Canadian Musician - January/February 2019 | Page 29

WOODWINDS
Dr. Daniel Schnee is a multi-instrumentalist who has performed worldwide with 21 different JUNO
and Grammy Award-winning musicians. He has been internationally recognized as a graphic score
composer and is a former student of Pulitzer Prize-winning jazz musician Ornette Coleman.
By Dan Schnee
The Algebra of Indian
Music
T
hough there are innumerable ar-
ticles on Indian music available
to woodwind players, few discuss
how to apply the more conceptual
aspects to practical scale studies in
non-Indian music.
This is unfortunate, as merely running up
and down a melodic pattern (raga) in differ-
ent keys does not provide the student with
the most valuable lesson: how to grasp and
utilize the intellectual power of Indian rhythm
in one’s musical studies. And a key ingredient
often missing in such study is the mathematical
underpinnings of Indian music, and how they
can be applied to practical scale practice.
First though, we must know a little about the
principles of rhythm in the various Hindustani
(Northern) and Carnatic (Southern) styles of music.
The Concepts
In Carnatic music, these principles are called
the Dasa Prana, the 10 vital elements of rhythm.
Among the ideas discussed are the various
modes of indicating rhythm, subdivision,
tempo, classification, and the idea of “time” in
general. The beat cycles in South Indian mu-
sic (talams) are considered to have developed
over time from Sanskrit poetry, and out of this
system, five basic lengths of time known as jati
developed.
These are: chatusra (4), tisra (3), mis-
ra (7), khanda (5), and sankirna (9). Groupings
of beats and notes can be arranged quite cre-
atively using the Dasa Prana, and thus I will dis-
cuss them in terms of how you can begin to
use such groupings to your advantage in jazz
improvisation.
Basic jatis, and how you group them within
a talam, are a major part of the incredible cre-
ative science of Indian music. And the key to
understanding the power of jatis lies in under-
W W W. C A N A D I A N M U S I C I A N . CO M
standing structure.
For example, Chatusra Jati is a grouping of
four notes or beats, and so a talam based on it
will contain at least one or two groupings of
four. This is extremely important to know, as
talams are algebraic: they can be expressed as
symbols which, when memorized, can give a
musician an advanced level of control in both
melodic and rhythmic improvisation.
For example, the talam known as Dhruva
contains the form X+Y+X+X, or XYXX; thus, if
we assign both X and Y numbers, the form stays
the same but the length changes.
Dhruva Talam, when based on Chatusra Jati,
is 4 + 2 + 4 + 4, a 14-beat cycle. But if Dhruva is
based on groupings of three (Tisra Jati), it be-
comes an 11-beat talam (3 + 2 + 3 + 3). In fact,
one of my favourite talams is Dhruva when it is
based on Misra Jati (7), which produces a flow-
ing 23-beat cycle (7 + 2 + 7 + 7).
The Equations
Taking this into consideration, we can then an-
alyze talams as algebra, and memorize/utilize
this information for improvisational or compo-
sitional purposes.
For example, Matthya Talam can be ex-
pressed as XYX, so Matthya is a 10-beat cycle
using Chatusra (4 + 2 + 4), an eight-beat cycle
using Trisra (3 + 2 + 3), a 16-beat cycle in Misra
(7 + 2 + 7), and so on.
Another talam (Triputa) can be expressed
as XYY, and thus can become an eight-beat
Chatusra cycle (4 + 2 + 2), a seven-beat Tisra
cycle (3 + 2 + 2), a nine-beat Khanda cycle (5 +
2 + 2), and so on. This means we can also adapt
the alphabetical symbols in such a way as to
make memorization easier for our particular
style of learning.
Some people are better at visual learning, so
memorizing XYXX as images might make the
process easier. Imagine pieces of fruit (apple
+ banana + apple + apple), colourful shapes,
emojis, or even the faces of Star Wars characters
– whichever way makes learning symbols fun
and personal.
In Practice
The next step is applying such algebra to our
practice regimen, and the most effective way
to start is using the C major scale as our initial
note set. So, if we want to study Dhruva Talam
using Chatusra Jati, we can practice it in straight
eighth notes as such: CDEF – ED – CDED – CDEF,
then DEFG – FE – DEFE – DEFG, and so on (giv-
ing us the scale step pattern: 1234 – 32 – 1232
– 1234, 2345 – 43 – 2343 – 2345, etc.), moving
on to the remaining 11 keys.
This approach is an extremely effective way
of practicing scales and keys while getting used
to Indian rhythms. If we want to then move on
to another talam using Chatusra Jati (Aja Talam
for example: XXYY or 4 + 4 + 2 + 2) we can utilize
the same concept: CDEF – CDEF – GG – GG,
DEFG – DEFG – AA – AA, and so on (1234 – 1234
– 55 – 55, 2345 – 2345 – 66 – 66, etc.).
Another really powerful use of this approach
is in the study of the chromatic scale. Break-
ing it up into segments using talams and jati
reveals the power of chromatic patterns, giving
you very advanced technical control over your
instrument. For example, if you can run through
Dhruva Talam using chromatic Chatusra Jati
(CC#DE - DC# - CC#DE - CC#DE , C#DE E - E
E - C#DE E - C#DE E, etc.), in eighth notes with
a metronome (e.g. = 200 bpm), all other scales
will seem like child’s play in comparison.
The algebra of classical Indian music is a true
treasure and gift to the world, so I encourage
you to explore it deeply and thoughtfully.
Good Luck!
C A N A D I A N M U S I C I A N • 29