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IOLET :: Music from the world of Anathem

IOLET::Music from the World of Anathem

“IOLET::Music from the World of Anathem” is a CD that contains music to accompany Neal Stephenson’s book Anathem. Music is an important part of the cloistered world of the avout described in this book, and the pieces on the CD are meant to evoke the rich traditions of music that might exist there. A preliminary version of the disc shipped as an insert in the Advanced Reader Edition of Anathem, which was distributed to reviewers and other early readers; the final version, which contains additional music, will be released in September when the book is released to the general public.

After hearing a short verbal description of the core ideas for Anathem during a dinnertime conversation with Neal in 2006, I was completely captivated by the world that he was creating. I began to draft musical ideas to match some of the musical traditions that he had described, and meanwhile, Neal supplied draft copies of his book to me as it took shape. The experimental vocal music that you hear on the CD and at this webpage is the result.

Music from the world of Anathem

Music from the world of Anathem

It was clear from day one that the characters and institutions found in the book possess many musical traditions, each forged over thousands of years of isolation, and each strangely similar to, yet exotically removed from, the monastic traditions of Earth. As an active performer of Earthly vocal music, as a lapsed musicologist, and especially as a composer, I was excited by the possibilities opened up by Neal’s imagination: somber music to celebrate the mysteries of philosophy and mathematics within the soaring stone walls of a mynster; simple songs to ease the mathematical drudgery encountered when verifying theories; inward meditations upon truth and beauty; and finally, fiendishly difficult musical games designed to hone intellectual prowess.

All profits from the sale of the CD will be donated to the Long Now Foundation, an organization founded to highlight the importance of long-term thinking. Their “Clock of the Long Now” played an important role in Anathem’s genesis.


quaternion actions: the Amazon comes to Burien

The Burien/Interim Arts Space is an installation space by and for the current DIY/guerrilla generation. As far as I can tell, Kathy Justin and Dane Johnson, the project’s artist-instigators, sidled up to the city of Burien (directly next door to SeaTac airport) and said “hey, if you’re not using that empty city block, do you mind if we do?” They have successfully recruited sculptors to transform the wasteland into an urban sculpture park, with unapologetic emphasis on the grittiness of the site and the temporary nature of the installation, and have then hosted a series of live events in this open space.

“Pieces of Eight,” a B/IAS event that will occur on 15 and 16 August, highlights their DIY spirit: a sound installation that features 8 independent speaker stacks, driven by 10,000 watts of amplification. These formidable resources are being made freely available to local composers and performers – 18 at last count. There will be pre-recorded octophonic pieces played during the day, and on Saturday night a smaller number of artists will perform live.

The quaternion group

The quaternion group

Participating in this event was a foregone conclusion for me, since I love experimental public sound art and music. For the pre-recorded portion of the program, I have remixed Mascheroni Circles for eight channels, adding a low drone and some klang in the form of percussive metallic highlights to the voices of Linda, Melissa, and Rebekah. It sounds great in the studio – I can’t wait to hear it outdoors.

For the live performance, I have selected samples from Perri Lynch’s Amazon field recordings, which I will combine using Ableton Live into an 8 channel ambient mix according to the rules of the Quaternion group. (See the illustration, which shows this group’s multiplication table, which I lifted from the very useful open source software tool called Group Explorer.) The quaternion group is useful in this context since it has an order of 8, and its combination of non-abelian complexity and abelian subgroups make for interesting kaleidoscopic combinations of elements. The group action of these quaternions is to trigger samples; I begin by iterating through Cayley and cycle graphs for the group, and follow with algebraic manipulations that seem appropriate for the setting. Although this sounds as though it might be dry and lifeless, no one will know that there is abstract algebra involved! The aural experience is a slowly shifting juxtaposition of the intense sound of the Amazon rain forest set against the desolate urban performance setting of concrete, asphalt, and rusting metal.

As a side-note: quaternions, used as tools for rotational calculations, and the geometry behind Mascheroni Circles are both featured in Neal Stephenson’s Anathem, which is up for the Hugo award this weekend in Montreal. Good luck, Neal!

[Edit: No joy for Neal, but as suspected, the giant sculptures of rusting metal, bonfires, torn-up parking lot, power generators, hulked trucks and buses, and the overall desolate feel of the site made a great foil for electronic noise and loudly amplified insects. Below is a panoramic shot of the site.]

