STUDIES ON SOUNDS FROM
MUSICAL PILLARS OF
MAHAMANDAPAM OF
VITTHALA TEMPLE AT HAMPI
C. Babu Rao
T.Jayakumar
Baldev Raj
Indira Gandhi Centre for Atomic Research,
Kalpakkam-603102, Tamil Nadu, India
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 out
new uses for old technologies
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
One such question is …
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
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
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
CLASSICAL LITERATURE
Vayu Purana
Visvaksena Samhita
Naarada Samhita
Petrology
On 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 Æ Strength
Acoustic Impact testing
Sound of partly baked brick Æ bala
(young)
Deep sound
Æ yuva
(mature)
Anunasika Nasal sound
Æ vriddha (old)
(possibly due to presence of crack)
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
CLASSICAL LITERATURE
Silparathna
Ajithaagama
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
Plan of Mahamandapam
Present study is concentrated on the 11 most
popular pillars, which are associated with
sounds of specific musical instruments
STUDIES ON MUSICAL PILLARS AT HAMPI
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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 ?
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY - metallography
Optical micrographs
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY - metallography
Microcrack
Microcrack
at surface (Z=0 μm)
at sub-surface (Z=8μm)
Scanning Acoustic Microscopy
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY - metallography
Region-1
Region-3
Region-2
SEM Micrograph at low magnification
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY
– metallography
– elemental analysis
Detailed SEM micrograph of Region-1
QUARTZ
EDAX Spectrum from region-1
STUDIES ON MUSICAL PILLARS AT HAMPI
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PETROLOGY
– metallography
– elemental analysis
Detailed SEM micrograph of Region-2
FELDSPAR
EDAX Spectrum from region-2
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY
– metallography
– elemental analysis
Detailed SEM micrograph of Region-3
BIOTITE
EDAX Spectrum from region-3
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY – metallography SEM
Region-3
Biotite
Region-3
Biotite
Region-2
K-Feldspar
Region-1
Quartz
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
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
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 procedure
which 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.
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY – phase analysis
SEM / EDAX
XRD
Quartz
Quartz
Feldspar (Potassium /
Sodium aluminium
silicate)
Biotite
Sodium
aluminium silicate
(Albite low)
Potassium
aluminiumsilicate
(microclinic)
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY – phase analysis
TYPICAL
GRANITE
STRUCTURE
STUDIES ON MUSICAL PILLARS AT HAMPI
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PETROLOGY – elemental analysis
SEM / EDAX
Quartz
Si, Al, K, Ca, Na, Fe, Ni
Feldspar
Si, K, Al, Na, Ca, Fe, Ni
Biotite
XRF
Major Elements
Si , Al , Fe , K , Ca , Mg
Minor and trace elements
Mn, V, Cu, Pb, Ba, La, Ti,
Zn
Fe, Si, K, Al, Mn, Cl,
Ti, Ni
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
PETROLOGY – elemental analysis
Chemical Signature
which can be compared
with the spectrum of
granites quarried
across the Hampi
region / country
To answer the question
Which rock has been used ?
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Our question is …
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
CBR/IGCAR
Musical column of the Hampi
pillar can be modeled as a bar
of circular cross section
undergoing flexural vibrations.
Assumptions :
The pillar with the musical
column is monolithic structure
Æ 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 modulus
ρ is density
Κ Is radius of gyration
If we assume the cross section of pillar to be circular bar then
K = d/4
d is diameter of the bar
y(x ,t)
x
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
Harmonics
f2 = 2.75 f1
d
L2
cL
f3 = 5.40 f1
where
cL is velocity of longitudinal waves in the granite
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
STUDIES ON MUSICAL PILLARS AT HAMPI
4
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.
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Pillar
No.
Musical
instrument
pillar is
associated
No.of
colum
ns
Length
range
(mm)
Diameter
range
(mm)
Longitudina
l wave
velocity
range (m/s)
Sound properties
Frequency (Hz)
Lower
Higher
Decay time
(ms)
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
Damaru
9
1050 1100
97 - 106
5200 - 5700
273 - 375
739-786
515
3A
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
790 865
98 - 106
5300 - 5500
444 - 457
1148
227-567
6
790 865
102 - 111
5400 - 5740
533 - 656
953
889
5
11
Mridanga
Ghanta
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
Shankha
5
820 925
95 - 112
5200 - 5450
399 - 471
983 -1060
664
4200
680 - 760
20A
15A
Damaged
181
f1 = 0.89(d/L2)cL
STUDIES ON MUSICAL PILLARS AT HAMPI
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f1 = 0.89(d/L2)cL
Effective length may be
shorter Æ possible crack
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Effective length
may be shorter
Æ possible
crack
Visible crack
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Musical column of the Hampi
pillar can be modeled as a bar
of circular cross section
undergoing flexural vibrations.
