Sacred Geometry: An A-Z Reference Guide by Marilyn Walker PhD

Author:Marilyn Walker PhD [Walker PhD, Marilyn]
Language: eng
Format: epub, pdf
Publisher: Rockridge Press
Published: 2020-10-27T00:00:00+00:00

SEE ALSO: Atom; Molecular Geometry; Theory of Relativity

MUSIC

Numbers and geometry codify the hidden order of creation; many scientists and artists, including Euclid, Pythagoras, and Plato, consider mathematics to be sacred. As mathematics is patterns, so music is patterns—rhythm, melody, time signatures, overtones, tones, intervals, harmonies, and scales made in sound. The universality and concrete application of numbers and geometry are embodied in music in all traditions. In fact, all music is mathematics at some level. The 19th-century English mathematician James Joseph Sylvester described the relationship between music and mathematics this way: “May not music be described as the mathematics of sense, mathematics as the music of reason, the soul of each the same?”99

Sounds or notes may be harmonious or discordant. Pythagoras discovered that whole numbers, such as one, two, three, four, and so on, govern musical harmonies and produce harmonious sounds, whether these exist at the macro level of the planetary orbits or the micro level of the strings of a guitar and how they’re tuned. Only whole number ratios such as 1:2 and 3:5 produce harmonies. Ratios made up of other than whole numbers such as 3.7:4.5 produce dissonance. Whole number ratios are the basis of scales, and the ratios remain constant regardless of the key or the number of notes in a scale (which vary across cultures). Different scales and different keys produce different emotions; musicians explore the revelations that emerge when mathematical patterns are discovered and then transformed into music. Sometimes a composer will embed such patterns in their compositions to be discovered by the musician or the audience. In discussing the music of Johann Sebastian Bach, mathematician Mario Livio points out mathematical patterns on many levels, but particularly in Bach’s canons: “Canons in general were considered at the time to be some sort of symmetry puzzles. The composer provided the theme, but it was the musicians’ task to figure out what type of symmetry operation he had in mind for the theme to be performed . . . this is not very different conceptually from the puzzle posed to us by the universe—it lies in all its glory open to inspection—for us to find the underlying patterns and symmetries.”100

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