The Burien Interim Art Space

The Burien Interim Art Space

constructing a square with circles

Mascheroni Construction of the Unit Square

Mascheroni Construction of the Unit Square

The picture to the right is a simple but beautiful Mascheroni construction which results in the points for the unit square. (You can see lines for 2 sides of this square in the drawing.) Melissa Plagemann and Linda Strandberg sang a live musical rendition of this construction at the Anathem launch in San Francisco. A week ago, back in Seattle, they helped me by making a quick recording of the duet for my archives.

Here is a stream of my rough mix:

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why cellular automata work for music

Several people have suggested that I post about cellular automata and music, since two of the pieces on the IOLET CD, Simple Automata and Sixteen-color Prime-generating Automaton, use one-dimensional cellular automata to provide their underlying structure. The subject has also been in the news with recent blog posts about using two dimensional automata for generative music-making. So consider this post to be partly liner notes for the Simple Automata (which can be streamed in its entirety here), and part speculative ramble by a composer who is also a computer guy. How and why would a composer use cellular automata for generative music-making?

I’m not going to give a tutorial on CAs; there is a vast amount of information freely available on the web, up to and including Stephen Wolfram’s immense tome, in its informative, yet pompous, entirety. CAs are easy to understand, to notate, and to implement. Diversity and complexity can be generated by very simple machines, without the need for the complicated syntax and evaluation rules used by other common modeling approaches such as L-systems or Chomsky grammars. Perhaps as important as their ability to generate complex patterns from simple beginnings is their ability to generate interesting, yet repetitive, patterns, since the simple breaking of symmetry is far more fundamental to our human enjoyment of music than complexity.

Piano-roll view of Simple Automata

Piano-roll for Simple Automata

Automata are firmly established as tools for creating visual art and music. Musical applications of CAs appeared as early as 1988, and the popularity of Conway’s Game of Life rapidly made them truly commonplace. For this reason, when I decided to use CAs as a basis for the Anathem pieces, I wanted to appeal to listeners’ existing knowledge when present, and yet tread new aural ground. In Anathem, the avout sometimes use musical CAs to perform calculations on-the-fly as a group, and so the obvious place to begin my search was to consider how a group of people might perform continuously evolving CAs from rule notation, rather than from though-composed musical scores.

At the Anathem launch event in San Francisco, I demonstrated the results of this thought experiment, using members of the audience as individual two-state cells. Since not everyone is comfortable with singing, we used rhythmic clapping (8 claps to a cycle) to represent one state, and silence to represent the other. The CAs that we performed together were all synchronous one-dimensional machines, which made it very easy to propagate information left and right down a single-file line of people. (We also performed asynchronous turing machines as a demonstration of less rhythmically rigorous performance possibilities.)

Before starting each rule by counting off eight beats, I gave simple English explanations of the rules, such as the following for the symmetric and pleasing rule 126: “Start clapping on the next cycle if either or both neighbors are clapping. Stop clapping if you and both of your neighbors are all clapping. Otherwise, continue what you are doing on the next cycle.” The chaotic rule 30 was less simple, but still doable: “If one and only one of your neighbors is clapping and you are not, start clapping on the next cycle. If you are clapping, and the person on your left is also clapping, then stop clapping on the next cycle. Otherwise, continue what you are doing on the next cycle.” Even the notorious complexity-producing rule 110 was simple enough to perform: “If you are not clapping, but if either the neighbor on your right is clapping or both neighbors are clapping, start clapping on the next cycle. If you and both of your neighbors are all clapping, stop clapping on the next cycle. Otherwise, continue what you are doing on the next cycle.”

[Details for would-be experimenters: Before starting, you need to set the initial state by telling some members of the line to begin in an "on" state by clapping; you also need to decide how to handle the special cases at both ends of the row. It is also straightforward to have individuals represent more than one cell by cycling through them in order; in this way, small groups can perform large automata. Finally, the possibilities for state mappings that are more complex than simple on/off gestures are infinite and limited only by your imagination.]

Making music is especially enjoyable for amateurs when done in a group, and this experiment confirmed for me that performing cellular automata is a fun, unthreatening, group activity. As detailed above, each cell was represented by individuals clapping, but if those individuals were told to choose a note and sing it, rather than to clap, what would result is Simple Automata. In this piece, the “master of the automata” calls out a rule number (in Orth, on the recording), and the “cells” each pick a pitch before computing their way through a chordal landscape. The resulting chord is fixed until the next automaton is called, but the voicing of the chord changes as singers enter and exit. It is both an extremely simple approach and an interesting thing to which to listen. If the mental gymastics prove too hard, or if you want more control over tonality, the master can pre-assign notes; this is what we did to make the recording. Both approaches are fun to perform.

