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.

CONSIDER OLYMPOS

Consider Olympos is a preliminary paper to The Marwa Permutations and augments some details that might not be clear in general. First that a generator of a scale can be thought to be a variable within set limits and also shows how the chain can be used as a sequence to generate larger scales. 

Page one of Consider Olympos-a draft of a paper that would become his Marwa Permutations 

WILSON'S BASIC TEMPLATE FOR LATTICING 13-LIMIT HARMONICALLY BASED STRUCTURES

The Most Common Generalised Lattice used by Wilson.

It is hard to think of a microtonal theorist who has made more headway with developing lattices than Erv Wilson. Here the concentration will be on what he nicknamed  an “Euler“ lattice after where he drew his inspiration.

By working with a template where each prime harmonic has a unique spacing , he managed to avoid clashes when generating lattice of multidimensional harmonically-based structure

There are some other features worth pointing out.  For instance harmonically generated intervals will always appear above the fundamental and the subharmonics below. With a  9-limit system the direction will be both above and to the right , leaving the other quadrant for more complex ratios with the opposite with the subharmonic. This makes it quite easy to understand what is being represented.

Commonly he would use a 10 square to the inch graph paper which explains why he didn’t use a template where all the numbers where divided by 2. This way he had room to notate both ratios and often the scale degree. The latter always followed by a period or dot to separate it from the ratios.



Lately i have been using the following lattice which seems to overcome a few trouble spots. This was plotted using 20 squares per inch.

Alternative lattice by Kraig Grady in cases of slashes with Wilson's Lattice.

Paul Beaver

Wilson often referred to Paul Beaver, especially in making him aware of Pascal's triangle which might be the most important source for Wilson's work. This is one of the few references I know of Paul's work which until now was unknown to this archivist.

"Ohio’s Paul Beaver, meanwhile, was an important early proponent of the the synthesized film score, working on soundtracks for The Munsters and My Favourite Martian. A Scientologist and noted eccentric, he played on records by The Monkees and The Byrds, and set up the Moog patch heard on The Doors’ ‘Strange Days’. T

from
.http://www.thevinylfactory.com/vinyl-factory-releases/the-greatest-electronic-albums-of-the-1950s-and-1960s-2/

...More Like a Living Thing, Than an Inert Crystal.......

Addition To Wilson's Moments Of Symmetry Article

 A new file has been added to Wilson's Moments of Symmetry paper.

 Either you can download the complete paper here http://anaphoria.com/mos.pdf

or if you wish, you can upload only the appendix. http://anaphoria.com/mosgeneral.pdf

AN 11- Limit "Centaur" Implied In A Wilson Lattice-Update!

Thus scale would work quite well as an introduction and ear training scale for those interested in both 11 limit harmonic and subharmonic material with a limited amount of notes.

The bottom Diagram is a blank Lattice found among Wilson's papers. No copy of him filling it in has so far been found. Taking how he normally lattices scales it produced an interesting and unusual scale. It contains two full harmonic and subharmonic series up to 11th which enables many tetrachords of both or mixed variety.  One of the first things noticed is that the scale develops more in the direction of the 11th than the 7th limit direction which is a bit out of the ordinary. The bar at the bottom shows how well it fills space. 

I cannot but relate this scale to my own "Centaur" Scale as it would function extremely well for what "Centaur" hoped to examine. It explores on an 11 limit level what Centaur did on a 7 limit. If a keyboard would have been available to tune to 17 places , it is exactly this type of scale that would have be sought. Thus this scale would have easily been the very first scale i wished for. Giving access on a sustained instrument a bedrock of material i so desired to hear.

This scale will be included on the Centaur page for the reason sited.

UPDATE! As fate would have it, look what I  found only a few hours after posting. Here is an actual drafting of the scale above by Erv Wilson next to the blank that led to the scale. In this diagram the inversion is contemplated as an alternative which i had not pointed out above.