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Sacred Geometry

22 the ShaPeS oF SoundS and three quarters Geometry is number in space, music is number in time. The basic set of musical intervals is the elementary set of simple ratios, 11 unison, 21 the octave, 32 the fifth, 43 the fourth and so on. The difference between the fourth and the fifth, which works out at 98, is the value of one whole tone. Musical intervals, like geometrical proportions, always involve two elements in a certain ratio two stringlengths, two periods lengths of time or two frequencies beats per length of time. We can see harmonic musical intervals as geometrical shapes by swinging a pen in a circle at one speed, and a table in an circle at another speed a harmonograph. Shown opposite are two patterns from nearperfect intervals where the pen and table swing circles in opposite directions. The octave upper fascinatingly draws as a triangular shape, the fifth lower as a pentagonal form. Two octaves, 41, or a quarter, can be exactly defined by two triangles, four squares, or by a pentagon in a pentagram below. 23
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