Experimental investigations of t anpur a acousticshome.iitk.ac.in/~ag/papers/tanpura.pdfExperimental investigations of t anpur a acoustics Rahul Pisharody and Anurag Gupta Department

Experimental investigations of tanpura acoustics

Rahul Pisharody and Anurag GuptaDepartment of Mechanical Engineering,

Indian Institute of Technology Kanpur, 208016, [email protected]

Summary1

High-speed video camera recordings are used to ob-2

serve dynamics of an actual tanpura string. The tem-3

poral evolution of the frequency spectrum is obtained4

by measuring the nut force during the string vibra-5

tion. The characteristic sonorous sound of tanpura is6

attributed to not only the presence of a large num-7

ber of overtones but also to the dominance of certain8

harmonics over the fundamental, the latter manifest-9

ing itself as a certain cascading effect. The nature of10

sound is shown to be strongly dependent on the ini-11

tial plucking amplitude of the string. The stability12

of the in-plane vertical motion of the string is also13

emphasised.14

1 Introduction15

Tanpura (or tambura) is an unfretted long-necked16

lute, with four strings, used exclusively for provid-17

ing the drone in Indian classical music. The purpose18

of drone is to establish a firm harmonic basis for a19

musical performance by constantly playing a particu-20

lar note or a set of notes. The sound of a well tuned21

tanpura, and hence the resulting drone, is remark-22

ably rich in overtones and creates a pleasant “melodic23

background” for the performance [1, 2]. The tanpura24

drone is widely recognized for enhancing the musical-25

ity of the raga being played by constantly reinstating26

the notes which form the essence of the raga [3]. The27

distinctiveness of tanpura’s sound is due to the unique28

manner in which the strings interact with the sound-29

board [1, 4]. The strings pass over a doubly-curved30

bridge of finite width before reaching the board, see31

Figure 1, as is the case with other Indian string instru-32

ments such as sitar and rudra vın. a [4]. The curved33

bridge provides a unilateral constraint to the vibrat-34

ing string and, in doing so, becomes the source for an35

overtone rich sound of the musical instrument [5, 6].36

The characteristic feature of tanpura is however the37

cotton threads, known as jıva (meaning the “soul”),38

which are inserted below the strings on the bridge, see39

Figure 1. The correct placement of jıva, essential for40

obtaining the required drone from a tanpura, is when41

the string makes a grazing contact with the bridge42

before going over the neck of the instrument [1, 4], as43

shown in the bottom-most picture in the right side of 44

Figure 1. The purpose of this brief note is to present 45

certain experimental results which elucidate the na- 46

ture of tanpura sound while emphasizing the role of 47

jıva. 48

We use high-speed video camera recordings of the 49

vibration of a single tanpura string to capture the 50

string motion close to the bridge and at the nut (see 51

the videos provided as supplementary material). The 52

latter is used to measure the nut force and to subse- 53

quently plot 3-dimensional spectrograms. The previ- 54

ous tanpura experimental measurements were based 55

either on the audio signals [7, 8] or the sensors placed 56

between the string and the nut [9]. Our experimen- 57

tal setup provides a novel visualisation of string–jıva– 58

bridge interaction in an actual tanpura and can be 59

used to further the scientific study of the musical in- 60

strument. In the present paper, we use the nut force 61

measurements to establish a cascading effect of en- 62

ergy transfer between lower and higher overtones, re- 63

sulting in a strong presence of certain overtones, as 64

Figure 1: (Colour online) A typical miraj styletanpura (left); (right top to bottom) side view of thebridge with jıva, top view, close side view of the bridgewith one string and jıva.

