Odissi Dance Mathematics in Motion

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Odissi Dance: Mathematics in Motion Rohini Dandavate, Ph.D. Consisting of measured or improvised steps, body movements, and gestures,

dance is often described as mathematics in motion, "Many shapes familiar to

mathematicians arise naturally in dance," says Christina Soriano, professor of

dance. She refers to dancers and choreographers as "active practitioners of

three dimensional geometry." In addition to the geometry of movement the

influence of mathematics is also prevalent in Odissi dance. Body postures,

movement patterns, and intricately designed group formations reflect a geometric

structure; the cadenced musical accompaniment, metered rhythm, and pace

maintain a mathematical order. This paper illustrates and explains the use of

mathematics in Odissi dance, focusing on form, spatial exploration in movement,

and rhythmic patterns.

Geometry in form

The technique of Odissi dance evolved by borrowing postures from temple

carvings in Orissa. In his book, "The Hindu Temple," George Michell explains

that sacred mathematics in temple architecture “is composed of a language of

precise measurements, which permits a symbolic realization of the underlying

cosmic ideas”. The architecture of Hindu temples follow strict proportions and

measurements because it was believed that a disproportionate carving, painting,

or image would disrupt harmony with the universe and render worship ineffective.

So when the Gurus borrowed Odissi dance postures from temple architecture,

the canons of proportions and measurements inherent in the poses were

mirrored in the reconstruction of the dance. The structure of the Odissi dance

repertoire evolved into a progression of dance numbers, which start with

salutations and prayers, followed by pure and expressive dances in gradually

increasing tempos, and end with Moksha, the dance of salvation.

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The following illustration of carvings from panels in the Konark temple in Orissa

show dance poses which form the basic positions of Odissi dance. Figure two

shows dancers in positions correlating with the carvings. These positions are

then set with rhythmic transitions and flowing movements which create an array

of symmetrical and asymmetrical shapes.

Figure 1. Figure 2.

Photo Credit: Shailan Parker The two basic positions used in Odissi dance-- the chowk and the tribhangi—

reflect basic geometric shapes. The position of Chowk, meaning "the square"

emulates the image of Lord Jagannath, the deity for whom this dance was

performed. Figures 3 shows a comparison of Lord Jagannath and the position of

chowk.

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Figure 3- Comparison of Lord Jagannath and Chowk

Lord Jagannath Chowk The following diagrams of the position Chowk, drawn by Late Guru Debaprasad

Das clearly establish the geometrical lines present in this dance position.

Figure 4- Deconstructing the Lines of Chowk (Source: Nrutyanu Sarani)

The second basic position in Odissi dance is named Tribhangi, literally meaning

“three bends” in Sanskrit. The position consists of three bends in the body at the

neck, waist and knee, giving it a gentle "S" shape. The Hindu deity Krishna is

often portrayed in the tribhangi position, as depicted in Figure 5. Next, Figure 6

illustrates the geometrical lines that define the tribhangi position.

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Figure 5  

Figure 6- Delineating the Lines of Tribhangi (Source: Nrutyanu Sarani)

In the context of group choreography, the precisely defined bends of the spine

and body are used to create geometric three-dimensional tableaus. The following

photographs of group formations show Odissi postures employing the different

bends in their body.

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Figure 7- Dancers: Srjan Dancers: Orissa Dance Academy

Source: http://www.indovacations.net/english/AboutOrissa.htm The various bends (bhangas) seen in Figure 8 are characteristic of the Odissi

style and are also seen in Indian sculptures.

Figure 8

    Source: http://www.dollsofindia.com/read/indian-classical-dance.htm   In each of the poses depicted above, the division and bends of the body create

angles juxtaposed with curves and position the body perpendicularly to the

ground.

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The same ideas are applied in the dance choreography with preset orderly

movements, proportionate postures along with the facial expressions, gestures

and appropriate costumes. The following section will expound on the presence of

geometrical shapes in the movement.

Patterns in Spatial Exploration In temples a performance space was designated directly in front of the deity. Map

1 presents the inner sanctum and the outward radiation of energy released in

different directions from the centre of the sanctuary where the deity is placed. On

these lines of energy other secondary images of the main deity are displayed.

Map 2 illustrates the directions in which the basic steps and movements of Odissi

dance are performed. The similarities between the directions of movement and

energy radiation in the main sanctuary show the influence connection between

temple architecture and movements in Odissi dance.

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Map 1 Map 2

In Odissi dance, jumps, stylized walks, turns and spins are performed in all

directions following or tracing imaginary paths of squares, rectangles or circles by

placing the body at different levels. At times a single part of the body coordinates

to create angular, square, linear, or circular patterns on or above the ground

Audience  

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depending on the sequence of steps chosen. Some examples of paths are

illustrated below:

Figure 10- Circular paths for movement, Source: Nrutyanu Sarani

      Figure 11 Circular paths for hand movement, Source: Odissi Path Finder

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Figure 12- Body bending to make an arch, Source: Odissi Path Finder

To further illustrate examples of geometry in movement, Figures 13 and 14 show

examples of sideward, forward and diagonal paths of movement on the ground,

where again the dancer is trained to pay attention to geometric coordinates in

space.

