SOME COMMENTS ON THE HARMONIC AND SUBHARMONIC GRAPHS

Wilson is here showing how his logarithmic spiral was constructed as a visual aid using the logs based two. He treats the 360 degree circle as an octave and applies the logs to determine where they fall according. The spiral besides representing the size of the harmonics in relationship to each other also serves as a good learning tool in grasping octave equivalences for those just beginning an acquintance with it.

Generally Erv always preferred to think in log based two instead of converting it to cents or any other measurements. Stopping there instead of continuing the cents cut down possible accumulated errors and always thinking interms of 12 tone grid

10 inches was the most common measure he used for the octave with an architectural ruler that divided the inch into 10 parts in order to place notes on the graph. He would use these to sing in order to develop a visual sound interface for himself.

It should also be noted he made [and had myself and others make as a lesson] a harmonic ruler showing the series from 4 or 8 to 64 that one could use a reference to quickly convert cent measurements to the closest ratios. Flipping the ruler it was also useful for subharmonic series.

For pages 4 and 5 the graph is for 4 octaves instead of 1, he reduces the octave accordingly [2.5 inches] or doubling that [5 inches] smaller charts contained here.

For those familiar with the metric systems we recommend 24 centimeters being closest to the 10 inch size.