Proceedings of the Second Vienna Talk Sept 19ndash21 2010 University of Music and Performing Arts Vienna Austria

CONTROL AND COORDINATION OF COMPLEX BOWING PATTERNS

Erwin Schoonderwaldt

School of Computer Science and CommunicationRoyal Institute of Technology (KTH) Stockholm Sweden

schoondwkthse

ABSTRACT

JS Bachrsquos Preludium of the third Partita for solo violin con-tains passages with complex periodic bowing patterns involv-ing combinations of bow changes and string crossings acrosstwo and three strings The recorded bow motion revealed spa-tial patterns in the form of circles and figure-of-eights Closerinspection showed that string crossings consistently led changesin bowing direction in performances by advanced players It isplausible that this behavior is necessary for the production ofclean note transitions and attacks and it can therefore be con-sidered as a good example of optimization in human sensori-motor learning Comparison of performances by two advancedplayers one of them familiar with the piece and the other sightreading it as well as a performance by an amateur player re-veal clear differences in the stability and consistency of bowingpatterns

1 INTRODUCTION

During the execution of a musical piece on a bowed-string in-strument the bow is constantly in motion The spatial trajec-tories followed by the bow (bowing trajectories) are not onlydirectly related to the control of the loudness and the quality ofthe tone but also reflect past and future events as a result ofco-articulation and preplanning For example bowing trajecto-ries in the vicinity of string crossings often show lsquorudimentaryrsquocircular patterns as demonstrated in the 1930s by Hodgson [1]The effects of co-articulation and preplanning were also clearlypresent in recent visualizations of measured bowing gestures bySchoonderwaldt [2 3]

Repetitive bowing patterns containing simultaneous bowchanges and string crossings form a particularly interesting classof bowing gestures in which continuous control forms an inte-gral part with past and future events A common type of suchpatterns consists of fast notes alternately played on two adja-cent strings This is often used as a compositional technique inbaroque music in which the notes on the respective strings formtwo intertwined voices (eg melody and accompaniment) An-other type of repetitive bowing patterns are series of arpeggiatedchords extending over three of four strings Many examples ofthese types of repetitive bowing patterns can be found in theSonatas and Partitas for solo violin by JS Bach

Earlier research on bowing gestures has mainly dealt withthe analysis of isolated bow strokes with the focus on the useof bowing parameters [4 5] or specific bowing techniques [46 7 8] Furthermore bi-manual coordination of bowing andfingering has been subject to study in simple musical sequences[9 10] In this paper a preliminary analysis of repetitive bow-ing patterns in a complex musical context will be presentedin which bow strokes cannot be considered as separate eventsThe focus will be on the coordination of string crossings andbow changes

2 METHOD

Recordings were made of performances of JS Bachrsquos Preludiumof the third Partita for solo violin by three violinists Two of theplayers were advanced students one of them (player A) wasfamiliar with the piece the other (player B) was sight readingThe third player (C) was an amateur player who was familiarwith the piece The musical fragments selected for analysis areshown in Fig 1

Figure 1 Selected fragments of JS Bachrsquos Preludium of thethird Partita for solo violin Fragment 1 (upper staff) rep-resents a repetitive pattern across two strings and Fragment2 (lower staff) is played as an arpeggio across three stringsBoth fragments start on a down bow and are played deacutetacheacute(a single bow stroke per note with the bow always attachedto the string) The roman numbers indicate the strings E(I) A (II) and D (III) [Score adapted from Mutopia projecthttpwwwmutopiaprojectorg]

The bowing gestures were recorded using an optical motioncapture system (Vicon) in combination with sensors on the bowfor measuring bow force and acceleration The measurementmethod allowed for an accurate definition of all relevant bowingparameters including bow velocity bow-bridge distance andbow force as well as the angles of the bow relative to the vi-olin [11]

A qualitative analysis of the measured bowing patterns willbe provided from two visual representations (1) direct visual-izations of the spatial trajectories followed by the frog of thebow (corresponding to the motion of the hand of the player)and (2) phase plots showing trajectories of the inclination ofthe bow versus bow velocity [2] A useful property of the lat-ter representation is that it clearly reveals the moments that thebow changes direction by the intercepts of the trajectory at zerobow velocity making it suitable for studying the coordinationbetween string crossings and bow changes in cyclic bowing pat-terns

