Stravinsky's Prediction

With an extensive history of music already in place, one might wonder, what more could possibly be accomplished? Are there really any musical components left for radical exploration? Here is how Igor Stravinsky, one of music's most historically celebrated composers, decisively answered a similarly posed question:

“Yes, pitch. I even risk a prediction that pitch will comprise the main difference between the “music of the future” and our music.”

— Igor Stravinsky, Memories and Commentaries

Why would Stravinsky say that the transformation of pitch is the future of music?

If we look at the components of a single musical tone, whether it be from the voice or any instrument in the world, we see an endless series of pitches, many of which have still never been heard consciously in isolation, let alone heard in a musical or harmonic context. These sounds within one sound, or pitches inside one tone, which I will now refer to as partials, could be the music of the future that Stravinsky predicted. Partials work with largely different rules and principles than those that have already been established.

One reason for the discovery of additional partials, along with the expansion of what pitches are deemed acceptable, is modern technology. In Stravinsky's time, along with all the ages before, there was not an efficient way of isolating, and thereby hearing and discovering, complex partials. Only with relatively recent advancements in science and technology are we able to bring the more complex and higher partials into our listening experience.

With further advancements in technology, modern instruments can play nearly any combination of tones and partials that can be conceived. As in many areas of life, the modern era is a unique time for musicians to be alive due to the contemporary opportunities and changes that only this period has yet been able to provide. Certainly, a number of musical creators from the past would be envious of our current circumstances, for many of those prominent composers and players felt limited by the constraints of their generation. Even Arnold Schoenberg, a true innovator in his time, articulated:

“We ought never to forget that the tempered system was only a truce, which should not last any longer than the imperfection of our instruments requires. I think, then, contrary to the point of view of those who take indolent pride in the attainments of others and hold our system to be the ultimate, the definitive musical system—contrary to that point of view, I think we stand only at the Beginning. We must go ahead!”

— Arnold Schoenberg, Theory of Harmony

Perhaps we are entering that age where imperfection need not last any longer.

Theoretical Music - A Definition

           Those who have discussed the subject of music with myself recently know that I prefer to use the term "theoretical music" (TM) when describing musical functions. Naturally, this phrase is met with slight confusion, as I am currently unaware of its usage anywhere else.

Theoretical Music: 
            A division of music that uses cognitive processing, mathematics, and aspects of the scientific method to understand and explain musical phenomena.

            Along with the simple definition above, theoretical music attempts to examine music from alternate systems and perspectives. For example, approaching certain musical concepts in a mathematical, physical, or even philosophical way can provide new insights. It's not just intellectual comprehension that these multiple perspectives provide. They also present ways to enhance and progress the practical, creative musical landscape. See my post titled M=m for a more in-depth look at how mathematical operations support music, and vice versa.

            A theoretical musician studies how music works with a scientific and evidence-based, while at the same time open, mindset. She forms ideas from creative thinking, then tests and validates these theories through reasoning and experimentation. Curiosity is vital, and with the consistent practice of theoretical music, she continually questions and shapes the existing musical understanding found in modern society.

            Other terms that deal with explaining musical functions are often rigidly entrenched and settled through years of cultivation and tradition. Theoretical music offers a chance to doodle and muse about the workings of music with a "clean slate," where the ideas therein carry no offense to any establishment. In other words, TM is its own practice with unique skills and interests. Being a theoretical musician is as simple as applying and utilizing the definition above. If these principles already come naturally to you, it is surely already adding to our understanding of how music works. If this is the first time hearing about these ideas, welcome to the world of theoretical music!

Going Around in Circles (Of Fifths)

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     Many ideas in the world are superficial constructions created to simplify and avoid the complexities of life. What's more, some of these ideas go largely unexplored and unquestioned. A concept in music known as the circle of fifths (COF) could qualify as one of these ideas. Indeed, a number of musical theorists elegantly simplify music into this single circle, and it has become a foundational symbol of most modern music and theory. While the COF has been useful to a degree, like most complexity-simplifying concepts, might it stifle deeper understanding?

      First off, what is the circle of fifths? It is a repeated cycle of one of the most, or if not the most, important musical intervals known as the "perfect fifth." Musicians throughout history have analyzed where, and how, fifths shed light on music. In modern music theory, when the fifth of every tone is taken consecutively, it circles back around to the same tone. At least, it seems that way. Curiously, it takes twelve successive fifths to complete a circle. Hence, the result is the twelve-tone scale found in most modern music. This, in theory, makes music more understandable and practical, because any musical pattern or song can then be taken through only twelve permutations (keys) before returning to square one.

