# Applications Of Trigonometry In Music Essay

1294 words - 5 pages

Trigonometry is the branch of mathematics that is based off on the study of triangles. This study help define the relations between the different angle measures of a triangle with the lengths of their sides. Even though trigonometry is the study of triangles, it is mostly used to study right angled triangles with the six functions: sine, cosine and tangent, and their reciprocals cosecant, secant, and cotangent. These functions are made by the corresponding points to the infinite number of angles that are present when continuously rotated in the unit circle. Because of this, each of the trigonometry functions has a tendency to repeat itself after every complete rotation around the unit circle. (Pierce) Since everything in math can be applied in real-life situations and problem, trigonometry has many applications in the real world as well, such as in architecture, astronomy, and in music. Likewise, the purpose of this essay is to further explore and research the real world applications of trigonometry in music. Music is a subject that intrigues me because it is like a whole other language on its own. It is very unique with its notation system and different styles, just like in literature. Thus, I wanted to learn more about its background so it can help me to better understand its concepts, like how the human ear receives music and how it can interpret high notes and/or low notes when it is by itself or when it is harmonized with others.
Speaking of how the human ear receives music, sound is produced by vibrations that transmits energy into sound waves, a form of energy in which human ears can respond to and hear. Specifically, there are two different types of sound waves. The more common of the two are the transversal waves, which are sound waves that move up and down. Despite being more common, this type of wave makes it easier to decipher different sounds/pitches. The other type of wave is the longitudinal wave. Instead of having sound waves that move up and down, these sound waves move back and forth. (Kessler) In spite of their differences, both of these waves have amplitude and frequency which in turn have their own separate effects on the properties of sound. Amplitude determines the intensity, in other words, the “loudness” or “softness,” of a sound. The higher the amplitude, the louder the sound is and naturally, the lower the amplitude, the softer the sound will be. Amplitude is usually measured in decibels (dB), where 80 dB would be equivalent to the sound of the vacuum cleaner while 160 dB would burst our eardrums. (Kessler) Amplitude and frequency are properties of sound waves that are independent of each other, meaning a note can have low amplitude but still have a high frequency, like high C played very softly. On the other hand, frequency, how often the object vibrates when a sound wave passes through the medium, determines the pitch of a sound. Similar to how the amplitude affects the intensity of sound, the higher the frequency...

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