VITA-1

133

Proceedings of the Second Vienna Talk Sept 19ndash21 2010 University of Music and Performing Arts Vienna Austria

minus100 minus50 0 50 100

minus22

minus5

Bow velocity [cms]

Incl

inat

ion

[deg

]

II

I

II

I

Figure 2 Performance of Fragment 1 by player A The phaseplot shows bow inclination versus bow velocity The trajec-tory shows a couple of cycles of the repetitive bowing patternsthe directions are indicated by the arrows The angles corre-sponding to string crossings (measured for the open strings) arelabeled at the y-axis Bow changes occur where the trajectoryintersects with the thick vertical line corresponding to zero bowvelocity The small plot on top provides a more intuitive spatialrepresentation of the bowing pattern more or less as seen fromthe playerrsquos point of view The dashed lines show the bordersof the fan-shaped string zones on the violin and correspond tothe labeled inclination angles in the phase plot The strings areindicated by roman numbers

3 RESULTS

31 Circular bowing patterns

Figure 2 shows the performance of Fragment 1 by player A Thespatial bowing trajectory (small panel on the left side) shows aclear circular pattern which can be explained as follows Thebow motion can be decomposed into a radial and a tangentialcomponent where the string forms the axis The radial com-ponent corresponds to the displacement of the bow which isdirectly related to sound production or more precisely the ex-citation of transverse vibrations on the string The tangentialcomponent (inclination of the bow) corresponds to the motionused for selecting the string In the tempo the piece was played(about 7 notes per second) both components can be character-ized as simple sine-like time series and as their periods areequal (2 notes) they add up to a circular spatial trajectory

The phase representation (main panel of Fig 2) of the bowmotion is derived from the spatial trajectory by taking the po-lar representation of the tangential component (bow inclination)versus the time derivative of the radial component (bow veloc-ity) The trajectory in the phase plot shows a narrow ellipticalshape This might be surprising at first consideration as this in-dicates that string crossings and bow changes are not perfectlysynchronized In case of perfect synchrony one would expectthat the two movement components would be exactly in phasewhich would yield a diagonal trajectory The hysteresis in thephase plot indicates that the bow changes lag behind the stringcrossings in the performed bowing pattern

This behavior was highly consistent in the performance ofplayer A Given the high quality of the performance it is un-likely that this behavior is erratic or that it reveals a lack of con-trol On the contrary there might be good acoustical reasons for

minus200 minus100 0 100 200minus44

minus22

minus5

13

36

Bow velocity [cms]

Incl

inat

ion

[deg

]

III

II

I

II

III

I

Figure 3 Performance of Fragment 2 by player A (see Fig 2for an explanation of the graphs)

the observed behaviorA possible explanation can be provided by closer consider-

ation of the mechanics of tone production during string cross-ings Firstly it should be realized that the string crossings do notoccur instantly but that they take place during a finite amountof time due to the bending of the strings and the bow hair at thecontact point During the transition the bow force is transferredfrom one string to the other It is then plausible that the optimalmoment for bow reversal is at the end of this transition ratherthen the beginning or the middle for two reasons (1) the bowforce acting upon the old string is released before bow rever-sal preventing the vibration from being lsquochokedrsquo [12 13] and(2) the bow force is built up on the new string providing thenecessary conditions for a good attack [14]

From these considerations it follows that the observed lagof bow changes might in fact reflect an optimal strategy for pro-ducing clean note transitions At the speed of the performancethis timing profile is achieved by the player by maintaining aroughly constant phase difference between the two movementcomponents Given that this strategy has developed by prac-ticing under influence of auditory feedback it is a convinc-ing demonstration of the level of sophistication of performanceskills internalized by sensorimotor learning

