STUDIES ON SOUNDS FROM MUSICAL PILLARS OF MAHAMANDAPAM OF VITTHALA TEMPLE … · 2012-07-26 · STUDIES ON SOUNDS FROM MUSICAL PILLARS OF MAHAMANDAPAM OF VITTHALA TEMPLE AT HAMPI

STUDIES ON SOUNDS FROM MUSICAL PILLARS OF MAHAMANDAPAM OF

VITTHALA TEMPLE AT HAMPI

C. Babu RaoT.Jayakumar

Baldev RajIndira Gandhi Centre for Atomic Research,

Kalpakkam-603102, Tamil Nadu, India

CBR/IGCAR

STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR

Why these studies ?Like some other interesting questions :• Why the wortz steel produced about ages back

is one of the strongest steels ?• Why the Delhi iron pillar forged centuries ago

is not rusting even now ?This technology is almost lost. And we are not able to answer some of these

questions satisfactorily. Answering them helps in understanding the past

STUDY OF DEVELOPMENT OF SCIENCE AND TECHNOLOGY


STUDY OF DEVELOPMENT OF SCIENCE AND TECHNOLOGY

May also bring outnew uses for old technologies

One such question is …

CBR/IGCAR

One such question is …

How the Hampi musical pillars, sculptured out of granite stone, are able to produce musical sounds similar to those produced by various musical instruments ?

Our work is a starting point in this direction

STUDIES ON MUSICAL PILLARS AT HAMPI


Vithala temple (1422 AD) at Hampi is one of the world heritage sites.

Musical pillars on the Mahamandapam (great-stage) of the temple made of granite stone.

Solid stone columns in these pillars produce audible sound, when struck with a finger.

A great attraction and surprise for tourists from all over the world.

Present study is the first ever attempt to scientifically investigate the acoustic properties of the musical columns in the pillars

CLASSICAL LITERATURE Vayu PuranaVisvaksena SamhitaNaarada Samhita

PetrologyOn how to choose : Geological indicators (Location etc)Stone Physical indicators of polished and unpolished stones

Testing methods : Visual inspection for major defects Smearing techniques to detect defects

(surface bearing cracks) This is equivalent to modern practice of leak penetrant testing.Smearing liquid - different varieties of milk (cow milk. human milk etc)

Should break only after several blows Strength Acoustic Impact testing

Sound of partly baked brick bala (young)Deep sound yuva (mature)Anunasika Nasal sound vriddha (old)

(possibly due to presence of crack)

CBR/IGCARSTUDIES ON MUSICAL PILLARS AT HAMPI

CLASSICAL LITERATURE SilparathnaAjithaagama

Regarding Musical Pillars

Pum sila (male) perfectly cylindrical gives sound of elephant bell

Sthri sila (female) wide bottom and narrow head gives sound of cymbal

Napumsika sila (neutral) narrow top and bottom and wide middle part give off no sound



Plan of Mahamandapam

Present study is concentrated on the 11 most popular pillars, which are associated with sounds of specific musical instruments

PETROLOGY

• Metallography– Optical microscopy– Scanning Acoustic Microscopy (SAM)– Scanning Electron Microscopy (SEM )

• Elemental Analysis– X-ray fluorescence spectroscopy (XRF)– Scanning Electron Microscopy (SEM )

• Phase Analysis– X-ray diffraction (XRD )– Scanning Electron Microscopy (SEM )


To answer the question

Which rock has been used ?

CBR/IGCAR

PETROLOGY - metallography

STUDIES ON MUSICAL PILLARS AT HAMPIOptical micrographs

CBR/IGCAR



at surface (Z=0 μm) at sub-surface (Z=8μm)

Microcrack Microcrack

Scanning Acoustic Microscopy

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Region-1

Region-3

Region-2

SEM Micrograph at low magnification

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PETROLOGY – metallography

– elemental analysis


Detailed SEM micrograph of Region-1

EDAX Spectrum from region-1

QUARTZ

CBR/IGCAR






FELDSPAR

CBR/IGCAR






BIOTITE

CBR/IGCAR

PETROLOGY – metallography SEM


Region-3Biotite

Region-1Quartz

Region-2K-Feldspar

Region-3Biotite

CBR/IGCAR

PETROLOGY – elemental analysis XRF


PETROLOGY – elemental analysis XRF


PETROLOGY – phase analysis XRD






X-ray diffractograms were recorded in the angular range of 12°-70° using CuKα radiation with a step size of 0.02° and dwell time of 4 seconds at each step

Phase identification was carried out based on Hanawalt search procedurewhich compares the peaks from the spectrum with peaks from the standards of different phases published as Powder Diffraction File (PDF) cards from ICDD (International Centre for Diffraction Data) showed presence of 3 phases

Since, a volume percentage of above 2% is required to detect phases present in the sample by XRD, some of the other minor phases which might be present could not be detected.

