MUSIC and MATHS
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By JULIAN HANCOCK
I have often heard it said that if a person is good at mathematics, then they will also be musical. There is no random coincidence to this relationship between music and mathematics. My comments are limited to Western music as I have not explored other forms of music. The basic premise of my discussion is that music was not so much composed by brilliant musicians, but evolved inevitably according to fundamental mathematical principles.
The crux of my postulation lies in the fact that, the simpler the ratio between the frequencies (cycled per second) of any two or more notes, the more pleasing the combination to the human ear. I am also assuming that the creation of music preceded both the development of a system to write it down (notation) and an understanding of the theory that developed to explain the composition.
The development of the eight note 12 semitone octave fundamental to Western music was inevitable, as it is based on precise mathematical ratios. The octave represents the simplest of all ratios, 2:1. But as we continue through the common intervals, we can see the principle of ratios demonstrated further. Thus the interval of a fifth has a frequency ratio of 3:2, the fourth 4:3, and the Major third, 5:4.
Further intervals are the Minor sixth (8:5), Minor third (6:5), Major sixth (5:3), Major second (9:8), Minor seventh (16:9), Diminished fifth (7:5), Augmented fourth (10:7), Major seventh (15:8) and Minor second (16:15).
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MATHS CREATES A BETTER PIANO
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The link between maths and music is well established: if you're good at maths, chances are you'll find learning music easy.
What is less well known is that mathematicians have been behind the development of some of the great breakthroughs in musical instrument design.
An Australian example is the Stuart & Sons Piano, which is revolutionising the harmonicity and sustain of the sound of grand pianos. With its vertical zig-zag clamps, nine extra keys and a fourth pedal, the Stuart and Sons piano establishes a new musical aesthetic for piano sound.
CSIRO Mathematical and Information Sciences has been working with piano maker, Wayne Stuart of Piano Australia, to develop instruments with extraordinary clarity of tone - and their work is attracting international interest.
At the International Congress of Industrial and Applied Mathematics (ICIAM) in Sydney on July 11, CSIRO researcher Bob Anderssen and three of his colleagues shared insights from their work into the maths of pianos, drums, gongs and vibrating strings with colleagues from around the world.
"Each musical instrument radiates its sound in a different way; so each requires a different type of mathematics to explain its harmonicity, sustain and singing quality," Dr Anderssen said.
"From a design and engineering perspective, a rigorous understanding of how an instrument radiates sound as it is played gives us a sound basis for better design.
"In the case of the Stuart Piano, we have been able to explain why it sings better than other pianos, giving greater confidence about how to refine and exploit Wayne Stuart's extraordinary invention."
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