Dear Lyle and Group,

Thank you very much for your document, which I have reformatted and will
pass on in its entirety to the Group here. It is fascinating. Ernest ought
to go nuts (in a very positive way) over this information.

The amazing thing to me is that I understand most of what is being said,
even if many of the Indian terms as such are yet unknown to me. Here you
offer another theoretical possibility related to the number 22, and once
again one based on tuning. Perhaps one may already hypothesize that in the
conceptions of various peoples, 22 relates symbolically, one way or another,
to the "harmony of the spheres". [As an aside: the very practice of Egyptian
chironomy in antiquity was so related. The goddess of music was said to have
ordered the cosmos by her musically-based gestures. It's noteworthy in this
light that the Egyptian chironomic scale was pentatonic, and had 11 degrees.
Both in its particular intervals and in its total range, harmonicity was its
hallmark.] Intuitively, that makes a great deal of sense to me. Perhaps the
fact that biblical Hebrew has 22 letters, no more, no less, was meant by the
Israelites to symbolize the order of the physical and spiritual world (cf.
the comparison made between heavenly order and Divine =torah= in the text
and music of Psalm 19, for example). As little as I know of kabbalistic
thought, I nevertheless suspect that there one could find ample
documentation of such a conceptual connection between the alphabet and the
order of the cosmos (again, both physical and spiritual).

It appears that the problem with tuning a =tamboura= lies not in tuning the
strings -- that should be a straighforward job once the tonic is determined
-- but in adjusting the bridge so that the proper overtones are produced.
The need to be careful about choosing the wires (strings) is noted also, and
this too makes sense. Something else is intriguing: it appears that the
tonic pitch and all the intervals (each interval being a =sruti=) that
relate to it are in some way derived from or harmonized with the natural
resonance frequencies of the player himself, and indeed of his environment.
That is remarkable sensitivity! Here the idea of =ethos= or moral force in
music is being extended to the greatest limits of any culture I know
of...something Curt Sachs' old book THE RISE OF MUSIC IN THE ANCIENT WORLD:
EAST AND WEST presaged for me a while back.

Which reminds me: a minister/musician friend asked me, "What pitch standard
would the Hebrews have used in their cantillation?" The only possible
alternative that the Bible actually mentions lies in the paired silver
trumpets, which (according to Josephus) were just under a cubit long. Now it
so happens that one may mathematically calculate the basic (and uncorrected)
pitch of such an instrument according to the air temperature and the length
of the vibrating column. The resultant pitch will change according to the
air temperature. Perhaps using such a set of relative rather than absolute
"pitch pipes" was a simple, practical way not only of tuning the instruments
and voices to a tonic -- that much would be obvious -- but to idealizing
that pitch to the outdoor conditions.

Sachs thankfully tells me (op. cit., p. 28) what a "cent" is. 100 cents
equals a half-step or semitone on an equal-tempered piano scale. One octave
is 1200 cents. As Sachs says, single distances as well as complicated scales
become (for us in the modern West) simple and intuitively evident by this
means. (The actual numbers of cents cannot be derived directly from a voice
or a measuring device; they must be calculated mathematically from the
vibrational frequencies.) So 24 cents (a microtonal interval mentioned in an
interviews you cite) goes into a piano's half-step 4-1/6 times.

Best wishes,

John Wheeler
King David's Harp, Inc.
http://www.kingdavidsharp.org
http://www.rakkav.com/kdhinc/

===========================

http://www.ragascape.com/Ragascapes/4.html

Tambura

It seems appropriate to write the first ragascape essay on the tambura, as
the all-encompassing sound of this instrument is the source from which arise
the melodic centers (notes) of Indian music. The tambura is more than just a
four-stringed instrument providing the sonorous drone and the basic
environment in which the music enfolds.

The tambura is the acoustic potential for the whole harmonic series; and, as
such, represents the cosmic potential for all apparent phenomena. Although
the tambura is tuned with three strings tuned to the tonic (in Indian music
we call this tonic Sa or shadja) and one string to the fourth or fifth, we
can find all twelve notes in the harmony that is created by the four strings
vibrating simultaneously. This acoustical phenomena occurs because the
harmonic series is activated through a process called jawari or cyclical
wave formation in which the bridge upon which the strings are resting is
filed into a particular curve. When this process is completed properly, the
notes are no longer just blunt tones but rather rich tonal landscapes with a
precise sharp center and expanding periphery.

