Loopseque on the iPad. Courtesy the developer.

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.

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:


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.


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.


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.

  • No mention of Raymond Scott's Circle Machine? Or the Buchla 250e?

  • D'Oh! You mean I have to actually read the words?

  • Peter Kirn


    I don't think the original Buchla had any sort of radial layout like that, not on any of the modules I used. I assume Don Buchla must have been familiar with the Circle Machine, though. The 250e is absolutely an excellent example. Like the FutureRetro, I think it should be considered a descendant of the Circle Machine … well, and most clockfaces!

  • Art
  • Wonderful article! In the written-music world, Terry Riley wrote some of his Keyboard Studies on a circular stave. Also George Crumb has used circular staves quite often. Really helps to get to the heart of the music! Back in the software world, there is also the excellent Reaktor sequencer, Spiral, and the old c74 program, radiaL, whose gui had circular audio files.

    After all, beginnings and endings are just perceptual constructs. Using circles helps to underscore that music (and life!) is about the journey, not the destination!

  • I'm going to add here my own Seeq-it analog circular sequencer: http://unatronics.com/store/index.php?route=produ

  • Yasha

    The VST Eckel by Shuriken.se (Mac & Windows) functions as a Euclidean Rhythm sequencer. There's no visualization of the circular cycles, but a circular motif was used for all of its controls.

  • The Domino Factory piece is fantastic, very impressive indeed.

    I *cough* made an interactive installation based on this circular sequencing idea actually, using arduino/processing and pure data – video here: http://vimeo.com/12763642 The fascinating aspect of this approach is that you have a natural visual tendency to loop and repeat and "manage" your music in a slightly different way than usual. As a result the interface leads you in a certain musical direction, which I find quite interesting.

  • joost

    Interesting article! You can also get LoopSeque Mini for the iPhone now.

  • ash

    I don't get the point of a circular sequencer vs square track. They both have equivalent loop points and resolution, so is it just a question of aesthetics?

  • Tim

    Dear Americans
    Your date formating of [month] / [day] makes no sense. Everyone else says [day] / [month] / [year], it's a logical order as each is bigger than the other. It's not cute and idiosyncratic like the way we have unnecessary vowels in words like "colour" or "analogue", it's just wrong.
    I look forward to celebrating Pi day in its god-given chronolocation of the 3rd of Fourteenuary

  • Peter said: "I’m going to turn loopy if I keep going, so I’ll leave it there"

    Don't do that, it's crowded enough in my head! 
    Seriously, fantastic article (all the PI day stuff was great). The appeal to me specifically should be obvious but really a nice way overall  to re-visualize (as Henderson already mentioned) musical relationships and how both interface design then changes and how you interact with the materials.

  • Peter Kirn

    @Tim: Actually, we're both wrong. See ISO 8601:
    Descending order of quantity makes more sense than ascending ordinality and certainly more sense than the illogical American method.

    And best of all, it protects Pi Day. 

    And it's an official standard.

    @Loopy C: Ha! And thanks!

  • lodsb

    also http://sourceforge.net/projects/iannix/
    as quite mature app  with more vocabulary+additional physics. its also cool, since it is an osc sequencer 😉

  • Jonah

    It's late, but  360 Drum Sequencer in the Mac App store is cool. http://360drumsequencer.blogspot.com/

    The demo I tried was a bit fiddly, but the new features in version 1.0.5  are enough for me to buy it when I get my mac hooked back up to the net. Last I checked it was by far the best music program in the app store. But there were only two good apps. 🙂

  • Cretin Dilettante


    Not really circle related, but does anyone know where I could get the first version of this? The most recent one isn't really a sequencer so much as a mangler for a single sample. I'd really love to try making some tracks using the original Narrativas Sonaras alone.

  • here's another Python implementation of bjorklund's algorithm for Euclidean rhythms:&nbsp ;http://brianhouse.net/software/#bjorklund

  • sr.proxerino

    here's a draft of the bjorklund algo for supercollider:


  • What about the genoQs Octopus?


  • Jonah! Thanks so much for the recommendation of 360. Grabbed it out of the app store and am having fun! It's a bit of a heavy app for what it does, but there's a lot going on, on screen. Fun sequencer!

  • My iPhone app Tondo is a circular sonogram painting program – in the sense that a sonogram loop is a sequence , I suppose it could be called a sequencer.  You can constrain the time dimension to map out polyrhythms if you want to.