# Musical Excellence of Mridangam by Dr. Umayalpuram K Sivaraman, Dr. T
Ramasami and Dr. M D Naresh

An introductory review by Dr. Arvind Shankar Kumar

To Sivaraman Sir, whose evergreen enthusiasm and quest for excellence
continues to inspire and astound in equal measure.

###### Contents

  1. 1 Preface
  2. 2 Introduction to Musical Analysis
    1. 2.1 What makes a musical note? - A primer on harmonics
      1. 2.1.1 Visualizing sound
      2. 2.1.2 Periodic signals and spectral analysis
      3. 2.1.3 What does this have to do with music?
      4. 2.1.4 Producing a musical note
      5. 2.1.5 What of drum instruments?
    2. 2.2 A unicorn in the world of percussion instruments
  3. 3 Can Science and Aesthetics Coexist? - History of Scientific Work on the Mridangam
    1. 3.1 Laying the Foundations - Dr. C.V Raman
    2. 3.2 Building on Raman’s work
    3. 3.3 Current Research Questions
  4. 4 Musical Excellence of Mridangam - Materials and Making
    1. 4.1 Structure of Mridangam
    2. 4.2 Traditional Construction of Mridangam
    3. 4.3 Rational Choice of Materials
      1. 4.3.1 Wood
      2. 4.3.2 Parchment
      3. 4.3.3 Minerals
      4. 4.3.4 Adhesives
      5. 4.3.5 Straps
      6. 4.3.6 Annular Space
    4. 4.4 Elements of Construction
      1. 4.4.1 Preparation of parchment
      2. 4.4.2 Preparation of Minerals for Application in Black Patch preparation
    5. 4.5 Chapter summary
  5. 5 Musical Excellence of Mridangam - Understanding the Unique Tonal Properties
    1. 5.1 FFT Spectrum and Decay Profile Analysis
    2. 5.2 The Seven Strokes
    3. 5.3 Kucchi vs Thool Mridangam
    4. 5.4 Cow-based membranes vs Goat-based membranes
    5. 5.5 Building on Raman’s work
    6. 5.6 Chapter Summary
  6. 6 Towards Musical Excellence
    1. 6.1 Characterizing Mridangams - Spectral ratios and time decay
    2. 6.2 A comparison of Mridangam and Tabla - A case of resonating columns
    3. 6.3 Search for the fundamental mode - odd-even hypothesis
    4. 6.4 Alternative materials for resonating column, membranes, black patches and insertion materials
    5. 6.5 Alternate Mridangam Designs
    6. 6.6 SRI Mridangam - a vision to the future
    7. 6.7 Chapter Summary
  7. 7 Epilogue

##  1 Preface

Musical Excellence of Mridangam is a treatise by the legendary mridangam
artiste Padma Vibhushan awardee Sangeetha Kalanidhi Dr. Umayalpuram K
Sivaraman in collaboration with eminent scientists Dr. Ramasami and Dr. Naresh
of Central Leather Research Institute Chennai, whose grand ambition is to
redefine our understanding of the ancient instrument that is the mridangam,
using both modern scientific tools and artistic insight. One of the most
challenging aspects of such an ambitious undertaking is to interpret the
subjective experience of music using tools designed for objective analysis.
Given this paradox, there are bound to be gaps in our interpretation and
understanding that cannot be bridged. However, as Musical Excellence and
previous undertakings of such nature - mostly confined to Western music - have
repeatedly shown us, there is tremendous insight to be gained through such an
analysis. However, such scientific analysis is quite sparse in the field on
Carnatic music, whose beauty and uniqueness still remains shrouded in myth and
mystique. In the case of the mridangam, the famed physicist Dr. CV Raman was
the first to pursue this avenue, and he made important discoveries in the
1920s regarding the unique nature of the mridangam within the world of musical
instruments, which have been carried on by researchers in the following
decades. Musical Excellence builds on this and delivers a treatise which
comprehensively analyses the unique tonal properties of the mridangam,
unravels the role of various materials and traditional fabrication
methodologies, and proposes new designs for travel-friendly mridangams and
methods of standardization of materials and manufacturing which preserve the
musical experience produced.

The primary value of such an enterprise as Musical Excellence of Mridangam is
expected to be 1) to the rasika, who can gain a new appreciation which
enhances their experience of music, 2) to the artist, who can use the enhanced
understanding of their instrument to develop new techniques to produce musical
experiences and finally 3) to the makers of the instruments, who can use the
understanding of the role of various materials, designs and fabrication
processes to improve and innovate new designs to enhance the quality of
musical notes produced. One aspect that we note about these three categories,
which is not typical of the audience of any other kind of scientific treatise,
is that it does not include trained scientists. However, the rigour of
scientific analysis requires that new discoveries and insights are presented
in a language that reflects said rigour and understanding of the analysis
techniques used, and thus may not be directly accessible to people in any of
these categories.

This review thus aims to bridge the gap between the primary intended audience
of Musical Excellence of Mridangam and the scientific rigour with which the
original treatise is written by introducing the subject of musical analysis
and presenting the discoveries made about the wonders of this unique
instrument in Musical Excellence to rasikas, artistes and makers alike. The
first three chapters of this review (including this one) introduces the basic
scientific concepts used in Musical Excellence of Mridangam and provides
background to previous scientific research into this instrument, starting from
the seminal work of Dr. CV Raman. This also includes brief discussions of the
corresponding chapters in Musical Excellence of Mridangam. The next chapters
all serve the purpose of explaining the main scientific results presented in
Musical Excellence of Mridangam in each of the corresponding chapters in the
treatise, and finally summarizing the relevance of the work.

##  2 Introduction to Musical Analysis

###  2.1 What makes a musical note? - A primer on harmonics

Sound is nothing but variations of pressure in the atmosphere, that are picked
up by the sensitive instruments that are our eardrums. However, certain sounds
are pleasant to hear - which we call ’musical’ - and certain sounds unpleasant
- which we call ’noise’. Our ears are therefore able to make qualitative
distinctions between different kinds of pressure variations in the atmosphere.
In this chapter, we will see that this qualitative distinction has a basis in
the theory of waves and our ears are, in a sense, a form of spectral analysers
(a sophisticated scientific instrument found in electronics labs).

####  2.1.1 Visualizing sound

These days, the most direct way of visualizing a sound signal, is by
converting it to an electrical signal or voltage. This is typically done
through a microphone which has elements inside it which produce an electrical
signal in response to pressure variations, called piezoelectric materials.
Here, the magnitude of the pressure signal at any instant in time directly
corresponds to the voltage value of the signal at that time. The electrical
signal - typically quantified as a voltage - can be viewed on an instrument
called an oscilloscope, where the voltage - on the y-axis - is plotted against
time on the x-axis. Figure 1 shows an image of a typical oscilloscope screen.

Figure 1: A typical Digital Storage Oscilloscope (DSO). Image credits: [1]

####  2.1.2 Periodic signals and spectral analysis

One common category of signals are ones that repeat themselves after a certain
fixed amount of time. These are called periodic signals (or - more
colloquially - waves), and the time after which a signal repeats is called the
period. We will see that these signals play a crucial role in our
understanding of sound. An example is seen in Figure 2, where we see a
periodic signal of period given by $T$.

Figure 2: A periodic signal of period $T$. Image credits: [2]

There are many common examples of periodic signals (triangle waves, square
waves etc.), but one special set of such periodic signals are sine and cosine
waves (Figure 3). These sines and cosines are the same ones you might have
encountered in a trigonometry class, but their exact form is not important for
our purposes.

The parameters of a sine wave are its amplitude and period - all marked in
Figure 3. The period can also be written as a frequency, which is the inverse
of the period. The unit of frequency is Hz or s-1, which represents how many
periods can fit in one second of the signal.

Figure 3: A sine wave signal with amplitude and period (one cycle) marked.
Image credits:[3]

Our ears are especially good at distinguishing these sine waves from other
signals. In fact, we hear sine waves as a pure note, with the pitch of the
note determined by the frequency of the note. For example, if ’Sa’ has a
particular frequency, ’Ri’ has a higher frequency, and so on, until the ’Sa’
of the next octave which has exactly twice the frequency of the initial ’Sa’.
Tuning forks, for example, are instruments which produce pure sine waves of a
given frequency.

The remarkable quality of sine/cosine waves, that can be proved
mathematically, is that any periodic signal can always be broken down into a
weighted sum of sines and cosines of different frequencies (i.e) sines and
cosines of various frequencies added up in different proportions known as
weights. This process is called a Fourier Transform, and is a common tool in
science and engineering. Therefore, instead of representing a signal as a
voltage versus time, we can instead represent it as the weights (in voltage)
of the sine waves that make up the signal (on the y-axis), and their
corresponding frequencies (on the x-axis). This representation is typically
called the spectrum of a signal. It is shown for sine wave, triangle wave and
square wave signals in Figure 4 \- the graphs on the right are the spectra of
the signals on the left. We see, for example, that a sine wave has a single
peak corresponding to the frequency of the wave.

