Forward (excerpt) to ‘Microtonality and The Tuning Systems of Erv Wilson’

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



Erv Wilson Remembered

ERV WILSON, COSMIC DREAMER (1928-2016) by Gary David



I knew Erv Wilson for over fifty years starting in 1964. He was my guide into the world of pitch fields, his fields of dreams. Each one who knew him has a different story. This one is mine. In the 1960s and early 70s, I led an experimental vocal-instrumental jazz group called The Sound of Feeling. I had been interested in tunings that deviated from the accepted 12 equal system the prevailed in Western cultures. Erv stewarded me into the methods of making scale formation part of the creative act of composition. I feathered into our music what I learned with Erv, and it was the first time arrays such as hexanies were featured by a musical ensemble on a major label. The many hours of theory and ear-training with Erv changed the meaning of music for me. The great psychologist-researcher Silvan Tomkins said, “The world we perceive is a dream we learn to have from a script we have not written.” Erv Wilson was a weaver of dreams that embodied previously unheard or unrecognized webs of frequencies. In the process, I got to know one of the most coherent and unusual individuals of my lifetime.

Here is a short account of my experience of how that unfolded.

Is it knowing to contemplate while dreaming? Is it understanding? The eye which dreams does not see, or at least it sees with another vision. . . Cosmic reverie makes us live in a state (where) the communication between the dreamer and his world is very close in reverie; it has no distance, not that distance which marks the perceived world. — Gaston Bachelard

As I follow the curve of space-time, I spiral into my own movement, and there I become an eddy of space-time itself and I “disappear” into my own vision. —Gary David

On Dec. 8, Erv Wilson took his leave from planet earth. While I feel a sense of grief, I don’t mourn. My past with him lives now as I write. He is inextricably lodged as a basic element in my being. George Spencer-Brown wrote, “Each being experiences what he, she, or it regards as the world as if of a dream of one’s own creation, and each of us is also an appearance in the ‘dream world’ of another. When the other dies, we too are lost from the dream. If we were prominent in that dream, we feel the loss acutely, and call it ‘grief.’”

“I myself prefer to be known as a “natural approximationist of (the) Augusto Novaro school (circa 1927). I will not be the one to split hairs in this matter; it’s the way one splits the tones that really matter, and I prefer to split them lengthwise, as opposed to those who split them sideways, or not to split them at all, for that matter. My entire philosophy of musical intonation can be wrapped up in one succinct little quote: “Nothing that exists is un-natural.” This includes the arts and artifices and artificiality of the musical imagination. Or, indeed, “why settle for the real thing when one might as well be having artificial?” (Lou Harrison, the 2nd funniest thing I ever heard him say). All scales are artificial, as are all other great works of art and products of the human imagination. You want to know what “natural” is? Let me tell you what “natural is. You don’t want to know. Well, I’ll tell you anyway.”

Erv Wilson

He never did tell us. He showed us. It didn’t matter if it was pitch fields or corn fields, he was a unifying weaver of meanings. He uncovered unity wherever he found it. A friend of mine who met Erv said, “I never thought someone could render me so fascinated by the potential of individual corns on a cob! And his flying micro-tonal scales hanging from his ceiling amazed me.”

Once you become aware of this force for unity in life, you can’t ever forget it. It becomes part of everything you do …. my conception of that force keeps changing shape.

John Coltrane

I have written elsewhere about Erv Wilson’s work, but here I give you a mere taste of my sense, feeling, and experience of the man. I’ve told the story of my first meeting with Erv Wilson many times, and I never tire of repeating that memorable moment. Harry Partch, was among the first of modern American composers to systematize microtonal music. In 1963, he was living in a chicken hatchery in Petaluma California with all of his instruments. I was living in San Francisco, and Emil Richards urged me to visit him. I did, and we spent the day talking about music and tuning (and drinking). I told Harry I was moving to Los Angeles and he said, “You should look up Erv Wilson.” In 1964 I moved to Los Angeles from San Francisco. One of my priorities was to meet Erv. One day I went to his apartment on Poinsettia Drive in Hollywood. I knocked on the door, but no one answered. The door was ajar, so I pushed it open and walked in. No one was there, but there were some unusual instruments in the living room of the small apartment. I picked up some mallets and began to play a microtonally tuned marimba. I was engrossed in the sound when behind me I heard a gentle voice begin to describe to me what I was doing. We started talking about the tunings the sounds and numbers. No introductions. That initiated a 30-year conversation.
In all the years I worked with Erv and enjoyed our friendship, I learned that there was no difference between who he was and what he was. As far as I could tell, there was no division. I experienced an aura of emotional safety whenever we engaged. He treated the novice I was in 1964 the same way he would relate to a master. That made it both easy to learn, as well as to accept my inability to grasp his meanings beyond my experience. There was little shame in not understanding.

If. . . the being I love most in the world came and asked me one day what choice he should make– what refuge is the most profound, the sweetest, the most immune to attack — I would advise him to shelter his destiny in the haven of a soul devoted to noble growth. — Maurice Maeterlinck, Sagesse et destinee, 1902

One of the innate traits of human life is curiosity. Those who lose access to that live an impoverished life. That fate never befell Erv, even later in life when his resources began to fail. His curiosity and his humor and his minimal egoism were hallmarks of both who and what he was.

He was what I call a fluid learner. Human awareness is both explicate and implicate – focal and subsidiary. Erv relied heavily on subsidiary awareness, while his focal awareness was a guide. He took literally, “the world is a dream.”

