Purnaprajna Blends Geometry with Love of Music

LAWRENCE — Art and creative expression have often been used to further human understanding of science. A University of Kansas professor is now using his math prowess to push the boundaries of music creation.

Purnaprajna Bangere, professor of mathematics and courtesy professor of music, blends his love of geometry with his talent on the violin. A virtuoso trained in Indian classical music and with broad exposure to Western classical violin music, Purna, as he is known by many, has developed a meta-mathematical framework that supports creation of new music and also builds a bridge among musical genres of Western classical, jazz, blues and Indian classical.

“This geometric framework gives a grammar and a syntax and foundations for new music,” Bangere said. “Music is a personal statement, always. So is this, which in some way represents my experiences.”

A geometric light switch

Purnaprajna Bangere holding violinsTo better understand his work requires a trip back in time.

As a youth growing up in Mysore, India, Bangere had access to HKN Murthy, one of the top violinists in the nation, as his guru. Bangere's father, now retired, was a mathematician, and the family was always surrounded by people from humanities and sciences. His hometown regularly welcomed Western classical performances in the maharaja’s palace. Those early experiences and his own exploration with the craft laid the foundation for what was to come.

“For an Indian classical musician, it is quite difficult to play Western classical music and vice versa,” he said. “The whole fingering changes.”

The fingering and the tuning of the two styles are quite different, in such a way that few individuals around the world try to master both. Although a love for music filled his life, so, too, did his fascination with mathematics.

“The two threads in my existence are closely intertwined, I’ve done as much music as math,” Bangere said.

Eventually his mathematical pursuits brought him to the United States, where he was exposed to the profoundly stirring genres of jazz and the blues.  

In the math world of the 20th century, Bangere also found inspiration in the pioneering work of the math giant and geometer Alexander Grothendieck. But it would be years later before Bangere would face the epiphany that finally brought music and math together for him.

“Literally, one day, sitting quietly thinking of math, but with music in the background,” he realized that Grothendieck’s way of looking at geometry could be applied to music in a way that would lead to an integration of various genres of music. Bangere was stirred to create a meta-mathematical framework that incorporates aspects of Indian classical and Western music.

“I realized that his viewpoint, which is very radical, applies brilliantly to view music in a unified way, where we can reconcile some key elements in Indian classical, Western classical, jazz and blues.

“It’s a self-consistent system in mathematics. You can read from mathematical symmetries and mathematical structures back to music. … Seeing music, it gives new mathematical structure as well, so it’s also impacting both ways,” Bangere said. “It goes into concepts of space, ‘What is space?’ You know we all have concern about physical space, mathematical space and so on. There is also a notion of musical space that comes out from this, which is expressed and made more precise mathematically, inspired by viewpoints of Grothendieck’s work in algebraic geometry. It is essentially a meditation on structures. Musically western and Indian systems are quite different, in fact almost complementary systems. Structurally, (Western and Indian music) are not as different as they appear to be. It’s like human beings. They look very different, but the DNA is very close. So it is the underlying structures we look at, and there are structural similarities. But there are crucial differences as well. The Indian system is deeply concerned with space between notes, and Western system is concerned with polyphony, counterpoint and more. This new system reconciles aspects of these genres.”

To hear Bangere talk about his system, one might conclude he’s entered the digital rain scene from the movie “The Matrix,” but he’s quick to point out that this is still in its infancy and very abstract. And exciting.

“In any such work, there are also aspects from various genres that are not captured as well, but the synthesis is leading up to its own self-consistent musical space and a systematic framework rooted in geometry.  My heart is in it,” he said.

Worldly Collaboration

Bangere Purnaprajn with Jeff Harshbarger, David Balakrishnan, Amit Kavthekar with their instruments

Others in the music and math worlds share his excitement and are advancing the conversation.

“The work Purna is doing to explore commonalities between Indian classical music and jazz and other related improvised Western music is truly groundbreaking,” said Dean of Music Robert Walzel. “Purna is creating opportunities for new musical soundscapes by bringing together diverse musical styles in a revolutionary way. His work is amazingly creative.”

