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.

Two Papers on Partch's Tuning

   Erv is responsible for showing Partch the possibility of inverting the Diamond of what later became the Quadrangularis Reversum. He also helped Partch construct this Marimba. Erv's drawings is a constant contribution throughout the second edition of Partch's Genesis of a Music . Something one used to his style of drawing becomes easy to pick out. A rare double flute from Bolivia found by Erv's brother was another gift he bestowed upon Harry which he  used prominently in Delusion of the Fury.
   Here are two documents just a few years later commenting on first Partch's use of 392 that he felt too much was being made of, and provides an explanation here. The second paper shows a comparison of Partch's 43 tone scale  to a 41 tone space. Like a similar example also found with Novaro's 7 limit diamond [1927] this lead to reinforce his observations of Moments of Symmetry and Constant Structures as "naturally occurring' tendencies in how people construct scales. The latter he defined as when any interval occurs in a tuning it will always be the same number of steps. He found Partch and Novaro both taking their Diamond structures and intuitively filling the space with as close of a constant structure solution possible. He spoke on more than one occasion how he observed Partch following his ear using many  near pitches to simpler ratios rather than sacrifice a musical inspiration or inclination.

Wilson-On Partch's Use of G 392

Wilson's comparison of Partch's scale with 41 ET

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.