Figure 4: Various periodic signals on the left and their frequency spectrum
sketches on the right. Image credits: [4]

Spectra for a few common periodic signals is compared to that produced by a
stroke on the mridangam in Figure 6.5 in Musical Excellence.

####  2.1.3 What does this have to do with music?

As mentioned before, our ears have a keen ability to distinguish music from
noise. Therefore, in exploring how this is possible, it is reasonable to
expect that ’music’ and ’noise’ have distinct spectral signatures. In Figure
5, we compare the spectrum of a musical note generated from a tampura (taken
from Figure 5.5 in Musical Excellence) and noise generated from a white noise
machine. We immediately observe a few points of difference. The musical note
is only composed of sine waves of a few frequencies, which are called the
harmonics. Noise, on the other hand, is composed of sine waves of many
frequencies and one cannot distinguish distinct harmonics.

Figure 5: Top: FFT spectrum of a note on the tampura (taken from Musical
Excellence). Bottom: White noise signal and corresponding FFT spectrum. Image
credits: [5]

If we look at the spectrum of the tampura note in Figure 5(a) closer, we also
observe that all subsequent harmonics have frequencies which are integer
multiples of the first. For this reason, the first harmonic is called the
fundamental, and higher harmonics are called overtones. This is an important
feature of musical or harmonic tones. These harmonic sine waves have similar
nodes (points where the amplitude of the signal is zero - seen in Figure 6),
and hence sound similar to our ears. When these harmonic series are combined
in various ratios, the resulting wave retains the essential features of a sine
wave and hence sounds pleasing to our ears (see Figure 7 and caption for
details). Whereas, for an anharmonic sequence of peaks, the combined wave
looks more similar to the wave for noise as it lacks the periodic features of
the former and therefore, our brain interprets it as such. Another feature of
harmonic peaks is that, due to the aforementioned structure in the nodes, they
interfere constructively with each other and are much more stable than
anharmonic peaks. Thus, they are able to ’sustain’ for much longer.

Figure 6: A series of harmonic sine waves - from the top, the fundamental or
first harmonic, second harmonic or first overtone, and so on until the bottom.
Image credits: [6]

Figure 7: Left: Resultant wave of four sine waves with frequencies in harmonic
ratios (1:2:3:4) in arbitrary amplitude ratios. Right: Resultant wave of four
sine waves with frequencies in an arbitrary anharmonic frequency ratio
(1:1.27:3.82:4.27) and the same amplitude ratio as the harmonic case [7]

It is also a widely accepted fact that the number of overtones contribute to
the texture of the musical note, and in general, the more the number of
observable overtones, the more complex and pleasing the texture of the musical
note. In musical parlance, these sine waves with frequencies in integer ratios
correspond to the same note in different octaves. Hence, we see that a note
played in a particular octave has overtones in higher octaves. As an
illustrative example of this, we see in Figure 8, a note (’Sa’ for example)
played on a tuning fork used in laboratories as opposed to the tampura in
Figure 5. As we see, ’Sa’ by itself only corresponds to a sine-wave of a
particular frequency. However, to obtain the pleasantness of a ’Sa’ played on
a tampura, we also need to produce overtones of the sine-wave corresponding to
’Sa’, but in higher octaves, at specific amplitude ratios. The combinations of
the fundamental and overtones, at these specific amplitude ratios (which, of
course, vary according to the instrument used and even the musician), produced
by the same instrument, combining together give us the pleasant ’Sa’ played on
a tampura. Possibly, it is this texture, provided by the higher harmonics of
the particular note produced in ratios unique to the instrument that produces
them, that provokes in us the subjective experience of ’naadham’.

Figure 8: FFT spectrum of a note on a tuning fork. Image credits: [8]

####  2.1.4 Producing a musical note

Given that it is desirable to produce musical notes with a maximum number of
harmonics, how do we achieve this? For this, we have to understand how sound
is produced from instruments. Sound waves are usually produced by vibrating
membranes, with the shape of the sound wave being defined by the shape of the
membrane after exciting it. Thus, our objective is to look for systems which
can produce multiple harmonics upon exciting them in specific ways.

To solve this seemingly difficult problem, we look at the modes of vibration
of an instrument. These are the only possible sine-wave deformations that can
be done to the instrument that are stable, each characterized by the amplitude
and wavelength of the sine wave. In this case, wavelength replaces period
since there is a space axis instead of time, but the wavelengths are directly
related to the period (and hence the frequency) of the sound signal produced.
Some of these modes for a string clamped at both ends (similar to a guitar or
violin) are shown in Figure 9. An interesting result, whose intuition can be
understood based on our earlier discussion on the properties of sine waves, is
that any possible stable deformation of an instrument is a combination of
these modes of vibration. Therefore, the typical spectrum of the sound
produced by such an instrument will have peaks at the frequencies
corresponding to the sound produced by the modes of the instrument. If these
frequencies - termed as natural frequencies of the instrument - are in a
harmonic series (i.e) they are in integer multiples of the lowest frequency
(the fundamental), the note that we hear upon exciting the instrument will be
musical, with the texture of the note depending upon the number of harmonics
sufficiently excited.

Figure 9: First four modes of a string clamped on both ends. Image credits:[9]

####  2.1.5 What of drum instruments?

You will notice that so far, we have not at all discussed one important aspect
of music typically associated with drum instruments like the mridangam -
rhythm. Drum instruments typically involve a two-dimensional membrane
stretched across a surface, which is excited by striking it either using the
hand or an implement like a drum stick. These two-dimensional membranes can be
struck at varying pace, upto several times a second, and and their primary
role is rhythm and percussion, which involves a separate discussion on the
time evolution of musical and non-musical notes. However, their ability to
produce musical notes is typically very limited. This is because, unlike the
one-dimensional string, the uniform two-dimensional membrane does not produce
modes whose frequencies are in a harmonic series. Typical ratios of the
natural frequencies of the modes of a circular drum, as seen in Western
percussion instruments, are in the ratio 1:1.59:2.14:2.30:2.65:3.16:3.50 etc.

One unlikely advantage of this fact is that, because of the lack of resonance
or constructive interference between modes which is seen in the harmonic case,
the notes produced by a drum do not sustain for a long period of time and
decay fairly quickly. This allows the human ear to distinguish upto several
notes played within a second as independent notes, which is not possible if
the notes sustain for a longer period since the next note will start before
the first note decays and one hears a combination of both notes. This fact
particularly helps the drum players to play complicated rhythmic patterns and
fast tempos, which are still discernable to the listeners. An image of the
first few modes of a circular membrane are shown in Figure 5.6 of Musical
Excellence, and are also reproduced later in this review, in Figure 22 (These
are modes for the case of a mridangam, which we will see is not the same as a
uniform circular membrane. However, the shape of the modes remains similar).

###  2.2 A unicorn in the world of percussion instruments

As was explained in the previous section, it is not possible for a uniform
two-dimensional membrane to produce harmonics since its mode frequencies are
not in a harmonic series. But what would happen if we make the circular
membrane non-uniform? Could we engineer it to produce harmonics? This was the
ingenious thought that was had by makers of Indian percussion instrument
makers thousands of years ago, without the benefit of modern technology and
understanding. They found that, by adding an additional mass around the centre
of a uniform circular membrane (or ’centrally loading’), they were able to
produce notes which sounded harmonic or musical. Indeed, we will see in this
review that centrally loading a uniform circular membrane in particular ways
does make the anharmonic modes of a uniform membrane into a harmonic series.
Thus, in the world of percussion instruments, the mridangam and tabla are
unique because they are drum instruments used for percussion, which are also
able to generate musical notes with many harmonics.

Given this uniqueness in the method of producing musical notes, one also
expects the musicality of these notes to be similarly unique. We will take the
case of the mridangam and explore the unique melodic character of the notes
produced, and the various factors involved to produce a tone of high quality.

Figure 10: Image of right membrane of the mridangam taken from the cover of
Musical Excellence of Mridangam by Dr. Umayalpuram K Sivaraman, Dr. T Ramasami
and Dr. M.D. Naresh , with the prominent black patch seen which is responsible
for central loading

##  3 Can Science and Aesthetics Coexist? - History of Scientific Work on the
Mridangam

In the general public’s notion, art and science have always been seen like oil
and water - opposing forces that do not mix. This is mainly because art deals
with a subjective experience of aesthetic beauty and science deals with
objective empirical observations that are (as far as possible) independent of
the subjectivity of the scientist. While this fact will always keep a
separation between these disciplines, they are also - in a way - united by
their objectives. Both art and science are motivated by a sense of wonder and
exploration that seems to be innate to humans. Science pursues this wonder
through exploration of the beauty and mysteries of the universe around us,
while art pursues this through the exploration of the internal human
experience of aesthetic beauty in itself. With this perspective, it is maybe
not a surprise that many great scientists loved to spend time with their
musical instruments, and many great artists have taken an interest in science.

