Math is a subject that many people avoid or find frightening. However at some point in everyone’s lives there will come a time when math is required for accomplishing a seemingly difficult task. But, with the right skill sets and practice even the most difficult real world problems can be accomplished. There is nothing in this world that math doesn’t affect in some way, I challenge you to think of an activity in your day-to-day life that is’t affected in some way by matht Simple tasks such as walking can be explained with the use of math, How fast did you walk; speed, distance, time, All of these things are related to one another with an equation. If you walk 10 feet in 20 seconds, an equation can be used to find, the average speed you traveled at while walking that distance.
In this equation the speed is 1/2Ft per Second. Very slow. There are so many real world applications of math, Even aspects of music can be explained using math, In this paper I will discuss some of the math that appears in music. Sound Waves Music is sound, with the use of math and some physics we can explain how sound travels which in turn explains how music is made. Sound, when traveling through the air (or any object) is known as a sound wave (see figure 1). We hear sound at a frequency, the frequency is the number of wavelengths that reach your ear in a given amount of time (What is a wavelength? The unit used to measure frequency is Hertz. The equation for this is IHZ:1/Second. To explain frequency we can look at a piano. When a note is played on the piano, a part inside of the instrument known as a ‘drum‘ makes contact with the corresponding string to that note the string then vibrates at a frequency.
Each note has a different string which is used to make the sound we hear. When making music with a piano it’s important to note that not all the notes sound good played together, some notes however work wonderfully together. This is because the frequencies of the notes are related to each other by ‘simple fractions.’ These related notes work together to form what is known as a chord, Once, you know all the chords on a piano it is very easy to play a simple song, but, it takes many years of practice to to master the instrument. All music notes are somehow related, by frequency. The frequencies for each of the notes is available to anyone with a computer and internet access, With these frequencies 1 created my own instruments. By altering the lengths of a ‘/2 inch PVC pipe using an equation I was able to create Palm Pipes. Each pipe when hit on the end creates a different note.
When hitting the pipes in order you can create a tune. I look forward to implementing this as part of my presentation in class. Patterns And The Fibonacci Sequence Music also has a lot to do with patterns and numbers. The Fibonacci sequence is a series of numbers that appear in music ofteni “In 1202, Italian mathematician Leonardo Pisano (also known as Fibonacci, meaning “son of Bonacci”) pondered the question: Given optimal conditions, how many pairs of rabbits can be produced from a single pair of rabbits in one year?” (Lamb), when ‘pondering’ this question he came across the sequence, which was named after him. He did not invent the fibonacci sequence, he just came across it, the fibonacci sequence has existed in nature for Billions of years. The way the sequence works is that you keep adding the two numbers that came before to make up the next number in the sequence. 1+1=2 1+2=3 2+3=5 and so on It can go on forever.
On the piano a scale consists of 13 notes(see figure 3) there are 8 white keys and 5 black keys, these keys are arranged into sections of 3 and 2. Look familiar? It’s the Fibonacci numbers 13,8,5,3 and 2. Conclusion I enjoyed making the discoveries as I conducted research, math and music have so much in common that I didn’t realize before this project. I’ve had a basic understanding of music throughout most of my life, and it‘s been interesting to connect that to math; a subject that I have a rough past with. The Fibonacci sequence was in particular very interesting, I enjoyed reading about the golden ratio (618) and how the difference between each term in the Fibonacci sequence is almost exactly 618.‘ The palm pipes were also very fun to make and l enlisted the help of my little brother Josh to help cut and file down the rough edges of the PVC pipe after I measured each section. it gave us something to do on a rainy afternoon.
