THE SHELL... AND RELATIVE PITCH
A circle was drawn with the dividing by halves
principal. The quadrant on the left upper portion has divisions of nine parts.
These are marked 1, 2, and 3, etc.. The second rim is divided into eight parts,
numbered also. The ratios are read off a 1:1, 2:1, 3:2, 4:3, 5:4, 6:5 two blank
spaces for 7:6 and 8:7, as they are not used in this system, and 9:8.
next ring has six divisions, the next five, etc. Since the margin of error is
too great to deal with these proportions there is some distortion in the ray
measurements, when drawn. However, the combination of the ring measurements and
the ray measurements is so much like those of the shell that comparison can be
made. To the upper right 16 points were counted off the horizontal radius, and
the tones laid on them according to the ratios of their relative pitches to the
When colored rays are drawn to each tone and through to the
other side... at the twist point the tone spectrum is reversed.
At the lower right, the tones are placed as they would fall on a grid in a
wave form of crests and troughs. As would be expected tones B at 15:8, and Bb at
16:9 lie on a different plane... or dimension from the other tones.