The most notable feature of cellular automata is their synchrony: like all parallel computing activities, the cells of an automaton must share some notion of synchronization (which is, in this case, the pulse). For musical activity, unlike computing, synchronization is an advantage rather than an impediment.  Performing together is the whole point, after all! Musical performance, like any process unfolding over time, can be thought of as computation. What is interesting about using CAs in this way is that the computation can be purely abstract. The process doesn’t need to produce any results besides the execution of the rule itself, which helps to explain why many researchers working with automata think of them as a way to model life itself.

IOLET::Music from the World of Anathem now available

The mysterious cogs of the distribution system have whirred and turned, and the CD for the Anathem music project is now available from CD Baby [http://cdbaby.com/cd/davidstutz] and from the Long Now Foundation. The Internet tubes are also being filled as I post this, and so the album should also be available in digital form through other online retailers soon.

Get ‘em while they’re hot! Remember, all profits from this project go to the Long Now Foundation.

Anathem launch and CD availability

A picture taken by Toasty at the Anathem launch.

A picture taken by Kenneth Lu at the Anathem launch.

The Long Now Foundation hosted the launch event for Anathem on Tuesday evening in San Francisco, and as part of that event, I had the good fortune to present some of the Anathem math-music, live. All of the singers enjoyed having the opportunity to act as avout ambassadors to the event, and we appreciated the good will of the audience, which seemed to enjoy our performances despite having to endure some long delays and some pretty drastic problems with the sound system. I was impressed, in particular, with the spirited participation in our experiments at creating Turing machines and cellular automata directly out of the attendees themselves. Thanks to all who participated!

In Pursuit of Mysteries has a very nice write-up of the musical side of the event, complete with tasteful pictures of our stylish bolts (whose wrapping techniques were developed by Domini). The martial arts demonstration was also pretty fun, as shown in Kenneth Lu’s Flickr set, which captures some of the dangerous moves. Oh, and did I mention that Neal Stephenson, Danny Hillis, and Stewart Brand were in dialogue? They said some pretty interesting things as well!

I’ve received several inquiries about availability of the Anathem CD in the wake of this event. The copies that were available for purchase at the performing hall had just arrived from manufacturing on Tuesday, and copies from that batch are now available at the store at the Fort Mason pier. As soon as CD Baby has processed the CDs, they will also be available there and for electronic distribution. Meanwhile, you can also listen to most of the tracks as MP3 files, which are posted at the Anathem book site.

Despite the availability of the MP3 files, I still encourage you to buy the CD, since all of the profits from their sale go to the Long Now and also because the sound quality is better! The CD also contains a long and beautiful additional track for women’s voices, which is similar to the meditative duet that was performed Tuesday night.

Thanks to everyone at the Long Now Foundation who worked so hard to make this event possible.

mohr mascheroni – math in the music of Anathem

Many people who have heard pieces from the Anathem music project might think that the music is simply a fiction that accompanies the book, and that the science-related titles are a fanciful nod to the plot. As the composer, I certainly hope that the music stands on its own in this way, but for the geeks among us, I also think that I ought to explain that there is another level to the music. Most of the pieces are direct attempts at mapping mathematical structures used or named in the book into music.

Geometry is one of several mathematical disciplines that has proven fruitful during these experiments. Abstract musical space already contains common notions that relate directly to geometry: “line,” “point,” and “musical shape” are all commonly used terms for speaking about music. There are also less obvious, but still pertinent, concepts that map onto other important geometric entities, such as musical “events,” which map onto incidence, and various musical equivalence relations, which can map to congruence and similarity. The world of music has turned out to be a perfect fit for many forms of geometry: finite projective geometries, differential geometries, and non-euclidean geometries all relate well. I have experimented with each of these while attempting to fuse music, music history, math, and SF.

The most familiar of all geometries, however, plane old Euclidean geometry, has turned out to be a harder fit. And for reasons that will be obvious to those who have read Anathem, Euclidean geometry was important to me. An interpretation of the Adrakhonic Theorem (which on Earth goes by the moniker of “the Pythagorean Theorem”) seemed like required programming for inclusion on the IOLET CD. I tried a number of approaches to setting Euclid’s own proof to music (it is often called the “bride’s chair proof” for reasons that are lost to history), but none seemed entirely satisfactory. I even began setting of an entire book from his Elements, in order to derive a musical language.