CBR/IGCAR


PETROLOGY – phase analysis

SEM / EDAX XRD

Quartz

Feldspar (Potassium / Sodium aluminium

silicate)

Biotite

QuartzSodium

aluminium silicate (Albite low)

Potassium aluminiumsilicate

(microclinic)

CBR/IGCAR


PETROLOGY – phase analysis

TYPICAL GRANITE STRUCTURE

CBR/IGCAR


SEM / EDAX XRF

Quartz

Si, Al, K, Ca, Na, Fe, Ni

Feldspar

Si, K, Al, Na, Ca, Fe, Ni

Biotite

Fe, Si, K, Al, Mn, Cl, Ti, Ni

Major Elements

Si , Al , Fe , K , Ca , Mg

Minor and trace elements

Mn, V, Cu, Pb, Ba, La, Ti, Zn

PETROLOGY – elemental analysis

CBR/IGCAR


PETROLOGY – elemental analysis

Chemical Signature which can be compared with the spectrum of granites quarried across the Hampiregion / country

To answer the question

Which rock has been used ?

CBR/IGCAR

Our question is …

CBR/IGCAR

Our question is …

How the Hampi musical pillars, sculptured out of granite stone, are able to produce musical sounds similar to throse produced by various musical instruments ?



Musical column of the Hampipillar can be modeled as a bar of circular cross section undergoing flexural vibrations.

Assumptions :

The pillar with the musical column is monolithic structure

bar is considered to be clamped at both the ends to simulate the monolithic structure fused to other parts of pillar.

The vibrations are transverse in nature.

There is no tension in the bar and the restoring force is mainly due to elastic forces within the bar.


During transverse flexural vibrations the bar undergoes bending. In order to keep the bar in equilibrium a shearing force is developed. Restoring force is mainly due to elastic forces within the bar.


If y(x, t) is the time variant displacement at position x along the axis of the bar then the equation of motion governing the transverse vibration in the bar is given by

E is Young’s modulusρ is densityΚ Is radius of gyration

If we assume the cross section of pillar to be circular bar thenK = d/4

d is diameter of the bar

x

y(x ,t)


Equation of motion

Solution of equation of motion is given by

y (x,t) = cos (ωt + φ) [A cosh (ωx/v) + B sinh (ωx/v) + i cos (ωx/v) + D sin (ωx/v) ]

where ω is angular frequency A , B , C and D are arbitrary constants. v is velocity of transverse wave

Velocity of transverse wave v is a function of ω and velocity of longitudinal waves cL

v2 = ω K cL

= 2 π f E/ρ

where f is frequency of vibration ( ω = 2 π f )


Boundary conditions : Vibrating bar is clamped at both ends

at x = 0 and at x = L y = 0

= 0

These conditions will be satisfied only for certain values of f given by

tan (π f L / v) = ± tanh (π f L / v)

First three frequencies

Fundamental frequency f1 = 0.89 cL

Harmonics f2 = 2.75 f1

f3 = 5.40 f1

where cL is velocity of longitudinal waves in the granite

d

L2


Dimensional Measurements

The musical column of the pillar is a tapered structure (maximum at bottom) with an ornamental extension on either ends

The diameter of the column was measured at the lowest (maximum) and upper most (minimum) regions. The diameter was derived by measuring the circumference.

The length measured was that of the column excluding the ornamental regions on the top and the bottom of the column.


Measurement of Velocity of Longitudinal Waves in the Musical Column

A microprocessor based ultrasonic flaw detector (EPOCH-IV, M/s. Panametrics, USA) along with a pair of transducers of 500 kHz was used in through transmission mode to determine velocity of longitudinal waves (cL ) in the musical columns.