Musical Excellence of Mridangam (Musical Excellence for short) is a treatise
born out of such a shared sense of wonder and exploration between eminent
scientists Dr. Ramasami and Dr. Naresh, and the mridangam maestro Padma
Vibhushan Dr. Umayalpuram K. Sivaraman. Given that mridangam is an ancient art
and the science behind how the instrument works is still relatively recent,
Musical Excellence - throughout the treatise - uses inputs from Dr. UKS as a
starting point and initial hypothesis for all of its scientific investigation,
and builds on that though rigorous scientific analysis, to make new
discoveries and give new insight into the workings of this instrument and the
creation of ’naadham’. For this unique research setup to work, it requires an
artist who has a very good grasp of the science behind the instrument,
scientists who have a keen ear for music, and open conversation and flow of
ideas between the two.

The first chapter of Musical Excellence thus aptly begins with conversations
with both Dr. UKS and Dr. Ramasami which help to elucidate the objective and
motivation behind the treatise and also their philosophy of mridangam,
research, music, art, science and many more, with many interesting anecdotes
along the way. The conversation with Dr. Ramasami establishes the technical
base of the treatise, where he first explains the scientific background for
research into the mridangam, and goes on to expound on the various scientific
tools used in the current research work and summarizes the main findings of
the project. Along the way, we also get to learn his perspective on naadham
and the relationship between science and music. The conversation with Dr. UKS
explores the concept of musical excellence in the context of the mridangam and
includes discussions on his philosophy of naadham and mridangam, the role of
the mridangam in a concert, his role as a guru and many more practical issues
like sustaining energy for a long concert, various types of mridangams and
methodologies of accompaniment. Amongst these are sprinkled various
illuminating anecdotes from doyens of Carnatic music like Sri Semmangudi
Srinivasa Iyer, Sri Arriyakudi Ramanuja Iyengar, Sri Pallakadu Mani Iyer, Smt.
D.K.Pattamal and many more. In addition to this, Dr. UKS also explains his
motivation behind his ongoing pursuit of scientific research into the
mridangam and the innovations that he has made thus far, including the fibre-
glass mridangam, before going on to outline his objectives for the current
research project.

In this chapter, we will look at the existing body of literature on the
science of mridangam, sparked by the pioneering work of Dr. CV Raman, which
will lead us to understand the level of scientific understanding that
currently exists about this instrument, and what questions still need to be
answered.

###  3.1 Laying the Foundations - Dr. C.V Raman

Dr. CV Raman - the scientist of great repute for his discoveries on waves both
light and sound - through his keen musical intuition realized that the
Mridangam was not only a percussion instrument but a melodic one as well. This
motivated his foray into the harmonics of Mridangam strokes[10, 11], and
culminated in a landmark paper in 1935 [12], where he explains the results of
his experiments performed 1919 onward. Raman was the first to notice that the
mridangam could produce upto five harmonics, thus beating the no-go
theoretical result about the inharmonicity of 2D membranes. Raman was further
able to demonstrate the different shapes of the membranes corresponding to
each of the modes (Figure 3.1 in Musical Excellence ) and recognize the role
of a skilled player in exciting some of these modes. Additionally, he
hypothesized the role of central loading (which was later proven by
theoretical works) and the heavy wooden shell in the generation and sustenance
of these harmonic modes, and to top it all off, also noticed that the
fundamental mode is shifted in frequency by about 10 percent (The actual shift
is by seven percent). It is amazing that Raman was able to find out so much
without the aid of any electronic oscillators or spectral analysers and only
using his keen ears and physical intuition. The shifted fundamental is a
curious fact that has attracted the interest of future theoretical
investigation. It also means that the mridangam is tuned using the second
harmonic mode in the series, since the first harmonic’s frequency is offset.

###  3.2 Building on Raman’s work

Following Raman’s breakthrough findings on the harmonic nature of notes
produced by the mridangam, theoretical efforts by Ramakrishnan et.al in
1954-57 [13] modelled the black patch as a sharp increase in the density of
the membrane below a certain radius. With this model they were able to
reproduce the harmonic series of modes and also the degeneracy in modes
observed by Raman, and further predict values for sixth and seventh overtones
that were not observed by Raman. In 1994, Siddharthan et.al [14] were able to
calculate how exactly the central region has to be loaded in order to produce
the harmonics observed by Raman. As part of their study, they also observed
that the fundamental was shifted by 7 per cent and the rest of the series was
harmonic. Additionally, they found that the dheem stroke (see section 5.1.1 of
this review) primarily excites this shifted fundamental, whereas the chappu
stroke typically used to tune the mridangam to the pitch of the main artiste
primarily excites the second harmonic. This would imply that the mridangam is
tuned using the second and higher harmonics, but our ears are able to perceive
the fundamental that would correspond to this harmonic series and match the
frequency to the pitch of Sa. Further, in 2000, Malu and Siddharthan [15]
presented a model which accounts for the actual loading pattern of the black
patch on the mridangam and reproduce the harmonic frequency ratios. Further
studies primarily focus on comparing tonal properties between the mridangam
and tabla, and these are also catalogued in Chapter 6 of Musical Excellence.

###  3.3 Current Research Questions

After Raman’s initial work, there has been very few subsequent experimental
works that have emerged, which would reflect the level of theoretical
understanding we currently have about the origin of harmonics in the
mridangam. Systematic experimentation is required to distinguish between the
different theoretical models of harmonic production, and quantify the role of
different structural factors like the wooden shell and membrane materials, and
human factors like the expertise of the artiste, in producing tonal beauty.
Apart from this, there is ongoing effort to standardize the fabrication
methodologies of the mridangam, find alternative materials for constructing
the mridangam, and design a travel-friendly mridangam. It is with the goal of
addressing these questions that the authors of Musical Excellence of Mridangam
pursue their work, the results of which are summarized in the subsequent
chapters.

##  4 Musical Excellence of Mridangam - Materials and Making

The fourth chapter of Musical Excellence deals with the materials, structure
and construction of the mridangam, and investigates how these various factors
are involved in producing the tone of the mridangam. After introducing the
structure of the mridangam, Musical Excellence explains the traditional
process of constructing the mridangam in minute detail. Following this,
Musical Excellence delves into the six categories of materials used in the
mridangam and investigates the important material properties of each. Having
established these, it also investigates the elements of construction that
might be important to producing musical notes in the mridangam.

###  4.1 Structure of Mridangam

The basic structure of the mridangam consists of a wooden shell with two
multi-membrane assemblies on either side, which are held taut by straps
connecting them. On the right hand side or valanthalai - which contains the
black patch and is hence the major source of harmonics - the membrane consists
of multiple layers, the first of which is a disk of buffalo skin parchment
called ulkaraithattu, which is directly tied to the wooden barrel through
buffalo hide straps. Upon this is placed a full membrane typically made of
goat skin parchment, which also contains the black patch. This is the primary
membrane whose vibrations are responsible for the harmonic notes - hence
called paatuthattu or kottuthattu. Upon this membrane, annular rings made from
cow skin parchment are placed to create a space between membranes which is
filled with different materials to modify and fine-tune tonal quality. The
final layer - which is a disk typically made out of cow skin parchment -
called vettuthattu - is added. The annular space between the kottuthattu and
vettuthattu is filled with different materials like pine wood sticks or pieces
of black patch material to fine-tune and control the harmonics produced. The
black patch itself is made of a powder of ferric oxide and is applied on the
kottuthattu in sequential layers to create a density gradient that is
important to create harmonic modes - as seen by Malu and Siddharthan [15]. The
left membrane of the mridangam, or edanthalai, is typically used for playing
base notes, as opposed to the treble notes played from valanthalai. This
membrane is made from buffalo parchment which is typically thicker than the
right membrane. While this membrane is typically not centrally loaded with a
black patch since its primary role is not the production of multiple
harmonics, it is usually centrally loaded while playing through application of
a paste of semolina or cream of wheat (rava) to create base notes that have
increased sustenance and nevertheless produce some harmonic behavior.

Figure 11: Structure of the mridangam. Image taken from Figure 4.1 of Musical
Excellence.

