Wednesday, November 13, 2013

Mathematics and Music: A Search for Insight into Higher Brain Functions

Mathematics and Music: A Search for Insight into Higher Brain Functions

Authors: Wendy S. Boetcher, Sabrina S. Hahn, and Gordon L. Shaw
Source: Leonardo Music Journal, Vol. 4 (1994), pp. 53-58

“Until just before his sixth birthday, then, Wolferlled (Wolfgang) a happy and not too burdened life... He learned his lessons, whatever they were, easily and quickly. His mind was usurped by music until he discovered the rudiments of arithmetic. Suddenly the house erupted with figures scribbled on every bit of space walls,floors, tables and chairs. This passion for mathematics is plainly in close alliance with his great contrapuntal facility. Music, however, was his only real interest.

Throughout history, one of the most intriguing and common connections between science and the arts is the relationship of mathematics and music. This is no coincidence as physics and mathematics, explain acoustics, sound production and many other principles that are the foundations of music. Some composers such as: Gubaidulina, Bartók and Satie have even incorporated mathematical concepts into their compositions such as the Golden Ratio and Fibonacci sequence. Connections between mathematics and music are numerous but the aim of the article by Wendy S. Boettcher et al, is to examine these areas as processes of higher brain function.

Boettcher et al did not only base their research on previously raised points; they also presented results of interviews with 14 professors of mathematics concerning their research and relations to music. According to the authors, the cause of the higher brain functions that apply to mathematics and music is an abstract, spatio-temporal firing-pattern development by neurons grouped over large regions of the  cortex. In order to clarify development patterns in the brain besides music and mathematics, the authors analyzed chess-playing skill as a complex cognitive process equivalent to mathematics and music-related operations.

An insight into higher brain functions is discovered through accessing the Trion Model, which is according to the authors, a highly mathematical realization of the Mountcastle organizational principle. Vernon Mountcastle is an American neuroscientist who discovered, in the 1950s, columnar organization in the cerebral cortex. According to Mountcastle, cortical column is the basic neural network of the cerebral cortex and consists of subunit minicolumns called trions. Trions represent structured and intertwined bundles with the overall diameter of about 0.7 mm  containing about a hundred neurons. Each trion has three levels of firing activities and therefore, a cluster of trions can produce a complex and rapid firing pattern characteristic of higher brain function.

Music is comprised of melodic, harmonic, and rhythmic sequential patterns. Melodic patterns, or patterns of continuous notes, produce a frame that helps the listener recognize a familiar melody or make a distinction between two different melodies. Harmonic patterns relate to the  horizontal dimension of music, while rhythmic patterns involve the timing aspect of music. The authors discuss an experiment in which college students were exposed to the music of Wolfgang Amadeus Mozart before they were given intelligence quotient tests. The results of this experiment showed that the music of Mozart, which possesses natural complexity and structure, enhanced the abstract and spatial reasoning of the students. Even though music is highly organized by patterns, several studies have produced negligible results connecting computational and musical abilities in children.

The authors interviewed 14 mathematicians and posed the following questions: (1) “What is your math research?” (2) “What are some cognitive skills that are required to do this type of research?” (3) “Do you believe there is a connection between math and music?” (4) “Do you listen to music while doing math?” For the purpose of this text, probably the most important is the question number 3. Most of the mathematicians expressed their appreciation and knowledge of music but the majority said that the cognitive relationship between music and mathematics exists only at the level of detecting patterns.

As a musician and admirer of mathematics, studying this article has been of great importance and insight for me. Understanding the nature of sound and its fundamental relationship to physics and mathematics, being aware of the fact that some composers were successful in both areas, for some reason, never took my understanding in the direction of organizational patterns of music and math. In my opinion, the music of Mozart and other classical composers might be described as a sequence of predictable melodic, harmonic, and rhythmic patterns, but the exclusive implication of patterns can be found in the music of the contemporary composers. The music of the 20th and the 21st century, predominantly atonal or serial displays an even greater application of mathematic than tonal music. Focusing on the  proportions and relations of notes or sounds within bigger forms is one of the main characteristics of contemporary music. Graphic notation, symmetric structures, golden ratio and Fibonacci numbers are some of the fundamental techniques composers use today and even if no apparent pattern can be determined in writings of a composer, such an approach is a result of pattern-directed thinking. 

1 comment:

Pamela Lum said...

Hi Branko,

I believe that there is an underlying relationship between mathematics and music. Besides detecting patterns as the article indicates, there are many other aspects that relate such as probability in chance music and math sentences in completing measures.

I wonder if the results would vary if the study interviewed mathematicians who had music training and determined whether music training had assisted them to become a better mathematician. It would also be interesting to further investigate which area of the brain is related in terms of math and music.