Assumptions :
The pillar with the musical
column is monolithic structure
Æ 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
CLASSICAL LITERATURE
Silparathna
Ajithaagama
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
Pum sila (male)
Cylindrical
Elephant bell
Sthri sila (female)
Wide bottom
narrow top
Cymbal
STUDIES ON MUSICAL PILLARS AT
Napumsika sila (neutral)
Narrow top and bottom
wide middle
dull sound
CBR/IGCAR
HAMPI
Our question is …
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
CBR/IGCAR
Studies on musical instruments
string / wind /
percussion
Instruments
Characterisation of sounds
produced by musical instruments
Synthesis of sounds
produced by musical instruments
Synthesizer
Sounds similar to those produced by
musical instruments can be
artificially synthesized
Sounds similar to those produced by
musical instruments are now
artificially synthesized electronically
In an intelectual exercise this was
demonstrated about 600 years back.
Mechanical synthesizers were
successfully created by the great
sculptures of that time
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Sounds similar to those produced by
musical instruments are now
artificially synthesized electronically
I will demonstrate
that there are collective
vibrations
when one of the columns is struck other
columns also vibrate
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
VIBRATION ANALYSIS
I will demonstrate
that there are collective
vibrations
when one of the columns is truck other
columns also vibrate
STUDIES ON MUSICAL PILLARS AT HAMPI
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 the
antinodes 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.
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Pillar
No.
Musical
instrument
pillar is
associated
No.of
colum
ns
Length
range
(mm)
Diameter
range
(mm)
Longitudina
l wave
velocity
range (m/s)
Sound properties
Frequency (Hz)
Lower
Higher
Decay time
(ms)
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
Damaru
9
1050 1100
97 - 106
5200 - 5700
273 - 375
739-786
515
3A
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
790 865
98 - 106
5300 - 5500
444 - 457
1148
227-567
6
790 865
102 - 111
5400 - 5740
533 - 656
953
889
5
11
Mridanga
Ghanta
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
Shankha
5
820 925
95 - 112
5200 - 5450
399 - 471
983 -1060
664
4200
680 - 760
20A
15A
Damaged
181
VIBRATION ANALYSIS
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
VIBRATION ANALYSIS
10 7
9
6
5 2
4
1
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.
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
VIBRATION ANALYSIS
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.
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
VIBRATION
ANALYSIS
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.
3 m/sec2 to 6 m/sec2
Decay time
452 msec
STUDIES ON MUSICAL PILLARS AT HAMPI
VIBRATION ANALYSIS
6
5
Pillar 11 (Ghanta)
4
Acceleration responses
at other columns when
one of the columns,
marked with white dot,
is struck.
3
The diameter of the
blob is proportional to
the RMS acceleration of
the midpoint of the
column.
1
2
(a)
(b)
(c)
(d)
6 m/sec2 to 9 m/sec2
Decay time
889 msec
STUDIES ON MUSICAL PILLARS AT HAMPI
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
Further studies suggested
¾ Driving point impedence measurement
¾ Energy transfer between the vibrating column
and surrounding air
¾ Role of coupling between adjacent musical
columns
¾ Finite element analysis – Numerical simulation of
vibrations of models of musical pillars and synthesis
of resultant sound from multiple columns in a single
pillar
¾
Finally …….Proof of pudding …..…Replicate a
musical pillar with predefined musical
properties.
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Contributors
C.Babu Rao
Anish Kumar
T.Jayakumar
Govind K. Sharma
K.V.Rajkumar
S Mahadevan
S Sosamma
P. 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.Arundhati
ISVSA Project Scientist
Indian National Science Academy
New Delhi, India
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
Thanks to
Archaeology Department
Hampi
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR
MUSICAL PILLARS OF
HAMPI
STUDIES ON MUSICAL PILLARS AT HAMPI
CBR/IGCAR