Like a mirror, the tambura has the capacity to reflect whatever is sung or
played 'over' it. For example if you sing a note along with the tambura
other than the notes that are part of the tambura, you can hear the tambura
mirror that sound and 'sing' it back to you. The tonic in this instrument
has the capacity to appear in the form of whatever you place before it. It
is as if you took a piece of clear glass and put it on top of a blue cloth.
The glass does not become blue, but it appears blue. In this way the tambura
is an acoustical symbol of total integration. When tuned properly, the
tambura is a clear support for the vocalist or instrumentalist. He listens
to the tonic note of the tambura, integrates with it, and adjusts his 'sur'
so that each note finds a perfect resonance in the vibrational field of the
tambura. Notwithstanding the great support the tambura provides to a
musician, it is possible for Indian musicians to sing or play tunefully
without the support of the tambura. By tuning into the anahata (unstruck)
quality of the tonic, the musician becomes his own silent drone; and as he
begins to vibrate with the tonic, his tuneful precision arises. This is
obviously more difficult as there is no external support for the tuning.

The tambura, as a plucked instrument, is the acoustical metaphor for all
unstuck sound. It represents the empty side of clarity and the potential for
all apparent phenomena. It is the feminine space to be filled by the
masculine skillfulness of melodic form.

When a musician plays or sings along with the balanced stroking of the
tambura, it is not the case that he hears two different sounds-the droned
tonic of the tambura and the sound of his voice or instrument. He plays and
at the same moment releases the melodic configuration into the field of the
tambura. The artist blends with the space filled by the cyclical expansion
and contraction of the tambura and allows the tonal centers of his melody to
spread into that edgeless expanse. When he does this without conceptualizing
either the sound of his creation or that of the tambura, there is a moment
when the division between singer, song, and the act of singing dissolves.
The artist, fabricator of forms, suddenly jumps the hoop of time and space
and enters the dimension where pure sound becomes a vehicle to supersensory
cognition and awareness. Although conventionally we say that the singer is
singing a song, in this case it is as if the song is singing the singer.

Steve Landsberg
Santa Fe, NM USA
3-Sep-1999

http://www.peruvianwhistles.com/breath.html

Hazrat Inayat Khan taught that sound, in addition to creating its resonance
in the physical body, makes a particular impression upon the essence or
innermost Being of man. Music is a bridge over the gulf between the exterior
form of man and the formless world of the spirit. Although it suggests no
outward form, music creates a resonance which vibrates through every atom of
a person's Being, momentarily lifting thought beyond the denseness of
matter. That is why music is considered by the Sufis to be "the food of the
soul," and is employed by every religious tradition as a source of
inspiration.

Realized musicians reach the deepest levels in their listeners by
consciously expressing their relationship to their audience through an
ever-changing sense of harmony. The first thing that a player of Hindu music
does is tune his tambura (a stringed instrument). While doing so, the
musician is tuning his innermost Being to the quintessential moment to
moment, and this of course, has a great effect upon his listeners. The
audience can wait patiently, often for considerable lengths of time, until
the musician feels perfectly and wholly in tune with the entirety of his or
her environment.

A person with a sensitive heart listening to this will perceive the way in
which the musician tunes his own spirit, the way that he modulates his voice
into the chord that he has chosen to play. By the time the performer is
concentrated, he has tuned himself to all who are present. Not only has he
tuned his instrument, but the musician has "felt" the need of every soul in
the audience, and as he begins to play, it seems to touch everyone who is
listening.

This music is the answer to the demand of all of the souls gathered to
listen. There is no program in a performance of this nature, the musician
can not know in advance what he will play. Each performance is inspired by
the entirety of the moment, and ideally, is a flowing model of harmonious
Being. The musician is in fact the instrument of the whole cosmic system,
open to all inspiration and at one with the audience. When a musician has
reached this level of sympathy it is not only music that he plays, but
spiritual phenomena that he brings to life...

