Breakthroughs in Musical Geometry
The Visualization and Future of Musical Science
Researchers in American Universities have been developing precise mathematical formulations used to describe what is currently known about music, and to further human kno
Both mathematicians and musicians have known for thousands of years now that between their two subjects there was a very real connection - even if they didn't always know exactly what it was and how it was formulated.
Mathematicians and scientists throughout modern history have searched for new ways of quantifying and describing exactly what gives music an aesthetically pleasing quality - why some notes sound good together while others result in only ugly dissonance.
In physics there are answers to some of these questions - determining the wavelike nature of sound enables the understanding of note ratios - the wavelengths of some notes mesh with the wavelengths of other notes depending on their ratio with each other (a fact first noted by Pythagoras nearly 2500 years ago).
Geometry and Music?
Today, researchers such as Dmitri Tymoczko at Princeton University, Ian Quinn at Yale, and Cliffton Calendar at Florida State University have begun to take the next step in analyzing various forms of music from a mathematical perspective - geometry.
These researchers have begun to apply basic geometric principles to various musical ideas - describing various relationships between notes and musical formulations as pieces of three-dimensional structures. In this way, complex music can actually be represented in a purely visual manner (or both visual and audible).
Each note or structure of notes in a given piece is provided a mathematical formulation, which can then be translated to a point in three dimensional space (a task which needs only three coordinates, x,y and z).
Understanding Musical Reality
As the Princeton news release puts it, "Different types of categorization produce different geometrical spaces, and reflect the different ways in which musicians over the centuries have understood music." So, in addition to simply creating a way to add another realm of beauty and enjoyment to music, this line of thinking can actually benefit society by providing a new understanding of music itself.
By determining the geometrical formulation of certain musical qualities that are already known, researchers can then apply this to learning more about the qualities of musical itself - going even as far as to ask if there are any fundamental, aesthetically pleasing qualities of music that have not yet been discovered.
Are their chords with unique properties that have remained beyond the grasp of current musicians? Are their scales that might provide new musical insights? Would the creation of these new techniques require the creation of entirely new forms of instruments in order to harness all of the mathematical potential in music?
In addition, the researchers have noted that by perfecting this line of mathematical modeling, music education could also be enhanced in a meaningful way by allowing students another method of learning music - visually rather than audibly, creating another path toward musical enlightenment and understanding.
While this form of mathematics is still very new, it is especially intriguing in that it seeks to explore a familiar idea in an altogether novel way.
References:
"Researchers Map the Math in Music." News at Princeton.
