Alexander Chen, he of Kinect hacks and subways turned to strings, is back with another string visualization. Built in the browser (an interactive version is available), this work makes a visual accompaniment to Bach’s First Prelude from the Cello Suites. If you read music notation fluently, you may find the score itself suffices, but even so, the math to make this work – and the dance of circles across strings – is compelling. Alex, whose day job is with Google’s Creative Lab, talks to us a bit about the mathematics and process. First, his description:

baroque.me visualizes the first Prelude from Bach’s Cello Suites. Using the math behind string length and pitch, it came from a simple idea: what if all the notes were drawn as strings? Instead of a stream of classical notation on a page, this interactive project highlights the music’s underlying structure and subtle shifts.

Built in: HTML5 Canvas, Javascript, SoundManager
Made while a resident at Eyebeam

CDM: How did you settle on this particular visualization of this famous work? And how did you work out the maths, that is, why this specific number of dots, the distance from the strings, and the length of the strings themselves?

Alex: When I listened to the opening of the Bach, where it repeats the same bar twice, it made me think of a call and response. So I immediately pictured two wheels that echo each other, instead of just one wheel with four dots.

Figuring out the symbolic string lengths in pixels was a fun research project. I wanted explore the simple math behind string length. I learned that you can derive an entire chromatic scale just by using two fractions: 2/3 and 1/2. These correspond to the fifth and octave intervals. It’s called Pythagorean tuning. I stumbled onto this great little worksheet [PDF link] which seems to be intended for students.

Were there other things you tried, any failed experiments?

There were important learnings. It used to begin playing the piece right away. I started the opening tuning animation as an afterthought while I was preloading the strings. But that sequence became really critical.

What’s your sense of the music now having done this? Did it change your hearing of the piece

A lot of music visualization these days is linear, like reading a score. Logic’s editor, or even games like Guitar Hero, all follow that structure. And there’s a reason for that, as it’s convenient, for both computers and humans, since we can read it (and edit it) like a book. But I wanted to try something different. I think some of the magic of watching a performer is seeing such subtle, intricate finger movements produce such moving sounds. When I watch these strings morph, it feels more like the computer is performing, not just checking off notes one by one.

Seeing the Bach Prelude in groups of 8 notes gives me a bigger picture view of the piece. Instead of focusing on the individual notes, you can see each bar as a group. The strings start shifting very subtly, but as the piece builds, the strings seem to be panicking to me, shifting more rapidly. The computer is not expressive. All notes are played at equal volume. But the notes themselves, the data of the song, is inherently expressive.

http://blog.chenalexander.com/
http://twitter.com/alexanderchen
http://www.baroque.me/ [interactive - grab the ... circles ("grab the balls" doesn't sound quite right)]

You know you’re in for something different with an article that contains this line: “as 256 bytes is becoming the new 4K, there has been ever more need to play decent music in the 256-byte size class. ”

In just a single line of code, Finnish artist and coder countercomplex, working with other contributors, is creating “bitwise creations in a pre-apocalyptic world.” What’s stunning is to listen to the results, even if you have trouble following the code – the results are complex and organic, glitchy but with compositional direction, as though the machine itself had learned to compose in its own, strange language.

This is, naturally, the opposite of the musical coding in the previous post: in place of human-readable languages representing abstractions atop other abstractions, this is pure algorithm transformed into music. Geeky, yes, but it also says something about musical composition and thought independent of the computer. It is as compact an expression of a human musical idea as one could imagine.

I recommend reading the whole blog post (and following the blog for new developments). Embedded in this whole exercise are thoughts about musical algorithms, the history of chip and 8-bit music and the demoscene, and, most interestingly, the question of whether digital music might yet yield “new” (or at least largely unknown) discoveries:

Hasn’t this been done before?

We’ve had the technology for all this for decades. People have been building musical circuits that operate on digital logic, creating short pieces of software that output music, experimenting with chaotic audiovisual programs and trying out various algorithms for musical composition. Mathematical theory of music has a history of over two millennia. Based on this, I find it quite mind-boggling that I have never before encountered anything similar to our discoveries despite my very long interest in computing and algorithmic sound synthesis. I’ve made some Google Scholar searches for related papers but haven’t find anything. Still, I’m quite sure that at many individuals have come up with these formulas before, but, for some reason, their discoveries remained in obscurity.

Algorithmic symphonies from one line of code — how and why? [countercomplex]

But can you dance to it?

