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 ...
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What is trigonometry? Well trigonometry, according to the Oxford Dictionary ‘the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.’ Here is a simplified definition of my own: Trigonometry is a division of mathematics involving the study of the relativity of angles and sides of triangles. The word trigonometry originated from the Latin word: trigonometria.
For any individual who either avidly listens to or performs music, it is understood that many melodies have amazing effects on both our emotions and our perception. To address the effects of music on the brain, it seems most logical to initially map the auditory and neural pathways of sound. In the case of humans, the mechanism responsible for receiving and transmitting sound to the brain are the ears. Briefly stated, the outer ear (or pinna) 'catches' and amplifies sound by funneling it into the ear canal. Interestingly, the outer ear serves only to boost high frequency sound components (1). The resonance provided by the outer ear also serves in amplifying a higher range of frequencies corresponding to the top octave of the piano key board. The air pressure wave travels through the ear canal to ultimately reach and vibrate the timpanic membrane (i.e.-- the eardrum). At this particular juncture, the pressure wave energy of sound is translated into mechanical energy via the middle ear. Here, three small bones, the ossicles, vibrate in succession to produce a unique pattern of movements that embodies the frequencies contained in every sound we are capable of hearing. The middle ear is also an important component in what music we actually keep out of our 'head'. The muscles grasping the ossicles can contract to prevent as much as two thirds of the sound from entering the inner ear. (1, 2)
The concept of the Renaissance man is somewhat of a lost ideal, replaced by the specialized philosophy of the industrial era. From the 14th to 17th centuries; however, it would be common to find a man with a profound knowledge of both the Arts, music, poetry, literature, art, and the Sciences, mathematics, physics, chemistry, biology. The Renaissance man embraced all forms of knowledge, and through a deep passion for both the Arts and Sciences, used each discipline to expand the other. Unfortunately, in the 21st century, this same philosophy is far gone. Where these two fields once were used together to create an ultimate beauty, they are now pitted against each other by many scholars. It is not uncommon now for a mathematician or physicist to dismiss the Arts as a waste of time; or for an artist or musician to proclaim the Sciences as useless to them. As both an avid blues guitarist and an IB math student, I aim to contrast this modern opinion. I will do so by exploring the relationship between the Arts and Sciences; specifically mathematics and music. On a personal level, I find this to be extremely important, as I hold a deep value for all means of human expression and learning. I believe also that the Arts and Sciences hold one great unifying thing together, which is the search for Truth and Beauty. In a modernized world where ideas and creations can be shared so quickly; the potential for a profound knowledge and passion of both these fields has never been greater. Concepts I plan to explore are: how musical scales can be made using Fibonacci ratios, the Golden Ratio’s relationship with music, equal temperament, where else the Fibonacci numbers occur in music, the exponential nature of octaves, and how exposure to music help...
the directions of such waves. Eight balls were carefully balanced in the mouths of eight dragons placed around the outside of
Music and the relationships of music have changed drastically in our society. The course of studies and the evaluations of the applications of the technology of music, the making and the listening of music have changed in the way we listen to music, the styles of music in our society and in the media. The importance of the technology in music today, has, over the past century been charted through the study of musical examples and through viewing how human values are reflected in this century's timely music. There are very many different types of music that are listened to. There are readings, writings, lectures and discussions on all the different types of music.
Throughout the semester, various styles of music and the aspects of culture associated with these styles have been analyzed. Musical elements such as dynamics, texture, form, timbre, melody, instruments, etc., have been used to thoroughly explore each kind of music from different areas of the world, with an emphasis in music from Africa, India and Indonesia. These aspects of music go far beyond just music itself. Culture also plays a huge role in music and the accompanying musical elements. Each country and culture has a different style and distinctiveness that add to what makes the music of that certain culture unique. Music in Africa may differ dramatically from music in Indonesia or India not only due to those certain elements but also due to how it is interpreted by people and what it represents for those people. In addition to this, what one may consider music in one culture may not be music to another. These differences have been made apparent in the several demonstrations that we have been exposed to in class.
Realworldstudios.com. 2013. The Big Room - Real World Studios. [online] Available at: http://realworldstudios.com/recording-studios/the-big-room/ [Accessed: 25 Nov 2013].
http://www.musicianbrain.com/papers/Schlaug_Music_Child_Brain_NYAS2005.pdf>. " Scientific American Digital: Digital Archive of All Issues from 1993 to Present." Scientific American Digital: Digital Archive of All Issues from 1993 to the Present. N.p., Nov. 2004.
Through out the history of music, acoustics have played a major role. After all if it were not for acoustics the quality of sound that we know today would not exist. The word acoustics comes from the Greek word akouein, which means, “to hear”(Encarta Encyclopedia). Since music has to be heard in most cases for enjoyment, acoustics obviously take on a very important role in the pleasure that music brings to the ear. Acoustical architecture and design are two key elements in the way music sounds. For example, an electric guitar played in a concert hall would sound very different compared to the sound produced in a small room. These differences can be explained by the acoustical design of the room and the reverb created by both the instrument and the room in which it is played. These differences signify the importance of acoustics in music.
"The Purpose of Music." EzineArticles Submission - Submit Your Best Quality Original Articles For Massive Exposure, Ezine Publishers Get 25 Free Article Reprints. Web. 23 Feb. 2010. .
Dobrian, Chris. "Music and Artificial Intelligence.” In University of California, Irvine Department of Music. UCI.edu,
waves are further divided into two groups or bands such as very low frequency (
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics