Many musical composers have used mathematics in their compositions. Some artists

Question

Many musical composers have used mathematics in their compositions. Some artists have created artworks that use or reflect mathematical principles. Research one such composer or artist, and write an essay discussing the role of mathematics in the composer’s music or artist’s art. Make sure you describe the mathematical concepts that are present in the creative work and what you understand about the mathematics. Your paper must be at least one full, single-spaced page long. Include a citation and a link to the source(s) you used.

Explanation / Answer

Music and Mathematics

"There is geometry in the humming of the strings, there is music in the spacing of the spheres." — Pythagoras

Counting, rhythm, scales, intervals, patterns, symbols, harmonies, time signatures, overtones, tone, pitch. The notations of composers and sounds made by musicians are connected to mathematics.

Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, the Pythagoreans (in particular Philolaus and Archytas) of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, particularly the ratios of small integers.

From Pythagoras' observations of the fundamental mathematical relationship between vibrating strings and harmony to the digitized musical world we enjoy today, the Majesty of Music and Mathematics with the Santa Fe Symphony and the Santa Fe Institute will explore the remarkable interweaving of the languages of music and mathematics."

The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory. In [1] and [2], Reginald Smith Brindle,(British compositor and writer) have incorporated the popolar mathematic concept like golden ratio and Fibonacci numbers into their work.

Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of timeand frequency, offering ready analogies in geometry.

Expanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music. For example, the pitch classes in an equally tempered octave form an abelian group with 12 elements. It is possible to describe just intonation in terms of a free abelian group in [3],[ 4].

Transformational theory is a branch of music theory developed by David Lewin. The theory allows for great generality because it emphasizes transformations between musical objects, rather than the musical objects themselves.

The connection between mathematics and music has been explained in [5] with the help of videos and other contents.

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