Brownian motion & other aleatoric processes

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wellurban
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Brownian motion & other aleatoric processes

Post by wellurban » Thu Oct 24, 2013 9:39 pm

Hi all,

I'm very interested in generative music, algorithmic composition, self-running patches and the like. Analogue is great for some of that, but while other techniques tend to suit a software approach, I've been trying to work out what can be done in the analogue realm, and in Eurorack in particular.

Brownian motion or random walks (playing fast & loose with definitions here) seem like a useful building block for a range of such techniques, but I was surprised not to find much mention of it on Muff's. Maybe my search-fu is letting me down, but I could only find references to software techniques or to specific modules (e.g. Addac Complex Random) that have it as a pre-cooked option.

So I tried to cook up my own, thinking that setting up a feedback loop into a S&H, with a mixer to incorporate random bipolar voltages and get a random walk happening. It failed spectacularly at first, but once I put a quantiser in the loop (cheating?) and got the voltage scaling right it worked a charm. Here's a simple patch using Euro modules, but it should be fairly generic:

Image


Here's an audio demo with further explanation:

http://soundcloud.com/and-per-se-and/random-walk

A few questions:

- Is this pretty much old hat?
- If any of you have examples of similar concepts, I'd love to see/hear them.
- Are there simpler ways to do this? In particular, are there any Euro S&H modules that have low enough voltage droop to allow the elimination of the quantiser from the feedback loop?
- Has anyone tried generalising this to more complex sequences such as Nørgård's "Infinity Series"?

Anyway, here's another quasi-Brownian patch in a more "musical" context:

http://soundcloud.com/and-per-se-and/e-tude-brun

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Post by John Noble » Thu Oct 24, 2013 10:16 pm

I love generative methods and have been injecting some chaos into my patches lately. I use a quantizer most of the time to give it structure, and I don't think it's cheating so much as setting the stage for a (hopefully!) desirable set of possible outcomes.

Try varying a LFO's rate randomly and sampling/quantizng it at a fixed rate. :tu:

Quantizers with trigger inputs make thes methods simpler: A-156, Quantimator, etc. The A-156's trigger output is of particular interest here.
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Post by Dcramer » Thu Oct 24, 2013 10:48 pm

There was a good thread in the general modular section about this kind of stuff. Lots of cool ideas. I haven't seen it in a while and I find most of my searches yield the same results; every damn thread ever since Christ was a baby :omg:

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Post by Summa » Fri Oct 25, 2013 12:44 am

I love my addac 501 to death! I send the three outputs everywhere in my patches, modulating modulators, filters and straight up vco's. I'd dare to say I'm a big fan of randomness/chaos but the real interesting thing with modulars is the possibility to control that chaos!

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Post by Isolde and Isobelle » Fri Oct 25, 2013 2:59 am

Dcramer wrote:There was a good thread in the general modular section about this kind of stuff. Lots of cool ideas. I haven't seen it in a while and I find most of my searches yield the same results; every damn thread ever since Christ was a baby :omg:
This one maybe? - viewtopic.php?t=31698&postdays=0&postorder=asc&start=0

... I found it very useful when I planned my ''generative'' case recently. :tu:

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Post by Summa » Fri Oct 25, 2013 11:41 am

Isolde and Isobelle thanks! Made me decide to go for a RG-6, neeeeed mooooore RANDOM!

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Post by narwhal » Fri Oct 25, 2013 12:20 pm

Summa wrote:Isolde and Isobelle thanks! Made me decide to go for a RG-6, neeeeed mooooore RANDOM!
RG-6 is my second favourite module after d-lfo. it can do so much, fantastic design. btw. that clock out is perfect for pinging the res4 :tu:

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Post by Isolde and Isobelle » Fri Oct 25, 2013 2:14 pm

Summa wrote:Isolde and Isobelle thanks! Made me decide to go for a RG-6, neeeeed mooooore RANDOM!
Brilliant! :tu: That is a great thread, lots of gems of information in there.

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Post by waveglider » Fri Oct 25, 2013 2:25 pm

I have an ADDAC 501, got it specifically for the brownian motion function and I absolutely love it. It is really good that you can dial in the range of random levels and time interval, all CV'able as well.