      While the COF makes sense conceptually, the subject in question is this: does a consecutive series of fifths actually make a perfect circle? Surprisingly, mathematics shows otherwise. A true fifth originates from the third harmonic of a tone, which is measured at 702 cents. If a cycle of twelve true fifths is taken when measured at 702 cents, it very nearly shuts into a circle. The key word in the last immediate sentence is: nearly. When fully calculated, it is off from a perfect circle by a mere 23.46 cents, an interval that baffled Greek musicians over two thousand years ago. This seemingly minute difference is so important that the infamous circle symbol associated with the fifth completely depends on it.

       Consequently, if the math doesn't hold up to support the circle of fifths theory, then what symbol might best represent the concept of a series of fifths? If a closer look into nature is taken, one eventually finds a perfect fit: the spiral. A spiral always remains open, as do successive fifths. A spiral can expand or contract, as can successive fifths. A spiral can theoretically extend indefinitely, as can successive fifths. The parallels are clear.

       Symbols are powerful due to humanity living largely visual-based lives. With a simple change of musical imagery, the very nature of music becomes dramatically more mysterious and complex. When the spiral starts to symbolize the musical fifth, society may begin to visualize music in its true, boundless form. Indeed, the spiral can lead musicians away from circles, and straight into the unknown, spiraling as deep as the imagination allows.

Spiral of Fifths

The Music Diet

            The average American spends four hours and five minutes listening to music every day. On eating, drinking, and physical activity (moderate exercise), all of which are currently considered essential necessities of life, the average American spends roughly a combined one hour and forty-five minutes per day. On the latter examples, there have been countless studies, experiments, and theories as to how these activities affect overall health. Indeed, organizations and individuals worldwide continuously advise the population about healthy ways to eat and exercise. However, studies and governmental advice on what music is healthy to listen to is deficient, even though the average person spends nearly three times the amount of time on listening to music than these other absolute necessities. A short look at the influence of music on society and individuals shows just how important a musical diet can be.

            One of the top questions of the early twenty-first century posed by journalists was "what's on your iPod?" In other words, what music do you listen to (for four hours per day)? This question is considered relevant, and a favorite among interviewers and journalists, because it operates under the assumption that the music one listens to reveals much about that particular person. Naturally, many people do agree that music tells something about one's personality and character traits. An intriguing question that stems from this idea is: does the personality influence the music, or does the music influence the personality? It is quite possible that both scenarios are accurate.

            The effects of music on society is wide and extensive. Some of the most creative minds in the world have received profound insight and direction from music. Notably, this was true for Albert Einstein, who stated, "If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music." The enjoyment and inspiration Einstein derived from music cannot be overstated. Another more recent mind, Steve Jobs, said, "Music is so deep within all of us...", and he made it a key mission of Apple to expand music's role in society with products like the iPod and iPhone. He also received deep inspiration from Bob Dylan and the Beatles, who affected his personality and rebel outlook on life. The examples here are grand and positive cases, but for many individuals, music carries a wide range of effects. These effects contain a variety of emotions and feelings, including inspiration, joy, sadness, frustration, anger, and mental energy.

            Just how long has music been a major part of human existence? The discovery of a small bone flute calculates the range of musical influence to be at least forty-thousand years old. Not only that, but music played a role in many crucial time periods in history, including ancient Greece, where philosopher musicians such as Plato, Anaximander, and Pythagoras intently studied aspects of theoretical and practical music. The enlightenment was surrounded by brilliant composers like Mozart and Bach in Europe. At the end of the day, there are very few practices as ancient and modern as music.

            With the widespread impact music currently exhibits on society, as well as throughout history, perhaps listening habits are worth further examination. If the average person were to listen to four hours of healthy, mentally stimulating music per day, how might that influence human behavior and psychology? It is an interesting question. Unfortunately, a definitive answerwill have to wait until additional research surfaces. In the meantime, it is enough to note the significance of music on day-to-day life, and to contemplate what musical diet can help us along the way.

Citations:

Stutz, Colin. "The Average American Listens to Four Hours of Music Each Day." Spin. Spin, 19 June 2014. Web. 14 April 2016.

"American Time Use Survey." Bureau of Labor Statistics. ATUS, n.d. Web. 14 April 2016.

Isaacson, Walter. Steve Jobs. New York: Simon & Schuster, 2011. EBook.

