Music Is Math

Big thanks to the Behance Network for turning me on to the amazing work of Tatiana Plakhova, whose series “Music Is Math” is a meditation on the mathematical nature of sound, expressed in exciting and complex visualizations. Her work is grounded in exploring patterns and repeated forms, but she does so with a celestial eye and encourages us to consider tiny aspects of reality as being microcosms unto themselves.

The image above could fit equally as well in a NASA photo gallery as it could in a physicist’s treatise on string theory, yet it was inspired by music. Mathematical patterns and recursive vertices weave in and out of all three topics, but it took an artist as talented as Tatiana to bring the similarities into bright focus.

You can order prints and wallpapers at Complexity Graphics: http://www.complexitygraphics.com/

Wagner’s String Theory

Gesamtkunstwerk.

It’s the name Richard Wagner, famed German opera composer, gave to his concept of the ultimate artistic  synthesis–the successful integration of music, theater, visual arts, and poetry. Some argue that opera in general is an expression of this concept, but Wagner insisted that all artistic elements must be present constantly and simultaneously. His sprawling epic, Der Ring des Nibelungen, is his crowning achievement in this regard. It actually required him to build his own opera house in order stage it.

Wagner’s “string theory”–this common thread that ties the arts together–is not unlike “string theory” in the context of the scientific community.

I’ve touched on string theory in a few other posts: Musical Geometry and Music’s Hidden Dimension. String theory gets its name from the theoretical “fabric” that forms the essence of reality as we know it. Scientists postulate that the most basic elements of the universe are tiny vibrating strings, and the frequency at which they vibrate dictate the type of particle they imply. This, of course, is a very basic reduction of a very complex theory, but it does imply that existence is a result of cosmic music. These strings are the violins and harps of being.

String theory came about as a proposed solution to the inherent incompatibility of quantum physics and relativity: Relativity is a set of rules that have been proven to govern the celestial, and quantum physics is a set of rules proven to govern the tiniest of subparticles… but the two sets of rules don’t agree with one another! Reality cannot be understood by using both sets of rules together. String theory is one attempt to reconcile the two, and provide the holy grail of scientific effort: the so-called “Theory of Everything.” It would be the common thread tying together quantum physics and relativity.

The string.

For more information on string theory, check out the unbelievably accessible book The Elegant Universe by Brian Greene.

Music’s Hidden Dimension

When you play middle-C on a piano, you are not just hearing the note middle-C. You’re also hearing E, G, another C an octave higher, the D and E above that, F#… You’re hearing several different notes sounding simultaneously, all part of a single note.

It’s called the Overtone Series (also referred to as the Harmonic Series). Its implications are far-reaching: In my list of notes above, notes that the first 3 overtones of the note C are C, E, and G. These three notes form a “C-chord.” C is the tonic note, E is the third, and G is the fifth. The overtone series forms the foundation of Western music’s concept of harmony and chord structures. In this example, the note C is referred to as the “fundamental” of the series.

Overtones are also part of a note’s “timbre” or tonal coloring. Timbre is an instrument’s sound. It’s why a D# on a clarinet sounds different from a D# on a guitar. (“formants,” the resonating aspects of an instrument, also play a part.)

All of this seems somewhat logical, but the fact remains that a single note played on a musical instrument is not a single note at all–it is many notes. Our ears resolve an entire overtone series into one, single tone. Not only that, if you were to play the entire overtone series of C simultaenously, but leave out the note C, our ears will still hear everything as “C.” It’s as if our ears fill in the gaps where they expect the fundamental to be. The notes E, G, D, G, F#… all imply “C” in the world of harmony.

Why? How? These are deceptively deep questions about the nature of sound and human evolution and, like all deep questions, don’t yet have an answer…

Musical Geometry

The whole point of making these geometric spaces is that, at the end of the day, it helps you understand music better.

– Professor Dmitri Tymoczko, Princeton University

Recently, scientists have demonstrated that music has geometry. This Telegraph article describes the way in which music can be analysed and described visually, in what is being dubbed “geomtrical music theory.” The concept, pioneered by Princeton professor Dmitri Tymoczko in 2006, attempts to revolutionize the way music is described and perceived by using complex multidimensonal visual representations, instead of 2-dimensional musical notation.

This Time article from 2007 is a bit more enlightening. It points out that there has never been a way to explain how musical styles relate to one another, and Prof. Tymoczko states, “No matter where you go to school, you learn almost exclusively about classical music from about 1700 to 1900. It’s kind of ridiculous.” He’s right, and his new form of musical geometry can change all that:

Borrowing some of the mathematics that string theorists invented to plumb the secrets of the physical universe, he has found a way to represent the universe of all possible musical chords in graphic form.

Tymoczko’s calls them “orbifolds:” the multidimensional spaces that describe notes and chords. Thes shapes twist back on themselves, much like a Möbius strip. In fact, 2-note chords DO inhabit a Möbius space. The implications are huge, from both a music appreciation AND compositional standpoint.

For anyone interested in this concept, download Prof. Tymoczko’s “ChordGeometries” to see this effect as applied to Chopin and Deep Purple. It looks/sounds great.