Matt Ganucheau contributed to this story from San Francisco.

Perhaps channeling ancient cults of Pythagoras, the producer duo Kompal, based in Austria, have not only made an insane noise machine powered by light, but also ask you to hunt for triangles. Yes, the shape. Instead of a remix contest or photo contest or “like our Facebook page” business, they want you to take pictures of polygons.

First, about that sound-and-light-and-noise thing that will scare your friends. It is “a unique soundmachine controlled by light, containing controllable flashlights
as well as an optical filter, loudspeakers, an audio output and a hall effect drive. And last but not least the red “turbo button”.”

It isn’t entirely unique, in that it recalls designs like Bleep Labs’ Thinamagoop and the classic STEIM cracklebox, among others, but it is a lot bigger and more frightening. (I know at least one person trying to carry something like this through 9/11 security in NYC yesterday, and am curious how that went.)

The good news: you can win this:

Win the Kompalisator!
The Kompal producers Bernhard Belej and Jodok Dietrich have started a
galactic photo contest themed “Kompalisiere your world”. Those who
would like to join the contest should keep their eyes wide open and be
after any kind of triangle. Take a picture, upload it on Kompal fb or
www.kompal.eu and hope for plenty of user ratings. The pictures could
also be sent via mail to meinewelt@kompal.eu. A jury will choose the
winner of the fantastic “Kompalisator” out of the ten pictures
that got the most likes on September 30.

For more information about Kompal, their music and live shows visit
www.kompal.eu
YOUTUBE: http://youtu.be/AknizoL7zZY
Photos: http://gallery.me.com/bernhard.be#100144
“KOMPALISATOR”: http://kompal.eu/kompalisator.php
http://kompal.eu/kompalisator-postcards.pdf

Their music is actually rather lovely, not the mayhem of this particular box – think dreamy and slick, if thoroughly technological, sparkling and then adding in amiable beats and bass.

And full of triangles. A nicely-built, silly video, and some tracks:

Latest tracks by Kompal

I love this controller, but I think we should keep it Platonic. Solid.

Sorry, geometry humor. See, the controller in question is constructed as a convex regular polyhedron, such that all its faces are themselves congruent regular polygons meeting at each vertex, and … uh, never mind.

Above, a stunningly gorgeous video from Polish media art group panGenerator, with some lovely chiming music following by the evidently-now-requisite dubstep demo. (Tip all of us could use, guys and gals – makeup. Styling. Now, they just need some post-production so you can’t see the IR sensors or the wires.)

Hedoco, also based in Poland, is the manufacturing and distribution partner, and donated this prototype. I love their stated philsoophy: “a unique brand that connects two trends: open source design and fashion.”

No, seriously. And, seriously, why not?

The controller itself looks actually quite lovely – and it’s open source hardware, too, from top to bottom. MIT license for the source, Creative Commons for everything else. (One trick: by choosing “Non-Commercial,” they don’t technically qualify under the Open Sound Hardware Definition. I’d suggest keeping the ShareAlike, since any commercial user would have to share modifications. I know not all designers are comfortable with that, though.)

Designer Jakub Koźniewski and whole team of panGenerator, seen in these parts building a kinetic sound organ out of cans, is behind this project, too. Ingredients:

• Bluetooth. (The revolution will not have wires.)
• Infrared distance sensors. (Though if you know what those are, you already knew that.)
• Arduino, the open source hardware prototyping platform.
• Processing. (Whatever. No one cool uses that any more.)
• OpenSoundControl.

Source code is available now on GitHub, with hardware schematics coming soon. And that could lead to an all dodecahedronal music festival. You may recall the work of Ted Hayes, whose Neurohedron has the same shape. Ted’s work, by contrast, works with a drum sequencer — meaning these two could even play onstage together. Ted and Jakub each tell us that’s coincidence, and when Jakub did realize the form had been taken, the two connected. Now I say we just need more. Dodecahedronstock. Polyhedrapolaooza. Platonaroo. Euclid Fair. Let’s make it happen.

On Ted’s Neurohedron side, he tells us that his work, featured at a Handmade Music event I produced in New York as well as at NIME, has gotten significant updates, so we look forward to seeing that. Previously:

Pretty, Nodal, Non-Linear Music, on iPad + iPhone and Big Dodecahedrons

Handmade Music NY 8/29: Meet the Musical Inventors, Pong to Dodecahedrons

More:

http://www.pangenerator.com/

http://www.hedoco.com/

Sometimes, to quote Depeche Mode, words are very unnecessary. Instead, lose yourself for a few minutes in the vibrating mathemagical lands of numbercult, audiovisual immersions in which sound and geometry fuse in a strange, abstract dance.

