Getting to Know You Part 5

Gabrielle Antolovic #48

The Beginning Of My 'Musical' Life

I began learning to read music at age 5. Music has been a major aspect in my life and has been also been a major aspect in many other people’s lives throughout history. The earliest form of Music was drum based that came from Animal hides originating near India. By 4000 BCE the Egyptians had created harps and flutes with wood. By the European renaissance an instrument was popular by plucking a string as the player presses a key. The Harpsichord. Many don’t know that is why a piano is placed behind the strings in an orchestra. It is a string instrument. Music continued to evolve throughout time. In the 1980’s composing computer music became popular. No longer was a wooden frame, or animal hind required to make music. All you needed was a computer and some keys. The advancements in this industry are why it is worth $168 Billion today. It has gone from one beat to thousands of sounds blasting in your ears at lightening speed as you put your headphones in. The music achievements that I have witnessed in my lifetime have astonished me. As many others, I am looking forward to the future.

Understanding The Role That Math Plays

Mathematics has played the role of the beautiful and dynamic character of Juliet in the Music world. Music, or Romeo, could never function without his dainty lover in Romeo and Juliet. Without Juliet, Romeo would be only a lost boy, standing at the bottom of a balcony. With Math, Music could never be altered or evolved to what it has become today. It would never be something that has changed throughout my sixteen years as I recognized in Getting to Know You Part Two.

According to Mathematics Illuminated the world today knows three things: Sound is caused by compression and rarefaction of air molecules, we perceive the amplitude of a sound wave as its loudness, or volume, we perceive the frequency of a sound wave as its pitch. Frequency is the number of occurrences of a repeating event per unit time. In conclusion, the way an organism uses it’s sense of hearing to listen to music is in the form of a ratio; number of occurrences to the amount of time. By one altering the frequency, we are altering the sound that the listener will hear. This makes each song different. If the mathematical ratio of number of occurrences to the amount of time was not devolved, than no song would be different, in result music could never evolve. Music could never have enhanced to what it is today. It would be flat and dull, and uninspiring. Math has played the role of Juliet, changing Music, Romeo into a devote lover for all eternity. Math has changed the way music has not only affected my life, but the whole world’s.

Beethoven- Minuet in G

Music could not be altered to be something inspiring, or something moving if math did not exist.

The Math Behind Music

Math simply is the basic understanding of Music. Without math, one could not alter music to create different melodies to moves souls, to lift people up, or to inspire them. Society today would not be able to enjoy music in the manner that that it has grown accustom to; for a large music variety could not exist without math. The field in which I am focusing on relays so heavily on math, that if math did not exist neither could it. The relationship is powerful. Mathematics has played the role of the beautiful and dynamic character of Juliet in the Music world. As music, or Romeo, could never function without his dainty lover. Without Juliet, Romeo would be only a lost boy, standing at the bottom of a balcony. Without Math, Music could never be altered or evolved to what it has become today. Frequency, tuning, patterns, and harmony are only a few examples of the numerous ways that math affects the field of music.


According to Mathematics Illuminated the world today knows three things: Sound is caused by compression and rarefaction of air molecules, we perceive the amplitude of a sound wave as its loudness, or volume, we perceive the frequency of a sound wave as its pitch. Frequency is the number of occurrences of a repeating event per unit time. In conclusion, the way an organism uses it’s sense of hearing to listen to music is in the form of a ratio; number of occurrences to the amount of time. By one altering the frequency, we are altering the sound that the listener will hear. This makes each song different. If the mathematical ratio of number of occurrences to the amount of time was not developed, than no song would be different, in result music could never evolve. There would be no genres or different types of music. Music could never have enhanced to what it is today. It would be flat and dull.


