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.

Evangelina- Maybe Wilson's favorite

Evangelina-Wilson's 'Personal' Scale

Erv Wilson stated "The Evangelina tuning commemorates the work done by Evangelina Villegas and Surinder K. Vasal with quality protein maize in Mexico, Africa, India, Japan and China". It strongly resembles a 22 tone harmonic version of his diaphonic cycles. It might be thought of as his adaptation of the 22 shruti system of India as well as an expansion on Boomsliter and Creel's work on "extended reference". Wilson over time replaced the 5 and 7 limit intervals with the colored harmonics listed. Often these are within a cent or two. This was one of the scales he maybe played the most at home and once when a pair of Mormon missionaries descended upon his abode, he used the opportunity to have them sing pieces from the Mormon hymn book in this tuning which went on for months. In this diagram, I have taken his pencil notes and colorized them to accent the 3 harmonic series contained within. The diagram has been inserted into http://anaphoria.com/22tonescales.pdf where one can compare first his diagram of the 22 shrutis with other related scales he developed. The 7 limit one was used by a Los Angeles band 'Cypher' in the mid 80s on instruments built for guitarist Jose Garcia.