http://www.narada.org/kvn/address.html

Those who seek to learn South Indian classical music must aim at tonal
excellence in tune with 'sruti'. Let me share with you my thoughts. We must
learn to sing with a full voice and even those who learn instrumental music
must learn to play in perfect harmony with 'sruti'. They must learn to tune
the thambura and set it to the 'sruti' required for the occasion. To explain
this aspect, I wish to recall an incident which took place at the University
of Wesleyan in America in the year 1966 Dr. Robert Brown. then professor,
University of Wesleyan, told me that he would be sending an unusual student.
This person came and said that he only wanted to learn how to tune a
thambura and produce the required 'sruti' and not to learn vocal music,
violin or mridangam. I was pleasantly surprised. The trainee applied himself
totally to that task and within one month acquired mastery over tuning the
tambura and ensuring the required 'sruti'.

http://www.narada.org/kvn/intview1.html

Chief Casualties of Today's Music

Purity of sruti and purity of note positions on the scale seem to be the two
chief causalities in Carnatic music today, probably because of the demand
for spectacular music and the lack of time and patience on the part of
musicians, both young and not so young. What can be done to remedy the
situation ?

Yes, sruti suddham and swarasthana suddham are two areas in which we have
slipped badly in Carnatic music. Sruti is probably the most important thing
to a musician. For getting sruti gnanam, there's no better method than
tambura-playing. But the alignment of a tambura is a technically difficult
task for a new learners. Such people can use electronic sruti boxes, which
are easy to handle, or even the plain old-fashioned sruti box with bellows.
Staying perfectly in sruti and practicing-that's all there is to good music.

There are many overtones in the sound of a tambura. Therefore there is need
for one to be finicky about the wires to be used in the tambura. While I was
teaching in college, I used to devote one whole class-period to train my
students in this. I would say everyone should know how to handle a tambura
and align its sruti. Just as a mridangam vidwan attends to his mridangam and
keeps it correctly tuned and serviced, the vocalist should regard the
tambura as his instrument and keep it perfectly aligned and neat. The
tambura and sruti are what make the music possible.

I had once been to AIR-Bangalore where I met this tambura artist--I'm sorry
I don't remember his name. It was a joy listen to the sound of his tambura,
such was the flawless perfection with which he had both maintained it and
tuned it. He said to me: "This [keeping perfect sruti] means much more to me
than just a job."

On another occasion, a disciple of Pandit Jasraj strummed the tambura for me
at a radio recital in Bombay. After finding what my sruti was, he got the
tambura aligned in less than two minutes. It was absolutely miraculous, even
divine. I confessed to him: I can't do it so superbly or so quickly. I kept
watching him to try and understand the secret of mastery over the
instrument. At the end of the recital, he complimented me on my singing but
I told him that a lot of credit for it belonged to him and his tambura
expertise. Later I wrote to AIR-Bombay commending the supreme quality of
this tambura artist and telling them they were lucky to have such a gifted
person on their staff.

I must also mention this boy who was among those I was teaching when I was
in America. He wanted to be a tambura player only. Really! He said to me:
"Teach me to handle tambura perfectly. That'll do for me." I said I would do
that gladly and I taught him for a month. He perfected the art by constant
practice and could derive immense pleasure merely playing the tambura and
listening to its drone in perfect alignment with sruti.

One of my dreams--up to now unfulfilled, alas! -- is a each of us should
have a first-grade tambura, beautifully tuned and perfectly aligned and,
every day, we should go to sleep and get up in the morning listening to the
tambura sruti for a few minutes!

I shouldn't lose this opportunity to say that we need to improve the lot of
the artisans who make tamburas. Many of us are concerned with sruti and the
tambura but not about those who make the instrument. There are
government-aided institutions and fairly large commercial establishments
producing tamburas and other instruments but a large number the producers
are private individuals. They should be well supported with finance and
materials. Good jackwood and other tree wood which can be used for making
tamburas should be given to them in sufficient quantity and their craft must
be sustained and encouraged in other ways as well.

