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Math? In "My" Music? More likely than you think

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When approaching the topic of either music or math, both have a response as to what to expect when either are brought up, because of the structural priming (a process in which patterns get repeated until ideas are firm) we experience, math tends to have more of an academic response, while music receives an emotional one. In EFP’s article on “Working to Keep the Arts in Public Schools,” since 2008, almost 80% of school districts have had to work with budget cuts and most often, the first to go are art programs not having an impact on standardized tests (Jacob Shmitt). What should be understood is that music should have more of an academic response than just an emotional one; in other words, I argue that music should be seen as more than a humanity, it should be seen as a science as well.

The idea of music is most often related and attached to the concept of emotion. Due to an artist’s expression, Jay Schulkin and Greta B. Raglan’s article on, “The Evolution of Music and Human Social Capability” define music as, “… a core human experience and… functional because it is something that can promote human well-being by facilitating human contact, human meaning, and human imagination…” (Jay Schulkin). In other words, music is an important tool used to link personal feelings and expose personal emotions to the outside world. To use Schulkin and Raglan’s definition of music, it can be applied to support the definition of humanities. In humanities, the idea is to study different aspects of human society, and to understand human emotion and how to express it. Their definition of music fits into the definition of humanities as, society uses music to express: trouble, emotion, or political issues in a manner of “art” (Jay Schulkin). Applying Schulkin and Raglan’s definition of music, the interpretation of music being a part of humanities makes sense because the idea of emotion is seen as something stronger than logic. Although, if it indeed is true that music is nothing more than emotion and necessity, then it is implying that math is not included into music. Robin Hirsch, in her article, “Is Mathematics a Pure Science?” says, “Math is an integral part of virtually every science” (Hirsch). In other words, Math plays an important role in science, not only that, but math is factual math and is something that cannot get an emotional response.

In response to Hirsch’s statement above, math is pushed into an academic category that cannot be used to help and assist in other means besides purely on an academic’s basis. An example of this can be referred back to EFP’s article on school budget cuts. As said before almost 80% of school face those cuts and almost the first to go are art programs. The reason for this being is because in standardized testing, math can be tested by how an individual can understand and apply a formula to solve an equation, in science, the use of understanding graphs and knowing terms can understanding what can be done with theories are a way to test an individual’s flexibility of mind, in regards to arts, there is no real way to test how intelligent an individual is. When an artist paints a meadow or when a musician plays a melody, it connects with an individual and it creates negative or positive emotions to the individual that created it and to the individual that sees/listens to it.

Music is a combination of both math and emotion; to achieve the goal of a pleasurable, harmonic sound, there needs to be a pattern and system as to how the song will be sequenced. Without a pattern, music is nothing more than desultory notes, being played in a non-understanding and un-pleasurable experience. To put music in a constructional point of view, to create a sound, one needs to blow, hit, or strum; the outcome of this is called a note. There are 5 main classification of notes: whole notes, half notes, quarter notes, eighth notes, and sixteenth notes, each having their own counts. Whole notes going on for 4 counts (a count equaling a beat), half notes going on for only 2 counts, quarter notes only getting 1 count, eighth note only for 1/2 a count, and finally a sixteenth note only getting 1/4 of a count. In creating a melody an individual needs 4 total notes contained in a bar called a measure unless the time signature says otherwise. A time signature lets the musician know how many notes need to go in a bar and how to count them. It can go from 2/4, 3/4, or reach out to 6/4 time, but most musical pieces having a 4/4-time signature. Depending on how fast or slow the bar will go, each measure contains a count that will result in a melody. In continuation, a bar contains 4 notes that will be read out as 1, 2, 3, 4 in a pace that is called a tempo. The bar must be accompanied with the correct notes to create a pleasurable sound. To be more specific with using correct notes, key signatures are used to let the musician know what notes need to be played differently in the sharp or flat indication the key of composition. In music, the musician must also play the notes in the correct frequency called pitches. Using all these theories, it can be agreed that math plays an important role in playing, and reading music and that it can fit into Hirsch’s definition of math.

To have a better understanding of what pitches are and how to achieve them, Pythagoras invented the monochord. In Alexander Rehing’s article of “Instruments of Music Theory”, The monochord was a plank of wood with string attached to both ends of the board; somewhere in between, a movable bridge was attached underneath the string to change the sound the string makes when plucked. Only later was the monochord changed into a board with six strings attached. (Rehding). With more strings attached, the theory of octaves is integrated with the concept of music. Two notes that are “complimentary” together, one having twice or have the frequency of the note is important in understanding what octaves actually are. Another important piece of information is to understand that octaves rely heavily on math; to understand octaves, it is helpful to understand that the notes to create one are wave frequencies. Jeffery Rosenthal’s article, The Magical Mathematics of Music, describes wave frequencies as, “A sound wave [that] creates minute pockets of higher and lower air pressure… the sounds we hear are caused by these pressure changes.” Meaning, every note heard has a certain amount of air pressure that is being transmitted into an individual’s ear. An example would be “Middle C,” Rosenthal, states, that on a piano Middle C has the frequency of about 262 Hertz, so when Middle C is played, 262 pockets of high pressure strikes every 0.00382 seconds (Rosenthal). In order to create a pleasurable sound, there needs to be an understanding of which notes have more frequency in order to be able to match that particular note with one that has less than half or double of its frequency.