###  4.2 Traditional Construction of Mridangam

The main parts of a mridangam are a central wooden barrel which serves as a
resonating column - typically in three sizes -22”, 23” and 24” - whose
openings are covered by a multi-layered assembly of parchments made from goat,
cow and buffalo skin. The process of making a mridangam starts from the trunk
of a jackfruit tree, which is machined in order to make wooden barrels of
required height and diameters. For the left side membrane, buffalo skin
parchments are soaked overnight, and the layers are carefully assembled by
tying together with hoops and thongs. The right side membrane is also
assembled in a similar fashion. The buffalo hide straps are used to tie the
two membranes to the wooden shell in a plaited manner, through holes made on
the edges of the membranes. For the right side membrane, since equal
distribution of forces is critical, additional holes are punched and a rope is
run through them circumferentially - the number of points of insertion for the
right membrane is 48, while it is 36 for the left membrane - in order to
equally distribute the tension and allow for fine adjustments of shruthi. Once
the parchments are set on the shell and dried, the buffalo hide ropes are
removed. The process described thus far is called ’poi var pidithal’ since the
applied tension is not retained once the parchment settles on the shell.
Finally, the left and right membranes are joined through buffalo hide rope
which runs through 16 points along both membranes and is held taut so that the
right membrane has the necessary tension. The black patch is then applied to
the exposed region of the kottuthattu layer-by-layer, after cooked rice is
applied as an adhesive to the membrane. The annular space between the
kottuthattu and vettuthattu is then filled using radial strips of reeds
(kucchi) or pieces of black patch material (thool) according to the artiste’s
preference.

At the beginning of the fourth chapter, Musical Excellence explains this
process - which has been gleaned from extensive conversation and observation
of skilled artisans like Sri Johnson - in full detail, and includes images
which show the various steps being performed. Throughout the fourth chapter,
the authors consider the potential steps towards standardization of this
construction process and demystifying the myths that have invariably passed
down to us as well, which could - for example - lead to a future where we
could design and build this instrument using sustainable materials or make a
transport friendly version, while preserving the unique acoustic qualities. As
a first step in this direction, the authors suggest the use of Fast Fourier
Transform (FFT) techniques to extract and characterize the spectra of
different strokes played on the mridangam, along with time-decay profiles to
quantify the sustenance of different harmonic peaks. FFT is a computational
technique used for performing the Fourier Transform and extracting the
spectrum of a signal (see Chapter 1 of this review for an introduction to
Fourier Transforms and spectral analysis).

###  4.3 Rational Choice of Materials

There are six classes of materials in a traditional mridangam - wood (main
body), parchments (membrane), minerals (black patch), adhesives (binding black
patch to memberane), straps (binding membranes with desired tension) and
materials for filling the annular space (kucchi vs kappi). The authors study
each of these six classes of materials separately, and present rational
choices for materials based on such analysis. In addition to allowing us to
make rational choices about the materials currently used in a mridangam, this
section establishes the scientific method to studying these materials used in
the mridangam, thus establishing the grounds for discovering new such
materials which satisfy certain requirements like sustainability or transport-
friendliness or superior acoustic properties, and move us towards
standardization. Later, In the fifth chapter, dealing with tonal properties,
Musical excellence also addresses a few popular material-related issues like
goat vs cow parchments and kucchi vs thool mridangams.

####  4.3.1 Wood

Wood is the preferred choice of resonating column for the mridangam, and hence
represents one of the most important material choices. One of the unique
properties of wood is that it has different and independent mechanical
properties along three different mutually perpendicular directions
(Orthotropic), due to the formation of growth rings. This is well illustrated
in Figure 4.6 in Musical Excellence Musical Excellence, where we see different
patterns created by the growth ring fibres along different mutually
perpendicular surfaces, leading to unique mechanical properties along each
direction. In the case of the mridangam, the wooden shell is made in a
direction axial to the run of the fibres. To understand the orthotropic
effect, the authors conduct a study of the three-dimensional propagation of
sound for different types of wood typically used in the mridangam. Musical
Excellence further introduces the possible design choices in wood through
analogy with the role of wood in violin construction, particularly the famed
Stradivari. The wooden shell is made in the form of a frustum to ensure that
the buffalo hide straps are under tension, and it typically comes in lengths
of 22”,23” and 24” - depending on the required shruthi.

To study the role of wood, Musical Excellence uses the parameter of Sound
Radiation Coefficient (SRC), which has been previously used in studying the
acoustic qualities of wood used in xylophones and soundboards. SRC is a
measure of the vibrational response of a material to an input pressure signal
(i.e) sound wave. Higher SRC values are typically seen as ideal for musical
instruments as these correspond to more loudness for a given applied force.

Another such quantity used by the authors is Impedance (Z), which quantifies
sound propagation through a material. If sound moves from one system with
impedance Z1 to one with impedance Z2, the transmitted sound intensity drops
significantly if the difference between Z1 and Z2 increases. Thus, for
efficient sound intensity transmission, we want the impedance of different
parts of our system to be as close together as possible. In this case, the
authors compare the impedance of different directions of the wood (as
mentioned above), for different types of wood used.

Both these factors depend on the density,velocity and Young’s Modulus (a
parameter which quantifies response to external stress) of the wood, and these
are subsequently measured in order to calculate SRC and Impedance.

On a more practical note, it is worth to compare the hardness of wood to
ensure ease of machinability - as a step towards standardization. The authors
thus study this factor through the Janka Hardness Test, which is typically
used in the case of wood.

Through this study, the authors are able to conclude that jackfruit wood is
the favorable choice among the different types of wood studied, due to its
high SRC and similar Impedance in different directions. This seems to agree
with conventional wisdom, as traditional makers have favoured jackfruit wood
for the construction of the mridangam barrel. The comparatively low density of
this wood also reduces the total weight of the instrument.

####  4.3.2 Parchment

Parchment has emerged as the membrane of choice for the mridangam, and is also
used for the straps which adjust the tension of the membrane (typically made
from buffalo hide). In Musical Excellence, we see that parchment made from
different animals, and even different part of the same animal (particularly,
back and belly), can be used to generate different musical outcomes based on
their unique properties. To bring these on a common footing, Musical
Excellence categorizes these different skins based on the thickness of the
skin, the diameter of the fibre bundles that run along the skin, and the angle
at which these fibres are weaved together. The effect of processing these
skins by treating with lime (calcium hydroxide) is also explored. It is noted
that skin from the back region of the goat might be more suitable for
producing resonances due to the better compaction of fibre bundles in that
region, and hence it is used for the kottuthattu of the right membrane of the
mridangam which contains the black patch and is used to create the treble
notes. On the other hand, the skin from the belly region, having lesser
compaction of fibre bundles, is more suitable for the left membrane which is
used to produce bass tones.

The study of different parchments is done in Musical Excellence through
comparison of their visco-elastic properties, which quantifies how the
membranes respond to an external force (in this case, the force applied by the
artiste) (i.e) whether the membrane relaxes to it’s original position in the
same configuration after deformation (elastic) or undergoes a permanent
deformation (plastic) or returns to the same position but there is a permanent
rearrangement of molecules within the membrane (viscous). It is found that
skin from different regions of the goat all have similar distributions of
deformation across the three types discussed, which implies a significant
contributions from elastic deformation which is required for a membrane
material. The plastic and viscous contributions imply that the membranes
deform over time and their tension will have to be re-adjusted from time to
time. The buffalo straps of the mridangam allow for this to be done, in a
process called ’var pidithal’.

An anisotropy is also found in the material properties of the membrane between
perpendicular directions, attributed to the orientation of the fibres parallel
or perpendicular to the direction of deformation. It is also found that liming
marginally increases the elastic component of deformation, which might make it
more suitable for sound generation.

Additionally, Musical Excellence compares the frequency spectrum of a ’chappu’
note (a method of analysis heavily used in the fifth chapter) played on
membranes made from both cow and goat parchments and finds sharper resonance
peaks for the goat parchment membrane, which indicates its relative
suitability for resonance production and hence for its use on the kottuthattu
of the right membrane of the mridangam with the black patch. This conclusion
is further explored in the fifth chapter, where other strokes are compared as
well.

####  4.3.3 Minerals

Minerals are used to create a black patch on the right membrane, to load it in
such a way that it produces harmonic tones (as discussed earlier). Primarily,
Ferric oxide sourced from rocks on river belts like the Ganges and Cauvery are
used to make the black patch. Upon analyzing the composition of minerals
sourced from these locations, the authors find the samples from Cauvery to be
more rich in iron, whereas the samples from the Ganges are found to be more
rich in Silica. The tonal consequences of these are discussed in the fifth
chapter of Musical Excellence, and will be alluded to later in this review.

Additionally, the authors also use X-Ray diffraction - a technique used to
analyze the crystalline nature of a sample and find the crystal lattice
structure - to analyze these samples. In X-Ray diffraction, light is shined
along different directions relative to a sample, which if it is crystalline,
causes the light to diffract due to its periodic structure. This creates a
pattern of dots on a screen, which correspond to peaks of light intensity.
Sharper peaks indicate a more crystalline nature of the sample, and the
position of the peaks indicates the crystal structure. The authors in Musical
Excellence compare the mineral samples taken from Ganges and Cauvery and
compare it to pure Ferric oxide. It is found that the samples of black patch
are indeed primarily composed of Ferric oxide, but they are not as well-
ordered when compared to the pure crystalline Ferric oxide samples. It is also
interesting to see the similarities and differences in the diffraction
patterns, and this analysis in Musical Excellence introduces X-Ray diffraction
as a method of analysing minerals used for the black patch.