32 Figure-of-eight patterns

The bowing pattern of Fragment 2 is more complex as thereare three strings involved and it is therefore considerable moredifficult to play Again it is helpful to decompose the bow mo-tion in a radial and a tangential component However in thiscase the periods of the two components are not equal the tan-gential component has a period of four notes corresponding tothe sequence of strings (II-I-II-III) which is twice the periodof the to-and-fro motion (down-bow up-bow) for playing thenotes Thus the total bow motion forms a spatial pattern witha figure-of-eight shape as shown in Fig 3 (small panel on theright side)

Again the phase plot (main panel in Fig 3) revealed a smallphase difference between the two movement components insuch a way that bow changes lagged behind string crossingsThis indicates that the player used a similar strategy to achieveclean note transitions Even though some local deviations couldbe observed within the whole 12 measures arpeggio passageplayer A was able to maintain this strategy which is indicative

VITA-2

134

Proceedings of the Second Vienna Talk Sept 19ndash21 2010 University of Music and Performing Arts Vienna Austria

x = sin(t+δ)y = sin(t)

x = cos(2t+δ)y = sin(t)

δ = minus10deg

Figure 4 Lissajous patterns A high degree of similarity to theobserved bowing patterns is obtained by introducing a phase lagof about 10 deg to the x-component The dotted lines indicatethe Lissajous patterns without phase shift In the right panel thedashed lines indicate the positions of the string crossings

for a high level of controlFigure 4 shows how the phase plots of both bowing patterns

can be reconstructed by introducing a phase lag of about 10 degto the x-component of the shown Lissajous patterns Howeverit is possible that the optimal amount of phase delay depends onperformance variables such as bow force

33 Inferior performances

Figures 5 and 6 show performances of the two fragments bytwo other players Player B ndash an advanced student ndash was sightreading the piece at the time of the recording Player C ndash anamateur player ndash was familiar with the piece

The phase plots in Fig 5 reveal that there was a high degreeof similarity between the performances of Fragment 1 by allthree players (cf Fig 2) All performances exhibit hysteresis inthe phase plot indicating that bow changes lagged behind stringcrossings However there were also some discrepancies Thepattern of player B was slightly irregular which might be due tounfamiliarity with the piece Furthermore the phase plots showsharp cusps at the down-left end of the patterns most notably inthe performance of player C Inspection of the separate move-ment components showed a variable phase lag throughout thecycle At the cusp the minima of the time series were in phasewhereas there was a clear phase difference between the maximaThis implies that the movement components deviated somewhatfrom a perfect sine shape and it is tempting to speculate that thevariable phase behavior reveals a less efficient movement strat-egy However no definitive conclusions can be drawn based onthese examples

minus100 0 100Bow vel [cms]

Player C (amateur)

minus100 0 100Bow vel [cms]

Incl

inat

ion

Player B (sight reading)

I

IIII

I

Figure 5 Phase plots of performances of Fragment 1 by playersB and C

The performances of Fragment 2 shown in Fig 6 revealgreater discrepancies between the playersrsquo performances Player

Player B (sight reading) Player C (amateur)

III

II

I

III

II

I

Figure 6 Spatial trajectories of the bow motion of performancesof Fragment 2 by players B and C

B made many mistakes and did not manage to develop a stablecoordination pattern Player C did develop a somewhat stablecoordination pattern However the shape of the spatial trajec-tory is clearly different from the performance of player A (cfFig 3) Player C made larger excursions on the outer strings(I and III) which is indicative of a less efficient movementstrategy Furthermore it was found that the phase lag betweenthe movement components was inverted in the performance ofplayer C ie bow changes were leading string crossings Bylistening to the audio recording it could indeed be noted thatthe quality of the note transitions was inferior compared to theperformance by player A confirming the significance of the ob-served phase behavior for the control of note transitions

4 DISCUSSION AND CONCLUSIONS

This paper presented preliminary analyses of coordination ofcomplex bowing patterns in musical performances by three vi-olin players The bow motion was decomposed into two com-ponents a radial component related to sound production and atangential component related to selection of the string playedIt was demonstrated that the two motion components showeda systematic phase relation in such a way that the timing ofbow changes lagged behind string crossings It was hypoth-esized by considering the mechanics of the bowed string thatthis most likely reflects an optimal strategy to obtain clean notetransitions This needs to be further investigated by analysis ofthe synchronously recorded sound possibly complemented bybowed-string simulations