As regards swarasthana suddham, there is nothing else that will help a
musician to achieve it except practice. When we were in San Diego a year or
two ago, we stayed with an Indian compatriot --Ananthan-- in his house. He
told us about an experience he had when Bhimsen Joshi and his party were
similarly staying with him earlier on. As he narrated it, Panditji was
occupying a room in the basement. Every morning he did riaz from four to
six. He did sadhakam only in the mandhra stayi [lower register], staying
long in each swarasthana, all the time perfectly aligned to sruti. Anantha
would listen to Joshi Saheb for the entire two hours as he practiced
'aakaram' and 'eekaram'. Now, how can a musician stray from sruti or the
correct swara position if he is so painstaking?

http://encyclopedia.thefreedictionary.com/sruti

A sruti is an interval between two consecutive notes in music. There are 22
srutis in an octave, in traditional Indian musical tuning.

http://www.microtonal.co.uk/start.htm#JI
on various tuning systems

http://www.themusicmagazine.com/kvranganint2.html

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Discernment. Online

Varadarangan lives in Bangalore, and works for Harita Networks, a private
firm with an office near Double Road

'Ancient musicologists, who had deep insight, used special instruments like
the dhruva (fixed) veena and chala (movable) veena to arrive at 22 srutis'

'The 22 srutis are actually frequency intervals and hence the adhara shadja
should not be included in their reckoning'

'A clear understanding of the 22 srutis will enable us to sing and play the
ragas better and with greater feeling'

'Because of the Western tempered scale, individual notes lost their melody
to a noticeable extent''

'Veenas with 22 frets have been built, but they are impractical when it
comes to actual playing'

'Dissonance in orchestral music may be avoided by carefully tuning our
instruments to a reference frequency standard. This implies that we
understand the 22 srutis correctly so that we can create a frequency
standard of our own'

Quick link

Read earlier interview with Dr K Varadarangan

Review

Eureka! It's 22 srutis

An excited Dr K Varadarangan talks about his 'tryst with truth' that could
help settle an ancient debate about the octave, and validate the greatness
of ancient Indian musicology

Dr K Varadarangan wrote in a couple of months ago about what he described as
a breakthrough in musicological research -- he had, by using a software
program he had developed, arrived at conclusions that could settle a crucial
debate that had engaged the minds of musicologists for centuries. When I
spoke to him over the phone, he was all excited. He said he had come "face
to face with the truth", and was confident he could now once for all answer
the question why Indian musicology believes in the idea of 22 srutis an
octave.

I then sent the researcher-musician some questions from a non-mathematician
perspective, and he promptly e-mailed his answers. The issues he speaks
about call for some acquaintace with music theory, but he states his case in
plain words, and looks at questions that even popular music lovers would be
curious about -- like whether his discovery could give rise to a new
generation of synthesizers with 22 keys in an octave instead of the present
12.

For those who haven't been following Varadarangan's career -- he lives in
Bangalore, and works for Harita Networks, a private firm with an office near
Double Road. He comes from a family of writers. Pu Thi Narasimhachar, his
uncle, wrote several operas, one of which (Gokula Nirgamana) has seen a
revival in recent days, thanks to the Ninasam theatre institute in Heggodu.
Their recent show in Bangalore and other cities won audience praise for
lilting music composed by B V Karanth.

Varadarangan's office was earlier on Bannerghatta Road, where I met him a
couple of times. He is very happy interacting with readers of The Music
Magazine, many of whom keep in touch with him and update themselves on his
research.

You say you have arrived at a breakthrough that settles an age-old debate
about the number of srutis in an octave. Indian musicology had arrived at
22, and you now say you have mathematical evidence to prove this right. How
did you arrive at this discovery?

The concept of 22 srutis has existed for a long time in Indian musicology.
Ancient musicologists, who had deep insight, used special instruments like
the dhruva (fixed) veena and chala (movable) veena to arrive at this number.
It is difficult because of their subtlety to show the existence of these
microtones, and this has perhaps led to conflicting observations about the
number of srutis within an octave.

The subjectivity vanishes once we formulate the srutis mathematically, when
every sruti is quantified precisely. This is exactly what I have done. In my
earlier work I had derived the relative frequencies of the 12 swarasthanas
by using traditional srutibedha formulas found in our musical literature and
known very well to our musicians. I have now prepared a srutibedha chart for
these 12 swaras. It is a comprehensive chart which takes each of these 12
swaras as a moorchana swara, and tabulates the new relative frequencies that
result from a shift of tonic. (For example, suddha madhyama sounds exactly
like sadharana gandhara when the tonic is changed to chatusruti rishabha).

