amplitude of blow and draw reeds durseveral partial entries and exits of hole 6 draw bend. Note reciprocal shifactivity of the two reeds. Note the blow reed is the dominant actor indraw bend, as indicated in Table I.

FIG. 13. ~a!, ~b! Relative vibration of reeds during a consonant~a! anddissonant~b! overblow on hole 3. During the dissonant overblow, the drareed, with a natural pitch of B~494 Hz!, vibrated at 518 Hz, but the blowreed with natural pitch of G~392 Hz! vibrated at 358 Hz~approximately F!with an apparent 25% modulation in its period from cycle to cycle. Inconsonant overblow, the draw reed vibrates at 523 Hz (C5) and the blowreed vibrates at the same frequency but with diminished amplitude.


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II. DISCUSSION

For over a century harmonica players have manipulathe harmonica to produce a wide variety of tones, glides,slurs. The resulting effects reflect the dynamic interplayphysics and acoustics of the harmonica coupled to the bof the musician.

To understand the dynamics of music production wthe harmonica it is essential to understand the behavior ofinstrument. In these studies we have focused on the dynics of the reeds themselves and of their function as a plaachieves desired notes through the combination of blowdrawing, bending, overblowing, and overdrawing. The infomation obtained has shown how an array of sounds canaccurately produced with a single channel and a pairreeds. For example, in the third hole of the popular diatoharmonica, two natural notes~blow and draw!, one-, two-,and three-semitone bends, and an overblow can be prodwith the two reeds by alteration of the vocal tract of tplayer. The new group of tones introduced in the last quacentury, namely overblows and overdraws, have been shto be effected primarily by only one reed which functionsan opening reed—the normal function is closing—at a pioutside the interval of the two notes in the hole. Better uderstanding of these new tones provided the motivationthe authors to undertake the studies described here.

The common rule that bent notes are limited to withinsemitone of the opposite note of the hole was substantiin these studies. This is partially explained by the theoretmodel of Johnston which describes the range of pitcwhich are producible from a single reed. His analysis deonstrated that closing reeds can be flatted a semitone obelow their natural resonant pitch. Johnston’s theoretmodel unfortunately did not account for this possible copling between the two reeds. The reed-blocking experimereported above demonstrated that the presence of a lopitched, opening reed in the same hole appeared to dimithe potential range by imposing a lower limit on the benSimilarly, the presence of ahigherpitched opening reed wafound to virtually obliterate the blow bend of the closinreed in holes 1–6 and the draw bends in holes 7–10.

Due to the simplifying assumptions associated wJohnston’s model, it is also not capable of accountingmany of the nuances of the construction of the harmonitself. Therefore, additional modeling will be necessaryorder to understand how the geometry, physical propertand air flow combine to produce the observed phenominvolved in producing tones on the harmonica. In spitethis instrument’s apparent simplicity, there is a multitudemodifications that have been introduced, or proposed, to athe timbre and improve the ease of achieving certain noThe aerodynamics associated with increasing the reed pthickness, the shape of the air hole in the comb, or theentation of the reed pairs, for example, would make an inesting topic of study if a more elaborate mathematical mowere developed.

Our quantitative measurements of reed dynamics hsubstantiate some of the suspected relationships betwreed primacy and the fundamental tone that is generaSince the trajectory of the reed determines the flow of air,

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fundamental frequency of the reed displacement determthe frequency of the tone that is generated. However,reed motion was observed to contain overtones. The cauthis distortion could be explained by the nonlinearity ofther the displacement measurement system or the reed olator itself. In the case of the draw reed, a significant infltion in the displacement tracing occurred in close proximto the zero-crossing point of the reed with respect to the rplate. The calibration of the displacement transducers didreveal any discontinuity at the zero-crossing point whcould explain this inflection. Accordingly, this ‘‘hesitationin the reed motion is most likely caused by either the aedynamic disturbance or instability of the jet of air whicresults in the constricted reed slot.2

The paradoxical behavior observed with respect toparallel motion of some of the reed pairs may appear coterintuitive and initially seems to contradict the fact that tblowing pressure or drawing pressure causes one reeopen when the other one closes, and vice versa. Howevcan be explained through the small-signal theoretical moof Johnston3 which predicts the relative phase of the remotion with respect to the acoustic pressure in the hole.would be expected from a nonlinear dynamic system,phase relation at higher amplitudes~greater pressure or aflow! was observed to differ slightly from the low amplitudresponse. In particular the closing reed was observed toslightly further behind the opening reed for the draw adraw-bends when high pressure was applied. The slvariation of phase observed in response to increased air psure can easily be explained by the well-known influencedamping on resonant frequency and phase angle; see Refor example.

