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Sacred Number

29 28 The QuadriviuM four liberal arts How do we get a feel for numbers other than by their quantities What are their qualities One traditional method is by way of the seven liberal arts. Three of these, the Trivium of logic, rhetoric, and grammar, cover the gift of the gab, including poetry, while the remaining four, the Quadrivium, investigate number itself, geometry number in space, music number in time, and cosmology number in space and time. Number itself, outside space and time, forms the subject of the study of factors, prime or perfect numbers, and numbers like those found in the Fibonacci and Lucas sequences see page 58. The numbers of space are a distinct and fascinating bunch. How does space carve up Opposite we see some of the limits placed by space on number. There are three regular grids top left, five regular solids top right, eight semiregular grids center left and thirteen semiregular solids center right. Each of these helps to color the qualities of the numbers they invoke. The numbers of music lower opposite begin their amazing journey as the most simple ratios possible, 11 unison, 21 the octave, 32 the fifth, and 43 the fourth. The frequency of the fifth differs from that of the fourth as 98 the wholetone. Thus the numbers of music unfold as the spaces between fractions. These numerical facts of space and time are universal. They may or may not play the same tunes in the nearest intelligent galaxy, but they will agree that fifths and octaves sound good, and they will probably recognise the five simple regular solids.
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