####  4.3.4 Adhesives

Cooked rice is generally the preferred adhesive used for binding the particles
of black patch together and the black patch itself to the goat-based
parchment. With the objective of finding other alternatives to this, Musical
Excellence examines various adhesive materials using standardized tests for
evaluating binding properties. The generated alternatives are examined in
subsequent chapters.

####  4.3.5 Straps

Buffalo hide is usually used for the straps which connect the membrane to the
wooden barrel, and are used to adjust the tension of the membrane which
changes the frequency of the harmonics (i.e ’shruthi’ or tone of the
instrument) and thus tune the instrument. These are used for their high
tensile strength and durability. Musical Excellence quantifies the tensile
strength of these straps and discusses the possible role of traditional
processing steps like treating with curd.

####  4.3.6 Annular Space

Annular spaces between parchment membranes on the right side of the mridangam
are typically filled with insertion materials to fine-tune the harmonics
produced. These are also known to either dampen or amplify different strokes
played on the mridangam. These include thool (particles left behind after
sieving the black patch minerals) placed uniformly throughout the annular
space, kucchi (strips of palm stems) placed radially at equidistant points
along the membrane, grains of sand etc. Musical Excellence quantifies the
properties of the traditionally used annular materials, and discusses the
musical outcomes of thool vs kucchi - a popular issue - in the fifth chapter,
which will be explored later in this review.

###  4.4 Elements of Construction

####  4.4.1 Preparation of parchment

Parchments used for the right and left membranes are prepared using standard
means by soaking in water to clean and remove salts used for preservation, and
treatment with lime. This is followed by removal of hair and flesh, and the
added lime using ammonium chloride as an acidic salt. They are then adjusted
to the required thickness and dried. Following this, they are cut into the
required shape, according to their usage.

####  4.4.2 Preparation of Minerals for Application in Black Patch preparation

The black patch is one of the most important and unique parts of the
mridangam. Therefore, the scientific study of its construction is of paramount
importance. We saw that the introduction of a central loading (like the black
patch in the case of the mridangam) to a uniform 2D membrane shifts the
anharmonic frequency spectrum to harmonic. Most of the mathematical models
which prove this effect have considered layers of black patch applied in a
gradual manner, with sequentially decreasing diameters for subsequent layers.
This results in a type of loading where the maximum load is at the centre, and
it gradually tapers off along the radius as we get closer to the edge of the
black patch. However, this is not how the black patch is traditionally
constructed in the mridangam. Instead, layers with smaller and larger diameter
are alternated in a specific way, before applying the last few layers in a
sequential fashion (see Figure 4.15 in Musical Excellence for an
illustration).

Musical Excellence has done a systematic study of this method of loading,
through an interesting experiment with a tuning fork - which is an instrument
used to produce a tone of a given frequency. In this experiment, they apply
the layers of the black patch with varying densities in the same sequence as
is seen in the mridangam, and measure the change in frequency of the tuning
fork. It is found that, while the frequency decreases with loading as
expected, there is a fluctuation in the rate of decrease. This fact has been
used intelligently by artisans to produce overtones (which are initially
anharmonic) that are harmonic.

Similar studies are conducted which now measure the change in frequency of
different notes like dheem, nam (meetu) and chappu upon applying successive
layers of black patch, and a similar decrease in frequency is found.
Interestingly, the ratio of frequency between dheem and chappu is found to
oscillate as more layers of black patch are applied, until it stabilizes at a
value of 0.535 after a certain number of layers. This stabilization might be
used to infer that sufficient layers of black patch have been applied. Also,
the value of 0.535 in the ratio of frequencies of dheem to chappu (first and
second harmonics respectively) is characteristic of the mridangam, due to the
first harmonic or fundamental (i.e) dheem being shifted - as explained earlier
(Other wise one would expect a ratio of 0.5 between these harmonics). More
detailed study reveals that this ratio is accurate to within 0.05 over a range
of different mridangams. Similar ratios for non-observable fundamental to
dheem (discussed earlier) - 1.07 $\mp$ 0.01 and nam to chappu - 1.5 $\mp$
0.012 are reported in Chapter 6 of Musical Excellence. This fact provides us
with a method to characterize mridangams made from alternate materials and
design. This would be the first test for these new instruments to pass to be
considered equivalent to a traditional mridangam.

###  4.5 Chapter summary

This chapter of Musical Excellence thus examines the role of various materials
used in the mridangam, and characterizes each of these materials according to
their role, using scientific tools, in order to understand the relevant
material properties and come up with alternatives for standardization.
Additionally, this chapter also explores the various construction processes
like preparation of the black patch, which are crucial to producing the unique
tone of the mridangam. The next chapter further explores this unique tonal
quality through similar scientific tools like Fourier Analysis.

##  5 Musical Excellence of Mridangam - Understanding the Unique Tonal
Properties

As Musical Excellence states beautifully in the first line of Chapter 5, ’the
uniqueness of the Mridangam emanates from its potential to combine the
generation of harmonics like string instruments, create frequency diversity
like wind instruments, and offer rhythmic beauty of percussion.’ Just like the
seven notes of within an octave, there are seven notes played on a mridangam -
each with its own unique tonal signature. The origin of the tonal beauty of
these strokes is explored in Chapter 5 on Musical Excellence.

###  5.1 FFT Spectrum and Decay Profile Analysis

In order to decode the different strokes played on the mridangam and further
study the effect of materials and construction, Musical Excellence uses Fast
Fourier Transforms (FFT) - explained in the first chapter - to extract the
spectrum of each note and make comparisons. Additionally, the authors also
measure time decay profiles, which measure how the intensity of the primary
harmonic peak for a particular stroke changes with time, to quantify the
sustenance of the particular note. This is a very intuitive quantity to
measure, and is something both artists and scientists can relate to.

###  5.2 The Seven Strokes

In order to properly characterize the tonal quality of the different strokes -
given the various factors involved including background noise and expertise of
the artiste - Musical Excellence uses sound recordings of these notes played
individually by Dr. UKS in a studio for minimization of background noise. We
see the beautiful unique signatures of the different notes in Figure 5.1 in
Musical Excellence, with the ’open’ notes played on the right side eliciting
maximum harmonic features of sharp peaks separated in frequency by integer
ratios, and the ’closed’ notes on the right side showing broader features
characteristic of anharmonicity. Interestingly, the notes played on the left
side (’thoppi’) also show harmonic features, though these are broader than
those of the right side. These harmonic features are to be expected since the
membrane on the left side is also centrally loaded with a paste of ’rava’
(cream of wheat) which can be removed after a session. These figures are also
reproduced below.

Dheem
Dheem is the stroke played on the right side membrane that primarily excites
the fundamental mode of said membrane. Interestingly, Musical Excellence finds
that the frequency of this fundamental mode is shifted by 7 percent compared
to the expected fundamental frequency from the rest of the harmonic sequence,
and hence, when the mridangam is tuned to said harmonic sequence using higher
harmonics, the tone of dheem corresponds to the Rishabham note.

Figure 12: Dheem stroke with FFT spectrum

Chappu
Chappu (along with the Araichappu) is the primary tonal note of the mridangam,
played on the right side membrane. It primarily excites the second harmonic
but also has a rich polytonic structure. This stroke is used to tune the
mridangam so that the expected fundamental frequency corresponds to Shadgamam
or Sa of the main artiste. It is interesting that our ears are able to
perceive this ’ghost’ fundamental even though we are exciting only second and
higher harmonics using the chappu note. The second harmonic excited using
chappu sustains for the longest in comparison to other strokes (with the
exception of dheem) , for even upto a few seconds.

Figure 13: Chappu stroke with FFT spectrum

Nam
Nam is a stroke that is played on the periphery of the right side membrane,
that primarily excites the third harmonic. It produces a metallic sound that
does not sustain for very long, but is nevertheless harmonic. As seen in the
harmonic peaks for this stroke which tend to be broader, it requires a skilled
artiste to extract the naadham of nam.

Figure 14: Nam stroke with FFT spectrum

Araichappu
The Araichappu is a stroke that is unique to the mridangam, that has no
counterpart even in the tabla (as seen in Table 6.3 of Musical Excellence and
corresponding discussion). The araichappu primarily excites the third
harmonic, and hence corresponds to the upper octave Sa note. Additionally,
while the chappu note has a soft timbre, the araichappu has a sharp, metallic
timbre - even though it retains the rich polytonic structure of chappu.

Figure 15: Araichappu stroke with FFT spectrum

Dhi
While Dhi is a closed note played on the right membrane that does not sustain
for long, we see from the spectrum that it has clear harmonic peaks and is
thus a tonal note. The naadham of Dhi thus requires a skilled hand to produce
these harmonics even in a closed note.

