Walter O’Connell was a physics teacher at Los Angeles City College. Besides having his 'Tone Spaces' article published in vol. 6 of Die Reihe, he was also a physics teacher of La Monte Young [and yours truly and deserves the credit of introducing this latter to Erv Wilson ].

            The letter describes Wilson reinvention of a Stern-Brocot Tree, which he had called the Scale Tree. It would be some 20 years after this letter would he become aware of its pre-existence. There are some differences between the two. It is significantly important to scale theroy that he added at the bottom the series the set of noble numbers that the various zig-zags converged on. Often he would use these noble numbers by themselves.

Wilson elsewhere expands the use of the scale tree by using reseeding not found in the original in a fashion outlined in this blog post

The paper also shows his 1/x zig-zag pattern that tells one at how many places a particular generator will form MOS scales. Since these pattern occur quite abundantly in his papers, it seem a good point to explain what they are. They are discussed in the preceding introduction to the Moments of Symmetry.

            The reason why Erv states on the last page that the number is unusable is because one has subtracted most of the original data and one is left with a numerical artifact since a calculator only carries out an answer so many places.

He also points out what he always found a significant point in such patterns being the point before one moves a large number of zig or zags in the opposite direction. Basically this coincides with having to add an abundant amount of new tones to improve the accuracy of an ET of a convergent point.


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