Care was taken to position the displacement senconsistently in a similar relative location along the lengtheach of the reeds. The finite spatial resolution of the senresulted in an averaging effect of the displacement measment. For most of the reeds studied, the shape of theplacement trajectory did not appear to depend upon thecation of the transducer. However, the overblow in holeand 6 did demonstrate such a dependence. This observcan be taken to imply that one, or both of the reeds durthese overblows assumes an inflected shape. This wouldther imply that an overtone would be present. Basic betheory would predict the frequency of this overtone to6.26 times the fundamental.16 The absence of this observation for the other maneuvers could be attributed to thesence of this overtone or to the limited spatial resolutionthe sensor, as mentioned above.

The counterintuitive observations relating to the nomiposition of the reeds may be understood by consideringeffect of air flow velocity upon the local gradient of pressuAccording to the Bernoulli principle, increased velocialong a streamline of the flow, for example created byconstriction between the reed and reed slot, causes thesure to decrease; therefore, it is possible to create a pavacuum with positive flow. These results also shed solight as to the influence of reed offset upon ease of achievdesired notes. The common practice of adjusting the resposition of the reed, or reed offset, by gently bending


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reed into or out of the plate may, in effect, relocate the reto an equilibrium position more amenable to bendingoverblowing/overdrawing—but at the expense of increasthe difficulty of playing the natural tone.

The graphs of amplitude versus frequency of reed vibtion that were generated during bent, overblown, and ovdrawn notes were quite informative for demonstratingdistribution of reed primacy. As the linear acoustical modof Johnston3 would theoretically predict, the process of bening involved a smooth transition of primacy, whereas toverblows and overdraws demonstrated a more discontous, sudden jump in primacy.

The harmonica is nearly unique among musical instments in that the vibrating oscillator, the reed, which pduces the sound, is alternately upstream and downstrfrom the controlling resonating volumes. We have attempto qualify and quantify some of the phenomena of reed fution as the reeds react to this acoustical coupling. Johnst3

who provided the first scientific study of this phenomenodemonstrated that changes of pitch are effected by altethe acoustic impedance of the vocal tract, which in tudrives both reeds of the channel of the harmonica.

Similarly, the present investigation has centered primrily on the harmonica itself. However, in order to understathe dynamic function of harmonica playing, the human votract must also be studied. Clinch and associates17 haveshown with the clarinet, saxophone, and recorder thatgood quality notes resonant frequencies of the vocal tmust match the frequency of the desired note. The harmorequires pitch control of another order, for the acoustic ipedance of the vocal tract controls not only quality of tonbut it also raises or lowers the pitch in order to achiecertain notes. A wide variety of air flow rates, vocal cavvolumes and vocal configurations are compatible withproduction of natural tones from the harmonica. To produa more pure natural tone requires not only adequate shapthe vocal tract, but good musical sense and a sensauditory-vocal feedback mechanism. It appears that theume and shape of the vocal tract have only a slight effecthe natural tones, but the mode and frequency of the faioned notes—bent, overblown, or overdrawn—are causedchanges in the vocal tract.

In a preliminary study of one aspect of the vocal tranamely the volume of the oral cavity, a simple experimewas conducted in which a player, lying supine, played scific fashioned notes and then held the configuration ofvocal tract while the oral cavity was filled with water and threquired volume was recorded. Reproducible results wobtained with practice. The results of this preliminary expement are shown in Fig. 14. It is probable that actual playvolumes were larger than measured, since when waterinstilled, constriction of the glossopharynx and larynx ocurred in order to suppress the swallow reflex and prevaspiration. The volume of the anterior oral cavity was fouto be inversely related to pitch as modified by bending. Trelationship was not found with the straight notes whicould be obtained with a wide range of airway volumeChanges in configuration of the oral tract, however, demine the timbre of notes, which is a subject of further stu


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Upon delving into the physics and physiology of hamonica playing, the extent of the unknown phenomena ccerning this instrument became increasingly evident. Eexperiment, more times than not, revealed new groundunexplored. The authors now realize that this report doesinclude many of the additional features of sound affectthe timbre, modulation, or voicing. Most notably absentthese studies was the use of cupping of the hands. Mharpmen will use this technique to introduce vibrato aother forms of expression, as well as to alter the timbre ofsound. The answer to these and other questions regardinphysiology of harmonica playing will be further elucidatethrough systematic analysis of coupled interaction of the hmonica with the vocal tract—as revealed by videoenscopic, ultrasonic, and fluoroscopic imaging.