Figure 16: Dhi stroke with FFT spectrum

Ta
As seen in the measured FFT spectrum of Ta, it is a closed note that does not
elicit harmonics, played on the center of the black patch. It has a sharp
timbre due to its short sustenance time, which also allows it to be
distinguished even when played multiple times a second.

Figure 17: Ta stroke with FFT spectrum

Thom
Thom is an open base note played on the left side membrane. While popular
opinion suggests that the left membrane does not produce harmonics, we see
from the spectrum below that it is possible to extract harmonic peaks from
thom as well. Since the left membrane is not centrally loaded and thus is
anharmonic, one would not expect such harmonic peaks. However, these are able
to be created because the artiste applies a paste of semolina on to the left
membrane to mimic the role of the black patch of the right membrane. The
application of this paste is adjusted so that the base tone of this membrane
corresponds to the Pa note of the lower octave.

Figure 18: Thom stroke with FFT spectrum

Gumkki
Gumkki is another note that is harmonically unique to the mridangam (as seen
in Table 6.3 of Musical Excellence and corresponding discussion). Dr. UKS has
likened the naadham of gumkki to the ’cooing of the dove’. While it does
display some harmonic characteristics as evidenced by the spectrum below, its
primary use is to modulate the harmonicity of the thom strokes in-between
which it is played.

Figure 19: Gummki stroke with FFT spectrum

###  5.3 Kucchi vs Thool Mridangam

The issue of filling the annular space between membranes on the right side of
the mridangam has been a source of intense discussion in the Carnatic music
community for many decades. The reason behind this is likely due to the
clearly different tonal qualities between ’kucchi’ mridangams (annular space
filled with sixteen equidistant strips of pine wood placed radially) and
’thool’ mridangam (annular space filled uniformly with pieces of black patch
material). In the end, it is more a matter of personal preference and artistic
style as to which type is preferred, but it is important to understand the
tonal differences between the two.

In Musical Excellence, the FFT spectrum of both ’thool’ and ’kucchi’
mridangams are presented and compared. It is found that both in terms of
number of harmonic peaks observed and the intensity of the harmonic peaks, the
dheem and nam strokes are more prominent in the thool mridangam, whereas the
chappu and araichappu strokes are more prominent on the kucchi mridangam.

Additionally, Musical Excellence investigates the effect of inserting these
annular materials, by looking at FFT spectra and time decay profiles before
and after the insertion of ’kucchi’. It is seen that the insertion of ’kucchi’
not only improves the sharpness of the harmonic peaks and hence the tonal
quality, but also allows the note to be sustained for longer (seen through the
time decay profile) when compared to membranes without annular filling. These
annular materials can thus be used to adjust the sustenance of various notes
on the mridangam. Musical Excellence further compares the role of these
annular materials to that of the ’jeeva’ in a tampura through similar FFT
spectra. It is also interesting to see the sharpness of the harmonic peaks in
a string instrument like the tampura, which is used for a purely melodic or
tonal purpose, when compared to the mridangam.

While establishing the above facts about annular materials objectively is in
itself a significant development, Musical Excellence goes further to propose a
mechanism for the differences between thool and kucchi mridangams. To
understand these interpretations, one first has to understand the shape of the
modes excited by the different notes (fundamental/first harmonic for ’dheem,
second for ’chappu’ and third for ’nam’), seen in Figure 5.6 in Musical
Excellence (also included here as Figure 22). Insertion of ’kucchi’ prevents
the whole membrane from moving as one, so modes that correspond to this kind
of motion where either the membrane moves as a whole or the deformation is
symmetric along the radius (’dheem’ and ’nam’) are suppressed. For these types
of modes, we will find concentric circles on the membrane that are undergo no
deformation - called nodal circles. On the other hand, insertion of ’kucchi’
does not affect modes where there is no deformation of the membrane along the
diameter (where the kucchis are placed) - also called a nodal diameter. Thus,
the chappu and araichappu notes are not similarly suppressed in a kucchi
mridangam, and are in fact enhanced. In the case of ’thool’ mridangams, where
particles are distributed throughout the annular space, the modes where the
deformation is symmetric along the radius - which have nodal circles -
(’dheem’ and ’nam’ ) are enhanced, whereas the modes with nodal diameters
(chappu and araichappu) are suppressed. In Figure 6.5 (Chapter 6), Musical
Excellence also shows beautiful images obtained using laser interferometry (an
optical technique used to measure very small deformations), which show the
shape of the different harmonic modes of the mridangam, which also help to
illustrate this point. We also see, from the corresponding discussion, that a
majority of these deformations occurs in the black patch region, highlighting
its importance.

Figure 20: Shapes of first three modes of the mridangam, localized to the
black patch

###  5.4 Cow-based membranes vs Goat-based membranes

In addition to the annular filling material, the material used for the right
membrane as the kottuthattu represents an important parameter for tonal
quality. Traditionally, these membranes are made out of either goat or cow
skin, as mentioned previously. Upon comparing FFT spectra, Musical Excellence
finds that goat-based membranes seem to have sharper and higher intensity
harmonic peaks, especially for the chappu stroke. Further study of these goat-
based membranes using FFT spectra and time decay profiles reveals that thinner
membranes seem to have better tonal quality and sustain of notes, with the
chappu note sustaining without much loss of intensity for more than 1 second
in thinned membranes. Thus, when comparing membranes across different
materials or when proposing new materials to make these membranes, thickness
of the membrane is an important parameter, and it could be possible that - up
to a certain extent - thinner membranes allow for better tonal quality.

###  5.5 Building on Raman’s work

As explained previously, Dr. CV Raman’s work [10, 11, 12] established the
grounds for considering the mridangam as a harmonic instrument, unlike Western
percussion instruments. Following his work and subsequent investigations,
theoretical work by Malu and Siddharthan [15] has established the theoretical
framework for this, and shown that the central loading in the form of the
black patch is responsible for eliciting these harmonics, by considering a
model with where the density (within the black patch region) varies as a
function of the radial distance from the centre. With this model, they further
predict that the frequency of the fundamental mode is shifted by 7 per cent
when compared to the rest of the harmonics, which are in integer ratios as
desired.

At the end of Chapter 5, Musical Excellence compares the results of their
study using strokes played by Dr. UKS to this theoretical model, and find
remarkable agreement in the frequency ratios of all the harmonics, including
the seven percent shift in the fundamental. This further validates the
continuous central loading model for the mridangam, and so, one may be able to
use such a model to predict further musical outcomes (like the effect of
density variations in the black patch, for example). Further, in the same
section, Musical Excellence examines the time decay of various harmonics
excited by the ’chappu’ stroke, to investigate it’s polytonic nature. It is
indeed found that the second harmonic is the most prominent, and decays the
slowest (longest sustaining). However, it is also found that the chappu stroke
has a rich polytonic nature just after the instance of impact, with the third
harmonic even exceeding the second harmonic in magnitude over a short time
interval. The higher harmonics (including the third) decay faster than the
second harmonic however, resulting in a transition to a fairly monotone
sustained note after the first fraction of a second, which when tuned to the
’Sa’ of the singer, produces a very pleasing effect.

Finally, in Figure 5.13, Musical Excellence illustrates the importance of the
artiste’s expertise in creating these harmonics and other tonal qualities, by
comparing the FFT spectra of the chappu stroke played by two different
artists. The first one shows clear and sharp peaks at the harmonic
frequencies, which rise far above the background signals at other anharmonic
frequencies, while the second shows much broader peaks which are not as
clearly discernable since they are combined with background signals of
comparable magnitude at the anharmonic frequencies. Hopefully, having read
thus far, the reader can make a judgement on which is expected to elicit more
’naadham’!

###  5.6 Chapter Summary

This chapter of Musical Excellence thus uses the tools of Fourier Analysis and
time decay profiles to uncover the unique tonal signatures of various strokes
played on the mridangam and builds on the work of the previous chapter in
analysing the role of various material choices like cow or goat based
parchments, kucchi or thool etc, and other important factors like the skill of
the artiste on the tonal signatures produced by various strokes like dheem and
chappu. Further, it builds on the work of Dr. CV Raman by comparing various
models of central loading through the black patch to experimental data
obtained from advanced scientific instruments, thus giving further insight
into the source of harmonics in this instrument.

##  6 Towards Musical Excellence

The main thrust of Musical Excellence is to pioneer the use of scientific
tools in understanding the creation of naadham in the mridangam. To this end,
the authors have looked at each of the various factors involved - including
materials, construction, tonal properties and signatures and the skill of the
artiste. There have been insights gained from each of these perspectives about
the possible role of these different factors in creating the subjective
experience of naadham. For example, we have seen how the addition of
subsequent layers of black patch changes the frequencies of the strokes and
the ratio between them, until it stabilizes to a fixed harmonic value. We have
also seen how the insertion of kucchi creates sharper harmonic peaks for
chappu and araichappu strokes, and discussed the possible mechanism behind
this. The differences in tonal quality between thool and kucchi mridangams,
and goat and cow based membranes have also been quantified, and the importance
of the artiste’s expertise in producing these tonal outcomes has also been
qualitatively observed. The famed shifted fundamental has also been clearly
demonstrated, as has the rest of the harmonic sequence - validating the model
of Malu and Siddharthan [15]. These are a few of the research highlights of
Musical Excellence, scattered throughout the pages, in between elucidating
explanations and interesting conversations.