Figure 13-  

   Row 1: The feet position starts and ends in tribhanga position. Row 2:  The forward movement commences and ends in sama pada  (both feet placed together.

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Figure 14-

Row 3 and 4: Diagonal extension of the leg commencing and ending in Samapada These maps amply project the extent to which directions and geometrical

dimensions are defined and maintained in using space for the execution of the

footwork along with the whole body.

Measures, Division and Structure of Rhythm Other important aspects of mathematics, which form the basic framework for

dance choreography, are counting, dividing, adding, and multiplying beats to

maintain rhythm and tempo. Learning to count beats to set a dance is basic to

Odissi dance training. In the Odissi style, a dance is set to a specific category of

beats (Bols). Taal, the rhythmic cycle of beats (bols), is divided into units of

different counts and recited in various speeds. Each repeated cycle (avartan) of a

taal is generally divided into sections (vibhaags), which may have varying

numbers of beats and are recited or played on the pakhawaj (drum) at different

tempos (layas). Each taal cycle has two components: a sequence of notes, and

the definition of time intervals in which these notes are played. Steps are set

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either using fractions of notes when the tempo is fast or each step is danced to

just a full single note when the tempo is slow. Movements are set in three layas:

slow (vilambit), medium (madhya), and fast (druta). Although the tempo changes,

the fundamental taal cycle may be repeated.

In Odissi dance, the first lesson in understanding the divisions in notes of taals or

rhythmic cycles begins with the training of the basic steps in Chowk or Tribhangi.

Simple mathematical division of time within the recitation of the notes is used

while practicing the movement phrases. The other dance numbers in the

repertoire follow different permutations and combinations of beats. Measures of

beats are divided in 5 jatis or categories. There is a combination of beats under

each category creating 7 rhythmic patterns or taals. Choreographers use

combinations of taal cycles and the footwork and movement sequence is set in

correspondence to the rhythmic cycles. The following table illustrates the 35 taal

system.

Categories of Taal Tisra Jati Caturasra Jati Khanda Jati Misra Jati Sankirna Jati

3 beats 4 beats 5 beats 7 beats 9 beats Dhruba taal (3+2+3+3) (4+2+4+4) (5+2+5+5) (7+2+7+7) (9+2+9+9) Matha Taal (3+2+3) (4+2+4) (5+2+5) (7+2+7) (9+2+9)

Rupak taal (2+3) (2+4) (2+5) (2+7) (2+9) Jhampa Taal (3+1+2) (4+1+2) (5+1+2) (7+1+2) (9+1+2) Tripata Taal (3+2+2) (4+2+2) (5+2+2) (7+2+2) (9+2+2) Atta Taal (3+3+2+2) (4+4+2+2) (5+5+2+2 (7+7+2+2) (9+9+2+2) Ek taal (3 beats) (4 beats) (5 beats) (7 beats) (9 beats)

The counting patterns and sequence of beats shown in the table set the rhythm

for the dance movements. A dance number is choreographed based on the

rhythmic cycle played in the required tempo to express the plot or story.

Choreographing pure dance numbers requires mathematical acumen and

training. This table of counting system and rhythmic patterns is not exhaustive;

there are many more variations that are applied methodically in Odissi dance

choreography.

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It becomes clear that Odissi dance involves experiencing mathematics through

the body. French sculptor Rodin says, "I have come to realize that geometry is at

the bottom of sentiment or rather that each expression of sentiment is made by a

movement governed by geometry. Geometry is everywhere present in nature".

Odissi dance truly represents this thought. The Odissi dance repertoire creatively

explores geometry and mathematics in form, structure, and space to express

meaning.

References Das,Debaprasad(2002) Nrutyanusarani. Prachi Sahitya Pratisthan,Cuttack, Orissa Odissi Research Center(1988), The Odissi Path Finder, Vol 1 & 11 Bhubaneshwar, Orissa Michell, George(1988)The Hindu Temple: An Introduction to its Meanings and Forms. University of Chicago Press, Chicago Parsley, J. & Soriano, Christina Tsoules (2009). Understanding Geometry in the Dance Studio Wake Forest University, Winston-Salem, NC About the Author Rohini Doshi Dandavate holds a doctoral degree in Cultural Policy and Arts Administration from the Ohio State University. As an artist in the Arts in Education Program of the Ohio Arts Council, she has conducted workshops and lecture demonstrations in schools and colleges in Ohio on Odissi dance since 1994. She has offered courses in Odissi dance as a Visiting Faculty at Denison University in 2001, and continues to offer dance lessons. She received a graduate degree in Odissi dance from Kala Vikash Kendra, College of Indian Dance and Music, Cuttack, India. Her gurus are Guru Kelucharan Mohapatra, Guru Raghunath Dutta, Guru Ramani Ranjan Jena, and Dr. Menaka Thakkar.