Math and Music An Introduction and Mathematical Analysis...

Math and Music: An Introduction and Mathematical Analysis 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. Rhythm is determined by the periodicity of vibration of certain object in its surrounding substance, or medium. The vibration is repeated at a constant time length, thus creating wave motion. The repeated portion of the rhythm is referred as a cycle, or one wave. There are two types of wave motion: transverse waves and longitudinal waves. The particles in a transverse wave vibrate perpendicular to the†¦show more content†¦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, A# / A = h, A# = A†¢h A# = A†¢ h B = A# †¢ h = (A†¢h) h = A †¢ h2 C = B†¢ h = (A †¢ h2) h = A †¢ h3 †¦ Since there are 12 half steps in an octave, A* = A †¢ h12 Which means, A* / A = h12, h = (A* / A) ^ (1/12) Since A* / A = 2/1, h = 2^(1/12) = 1.059463094†¦ The frequency relationships within any octave are as follows: Intervals An interval is the scale between two tones. Basically, there are two kinds of intervals: Melodic interval and Harmonic Interval. Musical interval is distinguishable from music degree and music number, because they are indivisible. Since our ears have very complex structure, we are able to hear the harmony and melody very easily. Music is not a set of random pitch combined together. We could recognize different sounds, since our ears are extremely sensitive to intervals, unison and octave. Intervals play the main role in music ofShow MoreRelatedDebussys use of the Fibonacci sequence Essay1403 Words   |  6 Pagesï » ¿Ã¢â‚¬Å"I can count†: Mathematics in Music An Analysis of Debussy’s Nocturne Math has been associated with music for many years, particularly that of the Fibonacci sequence and the Golden Ratio. In Debussy’s Nocturne, composed in 1892, I look into the use of the Fibonacci sequence and the Golden Ratio. 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