In Chapter 6, Musical Excellence synthesizes these findings and puts them
together with a few more interesting ones - including a comparison of the
harmonic nature of the mridangam and tabla - to present a full picture of the
understanding that has been gained from this daunting undertaking. In addition
to this, the authors use this understanding to propose solutions to the
problems of standardizing the design of the mridangam, and finding alternative
and sustainable materials for construction of the mridangam. Chapter 7 of
Musical Excellence gives us a brief glimpse into this future, through a
discussion of the SRI (Synthetic Rhythm Indian) Mridangam created by Dr. K.
Varadarajan.

###  6.1 Characterizing Mridangams - Spectral ratios and time decay

As mentioned earlier in this review, Musical Excellence establishes ratios
between the frequencies of various strokes as characteristic of the mridangam,
within error bounds: dheem to non-observable fundamental (1.07 $\mp$ 0.05),
dheem to chappu (0.534 $\mp$ 0.005) and nam to chappu (1.5 $\mp$ 0.012 - (i.e)
third to second harmonic). To find additional parameters of characterization,
the authors further examine the time decay of the intensity of the dheem
stroke in Figure 6.9 and the corresponding discussion and find a
characteristic first-order decay rate constant of 2.02 s-1, in addition to
certain additional fine features like a beating pattern which could indicate
that the dheem stroke profile is actually a combination of two closely spaced
frequencies whose origin could well be related to the unique coupling between
the two membranes of the mridangam which share a single resonating column.
This bears further investigation, and is an interesting direction of future
research.

###  6.2 A comparison of Mridangam and Tabla - A case of resonating columns

The tabla, in many ways, is the counterpart of the Mridangam in Hindustani
music - due to its similar structure of membranes with a black patch, and
similar role in concerts. The major point of difference between the two is
that in the case of the table, the two membranes are contained in independent
resonating columns which are only coupled through the air between and around
them, whereas for the mridangam, both membranes share a common resonating
column and are thus more strongly coupled. Comparing the tonal properties of
these two instruments allows us to discern whether this coupling between
membranes is important to producing harmonics, a point that was alluded to
from the time of Dr. CV Raman. Upon obtaining FFT spectra for both Mridangam
and Tabla tuned to various frequencies, the authors of Musical Excellence find
that they are able to create a harmonic spectra in the tabla as well,
indicating that the coupling between the membranes through the resonating
column is not crucial to producing harmonics in these drum instruments, and
further highlights the role of the black patch in producing said harmonics.
Further, the authors are able to find notes played on the tabla that correlate
to those on the mridangam in terms of their frequency ratios to the unobserved
fundamental.

However, there are a couple of interesting points of difference as well. There
appears to be no equivalent note on the tabla for the Gumkki or Araichappu.
Also, the ratio of the frequency of Dhi (the closest note to dheem in tabla)
to fundamental is 1.12, which is different from the characteristic 1.07 for
mridangam. This also means that the other characteristic ratio we discussed
(dheem to chappu) would also be different for the table (In the case of the
tabla, the ’Tin’ note corresponds exactly to the second harmonic or chappu for
the mridangam), although the ’Na’ to ’Tin’ ratio corresponds exactly to the
Nam to Chappu ratio - reflected in the harmonic nature of the modes beyond the
fundamental for both instruments. Therefore, from this method of
characterization, Musical Excellence finds that the mridangam and tabla
produce distinct tonal outcomes - even though they are similar in construction
and production of harmonics.

###  6.3 Search for the fundamental mode - odd-even hypothesis

It is indeed an amazing fact that the shifted fundamental seen when playing
the dheem stroke exactly corresponds to the Rishabham or Ri note in Carnatic
music. In Chapter 6, Musical Excellence explores a hypothesis where the Dheem
note (which excites odd harmonics with a shifted fundamental) and the Chappu
note (which excites even harmonic) correspond to two independent harmonic
series - one corresponding to exciting axial modes and the other azimuthal
modes. It is seen that the fundamental of the latter is suppressed with
loading the black patch region, whereas the former remains prominent. Thus, it
is conceivable that the makers of the mridangam cleverly juxtaposed these two
independent sequences by accordingly adjusting the loading of the black patch
such that the fundamental of the odd sequence corresponds to the Ri note if we
fix the fundamental of the even note as Sa. This process - quantified by the
oscillations in dheem to chappu frequency ratio - is beautifully seen in
Figure 4.19 of Musical Excellence.

###  6.4 Alternative materials for resonating column, membranes, black patches
and insertion materials

Using the criteria of SRC discussed earlier, FRP (Fibre Reinforced Plastic)
and glass are presented as a possible alternative to wood for the resonating
column of the mridangam. These materials would render the mridangam much
lighter, and also allow for much smoother interiors of the resonating column -
which is expected to influence tonal quality.

As for the membranes, Musical Excellence discusses replacement of animal-based
membranes by Mylar and Remo FybreSkin and motivates these suggestions by
comparing the viscoelastic properties discussed earlier. It is found that
these alternatives can reach comparable ratios of elastic and viscous
deformations to the animal-based membranes, although the plastic component is
slightly higher. Additionally, these alternative membranes do not have the
same anisotropy in material properties along different directions as observed
in the animal-based parchments, since they are not dependant on fibre
arrangements and density. This also eliminates the non-uniformity in skin
between different animals and parts of the same animal, found in animal-based
parchments.

For materials which fill the annular space, the proposed alternatives are
divided into two main categories - materials that are distributed through out
the annular space (thool-like) and materials that are inserted radially with a
uniform separation (kucchi-like). Since the primary role of the annular
material seems to be to arrest or amplify different vibrations and harmonics
(As mentioned in Section 5.1.2 of this review, radial insertions enhance modes
with nodal diameters (i.e) Chappu and Araichappu whereas distributed
insertions enhance modes with nodal circles (i.e) Dheem and Nam ) , analysis
is done using ASDR profiles - a common type of time decay profile (which we
discussed in general before). ASDR stands for Attack, Decay, Sustain and
Release of the musical signal - with Attack referring to the initial run-up
from zero to highest intensity, Decay referring to the subsequent run-down to
the level of intensity that is sustained, Sustain referring to the level of
intensity maintained during the majority of the sound’s duration and Release
referring to the final run-down to zero intensity. A schematic of an ASDR
profile is shown in Figure 21.

Figure 21: Schematic of an ASDR envelope. Image credits:[16]

For the thool replacements, steel balls of various uniform diameters are
distributed throughout the annular space. For the kucchi replacement, Telfon
strips of various uniform thicknesses are placed radially in the annular
space, as metallic strips are found to add additional noise to the spectrum
due to their own timbre. The authors are able to generate comparable ASDR
profiles and FFT spectra for the various strokes using these alternatives,
which also have the additional advantage of being of uniform thickness and
material properties, which could potentially reduce tonal imbalances. In the
case of radial insertions, it is found that thinner materials which have no
metallic timbre of their own function well as dampeners.

The black patch is a crucial element of the unique tone of the mridangam, and
thus finding potential alternatives for the Iron oxide based black patch
material and the cooked rice adhesives is an important problem. Musical
Excellence examines various adhesive materials through their compressive
strength and found that polymers like Carboxyl Methyl Cellulose (CMC) and Poly
Vinyl Pyrollidone (PVP) performed better than cooked rice, and thus could be
potential replacements which prolong the life of the black patch. As for the
black patch material itself, replacement of the iron oxide with zirconium
salts to produce a white patch was experimented with. Upon constructing an
instrument with such a white patch, it was found that significant deviations
of the dheem stroke from the expected shifted fundamental was observed, even
though the harmonic nature of the higher harmonics was retained. This shows
that the material properties of the iron oxide black patch are important to
the tonal properties of the mridangam, and this is a promising direction of
further investigations.

Additionally, Musical Excellence also considers the effect of treating the
parchments with different tanning agents through comparing their porosity and
densities, and their viscoelastic properties. Even though it was found that
treating with tanning agents did not significantly affect tensile and other
physical properties, the tonal properties were found to be inferior to the
untanned parchments.