Some are using the meta-mathematical framework to analyze compositions both old and new.

“It turns out that what I’m doing in one of my compositions, there’s a close analog in this system to what Bach does in some of the fugues, when seen in terms of substratum structures,” Bangere said. “The strange point is that some of the crucial aspects of this integration of West and East is reconciled by blues. There’s a compelling social narrative that the East and West is reconciled by African sounds. Blues is a very primordial musical paradigm, fundamental in a profound sense, and it is not merely an aesthetic necessity for this new music, but a technical necessity.”

His work has been shared in scholarly circles — talks and demonstration at the Mathematical Sciences Research Institute at the University of California Berkeley, Brown University, University of Toronto, Tufts University, Clay Mathematical Institute, Chennai and National Institute for Advanced Studies in Bangalore, among others— as well as at concert venues in Boston, Kansas City, San Francisco and, of course, Lawrence. And he’s shared the performance space with impressive names.

“Working with violinist David Balakrishnan, founder of the acclaimed Turtle Island Quartet, Purna is combining complexities of the raga melodic structures in Indian music with modal structural concepts and inflections used by jazz improvisers,” Walzel said. 

Bangere's ongoing collaboration with Balakrishnan is a perfect opportunity to explore the boundaries of musical styles and improvisation and its deeper multidisciplinary aspects rooted in geometry.

“We started working together on this music that is neither Indian or Western, with a framework coming from geometry, actually,” Purna said. “It may be viewed as ‘integration’ by some or as another way of doing music.”

The KU community can hear the fruits of the collaboration at an upcoming performance of the Purna Loka Ensemble. On Sunday, Oct. 28, at the Lied Center Pavilion, Purna and Balakrishnan will be joined by Jeff Harshbarger, a lecturer in jazz studies, on bass; and Amit Kavthekar on tabla.

“The audience should feel what they feel. They might see that there are a family of things that they are familiar with going in and out. I want them to relate to the music in their own way, and hopefully I am able to touch their hearts.”


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Purnaprajna Bangere music

What others have said about Purnaprajna Bangere:

Peter Fribbins, the artistic director of London Chamber Music Society, King’s Place London 

“Purna Bangere’s new compositions have a palpable vitality, energy and profound sense of life and color, which is not only immediate, but emotionally moving. Whilst clearly informed by Indian musical practice, there is so much more, including strong American traits, which phase in and out throughout. As a global and geographically resonant 21st-century musical journey, the integration of these different styles implies the bringing of countries and different people together as well — hence there is a meta-politics here; but a positive and aspirational one, culturally and aesthetically.”

Fribbins, talking about “Syzygy,” Bangere's work with Balakrishnan 

“Intriguingly, this derivation from different musical styles and traditions is achieved without being derivative and with no discernable joins; it is on the face of it a musical ‘fusion,’ but of worlds that are generally too far apart to be fused in musical terms in one piece of predominantly the same mood and focus. The fact that a piece can accomplish this illuminates something of the skill, mastery and individually original voice of its creator. Philosophically, I am reminded of the Japanese composer Takemitsu and the concept of ‘swimming in the ocean that has no west or east.’”

Composer Jan Radzynski, professor of composition, The Ohio State University:

“Just like Conlon Nancarrow, the quintessential American original who lived most of his life in Mexico City, Purna Bangere escapes definition. Although he was born and schooled in Mysore, India, he settled in the United States only in 1991 and continued his musical activities as a violin virtuoso and a musical visionary. His vision includes integrating musical elements not only from his native India, but increasingly from his adopted country, the United States. He uses geometry to do this, which is his other passion. It is that essentially American meeting of cultural crossroads that reflects Bangere's deeply held belief in the brotherhood of humanity. That belief makes this music urgently emotional as it pulls the listener straight into the eye of the emotional storm."