Mathematics and Music

Scholars have attempted to understand the relationship between mathematics and music for many years. People in the field of music can readily understand the definite relationship between mathematics and music. In fact, some studies suggest that mathematics is in every field of study. Harmonic rations dominated music during the Pythagorean times. Studies have identified the relationship between tonal quality and mathematics.Advertising We will write a custom term paper sample on Mathematics and Music specifically for you for only $16.05 $11/page Learn More Tonal quality is responsible for creating the audible impression of music. These are â€Å"sound waves vibrating at distinct frequencies† (McPhee 1). Musicians believe that tonal quality creates enjoyable music to mathematicians. In order to understand the relationship between tonal quality and mathematics, we can focus on the concept of dissonance and harmony in music. Harmony and dissonance req uire specific notes to blend in music. Conversely, not all notes can blend in music. Ancient Greeks noted that mathematical integers relate to musical notes (Reid 1). In this context, Greeks observed that vibrating objects produced overtones. These overtones originate from a single object. As a result, the tones created harmonic series like 1/2, 1/3, 1/4, 1/5. Tuning practices control pitches of music in order to create a common tone between intervals. Therefore, tuning must have fixed reference. Music systems may have 440 Hz as equivalent to A. Tuning must control out of tune tones using specific reference pitch. Mathematical analysis indicates that integer multiples also generate their base frequencies, but with weak intensity. For instance, when a string with specific length generates â€Å"a frequency of 220 Hz, there are corresponding frequencies of 440 Hz, 660 Hz, and 880 Hz and others† (Hearle 1). Octave also highlights the relationship between mathematics and music. T his relationship is evident when creating high or low musical notes in vibration. Octave also creates both interval and chord depending on their numbers. Both musicians and mathematicians use the analogy of shortening or lengthening a string to explain the concept of octave. The idea shows that any change in the length of the string results into a new tone. Music and mathematics also relate in Pythagorean tuning. This explains the scientific relationship between human ear and sound waves. This idea resulted in a mathematical-based system of tuning. This is the rule of perfect fifths in mathematics and music.Advertising Looking for term paper on art and design? Let's see if we can help you! Get your first paper with 15% OFF Learn More It shows that intervals between â€Å"the first and the fifth note of the proposed scale would be tuned to a ratio of 2:3† (McPhee 1). In the same case, it uses the ratio of 1:2 to indicate the relationship between the first and eig ht notes. These ratios indicate the relationship between wavelengths of different notes. Tempering has mathematical explanations for creating harmonic and melodic pair of notes. These creations result into ratios and compounds. This is where musicians apply 12-tone scale through the octave and pure fifth with reference to rations of 2:1 and 3:2 (Hearle 1). Musicians use the Pythagorean scale to build music systems using integer notes. Developers of musical keyboards apply the idea of integer notes to develop the system. They use a system of tuning known as â€Å"tempering when creating even-tempered or well-tempered systems† (Reid 1). In this process, mathematical rules apply. In an even-tempered system, the system creates all equal or slightly different notes of the same tune and then distributes the error on an equal basis among all scale notes to create compound musical chords. There is also equal temperament mathematically defined as 1:12. This is the standard for Europea n applicable in Western music. This style is simple and versatile making it popular among users. All the ratios between 12 correspond to two as applicable in modern pianos. The development of meantone also has mathematical concepts. Meantone uses Just Intonation of the scale, but with pure thirds. The model has C, G, D, A followed by a pure major. Just Intonation has regular tones with harmonic numbers, which rely on a single primary frequency. This is the opposite of equal temperament. Writers argue that people tend to prefer the Pythagorean intervals. Therefore, we have to learn how to listen to other sour tuning from well-tempered music. Further, some studies have shown that musicians tend to apply sweet notes of Pythagorean. Mathematical aspects help in understanding the concept of wavelengths and musical notes. In this case, mathematical concepts help in discovery of various ratios, which can result into harmony in music. The musician must combine musical notes with complementa ry wavelengths to create both high and low waves, which must relate with each other for harmonic sound. This aims to avoid dissonance in music notes.Advertising We will write a custom term paper sample on Mathematics and Music specifically for you for only $16.05 $11/page Learn More Mathematics and music also relate on the golden ration and Fibonacci sequence. The above principles mainly focus on the aesthetic nature of music. Fibonacci sequence has systematic sequence of numbers in which every two preceding numbers add up to the next number (1, 1, 2, 3, 5, and 8 etc). These numbers help in comprehending musical patterns. On the other hand, the golden ratio is mysterious, scientific ratio responsible for aesthetic in music. These are mathematical concepts, which help people appreciate aesthetic nature of music. For instance, some groups of notes in a given scale show Fibonacci sequence as well as the golden ratio. Works Cited Hearle, Noah. The Relations hip between Mathematics and Musical Temperament. (n.d). Web. McPhee, Isaac. Music and Mathematics. 11 March 2008. Web. Reid, Harvey. On Mathematics and Music. (n.d). Web. http://www.woodpecker.com/writing/essays/math+music.html. This term paper on Mathematics and Music was written and submitted by user Douglas Velazquez to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Writing a Sample Letter Essay - Learn How to Write a Letter Essay That Compares

Writing a Sample Letter Essay - Learn How to Write a Letter Essay That ComparesFor students who want to do their homework before heading out to do a sample formal letter essay, it's helpful to first set a goal. Usually, the goal is to write a sample formal letter essay that you have to submit to a particular school. The first thing to do is gather information about the school by visiting its website and reading its latest releases.After doing so, you should make a note of the current required courses and the curriculum and inform your parents or guardians. Always bear in mind that college placement or examination is a combination of time and effort. If you want to make use of the time you have during this time, consider writing a sample letter essay on your own.You will also find that writing a sample letter essay can be difficult and complex. That's why it's important to do research and gather details about the school's college placement test. This way, you can determine if you'll n eed help with writing a sample letter essay. The research can be done either on the internet or through the newspaper.There are some basic facts that you will need to know if you want to write a sample letter essay. The first fact is the topic of the letter essay. The topic must focus on a particular aspect in the school curriculum. It is helpful to know more than one aspect because that way, you will have a better idea about how to write a sample letter essay that fits the school's requirement.As mentioned above, the second important detail is that you need to use words and sentences that are suitable for writing a letter essay. Because the topic of the letter essay is all about the school, you don't need to be too formal. This means that you can use a lot of informal and casual terms in your letter essays.Remember that your sample letter essay must have one subject in common and that is your name. You may also include your address and the date that the sample letter essay was writ ten. Lastly, you need to state why you are applying to the school. If you can find the reason to be the main reason behind your application, you can easily convince the school to accept you.Last but not least, in order to write a sample letter essay, you need to keep in mind the following points. First, it is important to determine your task because you will need to prepare everything before hand. Secondly, you must decide how to write a letter essay with confidence and ease. By following these tips, you will surely make your academic requirements fulfilled in your next year of college.