Their most recent creation, found via Richard Devine’s prolific Facebook wall and posted earlier this summer, explores an actual audiovisual sequencer. See it at top:

Connected is a graphical/musical sequencer system. a three way flow of information, between graphics, sound and external triggers shape the composition. Recorded in real-time.

But actual functioning interfaces aside, I’ll leave you with some other video clips that traverse similar territory, these syncing up separate visual and audio systems.

These folks make music, too – have a listen to their album, at bottom. And that shifts to body candy, as in, for your butt, with danceable grooves.

All three of the above videos combine vvvv – the Windows-only, graphical patching environment for powerful 3D effects – with Ableton Live for sound.

But lest you think it’s all abstraction, have a listen to their excellent dance release on Bandcamp. Downloading:

http://www.numbercult.com/

By the way, ever wondered what visual software people are using? So did we. Don’t miss this look on our sister site, Create Digital Motion, including where vvvv fits on the spectrum:
What Visual Software Readers Use: Some Clear Favorites, Plenty of Diversity, in Census Results

Full disclosure: I love waves. Analog, digital, acoustic, we’re talking vibrations in sound (and other substances, as well — and light). I don’t think you get into this area without having a certain wave addiction. If you love waves, you could easily get lost in exploring videos of vibrating guitar strings and pondering the physics of the string.

This story begins not with how guitar strings actually vibrate, but a curious phenomenon when combining the regular oscillation of the string with the rolling shutter of a CMOS digital camera — namely, the iPhone’s. To accurately capture motion, you need to record an image all at once (or at least come close). Rolling shutter or line scan as exhibited in a CMOS camera sensor like the iPhone is a side effect of the capture being scanned from top to bottom, so the bottom portion of the image is saved later than the top. That causes motion to skew across the image. (Long before digital, people played around with the same effect in analog video and even using film photography – all you need is something moving and a way of capturing the image that moves gradually in a different direction.)

When the regular oscillation of the scanning combines with the oscillation of what you’re filming – as with a vibrating guitar string, or the rotating propeller on an airplane — the two frequencies effectively phase, causing some curious distortion. In the case of the guitar, this means seeing the appearance of standing waves that, while they can occur in nature, don’t occur on any conventional guitar. (You can also think of the basic effect as aliasing, as seen optically when video shutters capture the frequency of rotation of a rotating car wheel in such a way that it appears to move backwards.)

As with many concepts in physics, it’s all easier to see than explain, so I’ll turn it over to some terrific videos. I’ve contrasted two at the top of the story; here are more examples.

Below, a high-speed camera operating at 600 and 1200 frames per second, played back 20x and 40x, respectively, slower than you’d see with your naked eye.

And here’s another example of how that might appear on a camera like the iPhone:

Of course, that means – fodder for our sister site Create Digital Motion – potential for more creative abuse, beyond the mere novelty.

What’s also amusing is the heated discussion this triggered as the iPhone video went viral. Read some angry comments – and some solid science among them — at Reddit:
Guitar string oscillations captured on video [reddit.com]

I’m glad people don’t behave (yet) in person the way they do on the Internet.

In person: “Excuse me; I think your fly is open.”

On the Internet: “That guy’s fly is open. He doesn’t even know his fly is open. That’s bullshit. I mean, what kind of person leaves their pants just *(&$#ing open like that? Look, look, look at his open fly. I’m never talking to him again. I’m not even going to wear pants from now on.”

(Seriously, happily, many of the comments are perfectly polite and well-informed!)

School’s out for just about everyone, but I’m going to remember to file this away for the next time I have to explain sound vibration. Now, back to the beach, or wherever you’re relaxing.

Thanks to Alexander Chen, from whom I lifted this via Google+. (See his own work on CDM here and here. Alex is just the kind of person I want to see this, as he’s been working with the aesthetics of vibrating strings! So, hurrah, Google+…

There’s something about symmetrical rhythms, it seems: through the power of math, these rhythms sound really good. We’ve looked a couple of times before at the spread of the Euclidean Algorithm for producing rhythms; see below. Wouter Hisschemöller has updated what began as an in-browser Flash tool to build an free and open source, Java-based MIDI utility. You dial in the rhythms you want, and now, with the addition of MIDI output, you can play those rhythms in any software of your choice. (Ableton Live plays the part of the MIDI recipient in the video above.)