A guide that can help understand what notes matches with other notes, can be seen in the 12 major scales. The 12 major scales are composed of 16 whole notes each, and seven octaves, these scales are important as they as a part of every instruments and is used to help learn notes as well as understand octaves. In these scales, eight notes on the scale are played in according to the selected note, only after reaching the eighth note does the octave go higher or lower according to what the scale the musician is playing. This is important because, the 12 major scales are not only used universally for every instrument, they have the correct notes for each octave and is the foundation of other music theories.

Although math and music are different subjects, the way an individual processes information is the same. The brain, when learning about a certain topic undergoes several steps to process it. An example to understand this, the theory of SSIRH is implemented. SSIRH stands for Shared Syntactic Integration Resource Hypothesis (Patel), or loosely, a shared of basic symbolic constants and their meaning. This particular theory is focused towards the relation of music and language, but can be closely related with math as well. The theory claims that most of musical and linguistic sequences we experience are put into a high structure based on domain-specific syntactic rules. (Joris Van de Cavey). Simply put, when both music and language are cognitively processed separately, the structure of each of the process is similar. In addition, this theory’s hypothesis is that because both music and language have a similar structural process, when one lacks it uses the other as a base, this is called dependency processing (Joris Van de Cavey). Music, is based on dependency processing as it alone cannot function without a stronger structural process. Each sequence in music has a “hole” in it, needing to be filled with linguistics as this theory states. As already stated, Music is based on dependency processing and relies on other stronger structural processing as it alone is weak. When it comes to the brain structuring math, the same process is applied. Reading math equations like eight times ten or 8 x 10 is broken down to an abstract process, later turning to a verbal thought using domain-specific syntactic rule.

There can be no mistake in understanding that music and math are different. Other arguments can be made that music, even though it contains math, is not seen as a science because it is based too heavily on creating and releasing emotion, and that math is only seen as concrete, only using intellect. Although it can be defined as such, Robin Hirsch writes in his article, “Is Math a pure Science?” that:

It is too wasteful keeping mathematics in its ivory tower where only a small elite are granted the privilege of access. It deprives those outside a powerful technique for understanding and, hence, changing the world. And it deprives mathematics of a vast pool of experience and intelligence which could raise the subject to hitherto unexplored heights. (Hirsch, Is Mathematics a Pure Science?)

To clarify what Hirsch “it” meant in the quote above, it can be referred to as the “hard” sciences. Math can be considered a science because of the concrete algorithms and because it is used in science as well, but if it people only see math as one thing, it makes it difficult for math to evolve and for science to evolve as well. Only seeing mathematics as a concrete science, makes it difficult to understand that math is in almost every aspect of societies lives, not only music. It can be seen in art, cooking, and geography as well.

It can be understood that music is a topic of both emotion and science. In EFPs article, “Working to Keep the Art in Public Schools,” it can be understood that when schools are told to make budget cuts, the first programs to go are usually the arts program. The reason for art programs being cut is because, there is no real way to test student’s intelligence with art. Music is under the category of art because, when playing music, a musician is encouraged to “play with emotion”. in terms of what people define art, it is usually based off of either made with emotion, reciprocated with emotion or sometimes both, made and reciprocated with emotion.

What makes music more of a science, is the mathematics used to create sounds and melodies. In creating a pleasurable and a likable song, patterns and arithmetic needs to be incorporated. Basic counting and understating wave sequencing while playing an instrument is also imperative in creating or playing any music pieces. When playing notes to create music, it is also important to understand pitches and octaves, which go hand in hand and are closely related to wave frequencies. According to Rosenthal, using the piano’s middle C, it is about 262 Hertz that strikes an individual’s ears every 0.00382 seconds (Rosenthal). Using octaves and pitches is also a good use for the sciences as perfect pitch helps in creating a harmony and having a positive reaction as well as correctly notes and melody.

In understanding how important pitches and octaves are, it can be dated back to Pythagoras when he created the first monochord- a plank of wood with strings attached at each end of the board was well as, a small wooden bridge underneath the strings that could move around, causing the strings to create different sounds when moved around (Rehding). Only being upgraded late with more strings, eventually creating pitches, and finally, the creation of the 12 major scales. The scales mainly composed of 16 whole notes, half one octave and the second doubled in hertz or half of it. These scales are the “backbone” in any music theory and are used most often in training with pitch technique and in muscle memory in musicians.

Another way to see music as a math is to understand the process of SSIRH or Shared Syntactic Integration Resource Hypothesis (Patel). Which was they theory that both music and language are cognitively processed separately, the structure of each of the process is similar. It is also said that music, lacks a strong structural base, often relying of another strong base, most often math. Music is under a type of processing called “dependency processing” where again, it lacks a strong structural process, so when processed alone, the thought is being processed with “holes” until a stronger process fills in those holes (math).

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