The study focussed on two typical bowing patterns Bothpatterns reflect expert behavior internalized as a result of long-term sensorimotor learning The circular pattern associated withFragment 1 (see Fig 1) represents a relatively basic skill andis encountered in a wide range of musical repertoire The figure-of-eight pattern associated with Fragment 2 is considerably moredifficult to master and requires deliberate practice even by ad-vanced players The analyses presented in this paper showed in-deed that the circular bowing pattern was mastered by all threeplayers whereas the figure-of-eight pattern was only performedwell by the advanced player who was prepared

The measurement method in combination with the visual-izations allowed to differentiate between subtle aspects of themovements of the three players and some inferences could bemade about the effectiveness of the strategies However furtherstudies are needed to shed more light on this largely unexploredarea In any case the presented analyses demonstrated that theused methods offer the possibility to analyse performance skillsat a high level of detail and as such possess promising peda-

VITA-3

135

Proceedings of the Second Vienna Talk Sept 19ndash21 2010 University of Music and Performing Arts Vienna Austria

gogical potentialOn a more general level it can be stated that there still exists

a wide gap between scientific performance studies and musicalpractice and pedagogy Bridging this gap will require effortsfrom both sides Some of the main challenges for scientistswill be to account for the complexity encountered in music per-formance to focus on topics relevant to music practice and topresent the results in an intuitive way understandable to musi-cians and music teachers Challenges for the latter will be tobreak through the barriers of traditional teaching to have anopen mind to scientific results and possibilities offered by tech-nology and to be willing to put popular beliefs and ldquoideacutees fixesrdquoto the test

AcknowledgmentsMany thanks to Lambert Chen for his invaluable input as aplayer

5 REFERENCES

[1] P Hodgson Motion study and violin bowing AmericanString Teachers Association Urbana Illinois June 1958First published 1934 by J H Lavender amp Co London

[2] E Schoonderwaldt Mechanics and acoustics of vio-lin bowing Freedom constraints and control in perfor-mance PhD thesis KTH ndash School of Computer Scienceand Communication Stockholm Sweden 2009

[3] E Schoonderwaldt ldquoBowing gesturesrdquo Youtube channelhttpwwwyoutubecomschoondw

[4] A Askenfelt ldquoMeasurement of the bowing parametersin violin playing II Bow-bridge distance dynamic rangeand limits of bow forcerdquo J Acoust Soc Am vol 86 no2 pp 503ndash516 August 1989

[5] E Schoonderwaldt ldquoThe player and the bowed stringCoordination and control of bowing parameters in violinand viola performancerdquo J Acoust Soc Am vol 126 no5 pp 2709ndash2720 2009

[6] N Rasamimanana E Fleacutety and F Bevilacqua Gesturein Human-Computer Interaction and Simulation 6th In-ternational Gesture Workshop Revised Selected Paperschapter Gesture analysis of violin bow strokes pp 145ndash155 Springer Berlin Heidelberg 2006

[7] M Demoucron On the control of virtual violins Physicalmodelling and control of bowed string instruments PhDthesis Universiteacute Pierre et Marie Curie (UPMC) Paris ampRoyal Institute of Technology (KTH) Stockholm 2008

[8] D Young A methodology for investigation of bowedstring performance through measurement of violin bowingtechnique PhD thesis Massachusetts Institute of Tech-nology 2007

[9] AP Baader O Kazennikov and M Wiesendanger ldquoCo-ordination of bowing and fingering in violin playingrdquoCognitive Brain Research vol 23 no 2-3 pp 436ndash4432005

[10] O Kazennikov and M Wiesendanger ldquoBimanual coor-dination of bowing and fingering in violinists-Effects ofposition changes and string changesrdquo Motor Control vol13 pp 297ndash309 2009

[11] E Schoonderwaldt and M Demoucron ldquoExtraction ofbowing parameters from violin performance combiningmotion capture and sensorsrdquo J Acoust Soc Am vol126 no 5 pp 2695ndash2708 2009

