RMIM Archive Article "23".
From the RMIM Article Archive maintained by Satish Subramanian
#
# RMIM Archives..
# Subject: Instruments: "ABC of Keyboards"
#
# Author: "Rajan P. Parrikar" (parrikar@mimicad.Colorado.EDU)
# Posted by: "Rajan P. Parrikar" (parrikar@mimicad.Colorado.EDU)
#
WARNING: No attempt has been made at clarity in exposition nor is the
treatment exhaustive. Comments/criticism most welcome. Flames will be
amplified and returned. Anyone considering a serious study in Indian
classical music would do well to never go near a keyboard during the
first 6/8 years of your training.
Rajan
=====
The Musical Scale:
-----------------
Start with an arbitrary note on your keyboard of frequency, say f1.
Now progressively increase the frequency (effectively, moving towards
the right on the keyboard) until you hit the note that is of a
frequency f2 = 2*f1. In doing so, you are said to have traversed
one octave (saptak).
The octave is sub-divided into 12 notes (swaras) out of which 7
are called "shuddha" swaras, 4 are "komal" and 1 is "tivra."
The shuddha swaras ( the "sa re ga ma" we are so familiar with)
may be viewed as being the "integers" of the musical scale.
(The Western notation is provided merely for comparison and may
be ignored). I am providing the terminology used in Hindustani
system; be informed that the Carnatic system calls the swaras
by slightly different names.
The Saptak
---------------------------------------------------------------
Hindustani Symbol Solfeggio Symbol
Swara Names
----------------------------------------------------------------
Shadja (Sa) -----> S -----> Do -----> C
Komal Rishab -----> r -----------------> C# or Df
Shuddha Rishab (Re) -----> R -----> Re -----> D
Komal Gandhaar -----> g -----------------> D# or Ef
Shuddha Gandhaar (Ga) -----> G -----> Mi -----> E
Shuddha Madhyam (Ma) -----> M -----> Fa -----> F
Tivra Madhyam -----> m -----------------> F# or Pf
Pancham (Pa) -----> P -----> So -----> G
Komal Dhaivat -----> d -----------------> G# or Af
Shuddha Dhaivat (Dha) -----> D -----> La -----> A
Komal Nishad -----> n -----------------> A# or Bf
Shuddha Nishad (Ni) -----> N -----> Ti -----> B
------------------------------------------------------------------
>From the table above, you will see that there are 4 komal swaras,
viz., komal re, komal ga, komal dha and komal ni, and, one tivra
swara, namely the tivra madhyam. The shuddha swaras are denoted
by caps and the remaining 5 notes are denotes by lower case.
(The "#" and "f" under the Western notation denote the "sharp" and
"flat" notes, respectively. For example, A# is "A-sharp"; it is the
same note as Bf (B-flat).)
To summarize: if you select any arbitary key to be your Sa then
the progression of notes in an octave will be:
S r R g G M m P d D n N S"
(The '"` tagged to S indicates the Sa of the higher octave; that is,
the frequency of S" is twice that of S). Now let's have a look
at the keyboard itself.
The Keyboard:
------------
The figure below shows a mapping of the octave on a keyboard along
with the corresponding Indian and Western notation. All the twelve
notes are indicated in the figure.
The "Safed Ek" (the first white key) is selected to be the Sa (also
called the "tonic.") The corresponding swaras of the octave, then, are
as shown. All the white keys will correspond to the shuddha swaras
while the black keys will be the komal and the tivra swaras. (Western
notation has been provided merely for comparison and may be ignored).
There is nothing sacred about selecting Safed Ek as your tonic Sa. In
other words, the Sa is not absolute. But once you establish your Sa,
all the other notes assume recognition _with respect to the chosen
Sa_ and fall into place accordingly. You could well have chosen Kali
Ek key to be your Sa. As Homework Assignment #1, figure out what the
corresponding shuddha swaras are with Kali Ek as the tonic. Do the same
with Kali Chaar. (BTW, the Western nomenclature is fixed; that is,
C always remains the key shown in the figure and so on).
(safed C# D# F# G# D#
ek) r g m d n
| _________________________________________________
| | | | | | | | | | | | | | |
|-----o | | | | | | | | | | | | |
| | | | | | | | | | | | | |
.---------o | | | | | | | | | | | |
| | |___| |___| | |___| |___| |___| | |
| | | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
| |_____|_____|_____|_____|_____|_____|_____|_____|
| S R G M P D N S" (--|Indian
(kali (Sa) (Re) (Ga) (Ma) (Pa) (Dha) (Ni) (Sa) (--|Notation
ek)
C D E F G A B C (--|Western
(Do) (Re) (Mi) (Fa) (So) (La) (Ti) (Do) (--|Notation
Important: Note that the above configuration has been arrived
at by fixing Safed Ek as the Sa. You could well select any
other Sa and arrive at a different configuration. In HW #1, you
are asked to make the r above (Kali Ek) as your new Sa and map
out the resulting scale.