The transducers were coupled to the musical columns using grease as couplant.


Recording of Sound Waves from the Musical Columns

The sound produced by striking at the centre of the musical columns with thumb was recorded in a laptop computer using a capacitor type microphone.

digitization 22 kHz

resolution 16 bit

Specific software was developed in LabVIEW with features for recording the sound waves and for analysis of the sound pattern in time and frequency domains.


1 2 3 4


Recording of Sound Waves from the Musical Columns

Peak frequencies and time for decay of amplitude to 1/20 of the peak in autocorrelation function were analysed for each of the sound produced by the musical columns.

Prior to recording the sound waves produced by the musical columns, the quality of the performance of the microphone was verified by recording and analyzing the sound waves produced by using a signal generator and a standard speaker.

Pillar No.

Musical instrument

pillar is associated

No.ofcolum

ns

Length range (mm)

Diameter range (mm)

Longitudinal wave

velocity range (m/s)

Sound properties

Frequency (Hz) Decay time (ms)

Lower Higher

2 Saptaswara 14 960 -1050 75 - 100 5300 - 5500 243 - 396 687-1000 452

3 Panchtala 9 750 -830 62 - 100 4600 - 5300 442 - 588 1046-1280 429

3A Damaru 9 1050 -1100 97 - 106 5200 - 5700 273 - 375 739-786 515

5A KeralaMridangam 5 960 -

1010 115 - 122 5500 - 5600 338 - 412 783-901 590

4 Jaltarang 7 760 -800 90 - 130 5400 - 5500 495 - 780 - 532

5 Mridanga 5 790 -865 98 - 106 5300 - 5500 444 - 457 1148 227-567

11 Ghanta 6 790 -865 102 - 111 5400 - 5740 533 - 656 953 889

14 Ghatam 12 1100 -1130 102 - 122 5300 - 5600 305 - 454 774 600

16 Veena 4 710 -860 100 - 106 5200 - 5500 745 - 821 - 499

24 Tabla 10 985 -1005 97 – 107 5200 -5600 296 - 407 - 376

20A Shankha 5 820 -925 95 - 112 5200 - 5450 399 - 471 983 -1060 664

15A Damaged 4200 680 - 760 181


f1 = 0.89(d/L2)cL


f1 = 0.89(d/L2)cL

Effective length may be shorter possible crack


Effective length may be shorter

possible crack

Visible crack


Musical column of the Hampipillar can be modeled as a bar of circular cross section undergoing flexural vibrations.

Assumptions :

The pillar with the musical column is monolithic structure

bar is considered to be clamped at both the ends to simulate the monolithic structure fused to other parts of pillar.

The vibrations are transverse in nature.

There is no tension in the bar and the restoring force is mainly due to elastic forces within the bar.

CLASSICAL LITERATURE SilparathnaAjithaagama

Regarding Musical Pillars

Pum sila (male) perfectly cylindrical gives sound of elephant bell

Sthri sila (female) wide bottom and narrow head gives sound of cymbal

Napumsika sila (neutral) narrow top and bottom and wide middle part give off no sound


Pum sila (male) Sthri sila (female) Napumsika sila (neutral)Cylindrical Wide bottom Narrow top and bottom

narrow top wide middleElephant bell Cymbal dull sound


Our question is …

CBR/IGCAR

Our question is …

How the Hampi musical pillars, sculptured out of granite stone, are able to produce musical sounds similar to throse produced by various musical instruments ?


Studies on musical instruments

Characterisation of sounds produced by musical instruments

Synthesis of sounds produced by musical instruments

string / wind / percussion

Instruments

SynthesizerSounds similar to those produced by

musical instruments can be artificially synthesized

In an intelectual exercise this was demonstrated about 600 years back.

Mechanical synthesizers were successfully created by the great

sculptures of that time

Sounds similar to those produced bymusical instruments are now

artificially synthesized electronically


Sounds similar to those produced bymusical instruments are now

artificially synthesized electronically


I will demonstrate

that there are collective vibrationswhen one of the columns is struck other

columns also vibrate

CBR/IGCAR


I will demonstrate

that there are collective vibrationswhen one of the columns is truck other

columns also vibrate

VIBRATION ANALYSIS

CBR/IGCAR

• The musical columns undergo flexural vibrations

• Since each pillar contains more than one musical column, it is likely that there will be coupling between the columns.

