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Measurements of the motion of the hand and

drumstick in a drumming sequence with

interleaved accented strokes - a pilot study

Sofia Dahl

Abstract

The motion of the hand and the tip of the drumstick in a simple repeated drummingpattern with interleaved accented blows have been studied using standard videoequipment. The vertical positions of the tip of the drumstick and a reference pointon the hand were measured. Typical timing relations and velocities are reported. Acharacteristic preparatory motion of the hand resembling a fishtail motion wasobserved for the accented blow.

IntroductionRelatively little is known about the biomechanicsof music performance. A basic observation isthat musicians at a professional level seem tohave acquired a technique which enables arelaxed and reliable execution of basic elementsin playing with a minimum of physical andmental effort. Typical examples would bechanging hand positions on a stringed instrument,or forming the attack characteristics of a tone ona percussion instrument. Both these examplesrequire close control and co-ordination of the

hand and arm motions. It seems reasonable toassume that in performance, these optimizedbasic elements of playing are used as buildingblocks in the execution of more complexstructures, such as phrases, a task which needsattentive planning over a longer time span.

Percussion players are particularly suited forinitial studies of the biomechanics of music per-formance. The body movements are generallylarge and basically limited to the arm and wristmotion in the vertical plane. The difficultiesinvolved in studying the small scale motion of thefingers characteristic for the playing of mostother instruments are thereby avoided.

ExperimentsA video recording of a non-professional player(the author) playing a repeated drummingsequence with a regular drumstick on a practicepad was made. The playing was recorded with astandard video camera, mounted perpendicularlyto the striking plane. The time separationbetween frames was 20 ms. Two centimetrescales were mounted vertically in the immediate

background, one placed at the tip of thedrumstick and the other at the hand.

For each frame of the recording, the verticalpositions of the tip of the drumstick and of areference point on the hand (the joint on the indexfinger next to the drum stick (Figure 1) weremeasured. The point on the finger will be referredto as the hand in the following. An estimationof the inevitable small horizontal movements ofthe hand was also made.

Figure 1. View of the drumstick and the hand.The arrows indicate the two reference pointsused for data collection (encircled); one at thetip of the drumstick and one on the index finger

at the joint next to the stick (referred to as thehand). The angle between the stick and thehorizontal plane is denoted by .

Based on the data of the vertical positions, thevelocity of the tip and the hand, as well as theangle between the drumstick and the horizontalplane were calculated (Figure 1). The velocitywas calculated as a three-point central-differenceapproximation. The reading error in verticalposition was estimated to 1 cm, giving acalculated error in velocity of

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0.5 m/s. The calculated error in ranged from2 deg (horizontal orientation) up to about 10deg (almost vertical orientation). The largeuncertainty for almost vertical orientation wasreduced by checking the calculated values againstthe recorded angular position on the screen. Theeffective length of the drumstick from the tip tothe reference point on the hand was 30 cm.

The recorded drumming pattern consisted ofrepeated single strokes at a tempo of150 beats/min (nominal beat duration 400 ms)with one strongly accented blow every fourthnote. The sequence was played with the righthand.

Results

General description of the sequence

The overall impression of the recorded per-

formance was that of a regular playing with arelaxed posture. A clear strategy for the prepara-tion of the accented blow was observed, bestdescribed as a fishtail-like movement of thehand.

A sequence of stylized pictures displaying theposition of the drumstick versus time is shown inFigure 2(a). The pictures were generated fromthe data of the vertical positions of the tip and thehand. The three successive soft strokes are of agentle, wave-like character. The amplitude of thehand movement is small, and so is the variationin the angle of the

drumstick with respect to the horizontal plane. Atthe last hit in the sequence of three soft strokes(S1, S4), the hand starts an upward movement asa preparation for the accented blow (A1, A2).This upward movement starts while the tip still isin contact with the drumhead.

