Math and Music: An Introduction and Mathematical Analysis

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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 direction in which it is traveling. In a longitudinal wave, however, the particles vibrate parallel to the direction in which it is traveling.

Consider the difference in human voice, animal noises and instrumental sounds. The unique characteristic of sound results from amplitude and frequency. Amplitude refers to the distance from crest or trough of the wave to its equilibrium position. Frequency is a term that describes the number of waves, or vibrations, that pass a given point per second (Stenstedt 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 resulta...

... middle of paper ...

...umentation) + (Lyrical Content) = Genre? T + K + R + I + L= G

Average results: Tempo: 84.6 bpm Key: Major Rhythm: Slow, Steady, less prominent, more background oriented Instrumentation: Acoustic guitar, steel guitar, bass guitar, Lyrical Content: Physical appearance, Physical relationships, summertime, the types of cars one drives.

References

Director, B. (1994). What mathematics can learn from classical music. Fidelio Magazine, 3(4).

F.Putz, J. (1995, October). The golden section and the piano sonatas of mozart. Mathematics

Magazine, 68(4), 275-282.

L.Crocker, R. (1964). Pythagorean mathematics and music. The Journal of Aesthetics and Art

Criticism, 22(3).

Loy, G. (2006). Musimathics: The mathematical foundation of music. (2nd ed., Vol. 1).

Cambridge: MIT Press.

Stenstedt, K. (1995). Math and music. Palo Alto: Dale Seymour Publications.

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