Yes, you can actually make music with these nifty geometric interfaces:
Euclidean Patterns Demo 1 by Wouter Hisschemöller

Euclidean Patterns Demo 2 by Wouter Hisschemöller

Lots of detail and documentation on how to use the tool on Wouter’s updated blog post from earlier this week:
Euclidean MIDI Patterns

Previously, on Euclid Music Television:
Euclidean Rhythms in Ableton MIDI Clips for Polyrhythmic Good Times

Circles and Euclidean Rhythms: Off the Grid, a Few Music Makers That Go Round and Round

Strings of numbers are everywhere in our world, tucked just outside our awareness alongside identifiers like bar codes. Dutch media artist and inventor Leo van der Veen simply plucks that information and brings it to the fore.

Barcodas is a barcode-scanning iPhone app that deciphers common EAN and UPC codes and translates them into musical patterns. Pick the scale you want, and out comes a melody. I’ve engaged in similar silliness myself, but in a sign of how handheld tech has changed, a project I did a few years back involved a USB scanner I purchased at an office supply store and a desktop computer running Processing; there simply weren’t readily-available, camera-equipped smartphones with useful multimedia capabilities. As a result, the work I did (sending MIDI to Ableton Live and doing a strange visual piece with a choreographer) wasn’t really all that practical.

By contrast, Leo’s project is elegantly-designed, with a beautiful, minimal, friendly user interface, and has some real use. You can transform an iPhone 3GS or 4 into a handheld melody-finding device, like a metal detector for tunes, and find order in the seemingly-chaotic. And most importantly, you can save and share your tunes, even spreading them on Facebook.

http://www.nr74.org/barcodas.html

There are other ways of making melodies, to be sure, but I think anything that raises awareness of the world around us and challenges us to be more creative is a good thing.

Developers: iOS devs, the work here is based on the excellent Zbar open source barcode framework; Leo says QRCode support is forthcoming. If you’re on Android, the free ZXing is also fantastic (and is the basis of Google’s own barcode scanning app).

Since it’sMathematics Awareness Month (whoo!), it’s worth noting that Leo is a fan of playing with numbers. He tells CDM he plays adding number games with barcodes over breakfast. (“I tend to sum all the individual digits up to zero using only the most basic operands. E.g. 8713091021473 would make 8-7-1 = 0; 3sq – 9 = 0; 1-2+1 = 0; 4-7+3 = 0, that’s a thing you do, too, right?”)

And he has a quite lovely math game that challenges you to make the value 15 out of randomly-chosen digits. It’s a bit like Blackjack for math nerds. nr15, another iOS app, isn’t strictly musical, but then, neither are barcodes, so perhaps this will lead someone to some new form of composition.

In the more strictly-practical end of the pond, Leo has also created the clever c74 app, designed to make control of Max 5 patches easy from iPhones and iPod touch.

Find many, many other fanciful projects from Processing to Max to hardware to imaginary, impossible inventions:
http://www.nr37.nl/

Ready to make your Ableton Live pattern programming a bit more polyrhythmic with the power of math?

In Monday’s reflections and round-up of cycles and circles, I mentioned Euclidean evenness and Godfried Toussaint’s research. The basic idea is that a mathematical algorithm for spacing pulses has a lot in common with traditional preferences for polyrhythms spanning everything from rock hits to conga patterns and musical cultures around the world.

Reader Tony Wheeler has turned those patterns into MIDI clips so you can drop patterns into Ableton Live. Drum patterns and dance music are obvious applications, but this could be an idea starter for melodic patterns or music in a variety of idioms.

Each individual pattern will sound like an isolated cycle; it’s often when you put them together that they’re most compelling. Here’s an example; Tony added a regular bass drum just to make things more grounded (it actually calls attention to the asymmetry of the other patterns).

ScaledKit by wheelmaker

Tony has another terrific tool for Ableton Live that generates the AMS files used by Operator to tune oscillators to alternative pitches, as we covered previously:
Free Utility Makes Endless Oscillators for Ableton Live Simpler, Sampler
Direct link: AMS File Utility for Ableton Live

And for harmonic experimentation, see the Circle of Fifths Chord Resource:
Circle of Fifths Chord Resource in Ableton Live

This is all fairly academic stuff, but the funny thing about it is there’s nothing stopping you from making either a dance music hit or some experimental new kind of music that doesn’t sound like it came from Ableton.