Instruments are how each musician translates their feelings to the audience melodically. Tuning is an essential part of a musician’s routine. The easiest example of how math affects music would be tuning a piano. As Zzsounds states, The interval between one piano note and the next should always be an octave. When it becomes out of tune, the octaves are no longer the proper length apart. There is also a set distance between notes like C and G and D and A; it should be a fifth. An octave corresponds to the ratio of 2/1; a fifth corresponds to 3/2. So, when someone is tuning a piano, they use the Pythagorean scale to measure the distance between the notes and adjust them properly. That is just one example of how a single instrument uses ratios for tuning. Other instruments use different ratios for their vital tuning according to the number of notes they posses. Again, math simply is the basic understanding of tuning; an essential to routine to all musicians.


Each song that one hears is a different arrangement of patterns of musical notes that create the chorus and verses of each song. Pattern is another way that math affects the field of music. The signature pattern is what differentiates a song from another. This is similar to many ideas in math. One example would be multiplication tables; each have their signature patterns that distinguish one from another. Like 9 multiples, in the second figure each number goes down consecutively: 9, 18, 27, 36 etc. Just as songs have signature note patterns that distinguishes one from another. An additional example would be a fractal. A fractal is a geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature according by the American Heritage Dictionary. Minuets are songs that have a pattern of three notes. The first and third notes being accented. This pattern distinguishes minutes from other types of music as do certain patterns in math.


As understood before, when a musical instrument creates waves of sound it produces the air to vibrate causing a frequency. The pitch of the note that a musician is playing is determined by the rate at which the sound waves are vibrating. ASA Educations defines harmony as “when a note with frequency "x" is produced, it has

overtones at multiples of x, at 2x, 3x, 4x, 5x, 6x, 7x, ...For example, if a musical note is produced by air vibrating 24 times per second, it will have overtones with sound waves (in air) vibrating at 48, 72, 96, 120, 144, 168, 192,...A major chord is formed by playing the 1-and-3-and-5 notes of a major scale at the same time. In a Pythagorean Scale, the ratios between the 7 notes of a major scale are 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 If the 1-note is produced by sound waves vibrating at 24 times per second, the seven scale-notes are: 24 27 30 32 36 40 45 48.” When this pattern is written out we can see the mathematical relationship between the overtones of the first, the third, and fifth notes. A persons ears recognize the "matching up" of overtone-waves as an enjoyable harmony that adds musical depth to any song. Harmony is crucial in any genre of music to create a more intricate, convoluted, and interesting to listen to a work of music.

"Mathematics and Music." Mathematics and Music. N.p., n.d. Web. 20 Feb. 2013. <http://www.math.niu.edu/~rusin/uses-math/music/>.

"Fractals." TheFreeDictionary.com. Farflex, n.d. Web. 19 Feb. 13. <http://www.thefreedictionary.com/fractal>.

"The Mathematics of Musical Harmony." Musical Harmony. N.p., n.d. Web. 22 Feb. 2013. <http://www.asa3.org/ASA/education/teach/harmony-cr.htm>.

"Music and Mathematics." Wikipedia. Wikimedia Foundation, 25 Feb. 2013. Web. 22 Feb. 2013. <http://en.wikipedia.org/wiki/Music_and_mathematics>.

MacPherson, Kitta. "Princeton University - Researchers Map the Math in Music." Princeton University - Researchers Map the Math in Music. N.p., n.d. Web. 21 Feb. 2013. <http://www.princeton.edu/main/news/archive/S20/83/65A48/index.xml?section=topstories>.

May not music be described as the mathematics of sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music -- music the dream, mathematics the working life.

Ideas for "The Project Phase"

Frequency

1. Utilize Violin, and give a physical demonstration

2. Give examples with a tuner- show different frequencies

3. Compare and contrast varying frequencies


Tuning

1. Utilize piano, and give physical demonstration

2. Show example or incorrect tuning, or incorrect note ratios

3. Show example of properly tuning, playing ratios


Musical Patterns

1. Demonstrate patterns within music, using varying examples that are known

2. Listening and recognizing patterns activities with songs on the radio

3. Within written music, highlight patterns


Harmony

1. Utilize piano or violin giving physical demonstration

2. Layer instruments, illustrating harmony

3. Show disharmony, and the mathem