A detailed description of the preparation forand execution of the second accented blow in the

recorded sequence (A2) is shown in Figure 2(b).The numbered frames show the successivepositions of the drumstick, some of themillustrated by inserted snapshots of the grip of thedrumstick.

During the first part of this preparatorymovement the hand moves rapidly upwardsmaking the drumstick follow, pointing down-wards (frame 1 - 12). The tip of the drumstickcatches up successively as the stick gains inangular velocity, but not until the hand hasapproached its maximum vertical position the

stick is levelled (between frame 12 and 13). Theangular motion of the stick continuesuninterrupted and the stick ends up pointingvertically (frame 19). By this time, the hand hasalready turned its vertical path (frame 15) andstarted a descending motion which initiates theactual downstroke. When the hand is lowered inthe initiation of the downstroke the wrist anglebecomes more pronounced (cf. snapshots C andD in Figure 2(b)). This is an effect of a relaxedwrist which allows the stick to reach its maximalvertical overshot. The small horizontalmovements during the stroke is seen as a loop inthe path of the hand.

Figure 2a. Motion sequence of the drumstick. Registrations of the motion of the drumstick and handduring repeated drumming with a strong accent every fourth stroke. The hits on the striking surface

(a practice pad) are indicated by arrows and marked with S for soft blows and A for accented. (Thehit of the first accented stroke was not recorded due to poor time resolution.) The figure is based onmeasurements of the vertical position of two reference points on the drumstick and hand,respectively (Figure 1), taken from a video recording with a separation of 20 ms between frames.

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By starting the upward movement of the handbefore the drumstick has left the drumhead theplayer ensures that there is ample time for thehand to reach a high starting position for theaccented blow. In the initiation of the down-

stroke, the hand drags the vertical stick down-wards before the stroke is completed by a twistof the wrist by more than 90 deg. Thecombination of a long vertical starting runfollowed by a large angular motion of the wristmakes a high impact velocity possible. Theresulting motion of the tip of the drumstick in theaccented strokes resembles a whiplash, while thehand performs a smooth, characteristic fishtail-like movement.

Accented strokes

Figure 3(a) shows the vertical positions of thereference point on the hand and the tip of the

drumstick versus time for the same sequence asin Figure 2(a). The strong angular component ofthe stick motion seen in Figure 2 is illustratedmore clearly in Figure 3(b), in which the timeseries of the angle between the stick and the

horizontal plane has been added. In Figure 3(c)the position and velocity of the tip are displayed.The accented blow is repeated every fourth

note, but the preparation for this stroke and thefollowing rebound influence more than a third ofthe repetition period of three soft strokes and oneaccented blow. Figures 3(a) and (b) show clearlyhow the hand starts the preparatory upwardmovement before the tip of the drumstick (see S4- A2). The lead of the hand is about 100 msbefore the tip is forced upwards. Both hand andtip then gain height quickly, and the angle changes rapidly from -50 deg up to a maximum

of about +90 deg. The maximum

Figure 2b. Detailed view of the second accented blow (A2) in Figure 2(a). The figure shows 22numbered frames separated by 20 ms. The total time-span is 420 ms, counted from the hit of the

preceding soft stroke (frame 1) to the hit of the accented blow (frame 22). The inserted snapshots (A- E) show the orientation of the drumstick and hand during the successive stages. Snapshot Acorresponds to frames 1-4 (initial positions), B to frames 12-13 (levelling), C to frame 18(approaching vertical orientation), D to frame 19 (vertical overshot), and E to frame 21 (point ofhighest velocity, just before impact). The small horizontal movements during the stroke is seen as aloop in the path of the hand.

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velocity of the tip reached on its way up to theturning point at about 70 cm above the strikingsurface is about 4 m/s. (Figure 3(c)). Incomparison, the highest position of the hand isonly about 50 cm and the maximum upwardvelocity 2 m/s.