When we look at my chart, we find that exactly 11 new frequencies result in
addition to the existing 11 srutis (excluding the adhara shadja), thus
making it exactly 22 sruthis, no more, no less! For example, anthara
gandhara sounds approximately like suddha rishabha when sadharana gandhara
is made the tonic. In fact, this approximate sruti is actually a new sruti,
which is higher than suddha rishabha by a pramana sruti (also known as a
Pythagorian comma).

In this way new srutis result. Note that our musicologists always
interpreted sruti as an interval. We should not consider adhara shadja as a
sruti by itself. This observation that the additional 11 srutis are embedded
in the already existing 11 srutis, and reveal themselves when there is a
modal shift of tonic, is the essence of my discovery.

As I have shown in my earlier work (readers may kindly refer to my paper
Determination of the Relative Frequencies and Fundamental Properties of
Swaras by Modal Shift of Tonic published in the Journal of Music Academy,
Madras, Vol LXXI, Year 2000), the interval between adjacent swaras in our
music scale is not a constant. It is either 90 cents or 114 cents and the
difference of 24 cents between these two is known as a 'pramana sruti'. The
11 additional frequencies mentioned above result from the "modulation" of
the existing 11 sruthis by the pramana sruti. The 22 srutis computed above
tally perfectly with those computed from the cycle of fourths and the cycle
of fifths.

They say many previous musicologists like Prof Sambamurthy had "adjusted" a
few frequencies to arrive at 22. You now feel this is erroneous and that
there is no need to "adjust" anything. Can you explain, for the benefit of
non-mathematicians, what the debate is all about?

Prof Sambamurthy's work is remarkable in the sense that the rather vague
subject of 22 srutis was given a clear mathematical foundation. However,
there have been two errors in his depiction of the 22 srutis:

The value of pramana sruti is actually 24 cents rather than 22 cents. This
error is negligible from a practical viewpoint but theoretically important
(see for example, page 47, Vol V of his South Indian Music ). Also, the
value of the nyuna sruti should be 66 cents rather than 70 cents. He gives
the value of the purna sruti correctly as 90 cents. Since the pramana sruti
interval was taken as 22 cents, he had to adjust the frequencies computed by
the cycles of fourths and fifths by 2 cents (see page 43 of the above book).
The 22 srutis computed by me agree perfectly with the cycle of fourths and
fifths and there is no need to adjust anything.

Secondly, a sruti with relative frequency of 678 cents (which is close to
panchama, being lower by a pramana sruti) is omitted from the list of 22
srutis for some mysterious reasons (see page 40 of his book). This frequency
comes both in my computation and in the cycle of fourths. He has probably
omitted it to fit everything into a 22 sruti system that includes the adhara
shadja.

As I have mentioned earlier, the 22 srutis are actually frequency intervals
and hence adhara shadja should not be included in their reckoning.

What bearing do you think your discovery will have on the practice of music?
Will it prompt musicians to reconsider the srutis they have been singing?
And if that happens, will it change the nature of ragas from what we now
know them as?

A clear understanding of the 22 srutis will enable us to sing and play the
ragas better and with greater feeling. It will also help immensely in
teaching our music to students. For example, we can tell the student that
the so-called suddha madhyama of raga Begada is actually higher and he
should use the next higher variety of madhyama (in the scale of 22 srutis),
and so on.

I don't think that we need to reconsider any srutis that we have been
singing. On the other hand this tells us what sruti we are using and we
become more aware. My discovery may not change the nature of any raga, but
may make it easier for us to teach the subtleties in ragas.

What does your study tell you about the history of the 22 srutis?

It is quite likely that many scholars have contributed to the evolution of
the 22 sruti system and Bharata was probably the first to describe it
systematically. When you look at the subtleties of this sruti system, it
appears to me that all of it could not have been conceived by a single
person in one shot.

Has any other musical culture arrived at 22? How is our division different
from the Western view of the octave?

When we study the evolution of musical scales we do find that more than 12
notes have been conceived by other cultures as well (see, for example,
Chapter 5 of the book Science and Music by Sir James Jeans). However,
Western music developed on the lines of polyphony and hence an equal
temperament scale became an absolute necessity. Once the scale became
tempered, there were exactly 12 notes, each placed 100 cents apart. Whatever
the key, the frequencies always match, producing harmony in a polyphonic
situation. However, because of this equal temperament the individual notes
lost their melody to a noticeable extent. As I have said, the interval
between adjacent srutis in our scale of 12 notes is not constant. It is
either 90 cents or 114 cents. It is precisely this difference that gives
rise to the additional 11 sruthis in our musical scale, totalling 22 srutis.
In the equi-tempered scale the difference between adjacent notes is
constant, and hence there is absolutely no scope for additional frequencies
or srutis to be generated.