[12] JC Schelleng ldquoThe bowed string and the playerrdquo JAcoust Soc Am vol 53 no 1 pp 26ndash41 1973

[13] E Schoonderwaldt K Guettler and A Askenfelt ldquoAnempirical investigation of bow-force limits in the Schel-leng diagramrdquo Acta Acustica united with Acustica vol94 no 4 pp 604ndash622 2008

[14] K Guettler ldquoOn the creation of the Helmholtz motion inbowed stringsrdquo Acta Acustica united with Acustica vol88 no 6 pp 970ndash985 2002

VITA-4

136

Proceedings of the Second Vienna Talk Sept 19ndash21 2010 University of Music and Performing Arts Vienna Austria

x = sin(t+δ)y = sin(t)

x = cos(2t+δ)y = sin(t)

δ = minus10deg

Figure 4 Lissajous patterns A high degree of similarity to theobserved bowing patterns is obtained by introducing a phase lagof about 10 deg to the x-component The dotted lines indicatethe Lissajous patterns without phase shift In the right panel thedashed lines indicate the positions of the string crossings

for a high level of controlFigure 4 shows how the phase plots of both bowing patterns

can be reconstructed by introducing a phase lag of about 10 degto the x-component of the shown Lissajous patterns Howeverit is possible that the optimal amount of phase delay depends onperformance variables such as bow force

33 Inferior performances

Figures 5 and 6 show performances of the two fragments bytwo other players Player B ndash an advanced student ndash was sightreading the piece at the time of the recording Player C ndash anamateur player ndash was familiar with the piece

The phase plots in Fig 5 reveal that there was a high degreeof similarity between the performances of Fragment 1 by allthree players (cf Fig 2) All performances exhibit hysteresis inthe phase plot indicating that bow changes lagged behind stringcrossings However there were also some discrepancies Thepattern of player B was slightly irregular which might be due tounfamiliarity with the piece Furthermore the phase plots showsharp cusps at the down-left end of the patterns most notably inthe performance of player C Inspection of the separate move-ment components showed a variable phase lag throughout thecycle At the cusp the minima of the time series were in phasewhereas there was a clear phase difference between the maximaThis implies that the movement components deviated somewhatfrom a perfect sine shape and it is tempting to speculate that thevariable phase behavior reveals a less efficient movement strat-egy However no definitive conclusions can be drawn based onthese examples

minus100 0 100Bow vel [cms]

Player C (amateur)

minus100 0 100Bow vel [cms]

Incl

inat

ion

Player B (sight reading)

I

IIII

I

Figure 5 Phase plots of performances of Fragment 1 by playersB and C

The performances of Fragment 2 shown in Fig 6 revealgreater discrepancies between the playersrsquo performances Player

Player B (sight reading) Player C (amateur)

III

II

I

III

II

I

Figure 6 Spatial trajectories of the bow motion of performancesof Fragment 2 by players B and C

B made many mistakes and did not manage to develop a stablecoordination pattern Player C did develop a somewhat stablecoordination pattern However the shape of the spatial trajec-tory is clearly different from the performance of player A (cfFig 3) Player C made larger excursions on the outer strings(I and III) which is indicative of a less efficient movementstrategy Furthermore it was found that the phase lag betweenthe movement components was inverted in the performance ofplayer C ie bow changes were leading string crossings Bylistening to the audio recording it could indeed be noted thatthe quality of the note transitions was inferior compared to theperformance by player A confirming the significance of the ob-served phase behavior for the control of note transitions

4 DISCUSSION AND CONCLUSIONS

This paper presented preliminary analyses of coordination ofcomplex bowing patterns in musical performances by three vi-olin players The bow motion was decomposed into two com-ponents a radial component related to sound production and atangential component related to selection of the string playedIt was demonstrated that the two motion components showeda systematic phase relation in such a way that the timing ofbow changes lagged behind string crossings It was hypoth-esized by considering the mechanics of the bowed string thatthis most likely reflects an optimal strategy to obtain clean notetransitions This needs to be further investigated by analysis ofthe synchronously recorded sound possibly complemented bybowed-string simulations