"Albert Einstein." BrainyQuote.com. Xplore Inc, 2016. 12 April 2016. http://www.brainyquote.com/quotes/quotes/a/alberteins692140.html

M = m

            The field of mathematics has been a source of monumental discovery and realization for over 3,000 years, especially when used in conjunction with another medium. Architecture, engineering, physics, and communication have all reached previously unknown heights when combined with mathematical thinking. Likewise, music has carried a tremendous amount of influence on humanity throughout the ages. It has especially stimulated art and creativity, while at the same time displaying the ability to transform emotions and shape behavior and personality. There are many aspects in the field of music that are still very mysterious. For instance, how is it that a simple combination of sounds from a piece of wood causes a person to cry, or dance, or both? Despite the rich history of these two fields, they seem in the public eye to have grown further apart over the years. In a recent TED talk, one professor frustratingly raised the question, "Why not admit there is a problem with mathematics and music?" (Formosa). With a little simple analysis of some congruent principles, one can see that there might not be a problem with math and music after all.

            One of the easiest shared concepts to understand between math and music is the idea of the octave, or doubling. In music, an octave is a musical tone seemingly the same as another, only higher or lower in pitch. In mathematics, the exponential function or, more specifically, doubling, functions in a highly similar manner. Just like the octave, any doubled number or multiple of two can easily be reduced, leaving the essence of the number intact. A musical octave is attained by dividing or multiplying a string or flow of air exactly by the number two. In other words, without the alternative musical terminology, one could say that the octave literally equals two!

            Like the octave, every other musical tone that exists can be defined using simple math terms. In the words of Harry Partch, a twentieth century pioneer of new music, "Tone is number, and since a tone in music is always heard in relation to one or several other tones­­­­­­­­­­­­­­­­­­­–actually heard or implied–we have at least two numbers to deal with: the number of the tone under consideration and the number of the tone heard or implied in relation to the first tone. Hence, the ratio" (76). Ratios, as Partch implies, contain valuable information about musical tones themselves: namely, they reveal the relationships of tones (intervals) through number interactions, and they relate the number of vibrations and cycles inherent inside all musical notes. Not only do mathematical ratios share scientific and intellectual information, but they also state the accurate physical measurements needed for tones and instruments. When the length of a string or sound hole are taken into consideration, ratios give the musician an exact dimension on where to place the fingers or frets. For example, to hear a sonic form of a mathematical ratio, simply pick a ratio of the total length of a string, say 3/4, measure it out with a ruler, and play. This successful experiment will render the whole musical spectrum of tonal relationships to be as simple as 1/1, 3/2, and 4/3.

            On a deeper level, math and music can work to explain the sonic and musical phenomena that escape conscious perception. This can be achieved through more research in the areas of string waves, string motion, the effects of music on the body and matter, and how sound distributes into the atmosphere. Studies on the effects of music on the body and neurology have lately been particularly prominent, as seen in highly successful books such as This is Your Brain on Music (Levitin). A study by the Academy of Finland has shown that music engages "wide networks in the brain, including areas responsible for motor actions, emotions, and creativity." These groundbreaking findings show what is possible when music, math, and technology work together. In addition, math and music have been instrumental in developing important theories in the field of physics, particularly wave theory. "Physics of music is really the physics of waves. We will concentrate on sound waves, but all waves behave in a similar way. Wave theory is probably the most important concept in physics and especially modern physics, much more so than projectile motion and classical mechanics" (Gibson). As shown, there have already been many breakthroughs from the empirical study of music, and perhaps the best findings are yet to come.

            After shortly examining the striking similarities between math and music, it is possible to find a new perspective on both fields. While music, presently perceived as a "right-brain" activity, and math, perceived as a "left-brain" activity, stand seemingly worlds apart in the public eye, they are in reality like the right and left hemispheres of the brain: part of a cohesive whole that work brilliantly together. In the end, math and music have always been part of a common goal: to understand, discover, and connect with existence more fully. When these two fields, of which separately have accomplished awesome feats for humanity, come together, their impact will be multiplied by two, or in other words, their impact will go up an octave. Same thing, right?

Works Cited

Formosa, Dan. "Why Not Admit There is a Problem With Math and Music? Dan Formosa at TEDxDrexelU." Online video presentation. YouTube. YouTube, 9 Jun 2012. 31 March 2016.

Partch, Harry. Genesis of a Music. 2nd Ed. New York: Da Capo Press, Inc., 1974. Print.

Levitin, Daniel J. This is Your Brain on Music: TheScience of a Human Obsession. New York: Penguin, 2006. Print.

Suomen Akatemia (Academy of Finland). "Listening to music lights up the whole brain." ScienceDaily. ScienceDaily, 6 December 2011. <www.sciencedaily.com/releases/2011/12/111205081731.htm>.

Gibson, George N. "Why Learn Physics Through Music?" Uconn. Uconn, n.d. Web. 31 March 2016. http://www.phys.uconn.edu/~gibson/Notes/Section1/Sec1.htm