I have always been attracted to those with both a high and vast sense of life. To the overly focused, they appear either crazy or dangerous. Jimi Hendrix depicted it this way:

I can see my rainbow calling me through the misty breeze of my waterfall.

Some people say daydreaming’s for the lazy minded fools with nothing else to do.

What Erv saw in his waterfall was no fantasy. He made it available to all of us. He created a unified field that we can mine for generations to come. I am ever grateful for his gift, and to have participated with him.

“I begin by imagining
The impossible
And end by accomplishing
The impossible.” ― Sri Chinmoy

“The earth has music for those who listen.” – William Shakespeare

Does not everything depend on our interpretation of the silence around us? — — Lawrence Durrell

Ervin Wilson

I consider myself one of those composers who is never happy with the established order of things. So when Erv Wilson invited me into his world of numbers and symbols and sonic codes, I was entranced with the vast array of stars in his sky, the zillions of unexplored planets out there with jewels just lying on the ground. His mode of distribution was straight up and simple,… he was very old school. He drew his treasure maps by hand, (http://thesonicsky.com/erv-wilson- diagrams/erv-wilson-diagrams/)  xeroxed them, and would mail them to whomever he thought would be interested. But he would leave it up to you to determine what to do once you get into the vicinity of each treasure site. Much of what was so unique about his approach to master pitch selection is reflected by his rejection of the notion of “The Truth”, (i.e. that there exists some ultimately superior scale or tuning system). He believed you don’t have to stay in any one system but should mine the resources of whichever ones you might need for a particular compositional purpose. Hence instead of handing people pre-drawn circles, he offered a larger context in which you draw your own circles. He advocated a process by which what you intuit can be systematized into a master set of musical pitches, then evaluated, changed and even discarded…. ultimately creating scales based on what you “feel” more than what you “think”. This now broadens a composer’s capacity to create color, novelty and interest. Ultimately the back and forth interaction between imaginative play and it’s systematization renders a dynamic flow of innovation that never gets stuck in a “way of doing things”.


Someone once told me Erv stole fire from the gods. I agree. Yet why would one believe such a thing? The light of the gods burns hot and cannot be held in the hand. For as soon as the hand opens to reveal the stolen prize, the fire immediately erupts, spreading itself into the room and beyond, revealing its infinite nature. Erv’s musical frequency structures contain this property of stolen fire. They are self-propagating yantras… the Scale Tree, Holograms, Pascal’s Triangle, The Coprime Grid, the Combination Product Sets (http://www.thesonicsky.com/photography/erv-wilson-diagrams/),… their numbers spill off the page as they go forth and multiply.  Most everyone who met Erv and saw his work, musician or not, would sense the presence of that fire., feeling this intuitively without having to understand the work itself. All of us who have explored his structures were drawn to him and his material not because of some intellectual curiosity but due to this feeling of “the emerging unexpected” that gets triggered when in the presence of one who has stolen fire.




The website, www.thesonicsky.com, is dedicated to explaining the musical breakthroughs of Erv Wilson and the larger cultural narratives implied by his work. Wilson can be described as a “musical cosmologist” who, by creating/discovering brand new pitch fields. has cracked open a vast unexplored mother lode of new musical note relationships for composers to use freely.

Many of his dynamic tuning systems have the organic property of spawning an infinite number of previously unknown musical scales nested within each other like Chinese boxes. The video interviews and other content on this site attest to the broad impact of his work.



From the Editor



It is with great pleasure that we relaunch Xenharmonikon. It has been a long journey of over a year and a half of working, planning and rethinking.

I am taking this opportunity to explain how Xenharmonikon will not only continue the work of the past but also be different in various ways. Most of these changes stem from a shift in format from print to online which makes possible new ways of organizing the journal. Innovation is a vital aspect of microtonality and intonational practice, thus the subject calls for innovative forms of presentation.

The new Xenharmonikon moves from an informal print journal to a single-blind peer-reviewed publication. Why single-blind as opposed to double-blind? Many individuals working in the field of microtonality have unique practices that would be difficult to discuss without being identified in some way. Contributors may still request to submit their work anonymously for the peer review process, but this will not be a requirement. Unlike some peer-reviewed publications, we will not be charging a fee to publish articles. We hope to be able to rely on donations to cover our costs.

While retaining the idea of volumes, these will be identified by tags along with keywords, which over time will be more useful in accessing articles on related subjects. Articles will be published online when the review process is complete. This prevents work being delayed due to the status of others. We also plan to take advantage of the online format by expanding Xenharmonikon to announce and cover microtonal activity around the world, especially the many festivals focusing on tuning as well as the latest developments in software and technology. Some of these will be dealt with in more detailed reviews.

It should remain clear that Xenharmonikon does not represent any single approach to the subject of microtonality or intonational practices and plans to be proactive in representing the field.

We do begin our first issue with a tribute to one of the important contributors to the original Xenharmonikon, Erv Wilson, who passed away while we were planning the relaunch of the journal. For the second issue, we are calling for articles relating to Heinz Bohlen who also passed away not long ago. For future issues, we plan to focus on the Helmholtz-Ellis notation and the school of composers who use it. Contributions beyond these specific themes are also encouraged and we welcome suggestions for other topics.

Lastly, thanks to John Chalmers, the former editor of Xenharmonikon, for making the transition possible through his support and suggestions. Also, giant thanks to Lucija Kordic who designed the website over many weeks and months and envisioned its possibilities, and to my fellow editor Terumi Narushima who provided invaluable feedback and criticism.

We now welcome the community to make Xenharmonikon their own. Comments and suggestions can be sent to xenharmonikon@gmail.com.


Kraig Grady