WIT Press


Design In Nature From Pythagoras To Helmholtz To The Cantor Musical Array

Price

Free (open access)

Paper DOI

10.2495/DN020211

Volume

57

Pages

Published

2002

Size

415 kb

Author(s)

B. F. Hero

Abstract

Our purpose is to illustrate how the laws of nature may be inherent in musical and mathematical systems. Pythagoras’s musical system, based upon numerical ratios, was intrinsic to a natural order called \“the music of the spheres”. Helmholtz’s musical system, based upon tonal laws, has an extremely important role to play in human adaptation. Georg Cantor, the metaphysical mathematician, developed an array of whole number ratios that follow the laws of microtonal musical harmonics and subharrnonics. While microtonal intervals play a limited role in Western music we fiid that they are intrinsic to a natural order. It is within the mathematical array that is called the Lambdoma Matrix where visual patterns of color-coding, Lissajous figures coding and angles coding -mirror nature’s laws. The Fibonacci series of ratios allows us to further explore laws of design and of nature. We have developed algorithms that generate the Cantor array in audible intervals that have not been heard before. The engineering of intervallic harmonic stimuli may create a sensation of tonal values that apply to both external and internal harmonics. These sounds and their patterns stimulate a new kind of sonification and visual experience that indicate an extremely important role to play in the human sensation of tone and laws of design. 1 Introduction Nature seems dependent upon an ordered set of harmonic ratios that may be directly related to the mathematics of music. Any number representing any phenomena in any scale from micron to light years may be translated into

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