• When struck, the vibrating columns develop a vibration pattern. If the structure of the pillar is such that theantinodes in the vibration pattern occur at other musical columns of the same pillar the note can be sustained for a longer duration.

• In order to verify this hypothesis,vibration analysis has been carried out on two pillars namely : Pillar 2 (Sapthaswara) with decay time of 452ms and Pillar 11 (Ghanta) with decay time of 889ms.


Pillar No.

Musical instrument

pillar is associated

No.ofcolum

ns

Length range (mm)

Diameter range (mm)

Longitudinal wave

velocity range (m/s)

Sound properties

Frequency (Hz) Decay time (ms)Lower Higher

2 Saptaswara 14 960 -1050 75 - 100 5300 - 5500 243 - 396 687-1000 452

3 Panchtala 9 750 -830 62 - 100 4600 - 5300 442 - 588 1046-1280 429

3A Damaru 9 1050 -1100 97 - 106 5200 - 5700 273 - 375 739-786 515

5A Kerala Mridangam 5 960 -

1010 115 - 122 5500 - 5600 338 - 412 783-901 590

4 Jaltarang 7 760 -800 90 - 130 5400 - 5500 495 - 780 - 532

5 Mridanga 5 790 -865 98 - 106 5300 - 5500 444 - 457 1148 227-567

11 Ghanta 6 790 -865 102 - 111 5400 - 5740 533 - 656 953 889

14 Ghatam 12 1100 -1130 102 - 122 5300 - 5600 305 - 454 774 600

16 Veena 4 710 -860 100 - 106 5200 - 5500 745 - 821 - 499

24 Tabla 10 985 -1005 97 – 107 5200 -5600 296 - 407 - 376

20A Shankha 5 820 -925 95 - 112 5200 - 5450 399 - 471 983 -1060 664

15A Damaged 4200 680 - 760 181

VIBRATION ANALYSIS


VIBRATION ANALYSIS


9 6 4 1

10 7 5 2

Acceleration responses at other columns when one of the columns, marked with white dot, is struck.

The diameter of the blob is proportional to the RMS acceleration of the midpoint of the column.

CBR/IGCAR

VIBRATION ANALYSIS


Pillar 2 (Sapthaswara)



CBR/IGCAR

VIBRATION ANALYSIS


Pillar 2 (Sapthaswara)



Decay time

452 msec

3 m/sec2 to 6 m/sec2

VIBRATION ANALYSIS


(a) (b)

(c) (d)

1 2

3

4

56

Pillar 11 (Ghanta)



Decay time

889 msec

6 m/sec2 to 9 m/sec2

VIBRATION ANALYSIS

• vibration analysis has revealed the existence of collective vibration modes in the columns of a pillar when one of the columns is struck.

• In particular coupling between near resonant columns is observed.

• Correlation between the degree of coupling and the sustenance of long duration vibrations is established.



Further studies suggestedDriving point impedence measurement

Energy transfer between the vibrating column and surrounding air

Role of coupling between adjacent musical columns

Finite element analysis – Numerical simulation of vibrations of models of musical pillars and synthesis of resultant sound from multiple columns in a single pillar

Finally …….Proof of pudding …..…Replicate a musical pillar with predefined musical

properties.

Contributors C.Babu RaoAnish Kumar T.Jayakumar

Govind K. SharmaK.V.Rajkumar S Mahadevan

S SosammaP. Sukumar

C Pandian M V R Prasad

P Parameswaran M Radhika

and Baldev Raj

Indira Gandhi Centre for Atomic Research, Kalpakkam-603102

Tamil Nadu, India

P.ArundhatiISVSA Project Scientist

Indian National Science AcademyNew Delhi, India


Thanks to

Archaeology DepartmentHampi


MUSICAL PILLARS OF HAMPI


Documents

STUDIES ON SOUNDS FROM MUSICAL PILLARS OF MAHAMANDAPAM OF VITTHALA TEMPLE … · 2012-07-26 · STUDIES ON SOUNDS FROM MUSICAL PILLARS OF MAHAMANDAPAM OF VITTHALA TEMPLE AT HAMPI