Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

A simple device for thesimultaneous registration of

bow motion and bow forceAskenfelt, A.

journal: STL-QPSRvolume: 25number: 1year: 1984pages: 044-057

http://www.speech.kth.se/qpsr

Musically, the motion pattern of the bow is of great importance in the performance of s t r i n g music, e.g., i n phrasing, t he motion of ten being carefully addressed by the composer i n the score. Physically, the momentary velocity of the bow is one of the player's chief controls of loudness, the excursion of the str ing being directionally proportional t o the bow velocity. The other avai lable control of loudness is the distance from the towing point to the bridge, the transverse excursion of t he s t r i n g being inversely proportional t o t h i s distance ( C r e m e r , 1981) . i

According t o the basic Helmholtz model of s t r i n g motion, the bow force does not influence the vibrat ions of the s t r i n g as long as the frictional force between bow and string is high enough to maintain the stick-slip process of the str ing under the bow. However, as familiar to a l l s t r i n g players, the bow force does e f f e c t the vibrat ions of the s t r i ng , an increased bow force giving a more b r i l l i a n t and carrying tone. A s sbwn by Cremer (1981), a higher bow force than m i n i m u m leads t o a resharpening of the c i rcu la t ing corner of t he s t r i n g during the passage under the bow, the corner being rounded off at the reflections a t the str ing terminations, mainly a t the bridge. This gives a boost of the higher partials with increasing bow force, an effect also available to the player by decreasing the distance between the bow and the kidge. However, this later strategy is accompanied by the increase i n loud- ness earl ier mentioned.

In the following, t he parameter (1) w i l l be referred t o as trans- verse bow motion although the motion takes place i n the longitudinal d i rec t ion of the bow. This is i n order t o avoid misunderstandings as the s t r i n g of ten is used as a d i rec t ion of reference i n s tud ies of the violin. A s regards parameter (2), the cor rec t term bow force w i l l be used instead of the customary term "bow pressure".**

Method

Bow motion The instantaneous transverse position of the t o w was measured by

means of the Wheatstone-bridge pr inciple , Fig 1. A t h i n res is tance wire was inser ted amongst the bow hairs . This wire is divided i n two parts by the string, the ra t io of the lengths of these two parts depend- ing on the transverse posi t ion of the bow. The two pa r t s of the wire

** I t would be desi rable t h a t the cor rec t term "bow force" be used consis tent ly i n s c i e n t i f i c presentations, as it is a force and not a force per unit area which is being measured. The reason for the persist- ance of the term "bow pressure" would be that t he player has good reasons to associate to pressure, as he actually presses the b w against the s t r ing.

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Fig. 1. Sketch of the equipent used for the simultaneous registration of bow motion, bow force, and pitch. The sensor for the transverse bow p s i t i o n is a thin resistance wire inserted m n g the bow hairs. This wire is divided into two parts by the string, the two wire parts constituting one branch of a Wheatstone bridge. Tne sensors for the bow force are four strain gauges munted on thin bronze strips through which the bow h a i r is fastened to the bow. The strain gauges are connected in another Wheatstone bridge. The pitch is registered by an accelerawter sensing the vibrations of the violin body. A l l three signals are re- corded on an ink writer.

make up one branch of a Wheatstone bridge, the other branch consisting of one fixed and one variable resistor, allowing for offset calibration.

With the midpoint of the bow resting on the string, the bridge is i n balance. When the bow is moved away from this point, a voltage is generated proportional to the distance from the midpoint of the bow. The signal is registrated on an ink writer. When the bow not is i n contact with the string, the ink jet is deflected away fran the paper, leaving no trace. The linear relationship between output voltage and transverse bow position is shown in Fig. 2.

This simple device makes it possible to register the player's matian of the bow without interfering with normal playing conditions. The player may wen use his own instrument as the only preparations needed are made on the bow. The only restriction necessary i n conjunction with the use of this prepared bow is the moderate use of rosin i n order to avoid intermittent electrical contact between bow and string.

Bow force The instantaneous bow force exerted by the player was registered by

the use of another Wheatstone bridge. The bow hair was cut a t the frog and the t ip and thin strips of phr>sphorus bronze were glued to the bow hair i n both ends. The bow hair was refastened to the bow via these metal strips. Four strain gauges were glued t o the str ips, one on each side, and connected in a Wheatstone bridge. When the player presses the bow against the string, the metal strips bend and the bridge generates a voltage proportional to the bow force. This signal is recorded on the same paper as the bow motion.

The output voltage is essentially a linear function of the b o w force, Fig. 2. The only deviations occur when using very high bow forces near the tip, a combination not used in normal playing.

The preparations of the bow described above did not change the normal playing conditions to any appreciable extent, according to pro- fessional violin players. For example, the total weight and the dis- tribution of the weight along the bow are essentially unaltered. The m o s t marked difference when using this prepared bow is the skrortening of the accessible bow length by a couple of centimeters, correspoding to less than 10% of the original length. The reduced length of the bow was 0.58 m.

Examples of registrations - K

The transverse bow motion and the bow force were registered on paper together w i t h other parameters of interest, in these experunents pitch or acceleration level i n the top plate of the instrument. The pitch a d acceleration were measured w i t h the aid of an accelerometer fastened to the violin top plate close to the bridge on the the bass h r side. The acceleration level was used as an estimate of the excitation of the instrument. Some examples of registrations are shown i n Figs. 3-

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8, displaying different manners of bowing as performed by two profes- sional players.

Typical values of bow force oberved during the experiments were *** between 0.5 and 1 N. The lowest bow force which s t i l l produced a steady tone was approximately 0.15 N. A bow force of 1.5 N and above is to be considered as high.