Pisharody and Gupta, p. 2

a distinguished feature of the tanpura’s overtone rich65

sound. In the absence of jıva, the overtones decay66

faster, the fundamental remains the dominant fre-67

quency, and there is no cascading effect. The ob-68

served richness of overtones, their slow decay, and the69

energy cascade effect are in fact confirmation of the70

findings in previous experimental [8, 9] and numerical71

[10, 11, 12, 13, 14, 15] work on tanpura.72

We demonstrate the dependence of tanpura’s73

sound, as evident from the spectrograms, on the ini-74

tial plucking amplitude of the tanpura string. We75

show that the effect of jıva in producing a desirable76

sound is lost for high plucking amplitudes, as is ex-77

pected from the actual practise of tanpura playing.78

We also establish that an arbitrary (out-of-plane) ini-79

tial pluck of the string eventually stabilises into an80

in-plane vertical motion. None of the previous works81

have discussed the effect of initial plucking amplitude82

and the stability of the in-plane vertical motion of the83

string.84

2 Experimental results85

The experimental setup consisted of a tanpura, with86

all but one string removed, two supports, to firmly87

hold the instrument, a high-speed camera, and DC88

light sources. The string was plucked at the center89

using the index finger as is done in actual tanpura90

playing. In doing so, the string experiences an initial91

vertical (in-plane) displacement of around 0.5 cm and92

a horizontal (out-of-plane) displacement of around93

0.2 cm. The tension in the string was measured by94

hanging a mass at the center of the string, observ-95

ing the angle between the string on either side of the96

mass, and using the principle of static equilibrium.97

The string was consistently tuned to F-sharp (using98

an electronic tanpura drone), having a fundamental99

frequency of around 92.8 Hz. The high-speed camera100

was triggered manually and was adjusted to capture101

10000 fps. The nut force was calculated as the verti-102

cal component of the string tension at the nut using103

the estimated tension value and the observed slope104

of the string at the nut. The temporal evolution of105

0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.2−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

Time (sec)

No

rma

lize

d T

ran

sve

rse

Fo

rce

Figure 2: Evolution of nut force, normalized with re-spect to string tension.

the nut force (normalized with respect to string ten- 106

sion) is shown in Figure 2. One can clearly observe 107

a high-frequency precursive wave, as reported earlier 108

by Valette [9, 16]. The presence of precursive wave 109

validates the role of dispersion in tanpura string vi- 110

bration and hence of incorporating bending rigidity 111

even for small vibration amplitudes. A video capture 112

of the string motion close to the nut is provided as a 113

supplement (video1.gif). The data was acquired from 114

the video experiments using MATLAB’s (version 9.0, 115

R2016) inbuilt image processing toolbox. The fre- 116

quency evolution of the nut force was plotted using the 117

spectrogram function, where the sampling frequency 118

was taken to be the same as in the video experiments. 119

We begin by comparing the spectrograms obtained 120

with and without the jıva. The 3-dimensional spec- 121

trograms are shown in Figure 3. The presence of 122

jıva, when positioned appropriately, not only brings 123

out a richer set of overtones but is clearly marked 124

by a definite change in the pattern of how overtones 125

evolve over time as well as how they interact with 126

each other. The interaction among overtones is clearer 127

in Figure 4 where the three important signatures of 128

tanpura sound are distinctively visible. First, there is 129

a characteristic reoccurring pattern of energy trans- 130

fer leading to a cascading effect with higher overtones 131

giving way to immediately lower overtones. A car- 132

toon of the effect is illustrated in Figure 5, where 133

the curves in green, red, violet, and blue represent 134

the nth, (n+1)th, (n+2)th, and (n+3)th overtones, re- 135

spectively, for n ≥ 3. Second, in the presence of jıva, 136

(a)

(b)

Figure 3: (Colour online) 3-dimensional nut forcespectrograms (a) without and (b) with the jıva.

