Techniques for Algorithmic Composition

This blog post marks a unique occasion. During grad school I wrote two unpublished white papers detailing a number of intricate design systems that I use to generate chord progressions and melodies for formal composition work. The systems outlined in these papers represent ideas that I came across as early as 1984, and continue to make use of in my current composition and analytical work along with new and revised systems that I have not yet committed to paper.

In particular, the second of these two papers (completed in 2006) shows the origins of a process I call “serial encryption.” Serial encryption is a revolutionary discovery. I do not view it so much as an invention of my own, but rather as a point of contact with the natural world that was waiting to be found.

Music theory hit a wall of sorts in the early part of the 20th century. Schoenberg’s exposition of serialism has been perceived for nearly a century as a kind of outer mathematical limit for organizational principles of pitch choice. The possibilities of 12-tone serialism were exhausted very quickly by Berg, Webern, and other compositional descendants of Schoenberg. Xenakis, Messiaen, Stockhausen, Cage, Reich et al made use of stochastic procedures and non-serial determinate systems with greater prevalence than serialism. In the digital age many composers have turned to random number generators as the utilitarian alternative to serialism.

In the later part of the 20th century, compositional techniques based on derivatives of serialism opened up in a sort of lateral evolution. Joseph Straus has very thoroughly documented the serial explorations of 20th century composers in his 2009 book “Twelve-tone Music in America (Cambridge University Press, 2009).” In particular, this quote by Straus is illuminating:

Instead of a rigid orthodoxy one finds in American twelve-tone serial music a flexible, loosely knit cultural practice. Composers within this culture share certain tastes and proclivities, and these in turn establish the vague and permeable boundaries of the culture.” (Preface, pp. xx-xxi)

This quote, to me, summarizes the heart of the issue, which is that composers and music theorists at this time in the earliest days of the 21st century have to some extent accepted serialism as a boundary beyond which there are no further real pitch organization discoveries to be made in the same realm of inquiry.

This is not the case. I humbly submit that the next great field of exploration for principles of pitch organization, the natural successor to serialism, is encryption. Specifically, what I have discovered in my own work is that a twelve-tone row may be transformed and permutated by passing it through a modified Vigenere cipher matrix such that a seemingly endless stream of harmonies mathematically related to the original row may be generated without exhausting the repetitive nature of the row structure itself.

There are [12!] (479,001,600) twelve-tone rows. By introducing a simple Vigenere cipher to the process, I submit that there are [(12!)!] possible combinations of all twelve tone rows, and it is the *combinations* that yield endless new and fascinating, non-repeating harmonic progressions, all interrelated to one another. [(12!)!] is a simply staggering number of possible combinations. It is a number estimated to be larger than [2x(10^3,000,000,000)] (go here and enter 479,001,600, then click submit):

Who would not want to explore a pitch space that large?

Furthermore, I am not a cryptographer. The Vigenere cipher is hardly state-of-the-art encryption, having been documented as early as 1553. Imagine what composers and music theorists could discover about new determinate pitch organization outcomes if partnered with actual cryptanalysts, working with the most state-of-the-art algorithms available in the field.

(Which raises an interesting aside, by the way: calling all mathematicians and cryptanalysts interested in music, please email me: <> I am simply dying to codesign additional algorithms to explore new cryptographic methods of generating harmonic progressions.)

And finally, who can say what applications the interface of music and cryptography may have beyond music theory and composition? I have no way of saying, but the possibilities are surely substantial.

To conclude: the basic foundations of serial encryption are laid out in the second of my two white papers: “Techniques for Algorithmic Composition, part II.” There are some very interesting ideas in the first paper as well, but part II represents the core of my life’s work as a theorist and an algorithmic composer.

I am in the midst of writing a new paper on the subject showing my revision and automation of the procedure using an elaborate Excel spreadsheet (special thanks to my uncle Tom Jones for the suggestion to make use of Excel). For prospective universities who may be interested in employing me in any capacity, I would be glad to discuss releasing new writings and composition work in this field under your imprint.

The links to both papers are as follows:

Techniques for Algorithmic Composition, Part I

Techniques for Algorithmic Composition, Part II

I owe my very good friend Tiffany Plunkett and my father Dennis Shere for their very well-reasoned and compelling arguments to release these papers (and my father in particular for his endless patience, having made this argument to me with tireless persistence for over a decade to date).

I owe the community of Music Center of the Northwest ( more than I can say for their endless support of, and enthusiasm for, my jazz theory classes. I owe executive director Chas Arnold, assistant director Kendal Keyes, Michael Alstad, and Kevin Fox for their friendship and administrative partnership.

And finally, I owe my graduate school mentors Jeremy Haladyna and Curtis Roads an endless debt of gratitude for showing me how to approach precompositional algorithms with scientific rigor.

Thanks for reading!

-David Matthew Shere, Ph.D.

Dec. 31, 2018


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