In the present example with a beat rate of150 beats/min (repetition period 400 ms), thepreparation of the accented stroke lasts 260 msapproximately, counted from the impact of thelast soft stroke (S1, S4) before the accented tothe maximum elevation of the hand. This leaving140 ms for the actual downstroke. The impactvelocity of the tip reaches about 13 m/s,compared to 1 m/s for the soft strokes. Thesevalues correspond to about twice the hammervelocity at string impact in pianos at ff and pprespectively (Askenfelt & Jansson, 1991).

Note also the oscillating motion of thedrumstick after the strong impacts (A1 and A2,Figures 2(a) and 3(a)). The tip of the reboundingstick bounces up to a position which is above theoptimal starting position for the following softblow. When not dampened by the players handthe rebound will carry the stick high enough foranother strong blow. (This is the mechanism theplayer takes advantage of when playing fast ordemanding patterns, for example rolls.) In thepresent case, the influence of the playersdampening of the rebound can be seen as oneperiod of an oscillating movement of the tip at

about 8 Hz, corresponding to about a third of thebeat period (400/3 = 130 ms).

Soft strokes

During the soft strokes, the position of the handstays essentially constant, with a variation ofonly 5 cm approximately around a mean positionabout 12 cm above the striking surface. Themotion of the tip is of course much larger, butgradually reduced during the sequence of thethree blows from about 25 cm at a maximum atthe first rebound to 10 cm at the third. As aconsequence, there is a slow drift in mean towards negative values superimposed on theperiodic pattern of the three strokes. The angle atthe impacts ( -25 deg) is not changed,however, as the elevation of the hand above thestriking surface is not changed markedly. Duringthe soft strokes the drumstick is consistentlypointing downwards (< 0), the strong reboundafter the accented blow excluded.

Discussion

The present study is of pilot character, utilizing asimple standard video recording with relatively

poor time resolution and a non-professionalsubject. Nevertheless, it seems reasonable toassume that it reveals some of the characteristicfeatures of a performance of a drummingsequence with accented blows interleaved in arepeated series of soft strokes.

The observed smooth and relaxed perform-ance could be assumed to be a general charac-teristic of professional drumming. A practicedplayer will try to minimize the use of sudden,forced, or jerking movements. If the drummertakes advantage of the rebound from thedrumhead, the hand can be lifted high withoutmuch effort as in the preparation for the accentedblows in the studied sequence. Not until the stickhas passed its upper turning point an actual forcedelivery may be applied by the wrist (or fingers)to increase the speed. The result is a whiplash

of the tip of the drumstick but the motion of thehand is smooth, resembling a fishtail-gesture.This characteristic fishtail motion of the hand

in the preparation and delivery of the accentedblow is certainly used in other ways indrumming, like reaching a position on anotherdrum far away in ample time. By starting themovement before the last note is finished theplayer gains time and thereby effort. While thehand and fingers still control the last stages of thepresent tone the lower and upper arm havealready started to move in position for the next.

In order to ensure a free retreat of the

drumstick from the drumhead the hand must berelaxed at impact. A strained hold of the stickwill increase the contact time between stick anddrumhead and cause a more dampened sound(which in some cases may be desired). Once,however, the rebound has carried the tip up andaway from the drumhead the hand has tostabilize the stick if the following stroke is to bemuch softer than the previous.

Further studies already under way - usingadvanced motion detection equipment - willprobably reveal more details in the motion of the

hand and drumstick, especially during the mostrapid events.

AcknowledgementsThe author is indebted to Markku Haapakorpifor assistance during the recording sessions, toSvante Granqvist and Jonas Beskow for pre-paration of picture sequences, and to AndersAskenfelt for valuable comments on the manu-script. This study is a part of the project Musicand motion supported by the Bank of Sweden

Tercentenary Foundation.

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ReferencesAskenfelt A & Jansson E (1991). From touch to

string vibrations II: The motion of the key andhammer, J Acoust Soc Am 90: 2383-2393.