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eikosany is an R package of tools for algorithmic composition with Erv Wilson’s Combination Product Sets (Narushima 2019, chap. 6). It’s meant to complement other microtonal composition tools, not replace any of them.

About the name: the Eikosany is a 20-note scale derived by Erv Wilson from the first six odd harmonics in the harmonic series - 1, 3, 5, 7, 9 and 11.

Other tools

  • Scala. Note: this is not the Scala multi-paradigm programming language that runs on the Java Virtual Machine. This is a specialized tool for working with musical scales.
  • Wilsonic. This is a free app that runs on iOS devices. I don’t have any iOS devices so I’ve never used this.
  • ODDSound MTS-ESP. This is a plugin for digital audio workstations (DAWs) that facilitates production of microtonal music. I own a copy and if you’re making microtonal electronic music, you should too. The Eikosany and other scales Erv Wilson developed all ship with MTS-ESP, so you don’t really need my R package to compose with them.
  • Sevish’s Scale Workshop. This is a web-based tool for working with musical scales.
  • Entonal Studio. Entonal Studio is a user interface package for microtonal composition. It can operate as a standalone application, a plugin host or a plugin. I own a copy of Entonal Studio and recommend it highly.
  • Universal Tuning Editor. Universal Tuning Editor is an application for computing and visualizing microtonal scales and tunings, and includes tools to interface with hardware and software synthesizers.

Some history

On February 4, 2001, composer Iannis Xenakis passed away. I’ve been a fan of experimental music, especially musique concrète, algorithmically composed music, microtonal music, and other avant-garde genres since I was an undergraduate. Xenakis was one of the major figures in algorithmic composition.

Reading the first edition of Tuning, Timbre, Spectrum, Scale 1 rekindled my appreciation for the microtonal music of Harry Partch. And so, armed with copies of Sethares (1998), Formalized Music 2, and Genesis of a Music 3, I embarked on a path that led to When Harry Met Iannis 4.

When Harry Met Iannis was premiered at a microtonal music festival in El Paso, Texas in late October, 2001. The Bandcamp version is essentially identical to that version; the source code is on GitHub at

At the festival, I met a number of composers who were working in microtonal and just intonation, and one name kept coming up: Erv Wilson. Wilson was a theoretician who developed keyboards, scales and tuning systems that several composers were using at the time, and are still using today. Terumi Narushima’s Microtonality and the Tuning Systems of Erv Wilson 5 is a comprehensive documentation of Wilson’s work and is the basis for the code in this package.


I have two main motivations:

  1. There’s an old saying that if you really want to learn something, teach a computer to do it. In the case of Erv Wilson’s musical constructs, teasing the construction processes out of his and others’ writings on the subject is a non-trivial task.

    For example, much of Wilson’s work consists of multi-dimensional graph structures drawn on flat paper. He did build physical three-dimensional models of some of them, but some can’t even be rendered in three dimension. And the graph theory operations that generated them and musical ways to traverse them are not at all obvious.

  2. The 20th anniversary of Xenakis’ passing and of When Harry Met Iannis occured in my second year of virtual isolation because of COVID-19. During 2021, I acquired two synthesizers that are capable of mapping the keyboards to arbitrary microtonal scales: an Ashun Sound Machines Hydrasynth Desktop, and a Korg Minilogue XD.

    The Hydrasynth ships with the tuning tables for many of Erv Wilson’s scales already in the firmware. For the Minilogue XD, the user can load up to six custom scales with a software librarian program.

    But I’m not a keyboard player, and even if I were, the remapping process for the scales leaves only middle C where a musician would normally expect to find it. All the other notes are somewhere else.

    So I need a translator for the music I want to write that doesn’t involve a lot of trial and error fumbling around on a remapped synthesizer or on-screen keyboard. CPS scales are aimed at harmonic musical structures like chords, and finding them on a remapped keyboard is tedious and error-prone.

    Music composed using Wilson’s musical structures is mostly played on instruments custom-built for them. There are keyboards designed for Wilson’s and other microtonal music; indeed, Wilson himself designed microtonal keyboards (Narushima 2019, chap. 2). But they’re quite expensive and, like the instruments, custom-built. I need tools to work with what I have.


The ultimate goal of this package is to compose music using Combination Product Set (CPS) scales. There are three milestones on that path:

  • v0.5.0: synthesizing tones in a CPS scale to WAV files that can be used in a sample-based workflow,
  • v0.7.5: creating MIDI files that can be imported into a DAW for editing and music production, and
  • v0.9.0: tools for creating and traversing diagrams of CPS scales and chords, using DiagrammeR (Iannone 2022).


Borasky, M. Edward (Ed). 2021. “When Harry Met Iannis.”
Iannone, Richard. 2022. DiagrammeR: Graph/Network Visualization.
Narushima, T. 2019. Microtonality and the Tuning Systems of Erv Wilson. Routledge Studies in Music Theory. Taylor & Francis Limited.
Partch, H. 1979. Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments, Second Edition. Hachette Books.
Sethares, W. A. 1998. Tuning, Timbre, Spectrum, Scale. Springer London.
Xenakis, I. 1992. Formalized Music: Thought and Mathematics in Composition. Harmonologia Series. Pendragon Press.