Pisharody and Gupta, p. 3

the fundamental decays faster than many of the over-137

tones so much so that it is completely overshadowed138

after a short initial span of time. This is in contrast139

to the situation without jıva where the fundamental140

remains the dominant frequency and the contribution141

of the higher overtones remains low in comparison.142

The coupling of various modes, and therefore of the143

overtones, is also present in this case due to the wrap-144

ping/unwrapping motion of the string on the bridge145

[5, 6]. With jıva, the interaction of the string with146

the bridge becomes more complex as it leads to a147

more impactful collision of the string on the bridge.148

This is clearly visible in the video recordings, pro-149

vided as supplementary files, of the string interacting150

with the bridge in both the cases (see video2.gif and151

video3.gif). Third, the presence of jıva clearly slows152

down the decay of overtones thereby adding to the153

richness of tanpura sound. Finally, we report the psd154

evolution as obtained from the numerical simulation155

based on the recently proposed penalty based models156

[10, 11, 12, 13, 14, 15], see Figure 6 (the details of the157

numerical model and the choice of parameters can be158

found is a recent thesis [17]). The numerical model is159

clearly able to capture the cascading effect, the domi-160

nance over the fundamental, as well as the slow decay161

of the overtones.162

The tanpura drone is very sensitive to the ini-163

tial plucking amplitude of the string. In fact, it is164

commonly said among the musicians that a tanpura165

should be played such that the strings should not166

know that they have been plucked. To support this167

argument, we obtain spectrograms when the pluck-168

ing amplitude is 2.5 cm (Figure 7(a)) and 1 cm (Fig-169

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−9

−8

−7

−6

−5

−4

−3

−2

Time (sec)

log(P

) (d

B/H

z)

fundamental

first overtone

second overtone

third overtone

fourth overtone

fifth overtone

sixth overtone

seventh overtone

eighth overtone

ninth overtone

tenth overtone

eleventh overtone

twelfth overtone

thirteenth overtone

fourteenth overtone

(a)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−9

−8

−7

−6

−5

−4

−3

−2

Time (sec)

log(P

) (d

B/H

z)

fundamental

first overtone

second overtone

third overtone

fourth overtone

fifth overtone

sixth overtone

seventh overtone

eighth overtone

ninth overtone

tenth overtone

eleventh overtone

twelfth overtone

thirteenth overtone

fourteenth overtone

(b)

Figure 4: (Colour online) Evolution of power spectraldensity (psd) for various overtones in the nut forcespectrogram (a) without and (b) with the jıva.

Time

psd

Figure 5: (Colour online) A cartoon of the reoccurringpattern in the evolution of psd for various overtonesof a tanpura string.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−12

−11

−10

−9

−8

−7

−6

−5

−4

Time (sec)

log(P

) (d

B/H

z)

fundamental

first overtone

second overtone

third overtone

fourth overtone

fifth overtone

sixth overtone

seventh overtone

eighth overtone

ninth overtone

tenth overtone

eleventh overtone

twelfth overtone

thirteenth overtone

fourteenth overtone

Figure 6: (Colour online) Numerical simulation of psdevolution for various overtones with the jıva using apenalty based model.

(a)

(b)

Figure 7: (Colour online) 3-dimensional nut forcespectrograms with initial plucking amplitudes of (a)2.5 cm and (b) 1 cm.

ure 7(b)), in comparison to 0.5 cm used to generate 170

the plot in Figure 4(b). The higher plucking ampli- 171

Pisharody and Gupta, p. 4

(a)

(b)

Figure 8: Out-of-plane motion of the tanpura string,with and without jıva, for (a) an in-plane initial pluck-ing and (b) an out-of-plane initial plucking of thestring.

