Use Of Mathematics In Music

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Math in Music Introduction The topic chosen is Math in Music. We decided to choose this as both of us learn music and we were interested to find out how math can be applied into it. We figured that it would be great if we could apply what we had learnt in school into our daily life. At the same time, we hope to be able to better comprehend some of the music concepts that may still be baffling us. Some of the first mathematical tools that music students learn about are transposition and inversion. In this coursework, we will learn about the mathematical concepts necessary to formalise these musical tools. These concepts include set, function, and modular arithmetic. Musicians will usually come into contact with transposition and inversion…show more content…
Background reading Numbers were the ruling principal of the universe. As the human ear is unable to numerically analyze sound, people turned to the vibrating string, explored the ideas of the length of strings and pitches, and found simple ratios relating harmonizing tones , a musical tuning system. The Pythagoreans of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, particularly the ratios of small integers. Their central doctrine was that "all nature consists of harmony arising out of numbers". Since Plato’s time, harmony was regarded as an important branch of physics, which is now known as musical acoustics. Early Chinese and Indian theorists also aimed to show that mathematical laws of harmonics and rhythms were important to both the way we understand the world and our well-being. One famous mathematician involved in this concept is Pythagoras. It was him who realised that different sounds can be made using different weights and vibrations. This led to him realising that the pitch of a vibrating string is proportional to and can be controlled by its length, meaning that the shorter the string, the higher the pitch. He also discovered that notes of that…show more content…
Key Signatures The top number of the is always telling you how many beats are in one measure of music. The bottom number always tells you what kind of note gets the beat in that measure. For example, if the bottom number is 4, it means the quarter note gets the beat. If the bottom number is 8, that means the eighth note gets the beat. If the bottom number is 16, it means the sixteenth note gets the beat. Pitch- Wave Frequencies A sound wave creates minute pockets of higher and lower air pressure, and all the sounds we hear are caused by these pressure changes. With music, the frequency at which these pockets strike your ear controls the pitch that you hear. For example, consider the note called "Middle C" (usually the first note learned in piano lessons). This note has a frequency of about 262 Hertz. That means that when Middle C is played, 262 pockets of higher air pressure pound against your ear each second. Equivalently, the pockets of air arrive so quickly that one pocket strikes your ear every 0.00382 seconds. We can draw a graph by putting an X at every time when a pocket of air arrives. The table of note

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