The study focussed on two typical bowing patterns Bothpatterns reflect expert behavior internalized as a result of long-term sensorimotor learning The circular pattern associated withFragment 1 (see Fig 1) represents a relatively basic skill andis encountered in a wide range of musical repertoire The figure-of-eight pattern associated with Fragment 2 is considerably moredifficult to master and requires deliberate practice even by ad-vanced players The analyses presented in this paper showed in-deed that the circular bowing pattern was mastered by all threeplayers whereas the figure-of-eight pattern was only performedwell by the advanced player who was prepared

The measurement method in combination with the visual-izations allowed to differentiate between subtle aspects of themovements of the three players and some inferences could bemade about the effectiveness of the strategies However furtherstudies are needed to shed more light on this largely unexploredarea In any case the presented analyses demonstrated that theused methods offer the possibility to analyse performance skillsat a high level of detail and as such possess promising peda-

VITA-3

135

Proceedings of the Second Vienna Talk Sept 19ndash21 2010 University of Music and Performing Arts Vienna Austria

gogical potentialOn a more general level it can be stated that there still exists

a wide gap between scientific performance studies and musicalpractice and pedagogy Bridging this gap will require effortsfrom both sides Some of the main challenges for scientistswill be to account for the complexity encountered in music per-formance to focus on topics relevant to music practice and topresent the results in an intuitive way understandable to musi-cians and music teachers Challenges for the latter will be tobreak through the barriers of traditional teaching to have anopen mind to scientific results and possibilities offered by tech-nology and to be willing to put popular beliefs and ldquoideacutees fixesrdquoto the test

AcknowledgmentsMany thanks to Lambert Chen for his invaluable input as aplayer

5 REFERENCES

[1] P Hodgson Motion study and violin bowing AmericanString Teachers Association Urbana Illinois June 1958First published 1934 by J H Lavender amp Co London

[2] E Schoonderwaldt Mechanics and acoustics of vio-lin bowing Freedom constraints and control in perfor-mance PhD thesis KTH ndash School of Computer Scienceand Communication Stockholm Sweden 2009

[3] E Schoonderwaldt ldquoBowing gesturesrdquo Youtube channelhttpwwwyoutubecomschoondw

[4] A Askenfelt ldquoMeasurement of the bowing parametersin violin playing II Bow-bridge distance dynamic rangeand limits of bow forcerdquo J Acoust Soc Am vol 86 no2 pp 503ndash516 August 1989

[5] E Schoonderwaldt ldquoThe player and the bowed stringCoordination and control of bowing parameters in violinand viola performancerdquo J Acoust Soc Am vol 126 no5 pp 2709ndash2720 2009

[6] N Rasamimanana E Fleacutety and F Bevilacqua Gesturein Human-Computer Interaction and Simulation 6th In-ternational Gesture Workshop Revised Selected Paperschapter Gesture analysis of violin bow strokes pp 145ndash155 Springer Berlin Heidelberg 2006

[7] M Demoucron On the control of virtual violins Physicalmodelling and control of bowed string instruments PhDthesis Universiteacute Pierre et Marie Curie (UPMC) Paris ampRoyal Institute of Technology (KTH) Stockholm 2008

[8] D Young A methodology for investigation of bowedstring performance through measurement of violin bowingtechnique PhD thesis Massachusetts Institute of Tech-nology 2007

[9] AP Baader O Kazennikov and M Wiesendanger ldquoCo-ordination of bowing and fingering in violin playingrdquoCognitive Brain Research vol 23 no 2-3 pp 436ndash4432005

[10] O Kazennikov and M Wiesendanger ldquoBimanual coor-dination of bowing and fingering in violinists-Effects ofposition changes and string changesrdquo Motor Control vol13 pp 297ndash309 2009

[11] E Schoonderwaldt and M Demoucron ldquoExtraction ofbowing parameters from violin performance combiningmotion capture and sensorsrdquo J Acoust Soc Am vol126 no 5 pp 2695ndash2708 2009

[12] JC Schelleng ldquoThe bowed string and the playerrdquo JAcoust Soc Am vol 53 no 1 pp 26ndash41 1973

