Is there a math in music?

mathtutordvd.com - Mathematics and Music - Math Tutor DVD

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Mathematics and Music

Although it might not be apparent on the surface, a strong and revealing link exists between the discipline of mathematics and the art of music. Whether we're considering the complexities involved in harmonics, the myriad ways in which musicians have incorporated the magic of numbers into their work, or the most rudimentary descriptions of sound, tempo, and vibration, mathematics has been interwoven into the fabric of music for thousands of years. This post will explore the profound relationship between mathematics and music. It provides an introduction to a rich subject, one that gives insights into both mathematics and music and can hopefully enrich your experience of both. And while you certainly don't have to be a mathematician to enjoy music of all kinds, we hope that after reading this post you'll be interested in the pursuing the subject further. Because this is an incredibly vast subject, we'll confine ourselves to an overview of it in this post. We'll begin with the musical theories of Pythagoras and a broad look at the importance of mathematics at key points in musical history. Lastly, we'll conclude with a summary of the links between mathematics and music theory.

Pythagoras, Math, and Music

The Greek philosopher Pythagoras was one of the first historical figures to emphasize the relationship between mathematics and music. Though his life and work are shrouded in mystery, Pythagoras lived during the 6th century BCE and is considered to be the “father” of philosophy and mathematics. Numbers were of incredible importance to Pythagoras and his followers. Their contribution to the science of mathematics is most visible in the Pythagorean Theorem, which is used to deduce the length of the hypotenuse of a right triangle by adding the square of its other two sides. Pythagoras made other contributions to mathematics as well, but his theories of music are what interest us here. Perhaps his most important contribution to our understanding of music were his discoveries in the realm of harmonics. Pythagoras realized that intervals of music could be expressed as numeric ratios. This discovery, along with many other accurate and inaccurate propositions, made Pythagoras one of the fathers of music theory. Building upon his work, succeeding generations of thinkers and musicians formulated the concepts that eventually became our modern understanding of music and music theory. It's important to keep in mind the “mystical” nature of numbers in the thought of Pythagoras. For him, reality itself (including music) was, in some ways, actually made up of numbers, not merely described by them. While modern science contradicted this postulation long ago, it is useful to use Pythagoras's musical theories as a touchstone for what came later.

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Math and the History of Music

Mathematics has played a key role in the composition of music as well as in its theoretical descriptions. Here are four moments in the history of music when mathematics contributed to an important movement or composition. In 1722, composer Johann Sebastian Bach used recent breakthroughs in root functions to compose his monumental and highly influential work “The Well-Tempered Clavier.” The Mathematical concept known as the “golden ratio” animated great musical works by composers as diverse as Mozart, Beethoven, and Bela Bartok. In 1980, Jonathan Harvey helped usher in the era electronic music by using mathematical techniques to combine pitch and timber on a computer in his “Mortuos Plango, Vivos Voco.” This development opened up a new world of possibilities for electronic composition. In the late 1980's, an influential sub genre of independent music known as “math rock” helped transform popular music. Though not derived as directly from mathematical concepts as the rest of our list, math rock did use quirky time signatures, atypical rhythmic structures, and dissonant chord progressions that built a new pop aesthetic upon conceptual work in mathematics.

Mathematics and Music Theory

As you're hopefully beginning to see, links exist between mathematics and music at a number of different levels. The most fundamental of these links exist at the level of music theory. Put briefly, music theory is a wide ranging term that denotes the study of the most fundamental qualities of music such as notation, harmony, melody, pitch, etc. Although even an introduction to this range of ideas is beyond the scope of this post, we'll conclude with a brief look at the close relationship between mathematics and these fundamental musical qualities. Here are just a few of the areas in which this relationship exists. Music can be thought of as sound that's organized in a specific way. And sound itself, which is a series of audible vibrations in the air, is best described in mathematical terms. The details are very complex, * but the vibrations that comprise sound can be described by using a trigonometric function called a sinusoidal wave. A specific type of sine wave, the sinusoidal wave describes sound in purely mathematical terms such as period, frequency, and wavelength.

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Mathematics also plays a pivotal role in musical harmony. Essentially, harmony is the combination of musical sounds as perceived by the ear and is analyzed in terms of math based concepts such as frequency, pitch, and chord progression. Mathematics is also deeply interwoven with the western notion of musical scale. Take the ‘diatonic scale,' for example. The diatonic scale is the most commonly used scale in Western music and is most easily expressed as a series of numeric ratios. The descriptions of the relationships between math and music theory could continue almost indefinitely, but you can perhaps already see how deeply interrelated the two disciplines are. And even though music theory is the analysis of music, there has been a fertile back and forth between theory and composition that has enriched our musical canon greatly and would not have been possible without the application of mathematical concepts.

Conclusion

Although we've only scratched the surface of an incredibly vast and intricate subject, you've hopefully gained the start of a new perspective on mathematics, music, and the relationship that exists between them. Mathematics can sometimes seem abstract and remote from everyday life. But as you can see from our discussion about its relationship to music, mathematics is a subject that actually plays an ‘integral' in our daily experience.

mathtutordvd.com - Mathematics and Music - Math Tutor DVD

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