Musical Notation

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!

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. <>.

Gibson, George N. "Why Learn Physics Through Music?" Uconn. Uconn, n.d. Web. 31 March 2016.