Comments on The Scale Tree and Horograms Section

~In Preparation~

Wilson appears to be the first person to realize the musical potential of what is known now as the Stern-Brocot Tree.

For the moment, it can be said that the Scale Tree is partially his reinvention of the Stern-Brocot Tree with the addition of the noble numbers of the first 12 layers. It was not known until the mid 90s that the tree had already been invented. Wilson though was the first to notice its application to musical scales and the charting of the Moments of Symmetry. The Noble numbers were added as they represented what was first thought to be the most dissonant points being the farthest one can get from simple ratios. That this feature did not turn out to be the case deserves further discussion elsewhere. Still theorist such as Kornerup had charted a noble number or two, but the over all scheme had not been noticed.

The scale tree is used not only to chart the Moments of Symmetries, but is also useful in finding the series of appropiate keyboards possible. This aspect will be covered by the release of Terumi Narushima's thesis on the subject in the near future.

Wilson in his inventiveness also invented trees that do not occur in the Stern-Brocot version. These he used to investigate periods besides the octaves. Some of the most interesting one involve ways to map out tetrachords . Some of these have been posted to the Gems of the Wilson Archives Blog. This will be added eventiallly to this section. An important example is http://wilsonarchives.blogspot.com.au/2013/07/triplet-sets-from-basic-scale-tree.html and http://wilsonarchives.blogspot.com.au/2011/08/lucky-accident-concerning-some-non.html show the process in the work of Novaro with scales bigger than the octave.

The Horograms represent a representation of various Moments of Symmetry scale how they occur on the scale tree. The First 64 represent the first 64 zig-zag patterns that come off the tree. Other Horograms of importance Wilson also mapped out.