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31 30 The laTeral fifTh 32 and the second overtone 31 The next interval to be tried is the dominant harmony of the fifth, intermediate between the simplicity of unison and octave and the more complex harmonies that follow. It will be seen from the open phase drawing opposite that the fifth has three loops along the horizontal side and two along the vertical. The number of loops on each side gives the ratio, 32. Looking back at the octave, there are two loops to one, and with Unison there is only one loop, however you look at it. This is the general rule for all lateral harmonograph ratios, and if a harmony appears unexpectedly during experiments, it can usually be identified by counting the loops on two adjacent sides. The fifth also appears as 31, the second overtone, a fifth above the octave see open and closed phase drawings of 31 on page 3. Drawing ratios outside the octave may require a twinelliptic harmonograph see page 58. The phaseshifted pair below are stereographic, if you go crosseyed they will jump into 3D.
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