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.

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.

Meta-Ptolemy [Some Collected Papers}

Chain of 7 tone scales within the 24 tone array in Wilson's Meta-Ptolemy

Wilson collected his papers on Meta-Ptolemy together. This is what is done here with some added notes http://anaphoria.com/metaptolemy.pdf The scale offers an interesting chain of  7 tones scales not unlike those we find on various African Ballophones and offer an exploration into like territory.  Composer Stephen Taylor has used this scale here. http://www.thesonicsky.com/music/microtonal-cartoon-cues/