Talking of practical applications, do you think your breakthrough could lead
to the designing of keyboards with 22 keys in an octave so that they can
handle all the nuances of Indian music? The harmonium, the piano and the
electronic keyboard, with 12 keys to an octave, cannot capture any of the
microtones that Indian music is famous for.

In fact such experimental veenas have been constructed. I don't know whether
it is practical to play such an instrument. The point, however, is that it
is possible to play the 22 srutis even on an ordinary veena by appropriate
pulling of strings. On a keyboard instrument this is not possible and we
should have separate keys. But even here, it may not be possible to handle
the nuances in ragas because of the instruments' inability to produce the
characteristic gamaka or meend. In other words, the 22 srutis are necessary
but not sufficient to make the intricate melody of ragas.

What is the next step in your research?

I would like to synthesize the srutis electronically to find out how exactly
the 22 srutis sound and interpret the srutis we use in various ragas. I
would also like to explore the concept of consonance in greater detail. I
feel we have not yet fully understood what really makes a frequency a
consonant one.

Do you plan to publish your work in book form? Your last book has caught the
attention of serious musicologists all over the world, some of who contacted
you after reading your interview in 'The Music Magazine'.

Yes, definitely. I am already in the process of writing such a book. I must
also thank The Music Magazine for giving wide publicity to my earlier work.

Do srutis change between instruments? In other words, would the gandhara of
a south Indian veena be different from the same gandhara on the sitar or the
nadaswaram or the flute? If the answer is yes, what happens during
orchestral compositions and jugalbandis? Is there a mismatch of shrutis that
our ears cannot discern, or have we learnt to ignore those differences?

I think this is quite possible. We tune our instruments purely by perception
and the tuning is within the limit of judgment of the player of the
instrument. I have heard many orchestras where I recognize some dissonance
because of the perceptional differences of individual players. Also, the
same raga (say Mohana/Bhoop) is played differently by Hindustani and
Karnatak musicians. Dissonance in orchestral music may be avoided by
carefully tuning our instruments to a reference frequency standard. This
implies that we understand the 22 srutis correctly so that we can create a
frequency standard of our own.

Tell us something about the Indian idea of consonance and dissonance -- the
concepts of vadi, samvadi and vivadi -- and how it is different from the
Western one.

The concept of consonance is fairly simple. Two notes are said to be
consonant if they blend melodiously when sounded together. This concept is
the same in Western music too. However, in Indian music this is further
elaborated by the introduction of the vadi, samvadi, anuvadi and vivadi
swaras. The vadi swara is a note which appears frequently in a raga and is a
vital note in that raga. A samvadi swara (relative to a reference note) is
essentially a consonant note. A samvadi note of the vadi swara is called as
an anuvadi swara. The vivadi swara is of course a dissonant note. Indian
musicologists have clearly defined consonance and dissonance in terms of the
differences in the srutis between them on the 22-sruti scale.

Western music does not have these subtle elements of consonance since they
have no concept of the raga. In our music consonance is intricately linked
to the raga. Interested readers may refer to an excellent paper on this
subject: Vadi, Samvadi, Vivadi, and Aanuvadi Swaras by N Ramanathan, pages
60-82, Vol LIV, The Journal of Music Academy, Madras, 1983.

Anything else you would like to add?

I would like to clear a common misconception that is associated with the
relative frequency ratios of our srutis. They say it is very difficult to
play or sing a complex ratio such as 729/512 (that of prati madhyama). This
is actually a misconception, which is removed once you see it as a number
and not a fraction. In fact we cannot produce exactly even the simple ratio
of 9/8 (chathussruti rishabha). The point is, while we sing or play we go by
perception and not by these numbers. It is however important that we stay
near these ideal values. The human voice can really make extremely melodious
music because it can hold on to these notes within the accuracy range of the
ear. Minor differences are ignored by our ear (actually the brain) and we
enjoy our music!

S R Ramakrishna

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