MAKING A DIAMOND SEEDED FROM A SCALE TREE LAYER

In this document novavotreediamond.pdf an inspection reveals that the sequence of notes is determined by common tone modulations of the top hexad. That is by shifting the hexad over one place at a time similar to going through the modes on a common tonic, a 23- note diamond like structure results illustrated at the bottom.

The Lone Page Showing a Unique 7 limit Diamond.  The Centerpiece of a File Now illustrating a Diamond Formed From the Scale tree or the Mt. Meru Triangle 

What is unusual is the choice of 6 notes that make up the seed to the process. It turns out this hexad is formed by the scale tree section seeded by 1/1 and 2/1 shown on page 2 and borrowed from another document. This section of the tree was the focus of Novaro who also played with some triangles that do not repeat at the octave mention in this blog in the past. so i have added an example of what type of result we can expect from that process. Here instead of using the tree  a reseeding of the meru triangle is used to show another way one can visualize the sequence. What occurs in on the other side of the 2/1 differs only by commas with the lower set of pitches. This could be used as possibly a layout where one only has rooom for centain notes in each traditional octave space.

What should not be lost is the unique type of diamond presented here. It is  neither a harmonically or melodically based one, but one that is formed by the tree or a descent down Mt. Meru triangle.

Triplet Sets From The Basic Scale Tree.

TETRACHORAL TREE

TRIPLET SETS FROM THE SCALE TREE

This top diagram has been a part of the 'tres.pdf' document for years but it was only after finding the second in his notes do certain aspects become clear. Wilson has taken a trio of terms found in the scale tree and proceeds to multiply them to where they can be easily used to generate a scale tree contained within a 4/3. The beginning set is formed by an outer pair of fractions with the medient being the third term. The top diagram is an example of the first formula realized. In the bottom half we see he also adds up the diagonals which give us different terms to the classic fibonacci series generated by the classic tree. The method in which he determines what ratio each side converges on is unknown. It is possible he might have figured it out just by hand.

A lucky accident concerning some non octave scales

 I happened upon two different Wilson documents which where quite separated but i had viewed recently enough to remember and realized their relationship which are  presented below.  First a letter which i assume was to Brian McLaren followed by the paper in Novaro referred to. The third is Wilson respelling of the two points in a scale tree type way that shows the relation of novaro's ideas to this series. It was lucky enough to stumble upon some time before and showed Erv how Novaro series can be generated as a Pascal triangle or in a series like this. He ran with it.
It also explains some of his other division of a tetrachord in a like fashion. The method shows a quite way of generating non octave structures.