Alternative tunings for Operator oscillators and Euclidean polyrhythms? There are many tools aside from Ableton that will work, too, but whatever your tool, this could be a great way to jump-start a musical idea. Airport layover, meet musical productivity.

Updated: Another great way to go is the Eckel VST plug-in, also donationware. It works on Mac (Universal) and Windows, and since you can dial up parameters, may be easier to use than the MIDI clips, depending on your workflow – especially since you can still choose pitch. (Or, hey, grab both!) Thanks to John Larsby for the reminder:
Shuriken.se: VST – Eckel

For Dr. Toussaint’s part, you can glance over his syllabus on Discrete Mathematics — and find a reference to Tony’s Ableton experiments.

Grab the download and read more on this topic (free, donations welcome):
Euclidean Rhythm MIDI File Resource in Ableton Live [Age of the Wheel]

We continue our 3.14 celebration with a round-up of circular logic.

There’s no reason apart from the printed score to assume music has to be divided into grids laid on rectangles. Even the “piano roll” as a concept began as just that – a roll. Cycles the world around, from a mechanical clock to Indonesian gamelan, can be thought of in circles.

Imagine an alternate universe in which Raymond Scott’s circle machine – a great, mechanical disc capable of sequencing sounds – became the dominant paradigm. We might have circles everywhere, in place of left-to-right timelines now common in media software. Regardless, it’s very likely Scott’s invention inspired Bob Moog’s own modular sequencers; it was almost certainly the young Moog’s exposure to the inventions in Scott’s basement that prompted that inventor to go into the electronic music business, thus setting the course for music technology as we know it.

See:
Raymond Scott’s Circle Machine
For more background: “Circle Machines and Sequencers”: The Untold History of Raymond Scott’s Pioneering Instruments [as reprinted from Electronic Musician]
One superb modern re-creation, via Synthtopia

Scott’s creation was shaped the way that it was partly out of mechanical necessity. Now we’re gifted with the ability to make any form we like for our electrified music tools. Circles can have appeal not because they’re somehow novel, but for just the opposite reason: they’re ubiquitous, intuitive, and geometrically elegant. So, let’s first consider these in their most abstract, in software.

Euclidean Rhythms

Incredible things are happening to our understanding of music theory as the gap between fields is shortened. Say what you will about the state of communication in our modern society; for the self-motivated, the trip “across the quad” (between academic departments) has nothing on the trip across the Internet.

Godfried Toussaint, a computer scientist with a strong math background based at Montreal’s McGill University, has a whole body of fascinating writing linking math, geometry, and music. One research paper has had a big influence on many of us, myself included. Here’s the beauty of math: an algorithm developed by Euclid in Alexandria around 300 BC also works for calculating timing systems in neutron accelerators and makes nice poly-rhythms for music. It’s rather amazing we don’t talk to each other about math more often.

Toussaint’s paper:
The Euclidean Algorithm Generates Traditional Musical Rhythms [PDF, 2005]

Our friend wesen wrote about the technique, suggesting it could be used to generate new rhythms, and included code in Lisp:
Generating african rhythms using the euclidean algorithm

wesen even made code for his amazing MiniCommand sequencing box, which I hope we’ll see more of this year. (I should have some time to work on it myself.) The actual demo is part of the way through the video:

The algorithm – the recent Bjorklund reinterpretation of Euclid’s millenia-old work – has in turn found musical life in other languages:

Python – the bjorklund algorithm and generative music[astomo.us]
Ruby – Rhythm Generation With an Euclidian Algorithm [Aleksey Gureiev]
More Ruby – jvoorhis GitHub
Java – Generating Musical Rhythms [Kristopher Wayne Reese]
Pure Data + Java – Dave Poulter
Flash/ActionScript (pictured above) – Euclidean rhythms [Wouter Hisschemöller]
Max for Live (pictured below) – Euclidean sequencer [Robin Price]

I’m implementing a touch interface for it now using Pd, Processing, and Android; I had hoped to share it by now, but I’m still fleshing it out – I’ll give it away when it’s done.

