THE WILSON ARCHIVES

Comments on The Scale Tree and Horograms Section

~In Preparation~

Wilson appears to be the first to realize the musical potential of the Stern-Brocot Tree and its application to musical scales in the charting of his Moments of Symmetry. The scale tree is also used in finding the series of appropiate keyboards for each of these Moment of Symmetry series. His inspiration fpr this was Yassers single zig-zag pattern starting with 5 and 7 and he saw the potential in treating it as part of a wider tree. It would take till the mid 90s before he would become aware that this basic tree had already been invented.

One difference between the Stern-Brocot Tree and Wilson's Scale tree was the addition of the noble numbers of the first 12 layers. The Noble numbers result from continuing the zigzag pattern to a point of convergence. If one took the assumption that tunings evolve to more complex forms by continuing down the tree, then the noble numbers represent where it would converge. Kornerup served as an example of this approach. Wilson in his inventiveness also invented trees that do not occur in the Stern-Brocot version which he did by reseeding. These he used to investigate periods besides the octaves. This is included in showing the relationship of the Scale Tree's to the Pascals Triangle (Meru Prastara) in the next section https://anaphoria.com/wilsondiamondcoprime.html . An interesting one involve ways to map out tetrachords . Some of these have been posted to the Gems of the Wilson Archives Blog. 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 grow from the tree. Other Horograms of importance Wilson also mapped out.