###  6.5 Alternate Mridangam Designs

To round off Chapter 6, Musical Excellence presents several interesting
designs for transport-friendly mridangams and evaluates the tonal properties
of these designs through constructed prototypes. We saw in earlier sections
that the nature of the harmonics produced by the mridangam are crucially
dependent on the black patch, but not significantly affected by the resonating
column. Musical Excellence uses this to its advantage by developing
alternative designs that modify the resonating column to make it more
transport friendly, thus hoping to retain the tonal qualities. These are then
characterized using FFT profiles and time decay of strokes played by Dr. UKS,
similar to analysis done in previous chapters. Design I considers a mridangam
that is split into four parts, which can then be reassembled easily. The
buffalo hide straps were limited to the parts on the extremities, while the
central wooden resonating column is bare. The tonal properties were reproduced
sufficiently well, with surprisingly sharp harmonic peaks. However, the
challenges in this design are the difficulty of fabrication and the still
insufficient tonality from the artiste’s point of view. Design II considers a
foam based resonator which can be attached on to and removed from the
mridangam body as required. However, the tonal quality of this design was
inferior as evidenced by broader harmonic peaks across most strokes played.
ASDR profiles also reveal that the sustenance is insufficient. Design III is
similar to Design I, but made so that outer parts go inside the inner
resonating column parts, making it further suitable for transport. The tonal
qualities and harmonic peaks were similar to Design I with similar drawbacks.
Design IV considers a telescopic design, and Design V considers a 3-in-1
mridangam with multiple heads with varying tonal properties being placed
inside the same body of the instrument. This design too produced sufficiently
sharp harmonic peaks, but the tonal quality was not sufficient from the
artiste’s point of view.

Thus, while the fundamental features like the shifted fundamental and the
dheem to chappu frequency ratios are demonstrated in these prototypes, their
tonal quality remains to be rigorously evaluated by artistes and scientists
alike. However, Musical Excellence does give us a lot of the tools necessary
for this task.

These alternative materials, designs and the analysis techniques used to study
them enable Musical Excellence to take a big step towards accomplishing its
stated goals of standardizing materials and fabrication of the mridangam,
develop sustainable alternatives and improve tonal outcomes. Along the way,
Musical Excellence has contributed greatly to understanding the tonal
qualities of this unique instrument.

Figure 22: Prototypes of various alternate mridangam designs discussed in
Musical Excellence

###  6.6 SRI Mridangam - a vision to the future

The final chapter of Musical Excellence concerns the SRI Mridangam, a design
established by Dr. Varadarangan, an excellent first step towards the
standardization of synthetic mridangams. Taking inspiration from Western
drums, the drum head is made out of polyester film and the black patch out of
a special type of rubber that is chemically bonded to the film. The wooden
shell is replaced with fibre glass, reducing the weight of the instrument
significantly. The drum head was attached to this shell with metal clamps
tensioned with nuts and bolts.

The overall final design was developed iteratively, and the whole process is
documented in an interesting way in the final chapter of Musical Excellence,
written by Dr. Varadarangan. The mridangam went through extensive testing to
ensure that it withstands wear and tear of daily use without damage, and the
final design is optimized to ensure such robustness. Further testing was done
to compare the tonal quality of the SRI mridangam to the traditional mridangam
across the various strokes played on the right drum head, and it was found to
have comparable tonal properties for each of the strokes.

The main advantages of the SRI mridangam are that it is environmentally and
animal friendly, light weight and easily transportable, has a consistent tonal
quality that is robust against external conditions, a wide tuning range, and
easier to maintain. While it is a great feat that a comparable tonal quality
to the traditional mridangam has been achieved in terms of FFT spectra and
time-decay profiles, it will be a test of both the instrument design of the
SRI mridangam and these characterization methods which we have extensively
discussed here, to see whether these results translate into a similar
subjective listening experience as the traditional mridangam.

###  6.7 Chapter Summary

The final chapters of Musical Excellence thus looks towards the future in
improving our understanding of this wondrous instrument by presenting
hypotheses and interpretations of the source of its unique tonal properties,
especially the shifted fundamental. Further insight is also gained by
comparing the tonal signatures to that of the tabla, which also allows one to
understand the role of the common resonating column in the case of the
mridangam versus the independent resonating columns in the case of the tabla.
The second major objective accomplished by these chapters is synthesizing the
knowledge gained from the comprehensive analysis done to propose new designs
for the mridangam that satisfy modern requirements of sustainability, animal-
friendliness and transportability, while retaining the essential tonal
qualities. Of course these designs and the materials involved will have to be
improved upon and optimized, but Musical Excellence offers both a great
starting point for new designs and solid framework for improving these designs
using objective scientific analysis that is augmented by artistic insight.

##  7 Epilogue

Scientific analysis of musical instruments is a field which has yet to reach
maturity both in terms of clearly establishing relevant scientific questions,
and the techniques used for such an analysis. While important scientific
breakthroughs regarding the structure and the production of musical notes have
been made especially in the case of the violin, a unifying framework of
questioning and analysis is still lacking. The fact that music is a subjective
human experience means that it is exceedingly difficult to establish what
questions can be asked that can be evaluated scientifically. These factors are
further magnified in the case of Indian instruments since the materials used
and processes of fabrication, which are millennia old, are typically only
known by generations of skilled artisans who learn these through an
experiential and oral tradition. Thus, the task set forth for Musical
Excellence is indeed a daunting challenge.

The main factor which has allowed Musical Excellence to surpass this challenge
is the close collaboration between a legendary artist in Dr. UKS, eminent
scientists in Dr. Ramasami and Dr. Naresh, and a skilled artisan in Sri
Johnson. Through this collaboration, the authors of Musical Excellence first
focus on establishing the current level of understanding about the
construction and music produced by the mridangam, and laying down the
important research questions that can potentially be addressed through
scientific analysis. The authors then go on to establish the current level of
scientific understanding and the scientific tools that could be used to
address the above questions. Then, following rigorous scientific
investigation, Musical Excellence is able to establish important results that
improve our understanding of both the construction and materials of the
mridangam and the unique nature of musical notes produced - like the
observation of the shifted fundamental excited by the dheem stroke, the role
of various annular materials like kucchi and thool and the importance of
layer-by-layer application of the black patch - thus validating and moving
beyond the work of Dr. CV Raman. Finally, the authors also use the improved
understanding that has been gained to propose new designs and standardization
techniques for the mridangam, laying the foundations for a future in which the
mridangam is both travel-friendly and made from sustainable materials in a
standardized fashion, yet preserving the signature naadham of the traditional
mridangam.

Musical Excellence of Mridangam by Dr. Umayalpuram K Sivaraman, Dr. T Ramasami
and Dr. M D Naresh is thus an important body of research in the field of
Carnatic music and even music in general, and is a shining example of how
scientific research can be done in a field that is built on human subjectivity
and whose subject is shrouded in ancient myths and mysteries.

## References

  * [1] “A practical guide to using an oscilloscope.”  Available at https://predictabledesigns.com/practical-guide-oscilloscope/.
  * [2] “Periodic signals.”  Available at https://cnx.org/contents/pgrh5dEe@15.5:-TFMBEPB@2/Periodic-Signals/.
  * [3] Available at https://vivadifferences.com/differences-between-periodic-and-aperiodic-signal.
  * [4] “Creating Rhythm games.”  Available at https://www.moddb.com/games/star-story-the-horizon-escape/news/reating-rhythm-games.
  * [5] J. Zhang, L. Zhang, X. An, H. Luo, and K. E. Yao, “Adaptive coupled synchronization among three coupled chaos systems and its application to secure communications,” EURASIP Journal on Wireless Communications and Networking, vol. 2016, p. 134, May 2016.
  * [6] “The Harmonic Series and its implications on composition.”  Available at https://www.zotzinguitarlessons.com/blog/the-harmonic-series-and-its-implications-on-composition/.
  * [7] The combination of different waves was done using the software package Mathematica. Code is available on request to corresponding author.
  * [8] “CUNY Physics Labs - Spectroscopy Experiment.”  Available at https://physicslabs.ccnysites.cuny.edu/labs/204/204-spectroscopy/spectroscopy.php.
  * [9] “Physics, guitars and pitch harmonics.”  Available at https://skullsinthestars.com/2008/09/30/physics-guitars-and-pitch-harmonics/stringmodes/.
  * [10] C. V. Raman and S. Kumar, “Musical drums with harmonic overtones,” Nature, vol. 104, p. 500, 1920.
  * [11] C. V. Raman, “The Acoustical Knowledge of Ancient Hindus,” Asutosh Mookerjee Silver Volume 2, p. 500, 1922.
  * [12] C. V. Raman, “The Indian Musical Drums,” Proc. Indian Acad. Sci., vol. A1, p. 179, 1935.
  * [13] B. S. Ramakrishna and M. M. Sondhi, “Vibrations of Indian Musical Drums regarded as Composite Membranes,” J. Acoust. Soc. Am, vol. 26, p. 523, 1954.
  * [14] R. Siddharthan Physics Education, pp. 304–310, Oct-Dec 1994.
  * [15] S. S. Malu and A. Siddharthan, “Acoustics of the Indian Drum,” 2000.
  * [16] T. Kvifte, Instruments and the Electronic Age: Toward a Terminology for a Unified Description of Playing Technique.  Solum Forlag, 1989.