Showing how "256/243" equals the limit of a cycle

256 represents a multiple inherent in the relative pitch of both D plus and Db (Eb or C#). By making orbits at each multiple on an angled square the patterns are formed. In this case the numbered axis extends far beyond the limits of the canvas. Each point is 4 of an inch apart, and extends to 90 points. Horizontally the number extends to 125... a ratio of hypontenuse to side of 125:90. At 125 the angle projects to right angles to form the other side of the square. The numbers then increase by 10 to 350 points. The orbits then reverse as if sound had hit an object and rebounded. The orbits are seen to fall in spaces between the orbits in contrary direction. The limit of 125 represents a cluster of tones which could be played as a chord.


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Web Pages Updated by: Kristi Borst. Ad·Mark·Com