Understanding the Realtion Between Math and Music Essay

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Math and Music: An Introduction and Mathematical Analysis
Galileo Galilei once said that the entire universe is “written in the language of mathematics”. Then, it is not surprising to learn that music is closely related to math. The mathematical application in music will be discussed in this essay.
Rhythm and Frequency To understand the relation between math and music, the primary step is to study the nature of rhythm, frequency and amplitude. Everything around us has its own pattern of rhythm, from the motion of protons and neutrons, to the beats in rock music. According to Garland (1995), rhythm is determined by the periodicity of vibration of certain object in its surrounding substance, or medium (p. 28). The vibration is
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Amplitude refers to the distance from crest or trough of the wave to its equilibrium position. Garland (1995) stated, frequency is a term that describes the number of waves, or vibrations, that pass a given point per second (p. 28). It is inversely proportional to the wavelength, which is the distance of one wave cycle. Frequency can be evaluated in the pitch of a tone: a higher pitch has a higher frequency. A simple tone has constant frequency and amplitude, and its graph is similar to a sine curve. Tones that are more complicated result from combinations of several simple curves. The smallest pure tone frequency in complex tunes is called fundamental frequency. Integer multiples of the fundamental frequency make the resultant tone musical.
The graph below shows the frequency data from A3 to A4 key. Note that A4 key has twice as much frequency as A3 key, because any two keys that are one octave apart have the frequency ratio of 2:1. Further inspection shows that two adjacent notes are in the ratio of 1.059…
For example:
Freq. of A#3 / freq. of A3 = 233.1 Hz / 220 Hz = 1.059…
Freq. of C4 / freq. of B3 = 261.6 Hz/ 246.9 Hz = 1.059…
Freq. of G4 / freq. of F#4 = 392.0 Hz / 370.0 Hz = 1.059…
The examples show that the frequency of any note is a product of the frequency of the adjacent note before it and the constant number 1.059.
Proof:
Let an octave start from key A. The ratio of frequency between adjacent keys is h.
Then,

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