The Equally Tempered Scale:
--------------------------
At this point, a curious mind will ask: Why is the octave divided
into 12 divisions? Why not more (or less)? After all, more the number
of divisions, better the resolution. While these are perfectly
legitimate questions the answers are not so straightforward. In the
interest of keeping this discussion short I shall not go into the
details of the origins and development of the musical scale. It is
an interesting topic but will have to wait for another day. However,
I shall briefly tell you how your keyboard scale is configured.
As indicated earlier, from S to S", the frequency ratio is 1:2.
Our task is to divide the octave into 12 equal parts such that
the interval from, say S to r and say, P to d, are equal. Let us
denote this interval by x. Now, if you assign a value of 1 to
S, the relative frequency of note r is x, R is x**2, g is x**3
and so on. By the time you have hit S", you end up with the
equation x**12 = 2. The twelfth root of 2 is 1.0594 and therefore
x=1.0594. When the octave is divided in this manner (there are other
ways too), the scale so obtained is known as the "equally tempered"
or "tempered" scale. Most commercially available pianos and electronic
keyboards employ this division scheme. (I should slip in the fact that
to classical Indian music, this kind of division is anathema but
we're not talking classical Indian music here and so....).
Once again, refer to the keyboard map above. What is typically done
in your Casiotones or Yamahas is, the key A of the "central octave"
is assigned a frequency of 440 Hz. With the ratio of 1.0594 obtained
above and a pocket calculator, you can easily calculate the frequencies
of all the notes in your "central octave." They turn out to be (approx):
C = 261.6 Hz F = 349.3 Hz B = 493.8
D = 293.3 Hz G = 392.0 Hz C"= 523.2(=2*261.6)
E = 329.6 Hz A = 440 Hz
The Grand Finale:
----------------
Now that you are done with all the foreplay it is time to prepare
for the climax. That is, actually start playing a song on the
damn keyboard. Before you do so, you need to recognize that Indian
music is "melodic" in nature and that you will have to first
extract the Sa out of any composition. Anybody with an ear for
music can do this with a bit of practice. Once the base Sa has been
identified you can then get into the act of notating the song. _This_
requires helluva lot of practice and years of musical training.
One of the great things about Indian classical music is that it
imbues in the musician the acuity to strip any piece of musical
melody into its constituent sargam (notes) almost instantaneously.
But this skill is by no means trivial to attain and is acquired
only after several years of thinking and training in the art.
Since you have confessed to being a puppy in sangeet-kshetra your
best bet is to try getting a song right by simple trial-and-error
if no notational information is available. Besides playing simple
tunes, you can do a lot more with an electronic keyboard, like
learn to play chord sequences etc. Maybe I'll tell you about
it after you have gotten through the basics.
I am appending the notated version of "Madhuban Me Radhika" that
I had posted some weeks back. As for your farmaiesh, I shall get
you started on the opening syllables and leave it at that. At this
point in time, I don't have the stomach (literally!) to notate
the entire songs. Finally, I have not bothered to re-read my
meanderings above so forgive me for any lapses.
You will have to do some extrapolating to get the timings right.
1) Ek do teen char paanch..
1 2 3 4 5 6 7 8 9 10 1...1 1...2 1...3
S R G... R G R G R S S R g R g R S
(Which luminary wrote these lyrics?)
2) Maine tere liye hi saath rang ke..
D P R G R G M P
3) Zindagi ek safar hai suhaanaa..
g R S g R S S R g M
4) Madhuban me Radhika..
Asthaaie:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
P . . . . . m P G M
ma dhu ba na me ra - aa dhi ka - aa
(N)D . N . S" . Pm P G M R . G MD P .
na - che - re - gi ri dha ra ki mu ra li ya -
G M R . S .
ba aa je - re -
Antaraa:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
P P P N D N .
pa ga me ghun ga ru -
S" . S" S" . . . . N D N D N S" R" .
ba an dha ke - - - - ghung ta - mu kha pa ra
N S" D P . . (G)MR P P (D)N D N D N S"
da aa ra ke - - nai - na na me - ka ja ra la
N D P . DN (R")S"
ga aa ke - re -
Rajan Parrikar
==============
Some more additions to the Keyboard concepts by Rajan (from another
post of his):
> Now here's my question : is the keybord typically made to follow
> human voice? Normally, (being a natural system), one would expect
> human voice to be capable of a continuous variation of frequency and
> not the discrete steps that a keyboard provides. If so, is it true
> that the keyboard plays an approximation of human voice when used to
> accompany a singer (or is it that the singer is expected to tune
> herself to the instrument)?
Let me try and keep this brief:
Yes, the octave is a continuum of frequencies and the keyboard
essentially discretises this continuum. In principle, we would require
an infinite number of points (and hence, keys) to accurately model the
octave. Fortunately, the response of the human ear makes this 'hair-
splitting` unnecessary. The following passage from an article I had
posted eons ago expands on this point very nicely:
*****
~From: The MUSIC OF INDIA: A SCIENTIFIC STUDY by B. CHAITANYA DEVA
(Munshiram Manoharlal Publishers Pvt. Ltd.) first published in 1981,
Chapter 8.