In retrospect, the factor that held me back was the problem of accurately representing length, which is central to Euclidean geometry, in the musical system. Certainly music has many different notions of length or distance, rhythm being one, interval another, but I found that to make these useful when doing musical geometry, more resolution and range was necessary than the listening and/or performing brain could handle. Hearing simple units when expressed as rhythms was not a problem, but more detailed roots and ratios (which are definitely needed to work the Pythagorean Theorem) needed more resolution, and the notion of rhythmic length was not up to the  task. Interval seemed a better choice, but by using interval to show length I bolloxed up the rest of the mapping: the representation of shapes then became difficult. One of my goals for this project was to try for morphisms resulting in music that humans can relate to, both in terms of performance and in terms of listening, and I was not succeeding. I wanted a generalizable construct immediately recognizable as a simple geometric shapes, but I couldn’t seem to make this work.

Enter Lorenzo Mascheroni. Lorenzo Mascheroni was an eighteenth-century mathematician who rediscovered what Georg Mohr seems to have known 125 years earlier but not received credit for: that any Euclidean construction can be executed using a compass alone. (Mascheroni has a name that is not an English homonym – hence my choice of naming conventions to Mohr’s detriment.) Mascheroni constructions can be visually quite complicated, but their layers of circles upon circles often paint a graceful picture, and significantly for me, they also translate into music more pleasingly than do measured line segments. A Euclidean construction can be seen as points of incidence and lengths, rather than lines. (Remember elementary school now: “two points define a line,” etc, etc.)

The compass is an instrument of measurement. A circle is nothing more than the sweeping out of a uniform distance from a center. So to sing a circle, one needs a center and a distance. I chose to represent musical circles as symmetric scales or patterns that revolve around a central pitch, repeating themselves over and over. More importantly, one don’t need no stinking straightedges or lines or triangles in a world of circles and points! As a result, I was able to draw the points needed for the Bride’s Chair Proof by starting with a single point and a single circle. (I’ve embedded the diagram below in this post.)

Mascheroni Circles

Mascheroni Circles

Armed with the construction, I then prepared to turn it into music by doing an analysis of the centers, radii, and incidences involved. In this particular construction, there were 22 circles and 22 important points. Some of the points were shared by many circles, some not. Some of the points were meetings between circles, some acted only as centers, and some fulfilled both functions. I created a chart based on this information, and started fitting musical patterns to the elements of the chart. And lo, after a few iterations, I had musical elements that were very pleasing to my own ear! As a final nod to the avout, I then turned these musical elements into a game that might be played by fids learning the Adrakhonic Proof. In this game, the musical circles are provided on the page, along with the points within them that are important. Finding the path through them, however, is left as a cooperative exercise to the performers. (See the score for details.)

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To my ears, the performance by Linda Strandberg, Melissa Plagemann, and Rebekah Gilmore on the CD is mesmerizing, and it demonstrates that purely mathematical structures can work well as the basis for music. Click on the arrow above to hear an excerpt from the beginning of this performance. The whole piece is fourteen minutes long, and can be found on IOLET::Music from the World of Anathem.

blurbing in America

In Cappella Romana, one of the ensembles that I sing with regularly, we have always been fiercely proud of the review that once branded us “hopelessly arcane,” and then went on to praise the performance so described.

It is in this vein that I cannot resist linking to Steven Levy’s great profile of Neal Stephenson at Wired, in order to capture the short blurb that it contains for my music:

“to the untrained ear it sounds like the neo-Gregorian chanting that accompanies ritual baby sacrifice in horror films”

Adding this to Al Billings’ “weird shit” and Cory Doctorow’s “spooky” and I’m starting to think a horror film soundtrack should be my next project. I’ve always loved performing vocal special effects for horror movies and singing on their over-the-top scores, so why not?

Just for the record, there are plenty of rituals and many kinds of sacrifice in Anathem, but none of them involve babies. Not in that way, at least.

Musical scores used in the Anathem music project

I’ve put together an RSS feed that contains some of the musical scores written for the Anathem music project, some of which didn’t make it to the CD. They are licensed using a Creative Commons “Attribution Non-commercial Share-alike” license, so try them out! (And let me know if you do – I’d love to hear other interpretations.)

Long Now Foundation to host Anathem launch

The Long Now Foundation in San Francisco has announced that they will hold the book launch for Anathem. This event will include some of the music from IOLET, performed live by a small group of singers.

Anathem advance reader edition

Thanks to Al Billings, who posted on his blog about the CD of music that was included in the Anathem ARC. His description of my music: “weird shit”, I take as high praise. He’s right about the Asian throat-singing influences. The mystery language is Orth, of course!

Thanks also to Cory Doctorow and Joey deVilla, whose subsequent postings on BoingBoing and on AccordianGuy did wonders for my traffic here.