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
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
STUDY OF DEVELOPMENT OF SCIENCE AND TECHNOLOGY
May also bring outnew uses for old technologies
One such question is …
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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
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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 )
STUDIES ON MUSICAL PILLARS AT HAMPI
To answer the question
Which rock has been used ?
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PETROLOGY - metallography
STUDIES ON MUSICAL PILLARS AT HAMPIOptical micrographs
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PETROLOGY - metallography
STUDIES ON MUSICAL PILLARS AT HAMPI
at surface (Z=0 μm) at sub-surface (Z=8μm)
Microcrack Microcrack
Scanning Acoustic Microscopy
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PETROLOGY - metallography
STUDIES ON MUSICAL PILLARS AT HAMPI
Region-1
Region-3
Region-2
SEM Micrograph at low magnification
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PETROLOGY – metallography
– elemental analysis
STUDIES ON MUSICAL PILLARS AT HAMPI
Detailed SEM micrograph of Region-1
EDAX Spectrum from region-1
QUARTZ
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STUDIES ON MUSICAL PILLARS AT HAMPI
Detailed SEM micrograph of Region-2
EDAX Spectrum from region-2
PETROLOGY – metallography
– elemental analysis
FELDSPAR
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PETROLOGY – metallography
– elemental analysis
STUDIES ON MUSICAL PILLARS AT HAMPI
Detailed SEM micrograph of Region-3
EDAX Spectrum from region-3
BIOTITE
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PETROLOGY – metallography SEM
STUDIES ON MUSICAL PILLARS AT HAMPI
Region-3Biotite
Region-1Quartz
Region-2K-Feldspar
Region-3Biotite
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PETROLOGY – elemental analysis XRF
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
PETROLOGY – elemental analysis XRF
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
PETROLOGY – phase analysis XRD
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
PETROLOGY – phase analysis XRD
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
PETROLOGY – phase analysis XRD
STUDIES ON MUSICAL PILLARS AT HAMPI
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.
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STUDIES ON MUSICAL PILLARS AT HAMPI
PETROLOGY – phase analysis
SEM / EDAX XRD
Quartz
Feldspar (Potassium / Sodium aluminium
silicate)
Biotite
QuartzSodium
aluminium silicate (Albite low)
Potassium aluminiumsilicate
(microclinic)
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STUDIES ON MUSICAL PILLARS AT HAMPI
PETROLOGY – phase analysis
TYPICAL GRANITE STRUCTURE
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STUDIES ON MUSICAL PILLARS AT HAMPI
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
STUDIES ON MUSICAL PILLARS AT HAMPI
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 ?
STUDIES ON MUSICAL PILLARS AT HAMPI
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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.
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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.
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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)
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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 )
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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.
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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.
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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.
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
1 2 3 4
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
f1 = 0.89(d/L2)cL
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
f1 = 0.89(d/L2)cL
Effective length may be shorter possible crack
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
Effective length may be shorter
possible crack
Visible crack
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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
CBR/IGCARSTUDIES ON MUSICAL PILLARS AT HAMPI
Pum sila (male) Sthri sila (female) Napumsika sila (neutral)Cylindrical Wide bottom Narrow top and bottom
narrow top wide middleElephant bell Cymbal dull sound
STUDIES ON MUSICAL PILLARS AT HAMPI 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 ?
STUDIES ON MUSICAL PILLARS AT HAMPI
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
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
Sounds similar to those produced bymusical instruments are now
artificially synthesized electronically
STUDIES ON MUSICAL PILLARS AT HAMPI
I will demonstrate
that there are collective vibrationswhen one of the columns is struck other
columns also vibrate
CBR/IGCAR
STUDIES ON MUSICAL PILLARS AT HAMPI
I will demonstrate
that there are collective vibrationswhen one of the columns is truck other
columns also vibrate
VIBRATION ANALYSIS
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• 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.
CBR/IGCARSTUDIES ON MUSICAL PILLARS AT HAMPI
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
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
VIBRATION ANALYSIS
STUDIES ON MUSICAL PILLARS AT HAMPI
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
STUDIES ON MUSICAL PILLARS AT HAMPI
Pillar 2 (Sapthaswara)
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
STUDIES ON MUSICAL PILLARS AT HAMPI
Pillar 2 (Sapthaswara)
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.
Decay time
452 msec
3 m/sec2 to 6 m/sec2
VIBRATION ANALYSIS
STUDIES ON MUSICAL PILLARS AT HAMPI
(a) (b)
(c) (d)
1 2
3
4
56
Pillar 11 (Ghanta)
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.
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.
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR
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
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Thanks to
Archaeology DepartmentHampi
CBR/IGCARSTUDIES ON MUSICAL PILLARS AT HAMPI
MUSICAL PILLARS OF HAMPI
STUDIES ON MUSICAL PILLARS AT HAMPI CBR/IGCAR