".......Also, by modern experiments with pure tones, it has been found
that a normal ear can discern a difference of nearly three cps to five
cps in pitch. That is, if there is a tone of 240 cps and another of
243 cps or 237 cps, the latter will be heard as different in pitch.
But if the other tone is, say, 241 cps or 239 cps, the ear cannot
distinguish between this and 240 cps. Of course, this is under
experimental conditions with very accurate instruments in the
laboratory with pure tones! But under ordinary conditions with complex
tones the differentiation will be definitely less. Again, even if the
number of different pitches within an octave which the ear can make
out may be more than 22, they may not be 'musically' different or
significant.
In this connection we may refer to an experiment by Ellis
(England, 19th Cent.)(6). He took a stretched string with moveable
bridges under it. By moving the bridges, the length of the vibrating
string could be altered, thus changing the pitch of its sound. He
found that to produce a just noticeable difference in the pitch of the
string he had to shorten the length of the string by 1/32 of its
*previous* length. For instance, let the wire be 1024 mm. long. Let
this be Sa. To get the next just noticeable pitch reduce the length
by 1/32 of this, that is by 1024/32. The new length is 996 mm. The
next length to produce a just noticeable difference in pitch will be
31/32 of this new length, i.e., 996 x 31/32 =964 mm. The next note
will have a length 31/32 of this, i.e., 964 x 31/32=932 mm. and so
on, till we get Sa' with length 512 mm.
We know that string length is inversely proportional to
frequency. So, every time we decrease the length by 31/32 of the
previous value, we are increasing the frequency by 32/31 of its
previous value. If we actually calculate the number of such steps
possible from Sa to Sa' we will find that there are nearly 22! (For
those who want to calculate these, here is the method. Let Sa be
l. The next audible 'note' will be 1x32/31. The third audible note
wi11 be (lx 32/31)x 32/31. The fourth audible note will be (1x 32/31 x
32/31)x 32/31, and so on. Now, Sa'=2. How many steps of 32/31 will it
require to get Sa'? Let this number be n. Then 1 x (31/32)**n = 2 and
n=21.98 or very nearly 22.)......"
*****
There have been harmoniums designed that incorporate 22 keys but were
so clumsy to be practicable that they are now extinct. Most of the
modern keyboards employ the division scheme you have cited (based on
the 12th root of 2) and this is known as the equally- tempered
scale. There are other possible ways of division (the so- called
justly-intoned scale, for example, which uses the frequency ratios of
smallest integers). The motivation for the equally tempered scale was
the ease with which you could handle harmony (chords) on the keyboard
(Why? Think about it).
The genius of Indian music lies is its recognition AND inplementation
of the fine microtonal intervals between two pure tones. These issues
were well-understood and developed by the ancient Hindus and form the
bedrock of our Raga-based music. This can be justifiably claimed as
one of the greatest contributions of Bharat to the global
civilization.
Since the keyboard is an approximation of the frequency continuum, it
is ill-equipped to handle the intricacies and nuances of melodic
Indian music and although the harmonium finds currency today as an
accompanying instrument in Hindustani classical music, its limitations
and deficiencies are known to the musicians. A good harmonium
accompanist will, therefore, maintain a volume low enough so as to not
intrude the main melodic vocal line, and will stick his neck out only
when the vocalist pauses (Contrary to popular belief, the harmonium is
not an Indian instrument though it primarily survives in India today;
it was brought into India by the Christian missionaries around the
18th century).
As an aside, we take pot-shots at Lata Mangeshkar today, but it was
this divine gift of high-shruti resolution and precision that
distinguished her from the rest of the flock. So great was her ability
in her prime that even formidable classical people were known to be
awed. Kumar Gandharva, for example, once remarked with a flourish: "I
have been blessed with just the Sa and Pa in my voice, but Lata! she
has them all!" To paraphrase Vamanrao Deshpande, author of 'Indian
Musical Traditions`, "it is as if Lata holds all the secrets of nada
in her throat." What they were talking about was the ability at the
precision in intonation. Try duplicating some of her earlier
classical-based songs on a keyboard and marvel at your impotence:-)
So to summarise: No, the harmonium or a keyboard cannot accurately
follow or simulate all that the human voice is capable of. A good
player, however, can, with dexterity of his fingers, do a good-enough
job at reproducing the human voice output.
If one is serious about Indian vocal music, it is best to never go
near a harmonium in the formative years of one's training. Why, it
should be apparent from the above discussion.
> Also, are there any instruments capable of a continuous frequency
> variation?
Oh yes, most of the stringed instruments - sitar, sarod, violin (NOT
santoor, however!). Wind instruments like the flute have the ability
too.
Rajan Parrikar
==============
From the RMIM Article Archive maintained by Satish Subramanian