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Symposium: Indian music and number theory (Leiden University – The Netherlands)

Posted by ElJay Arem (IMC OnAir) on September 25, 2006

Music is all about number theory.  For theoreticians of music in the Middle Ages, this was an obvious fact. A fact which the eminent mathematician Manjul Bhargava from Princeton will demonstrate on Thursday with the help of his Indian drums.

The tabla, the Indian drum is the most important instrument in Indian classical music.  A musician plays two drums, one for the right and one for the left hand.

Visiting Professor
Manjul Bhargava is a world-famous mathematician.  This numbers theorist already performed pioneering work during his doctoral research, won prestigeous prizes and, most exceptionally, was offered full tenure at Princeton Unversity just two years after his graduation in 2001.  For the past academic year he was visiting professor at the Stieltjes Instute, an inter-university research school in mathematics.

To bring his year in Leiden to a close, he will be returning this week and will appear on 14 September as one of the three speakers and performers in the public symposium ‘Mathematical Patterns in Indian Poetry and Music ‘, organised by the Stieltjes Institute, and two Leiden faculties: Mathematics and Natural Sciences, and Creative and Performing Arts.

Manjul Bhargava
Foto: The Daily Princetonian

Indian drum
Bhargava was born in Canada, the son of Indian immigrants, but grew up in the US.  He learned Sanskrit from his grandfather, a famous Sanskrit scholar, and from his mother he gained a love of both mathematics and the tabla, the traditional Indian drum. Number theory, which looks at the characteristics of and relations between integer numbers, is in Bhargava’s view closely related to classical Indian music, and could in fact have its roots here.

Unknown culture
The symposium is an initiative of Dr. Derk Pik, who was trained as a pianist and mathematician and gives lectures in ‘mathematics and music’ to his students at the Royal Conservatory and at Leiden University. Bhargava’s visit to Leiden was too good an opportunity for him to miss.  ‘Indian classical music is a very rich, and completely unknown culture.  In terms of cooperation between different disciplines, this subject is still in its early days.  I expect we will be able to learn a lot from one another.’

Symposium Mathematical Patterns in Indian Poetry and Music

Thursday 14 September 2006 19.45-22.30 hrs
Venue:  Kamerlingh Onnes Gebouw, Steenschuur 25, Leiden
Lorentzzaal (A 144)

Entry is free; you can reserve a ticket by create_mail(“secretariaat”,””, “email”)email.


Prof.  Manjul Bhargava (
Princeton University): Poetry, Drumming and Mathematics
Dr. Emmie te Nijenhuis: Metre in Indian Music and Poetry
Dr. Derk Pik (Leiden University): Indian Rhythm in Music by Messiaen

Further information on the lectures.

Prime number
And it goed further than theory. Pik: ‘It’s not without good reason that we have a Faculty of Creative and Performing Arts here. Manjul Bhargava will demonstrate with his tabla why it is so important that the number of units of a rhythm is a prime number.  And I will show using the piano how Olivier Messiaen used Indian rhythms in his music, and more importantly, why he did so.’

Pik is fascinated by the work of this French composer, whose life spanned almost the whole of the twentieth century. ‘Messiaen used many Indian elements in his music and has passed this on to students such as Boulez and Stockhausen. In his turn, Messiaen was influenced by Debussy, from whom he learned to regard musical phrases as units in themselves and not as steps to reach a subsequent point, as was common in nineteenth century western music until then.  As a young composer, Messiaen knew Indian music only from theory.  He had read an article in the French  Encyclopédie de la Musique from 1913. When he read this as a Conservatory student, he had probably never heard a tabla, and certainly had never heard the thirteenth century rhythms from the Sangita Ratnakara. He was fascinated by the constructions of these thythms, recognised them in other already existing music and used the theory to account for the magical nature of Stravinsky’s Sacre du Printemps.’

Strong rhythm
Messiaen, Pik continues, sees rhythms as personalities, each with its own character. ‘ He has studied all 120 rhythms of the Sangita Ratnakara in great detail, and recognises all kinds of general musical and mathematical principles: symmetry, palindromes, prime number rhythms.  A rhythm stands as a whole if it cannot easily be split into several equal parts: the rhythm is therefore strong if the number of units is a prime number.  Messiaen used the word prime mumber, but was, on the other hand, unfamiliar with many other mathematical concepts, such as symmetry and permutation groups. But he used them, with made-up names. For example, he called a collection of tones which is invariable under a shift – in other words, it remains the same – as an impossibility.  Although he does not refer to the things by their official mathetical name, he must have had considerable mathematical insight.

Derk Pik and Emmie te Nijenhuis. Pik: ‘Indian classical music is very rich, and is relatively unknown among western music lovers.  Cooperation between thesespecialist fields is in very early days.’ Te Nijenhuis: ‘Indian musicological works from the Middle Ages are full of mathematics.’

Pioneering work
The third performer at the symposium will be Dr. Emmie te Nijenhuis, pianist and musicologist, and member of the KNAW (Royal Netherlands Academy of Arts and Sciences) for her pioneering work in the field of classical Indian music.  Thirty years ago, as part of her doctoral studies, she went to India to study the country’s rich musicological tradition. Indian musicological works from the Middle Ages are full of mathematics.  ‘It is as if Indian music is more formal, more mathematical, if you like, than other musical traditions.’ says Te Nijenhuis. ‘Melodies and metres have been placed in lists in all conceivable combinations.  But these are all theoretical considerations, in which you find very little about practice.  Just as in Europe before the advent of modern science, musicologists were general scholars.  Theoreticians who were at home in didfferent disciplines.  Sometimes they were also musicians, and sometimes not.  Of the oral traditions, which also existed, a great many have disappeared.’

Text metre and musical rhythm
Te Nijenhuis’s lecture which will be interspersed with musical fragments on cd, will be about the relationships, and also tensions, between the metre of poetic texts and the rhythm of the music to which the texts are sung.  ‘The instrumental tradition, or drumming, and the textual tradition developed separately and then come together again at an appropriate point.  You then get a situation of polyrhythmics, with a text metre which extends beyond the border of a rhythm block.  But after a particular number of blocks – which can be calculated – they come together again.’

Leiden University
P.O. Box 9500
2300 RA Leiden
The Netherlands

Rapenburg 70
2311 EZ  Leiden
+31 (0)71 527 27 27 (operator)

For International Students:
Information requests and applications

Research in Leiden

Marieke van Eeden
 create_mail(“mr.vaneeden”,””, “”)
 +31 071 527 33 01

News and In Focus

Dini Hogenelst
  +31 071 527 33 45 / 06 52 58 24 26

Hilje Papma
 +31 071 527 32 82 / 06 11 35 15 62

Steven Hagers
 +31 071 527 46 91 / 06 52 33 72 21

 create_mail(“wetenschap”,””, “”)


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