[13] E Schoonderwaldt K Guettler and A Askenfelt ldquoAnempirical investigation of bow-force limits in the Schel-leng diagramrdquo Acta Acustica united with Acustica vol94 no 4 pp 604ndash622 2008

[14] K Guettler ldquoOn the creation of the Helmholtz motion inbowed stringsrdquo Acta Acustica united with Acustica vol88 no 6 pp 970ndash985 2002

VITA-4

136

Proceedings of the Second Vienna Talk Sept 19ndash21 2010 University of Music and Performing Arts Vienna Austria

gogical potentialOn a more general level it can be stated that there still exists

a wide gap between scientific performance studies and musicalpractice and pedagogy Bridging this gap will require effortsfrom both sides Some of the main challenges for scientistswill be to account for the complexity encountered in music per-formance to focus on topics relevant to music practice and topresent the results in an intuitive way understandable to musi-cians and music teachers Challenges for the latter will be tobreak through the barriers of traditional teaching to have anopen mind to scientific results and possibilities offered by tech-nology and to be willing to put popular beliefs and ldquoideacutees fixesrdquoto the test

AcknowledgmentsMany thanks to Lambert Chen for his invaluable input as aplayer

5 REFERENCES

[1] P Hodgson Motion study and violin bowing AmericanString Teachers Association Urbana Illinois June 1958First published 1934 by J H Lavender amp Co London

[2] E Schoonderwaldt Mechanics and acoustics of vio-lin bowing Freedom constraints and control in perfor-mance PhD thesis KTH ndash School of Computer Scienceand Communication Stockholm Sweden 2009

[3] E Schoonderwaldt ldquoBowing gesturesrdquo Youtube channelhttpwwwyoutubecomschoondw

[4] A Askenfelt ldquoMeasurement of the bowing parametersin violin playing II Bow-bridge distance dynamic rangeand limits of bow forcerdquo J Acoust Soc Am vol 86 no2 pp 503ndash516 August 1989

[5] E Schoonderwaldt ldquoThe player and the bowed stringCoordination and control of bowing parameters in violinand viola performancerdquo J Acoust Soc Am vol 126 no5 pp 2709ndash2720 2009

[6] N Rasamimanana E Fleacutety and F Bevilacqua Gesturein Human-Computer Interaction and Simulation 6th In-ternational Gesture Workshop Revised Selected Paperschapter Gesture analysis of violin bow strokes pp 145ndash155 Springer Berlin Heidelberg 2006

[7] M Demoucron On the control of virtual violins Physicalmodelling and control of bowed string instruments PhDthesis Universiteacute Pierre et Marie Curie (UPMC) Paris ampRoyal Institute of Technology (KTH) Stockholm 2008

[8] D Young A methodology for investigation of bowedstring performance through measurement of violin bowingtechnique PhD thesis Massachusetts Institute of Tech-nology 2007

[9] AP Baader O Kazennikov and M Wiesendanger ldquoCo-ordination of bowing and fingering in violin playingrdquoCognitive Brain Research vol 23 no 2-3 pp 436ndash4432005

[10] O Kazennikov and M Wiesendanger ldquoBimanual coor-dination of bowing and fingering in violinists-Effects ofposition changes and string changesrdquo Motor Control vol13 pp 297ndash309 2009

[11] E Schoonderwaldt and M Demoucron ldquoExtraction ofbowing parameters from violin performance combiningmotion capture and sensorsrdquo J Acoust Soc Am vol126 no 5 pp 2695ndash2708 2009

[12] JC Schelleng ldquoThe bowed string and the playerrdquo JAcoust Soc Am vol 53 no 1 pp 26ndash41 1973

[13] E Schoonderwaldt K Guettler and A Askenfelt ldquoAnempirical investigation of bow-force limits in the Schel-leng diagramrdquo Acta Acustica united with Acustica vol94 no 4 pp 604ndash622 2008

[14] K Guettler ldquoOn the creation of the Helmholtz motion inbowed stringsrdquo Acta Acustica united with Acustica vol88 no 6 pp 970ndash985 2002

VITA-4

136