You’ll notice in these, too, the similarity to the original Scott Circle Machine, down to the sweeping arm. But that’s a benefit: glancing at them on paper, Mozart and Haydn look the same, and they use the same musical technology, but think of the musical variety that results.

A Few Circular Sequencers

Circular sequencing interfaces are plentiful – indeed, I hope that this story prompts lots of people to say “hey, what about …?” Here are a few examples.

DominoFactory’s dial uses drifting circular geometries to control musical patterns. Created by Hiroshi Matoba, a young designer/DJ, it’s one of a body of work this student creator is building:

17 Dec, 2010
at ImageRama in Kyushu University(Fukuoka/Japan)

dial is a software sequencer using circle to control loop sequences in real time. I imply “speed sync” circular notation system which differ to “angle sync” in my past work “Overbug”.

Now under developing with openFrameworks and Bullet Physics. I use ofxConsole for custom CUI in this version.

*ImageRama is one night event hosted by Genda lab. in Kyushu univ., we setup surround sound(5.1ch) and 1 full HD projector. thank you for all stuff!!

See also Matoba’s earlier Overbug, which assembles polyrhythms in lacy, overlapping wheels, like some strange, elaborate clockwork:

Overbug

You can download it for yourself for the Mac; it even has Snow Leopard support.

Also from Japan, Nao Tokui has taken these ideas in another direction, still, with “mashup” application and, in three dimensions, his original Sonasphere. The latter was one of the first interfaces to really fire my imagination as far as alternative user interfaces and three-dimensional sequencing.

http://www.sonasphere.com/

For an instance of a commercial application, see the iPad Loopseque, the development of which we profiled extensively here on CDM in August:
Loopseque, New iPad App, Offers Circular Sequencing and Visual Inspiration

The one shortcoming for me of that application is the inflexibility of the grid, which is why the Euclidean ideas above interest me, but it’s still a lot of fun.

Dan Trueman (on the faculty at Princeton) built his own Cyclotron for experimentation with cycles, with work going back to 1996. The clever invention here is the use of the spokes themselves as musical information. Quite a lot more detail and code in Processing and ChucK:
Cyclotron project page

Rui Penha and Polygons

Rui Penha deserves his own category here, I think, as he’s done a great deal of research. He has worked with polygonal shapes as a way of displaying evenness in rhythms, and he’s built not only novel interfaces, but entire musical compositional environments using these paradigms. They’re all downloadable, too.

Instrument A, pictured below, uses sampled sounds and pre-composed loops which you can then assemble into a layered composition.

Gamelan, in the video at the top of this story, uses cyclic, circular notation to make interlocking parts of music more visible, in the style of an Indonesian ensemble. I was struck by this myself as I’d constructed a (much cruder) demonstration of the same idea for a talk in Ireland; here, Rui builds it into an entire interface. Also, there’s a meaning to the symbology of the circle: Gamelan looks for other networked players with which it can interact, making this a communal experience – and it can even be used to play a real gamelan ensemble, via robotic apparatus controlled wirelessly.

Políssonosis perhaps the most sophisticated of all of these, mapping those shapes into three dimensions and making the evenness of rhythms more apparent. See video, top, and the same ideas below.

Hardware and Kinectic Art

No discussion of circular design would be complete without the legendary synthesizers of FutureRetro, which uses a cyclical interface to divide patterns and even arranges synth parameters around the rotational theme. You can now pick up an Orb for $550.

http://www.future-retro.com/

It’s worth coming full (cough) circle here and revisiting the mechanical ideas, as I think part of what grounds these abstractions is the progression of time in physical contraptions. That’s what inspires the rotating arms above and so on. Because it’s so fundamentally tied to a motor, there are too many rotating soundmakers to name, but here are a couple. They’re inspired by a discussion following our post last month:

Music, Like Clockwork: Modular Music Boxes with Rotating Wheels, Inspired by monome

Invisible Rhythm worked from the notion of a music box to make their analog drum machine Rhythm 1001.

See also the Conspiring machine – thanks to an unfortunate use of Flash, I can’t link directly easily, but head to http://www.kristoffermyskja.com/, choose work, and then select Conspiring Machine (or some of the other, related ideas) from the left-hand column.

I’m going to turn loopy if I keep going, so I’ll leave it there. But have you found circular sequencers to be musically useful? Are there hardware or software designs you appreciate that I missed here? Research worth checking out? Or are you committed to the rectangle – and if so, can you explain why?

Happy PI day. May your oscillations always be in phase.