EXPANDING DIMINISHED ASCENDING SCALE CONTRACTING INCREASING DESCENDING SCALE...

This drawing portrays three different aspects of relative pitch. The long bar at the bottom shows the clusters of notes (arcs) at a point close to the left end of the module. These were determined by laying out the relative pitches from C on a numbered grid. These tones form an ascending scale with a gap between D (orange) and Cb (red-black). These form mathematically expanding radii, which diminish, in terms of time. The other side (right) indicates the difference between an infinite series (left side) and a finite length. The given, or finite length was divided into increasingly smaller sections based solely on the relative pitch, using exactly the same fractions as before. The pattern literally reverses before one¹s eyes, as the clusters of tones are at different places. The vertical bar modules also reveal this division of tones, but now the division is by halves going toward the the center of the circle, or multiplying going outward from the circle. One way of determining the division by halves was to lay all the tones in whole numbers out on the I Ching Hexagram grid. When the middle of this grid was used as a center point, each note found its orbit in a certain sequence. The sequence was found to coincide with a sequence formed of measuring arcs of polygonal shapes representing relative pitch. The sequence was also found to coincide with what was an evolution and involution axis, which will not be discussed here...