Typical values of b o w veloci ty were between 0.6 and 1.3 m / s . The lowestvelocitywhichstillproduced a steady tone w a s approximately 0.04 m / s , one f u l l bow s t roke l a s t i ng about 15 s. The highest bow veloci ty observed was almost 3 m / s , t h i s high value being reached i n sforzandi during closing chords of a movement.

The f i r s t example of reg is t ra t ions , Fig. 3, per ta ins to a r i s ing one octave G-major s ca l e s t a r t i n g on the low G-string. The sca l e is played legato, detache and staccato, respectively. The differences between these types of bowing are clearly demonstrated i n the figure.

The next f igure , Fig. 4, shows a sforzando i n two d i f f e r en t ver- sions, a short version with the bow leaving the str ing immediately af ter a rapid bow stroke, and a longer with the bow res t ing on the s t r i n g througbut the bowstroke. Note the differences i n the excitation of the instrument as displayed by the accelerat ion leve l curves. The long version consists of two portions with different decay slopes, emanatmg from a corresponding division of the bow stroke i n t w o portions w i t h a high and a slower velocity, respectively.

The r eg i s t r a t i on i n Fig. 5 i l l u s t r a t e s a crescendo - diminuendo made both the normal way, i.e., upbow - downbow, and also the m i t e way, downbow - upbow. Note the coordination of increase in bow force with the increase i n bow velocity, i.e., the force increases as the slope of the bow posi t ion curve increases. These gestures require a careful planning by the player as regards the consumption of bow length, i n order t o achieve a large dynamic span. In t h i s example, the span i n acceleration level is approximately 25 dB i n b t h versions.

An example of a usual accompaniment i n Mozart-style music is dis- played in Fig. 6, showing groups of notes played spiccato (eight-rmtes) and saltelato (sixteenth-notes). Note that the player increases the bow veloci ty i n crescendo by lengthening the bow strokes, t he t i m e f o r a stroke being constant. A matching increase i n bow force accompanies the increase i n bow velocity.

The registration i n Fig. 7 i l lustrates the typical accompaniment of Vienna-waltz, showing the after-beats played by the second violins. The bar is divided asymmetrically, the t i m e lengths from onset t o onset between beats 2-3 occupying 38% of the duration of a bar, leaving 62%

f o r the remaining two beats (cf., Bengtsson & Gabrielsson, 1983). The timing i n the f i r s t bar deviates from the following bars, indicating that the player adapts to the rhythm gradually.

*** The force un i t 1 N (Newton) corresponds to the weight of 100 g within an error of less than 2 8.

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The last example, Fig 8, shows the opening of the f i r s t movement of ~eethoven's violin concerto played in two different versions. The player w a s ins t ructed t o render one tender and one aggressive performarlce, respectively, maintaining an identical tempo and approximately the same loudness. A s seen i n the figure, the aggressive version is character- ized by a higher mean bow force as well as more rapid changes i n the force. Also, the player changes the bowing pa t te rn between the ver- sions, apparently i n order t o afford a f a s t e r bowing. The turning points of the bow are made a l i t t l e sharper i n the aggressive version, and a t one occasion the player l i f t s the bow from the str ing i n order to give an ex t ra s t r e s s t o the following note, s t a r t i n g t h i s note w i t h a sudden increase i n bow force.

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This l a s t example is perhaps the most interesting applicatian of the equipment described, giving insight into the bowing gestures used in playing music i n different moods

As indicated i n Fig. 8, the level of physical act ivi ty i n bowing is higher i n the aggressive version than i n the tender version. Interest- ingly, s imi l a r differences have been revealed between other motlon patterns performed under different emotions. For example, Clynes (eq., 1983), i n t he s tud ies of human touch expression, found the emotions "hate8' and "anger" t o be characterized by a stronger touch and, i n par t i cu la r , more abrupt changes i n the movements, as compared t o the emotions "love" and "reverence". The s ignif icance of the changes i n the s ignals , apparent both i n the touch experiments as w e l l a s i n the reg is t ra t ions i n t h i s study, suggests t h a t the der ivat ives of the pa- rameters registered w i l l offer informative contriht ions in a aontmued study of bowing gestures, the derivatives emphasizing the changes i n the signals (Askenfelt & Sjolin, 1980).

The r e s u l t s presented i n t he t h i s study show t h a t the method is capable of visualizing and discriminating well between the intangible differences i n bowing patterns associated with differing performances. Furthermore, the method does mt disturb the player i n his performance t o any appreciable extent. These features imply t h a t the equipment offers means to examine the art of the playing of bowed instruments more thoroughly i n t he future. Hopefully, such a study w i l l give ins igh t into the code used by musicians i n order to convey the emotional atmos- phere of a piece of music.

The author is indebted to violinists Semmy Lazaroff and Eiertil Orsin for their kind assistance in the experiments.

References Askenfelt, A. & Sjol in , ft. (1980): "Voice analys is i n depressed pa- t i e n t s : Rate of change of fundamental frequency r e l a t ed t o mental state", STGQPSR 2-3/1980, pp. 71-84.

Bengtsson, I. & Gabrielsson, A. (1983): "Analysis and synthes is of musical rhythm", in Studies of Music Performance. Publications issued by the Ibydl. Swedish Academy of Music, PJo.39, Stockholm.

Clynes, M. (1983) : "Expressive microstructure i n music", in Studies of Music Performance. Publications issued by the Ibyal Swedish Academy of Music, No.39, Stockholm. , . - . r - a $

Cremer, L. (1981) : Physik der Geige, S. Hirzel Verlag, Stuttgart. ,

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