tudes are given by pulling the string vertically at the172

center using a thread and then burning the thread.173

The desired pattern, and hence the desired drone, dis-174

appears as the amplitude goes above 0.5 cm. We have175

observed this conclusion to remain valid for different176

plucking positions on the string.177

Finally, we present some results on the out-of-plane178

motion of the tanpura string. The camera is now179

placed in the direction of the wire and a fixed point180

on the string is marked and then tracked during the181

vibratory motion. Figure 8(a) plots the locus of the182

point when the initial pluck is an in-plane triangle183

with a peak amplitude of 1 cm. Figure 8(b) plots the184

locus of the point when the initial pluck is as given185

in the actual playing of the instrument. In all the186

cases we note that the in-plane (vertical) motion of the187

string is stable with the point on the string eventually188

coming back to the vertical plane. The presence of189

jıva has no noticeable effect on the stability of the190

string. Our conclusion remains valid even when we191

varied the plucking position on the string.192

Acknowledgement193

We are grateful to Prof. Venkitanarayanan and his194

laboratory staff for helping us with the experiments.195

We are also thankful to Prof. Shakti Singh Gupta and196

one of the referees for their constructive comments on197

the manuscript.198

Supplementary material 199

(i) video1.gif: string motion close to the nut. 200

(ii) video2.gif: string motion close to the bridge with- 201

out jıva. 202

(iii) video3.gif: string motion close to the bridge with 203

jıva. 204

References 205

[1] B. C. Deva. Tonal structure of tambura. The Journal 206

of the Music Academy, Madras, 27:89–112, 1956. 207

[2] A. Ranade. Tanpura: A phenomenon. In Proceedings 208

of the ITC-SRA Workshop on Tanpura, pages 40–48, 209

1997. 210

[3] E. C. Carterette, K. Vaughn, and N. A. Jairazb- 211

hoy. Perceptual, acoustical and musical aspects of the 212

tambura drone. Music Perception, 7:75–108, 1989. 213

[4] C. V. Raman. On some Indian stringed instruments. 214

Proceedings of the Indian Association for the Culti- 215

vation of Science, 7:29–33, 1921. 216

[5] R. Burridge, J. Kappraff, and C. Morshedi. The sitar 217

string, a vibrating string with a one-sided inelastic 218

constraint. SIAM Journal of Applied Mathematics, 219

42:1231–1251, 1982. 220

[6] A. K. Mandal and P. Wahi. Natural frequencies, 221

mode shapes and modal interactions for strings vi- 222

brating against an obstacle: Relevance to sitar and 223

veena. Journal of Sound and Vibration, 338:42–59, 224

2015. 225

[7] H. V. Modak. Physics of tanpura: Some investiga- 226

tions. In Proceedings of the ITC-SRA Workshop on 227

Tanpura, pages 8–15, 1997. 228

[8] R. Sengupta, B. M. Banerjee, S. Sengupta, and 229

D. Nag. Tonal qualities of the Indian tanpura. In 230

Proceedings of the Stockholm Music Acoustic Confer- 231

ence, pages 333–342, 1983. 232

[9] C. Valette, C. Cuesta, M. Castellengo, and 233

C. Besnainou. The tampura bridge as a precursive 234

wave generator. Acustica, 74:201–208, 1991. 235

[10] M. van Walstijn and V. Chatziioannou. Numeri- 236

cal simulation of tanpura string vibrations. In Pro- 237

ceedings of the International Symposium on Musical 238

Acoustics, Le Mans, pages 609–614, 2014. 239

[11] S. Bilbao, A. Torin, and V. Chatziioannou. Numerical 240

modeling of collisions in musical instruments. Acta 241

Acustica united with Acustica, 101:155–173, 2015. 242

[12] V. Chatziioannou and M. van Walstijn. Energy con- 243

serving schemes for the simulation of musical instru- 244

ment contact dynamics. Journal of Sound and Vibra- 245

tion, 339:262–279, 2015. 246

[13] M. van Walstijn, J. Bridges, and S. Mehes. A real- 247

time synthesis oriented tanpura model. In Proceed- 248

ings of the 19th International Conference on Digi- 249

tal Audio Effects (DAFx-16), Brno, pages 175–182, 250

2016. 251

[14] J. Bridges and M. van Walstijn. Modal based tan- 252

pura simulation: Combining tension modulation and 253

Pisharody and Gupta, p. 5

distributed bridge interaction. In Proceedings of the254

20th International Conference on Digital Audio Ef-255

fects (DAFx-17), Edinburgh, pages 299–306, 2017.256

[15] C. Issanchou, S. Bilbao, J-L. L. Carrou, C. Touze,257

and O. Doare. A modal-based approach to the nonlin-258

ear vibration of strings against a unilateral obstacle:259

Simulations and experiments in the pointwise case.260

Journal of Sound and Vibration, 393:229–251, 2017.261

[16] C. Valette. The mechanics of vibrating strings. In262

A. Hirschberg, J. Kergomard, and G. Weinreich, ed-263

itors, Mechanics of Musical Instruments, pages 115–264

183. Springer, Wien, New York, 1995.265

[17] R. Pisharody. Experimental investigations on the266

acoustics of Tanpura. Master’s thesis, IIT Kanpur,267

2017.268