III. CONCLUSION

Artistry of harmonica playing is related to the interplabetween the player and the instrument. In this project,physical behavior of the reeds of the harmonica was invegated. Mechanical and acoustic aspects of reed dynawere elucidated during blowing and drawing, overblowiand overdrawing, and blow and draw bending. Throuknowledge of reed function, the artistry and process‘‘speaking’’ with the harmonica can be better understooand possibly mastery of this instrument will be enhanced

In the final analysis, the music created by the harmonconsists of more than the acoustic and physical function

FIG. 14. Volume of oral tract used to play the scale with 1 and 4 drbends. Harps keyed in the scale of F were used on which hole 1 draw~circles!, or for the higher scale, hole 4 draw bend~squares! were played.The resulting scale is in the key of F#. The player held the configuratiothe vocal tract as the volume of water required to fill the oral cavity wintroduced and measured. Pitch of notes was inversely related to volum


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the reeds. There is a synergy which causes the whole tgreater than the sum of the component parts and an artwhich cannot be quantified—dynamics which give personity to the instrument, reflecting individuality of the musiciaAs with speech which varies from person to person, therecertain tonal elements of harmonica playing which are silarly individualized. This dynamic interaction allows thplayer to speak with his instrument perhaps as with no othJust as no two voices are exactly alike, each player imphis own timbre, and one cannot expect to emulate exactlymusical tonality of another. This helps keep the harmoninteresting, and indeed has helped to sustain its enduprominence throughout the world

ACKNOWLEDGMENTS

The authors wish to acknowledge the willing and expassistance of Ricardo Schultz and Lee Denault who pformed much of the computer processing of the experimedata. The authors are also highly grateful to Howard Lefor participating in several unusual experiments involvedthese studies of harmonica physics, phonetics, and phyogy.

1K. Field, Harmonicas, Harps, and Heavy Breathers~Fireside, New York,1993!, Chap. 1, pp. 19–30.

2A. O. St. Hilaire, T. A. Wilson, and G. S. Beavers, ‘‘Aerodynamic exctation of the harmonium reed,’’ J. Fluid Mech.49, 803–816~1971!.

3R. B. Johnston, ‘‘Pitch control in harmonica playing,’’ Acoust. Aust.15,69–75~1987!.

4P. Duncan,Blues Harp for Diatonic and Chromatic Harmonica~Mel BayPublications, Pacific, MO, 1982!, p. 17.

5T. Glover,Blues Harp~Oak Publications, New York, 1965!, p. 32.6P. Duncan and C. Musselwhite,Power Blues Harp~Mel Bay Publications,Pacific, MO, 1990!, p. 13.

7S. McCloskey,Harping It Easy@cassette tape# ~Hohner, Richmond, 1983!.8T. Glover,Blues Harp Songbook~Oak Publications, New York, 1973!, p.10.

9F. Palmer,The Harp Styles of Sonny Terry~Oak Publications, New York,1975!, p. 47.

10S. Baker,The Harp Handbook~Hermann Demmler, Ludwigsburg, 1991!,p. 20ff.

11W. T. Yerxa, ‘‘Bending and overblowing—All one donut,’’ HarmonicInformation Press4, 35–42~1994!.

12M. Hiramo and D. Bless,Videostroboscopic Examination of the Laryn~Singular Publishing Group, San Diego, 1993!.

13J. Thaden, ‘‘Doctor Diatonic,’’ Harmonica Horizons5 ~1990!.14W. T. Yerxa, ‘‘The Overblow Harp,’’ Harmonica Information Press4,

4–7 ~1994!.15H. T. Bahnson, U.S. Patent No. 5,739,446~1993!.16S. Timoshenko, D. H. Young and W. Weaver, Jr.,Vibration Problems in

Engineering~Wiley, New York, 1974!, p. 74ff.17P. G. Clinch, G. J. Troup, and L. Harris, ‘‘The importance of vocal tra

resonance in clarinet and saxophone performance: A preliminarycount,’’ Acoustica30, 280–284~1982!.

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