Ervin M. Wilson was arguably the most creative music theorist in the world of alternative scales and tunings. He was also one of the least accessible because he chose to work alone and to share his prodigious discoveries and inventions personally, rather than teaching courses, writing formal papers, or publishing textbooks on his remarkably fruitful musical theories.

I first met Erv, as he preferred to be called, in the early 1960s when I was a graduate student in Biology at the University of California, San Diego. At that time, UCSD was located on the beach at the Scripps Institution of Oceanography, and the atmosphere was so intense that graduate students were given keys to the university library stacks. One evening I got tired of reading about molecular biology and genetics, so I decided to peruse the holdings of the Journal of the Acoustical Society of America. Soon I discovered that a certain Tillman Schafer had constructed a 19-tone electromechanical musical instrument at Mills College in the late 1940s, and that he had worked for the U.S. Navy in Point Loma, a suburb of San Diego. Hoping that he still lived in the San Diego area, I called the facility and asked to speak to him.

As it turned out, Schafer was still in San Diego and invited me to his home where I saw the instrument, but more importantly, was given the names of other people interested in microtonal music. One of these was Ivor Darreg, who then lived in Los Angeles; so I drove to LA and met Ivor, who in turn referred me to Ervin Wilson. Just prior to this meeting, I had attended a seminar at the Salk Institute by David Rothenberg, a composer and theorist from New York City, who is best known for his theories on the perception of musical tones in scalar contexts. Remarkably, David also knew Wilson and was visiting him the same time I was. So, through this network of associations, I met Erv Wilson and became one of the fortunate few who have had the opportunity to learn firsthand of his work.

As a graduate student, I had access to a large mainframe computer, so in 1968 I asked Erv if there were any computations I could do for him. We decided that a table of all the equal temperaments from 5 to 120 tones per octave would be useful, especially if I also computed the errors in a set of small-number ratios for each system. I did this, and at Erv’s suggestion, sent a copy to Professor Fokker in The Netherlands. Fokker was the leading proponent of 31-tone equal temperament in Europe, and the author of a number of articles as well as a composer in that system. Having finished this study, Erv and I also compiled a very large table of just intervals and distributed multiple copies to other workers. Other projects included equal divisions of 3/1 and other integers, as these can approximate divisions of the octave with improved representations of certain harmonically important intervals. In recent years, other composers such as Heinz Bohlen, John Pierce, Kees van Prooijen, Enrique Moreno, and others have also become interested in divisions of 3/1.

At this point, I had to stop and finish my dissertation, which was on the genetics of the tryptophan pathway in Neurospora crassa, if I were ever going to graduate from UCSD. (One of my graduate advisors had started referring to me as “graduate student emeritus”.) After getting my doctorate, I moved around the country, and became involved in research and teaching in the fields of microbial genetics, industrial microbiology, biochemistry, and biotechnology, eventually returning to UCSD. Through all of these peregrinations, I continued to correspond with Erv and pored over his sometimes puzzling letters, intriguing keyboard diagrams, and cryptic worksheets. An invitation from Larry Polansky to spend a summer writing at Mills College followed by a part-time research position again at U.C. Berkeley allowed me to complete my book, Divisions of the Tetrachord, a task that was originally suggested by Lou Harrison. Much of this book was directly concerned with Erv’s theories and musical discoveries. Central to Erv’s work and among his first discoveries are his keyboard designs. To play microtonal music with the same skill and expression as is done in 12-tone equal temperament, one needs instruments that are designed for alternative tunings.

Wilson was also one of the most intuitive mathematicians one is likely ever to meet outside of academia, though he had little or no formal training in the subject. In addition to being able to visualize and geometrically plot musical scales as objects in higher dimensional space, he rediscovered or reinvented a method equivalent to the approximation of irrational numbers by continued fractions (The Scale Tree), and characteristically applied it as an organized system for discovering new musical scales of the type he terms Moments of Symmetry (MOS). Dr Narushima’s explanation of this mathematical process is crystal clear without losing sight of its musical significance, particularly as it applies to keyboard design.

Other key concepts of Wilson’s musical theories are Constant Structures, which are scales in which every occurrence of a given interval is always divided by the same number of smaller intervals. These may be considered as a generalization of MOS and have comparable structural stability. They exist in both equal temperaments and ratiometric tunings (extended Just Intonation) as do another class of scales, the Combination-Product Sets.

CPS are found by multiplying a set of n harmonic generators, m at a time. The prototype is the Hexany, a six-note set generated from four integers representing harmonic functions such as 1, 3, 5, and 7, two at a time. The resulting set of pitches is partitionable into four pairs of (generalized) triads and their inversions. Others are the Dekany (two out of five or three out of five), and the Eikosany, four out of six. These in turn may be divided into smaller CPS: Dekanies into Hexanies, and Eikosanies into both. These structures are especially fascinating because they are harmonic without being centric as any note or none can function as the tonic. They are also defined in equal temperaments, but are generated by addition rather than multiplication.

Numerous composers have composed innovative and aesthetically significant music based on materials invented and discovered by Ervin M. Wilson, thus proving that his work is not empty speculation and audibly imperceptible theoretical invention.

John H. Chalmers, PhD.

Author of Divisions of the Tetrachord

Founding Editor of Xenharmonikôn

Rancho Santa Fe, CA, USA


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