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Harmonograph

32 The roTary fifTh 32 encircled hearts and fives The loudness of musical tones is represented on the harmonograph by amplitude, the relative sizes of the two circular motions. In rotary drawings this is much more important than phase which simply orients the whole design on the page. The third drawing below shows a rotary fifth in contrary motion where the higherfrequency, faster moving, pendulum has much the wider swing. In the spiky drawing to its right it is the other way round. At equal amplitude all lines pass through the centre see table on page 55. The top four drawings opposite show rotary forms of 32, concurrent on the left, and countercurrent on the right. The second row shows the effect of a nearmiss in the harmony, which makes the patterns spin. The lower two images opposite are from the 1908 book Harmonic Vibrations. They show the second overtone, 31, a fifth above the octave 31 21 x 32, concurrent on the left, countercurrent on the right. With concurrent pictures, the number of swirls in the middle is given by the difference between the two numbers of the ratio. So the concurrent patterns for the primary musical intervals 21, 32, 43. 54 and 56, all have a single heart at their centre. 33
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