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22 near unison lateral phases and beat frequencies A source of pleasing variety in harmonograph drawings comes from small departures from perfect harmonies. This seems to involve a principle widespread in nature as well as in the work of many artists. There is a particular charm in the nearmiss. An example from music suggests itself here. When two notes are sounded in near unison, the slight difference in their frequencies can often add richness or character to the sound. The two reeds producing a single note in a piano accordian have slightly different frequencies, the small departure from unison causing beats, a subtle warbling or throbbing sound see page 53. Set the weights for unison and then shorten the variable pendulum slightly. Swing the pendulums in open phase, producing a circle turning into an increasingly narrow ellipse and then a line. If the pen is allowed to continue, the line will change into a widening ellipse, circle and a line again at rightangles to the first. And so on. The instrument is working its way through the phases of unison shown on page 20. If the variable pendulum is then further shortened in stages, a series of drawings like those opposite will be produced. The repetitive pattern represents beats with increasing frequency as the discrepancy between the notes widens. Eventually the series fades into a scribble that is a fair representation of discord, though even here there is a hint of some higher number pattern. For most people this fading of visual harmony occurs at about the same point as the audible harmonies fade. 23
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