Mathematics in Art
My perception of mathematics is that it is abstractly intertwined in countless disciplines: science, economics, nature, and art – virtually anything. Therefore, everyone is an active participant in it in some discrete respect. This perception trumps my previous perception that math was only involved in objectively defined mathematics, and only useful to left brain dominated actions and individuals. However, as innovation is a crucial component of mathematical advancements, I have come to see where I commonly use math in my life. It applies not only to one aspect but two. These are music and literature, specifically poetry, due to counting rhythm and metre.
Music and literature have always been important components in my life. I have always enjoyed extensive writing and reading, a passion that has never faltered. Music has also always been very influential to me. Not only do I enjoy listening to music, but for five years I actively played the stand-up bass in a symphony. I would argue that the bass is the backbone of sound, and in classical music where precision is everything, synchronicity is crucial to the auditory pleasure of both audience and performer. Sound is the principle perception of music, but without math, we would never hear anything.
Sounds are sinusoidal vibrations measured in frequency and amplitude. Frequency is the tone pitch measured in cycles per second in hertz, and amplitude is the height of sinusoidal function detected as tone volume. Their respective equations are:
Frequency: f =1/T (f= frequency, T= time)
Amplitude: A sin (2pi ft + p) (p = phase shift)
A phase shift is timekeeping, as the physiology of our hearing naturally breaks sound into sinusoidal vibrations. These vibrations are localized on the basilar membrane of our brains that mirrors the Gabor Analysis Theory of Sound. This theory says that two pure sounds (or more) can be sounded together and perceived as one. Spectrographs have been used to provide quantitative dimensions in order to understand the artistry of compositions using the Fourier Series Analysis. This analysis, simplified, determines the sinusoidal frequency and phase content as it changes over time, thus making sense of waveforms that appears periodic, though they are not a pure tone. The Fourier Analysis states that any periodic function of frequency can be realized as a sum infinitely of sines and cosines (otherwise known as “Fourier coefficients) whose frequencies are multiples of f. Essentially, the analysis decomposes periodic vibrations into pure tones.
Now that it has been discovered how math is responsible for the understanding and manipulating sound, the focus can be shifted from science to art. Like math, music is dominated by patterns and ideas that must fit together harmoniously. There is symmetry in music, for a chosen theme can be transposed, inverted, and/or reflected in time to produce variations. Additionally, the generation of new harmonies is done within the Circle of Fifths. The 3:2 ratio of fifths that compose chromatic scales is rescaled, as well as octaves whose ratios are 2:1. Melodies also have a geometric shape, which can be physically seen through Parsons Code which uses rotations to identify music by the ascending and descending changed of pitch:
There exists probability in music as well. For example, the classical composer Joseph Haydn’s minuets have six parallel staves chosen by a dice roll. Since there are sixteen bars total, there are 2.7 trillion possible variations of the minuet!
Music is closely connected to math in its architectural design and numerous possibilities. Similarly is poetry. There are patterns in the rhyme schemes and meters, which include iambic, trochaic, anapestic, spondaic, and dactylic. Meters are determined by the stressed and unstressed syllable patterns in a verse that give the poem rhythm as well as rhyme. For example, an ode is a form of poetry with ten lined stanzas rhyming ababcdecde with the eighth line in iambic trimeter and the others in iambic pentameter. A ballad has a core structure of a quatrain with an abcb or abab rhyme scheme. The first and third lines are in iambic tetrameter, and the second and fourth in trimeter. The symmetry presented here is not just structural in meter, but also in idea. Like when solving both sides to find the solution to an algebraic equation, the reader examines both forms of meter in the stanza to come to the conclusion of what the poem is about. I have enclosed a ballad stanza to further demonstrate rhythm in poetry (the consistency of only one stanza is valid, for in a ballad there is no definite number of stanzas that is must be composed of; only how many it takes to get the narrative across) in one that describes the Fibonacci line:
“The Infinite Chrysanthemum”
Grow in golden angle
Imperfection is overcome
Colored spirals do form
The infinite chrysanthemum
Notice the appropriate rhyme and rhythm scheme, as well as mathematical muses. Finally, to best describe the relationship between mathematics and literature, the quote by astronomer Galileo Galilei artistically transcribes it best:
“The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.”
Words are as numerous in options as numbers, and can be used to artistically describe something as math does scientifically. Even prose, which is my personal specialty, which is seemingly without meter, still possesses a rhythm to it. Sentence length should vary to avoid making stocky or breathless phrases. There should be music to the flow of words. Such is it that math can be present anywhere, I would argue after writing this paper that all disciplines of science and talent are connected as they exist within each other.
Works Cited
Lynch, Peter. The Mathematicians Patterns, like those of the Composer, must be Beautiful. The Irish Times, 25 May 2017, irishtimes.com.
Austin, David. “No Static at all: Frequency Modulation and Music Synthesis.” Feature Column: Monthly Essays on Math Topics, American Mathematical Society, 2017, ams.gov.