RG-6 is on my wish list, that one seems killer in many ways.

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Post by Summa » Fri Oct 25, 2013 3:07 pm

Taking the concept of "Modulating the Modulator" I really like to use the simple random out of the A-118 into the Clk in of the 149-1, so basically "Randomizing the Randomizer" :party:

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Post by wellurban » Fri Oct 25, 2013 6:27 pm

Isolde and Isobelle wrote:This one maybe? - viewtopic.php?t=31698&postdays=0&postorder=asc&start=0

... I found it very useful when I planned my ''generative'' case recently. :tu:
Yes, that's a great thread, particularly for the analogue, emergent feedback chaos type of generative patch. I'm having fun playing with that sort of thing, and seeing to what extent I can replicate the likes of a Quantussy with a bunch of Euro modules (short answer: I'll never have enough S&Hs). Self-patching an A143-4 and putting it through an A156 generates a wide range of pleasant quasi-random melodies.

I guess what I'm leaning towards is incorporating more structured, mathematical, algorithmic forms of generative composition into that more organic approach. Not to the extent of Koan/Mixtkl etc: that would be perverse to attempt in the analogue realm when it's so suited to software methods. But I'm intrigued by the "Logistic Equation" Chaos Patch at the end of this Doepfer patching examples page. I don't think I have the right sort of clean linear VCAs required to implement the X^2 term, but the possibilities of that sort of analogue computation, combining mathematical chaos with the unique quirks of analogue hardware, are really exciting to me.

Has anyone tried Doepfer's Chaos Patch and got it to work? Are there any other interesting equations that might be used in an analogue generative patch?

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Post by Isolde and Isobelle » Sun Oct 27, 2013 10:14 am

wellurban wrote:


I guess what I'm leaning towards is incorporating more structured, mathematical, algorithmic forms of generative composition into that more organic approach. Not to the extent of Koan/Mixtkl etc: that would be perverse to attempt in the analogue realm when it's so suited to software methods.
...agreed - Noatikl/Mixtkl are far too feature rich for modular. Outside of the case bound logic/random modules, I use Charming Chaos on the Atari ST :eek: Still too many features - but it's ''DNA seed'' algorithmic tool, gives often beautifully melodic results without really having to know what is going on under the hood.

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Post by thermionicjunky » Sun Oct 27, 2013 10:27 am

Have you visited the chaos section of Ian's website?

http://home.comcast.net/~ijfritz/Chaos/ch_over.htm

Apparently, one can also modify a CGS gated comparator to turn it into a drunkard's walk module.


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Post by Navs » Sun Oct 27, 2013 11:03 am

thermionicjunky wrote:modify a CGS gated comparator to turn it into a drunkard's walk module.
Ooo. Any details?

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Post by thermionicjunky » Sun Oct 27, 2013 11:20 am

Navs wrote:
thermionicjunky wrote:modify a CGS gated comparator to turn it into a drunkard's walk module.
Ooo. Any details?
No, just Ken's video. He describes it as a minor modification. There are so many variations of the concept from Buchla's stored quantized voltages to the Klee. Someday I need to build something related to all of them, hopefully with this capability if Ken shares his mods.

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Post by kindredlost » Sun Oct 27, 2013 11:40 am

thermionicjunky wrote:Have you visited the chaos section of Ian's website?

http://home.comcast.net/~ijfritz/Chaos/ch_over.htm

Apparently, one can also modify a CGS gated comparator to turn it into a drunkard's walk module.

Yeah, dis' is it man.

Ian Fritz and Ken Stone have been at this for quite some time. A lot of DIY but worth it. The 5U world have had the Fritz modules available for some time and I'm sure many Euro projects have incorporated them as well. I use the ChaQuO quite a bit in my setup. I also have the MFOS quantizer in quad on a panel. The variable input attenuator helps to escape the ordinary 12tET tuning.

Another diversion from the straight-up analogue simulation (which is the point of this topic) are the Ardcore modules from 20Objects.com has some of this type of thing in scripts. Cheating, but the modules in your system is pretty cool.

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Post by oskies » Sun Oct 27, 2013 5:23 pm

Wellurban wrote: "Has anyone tried Doepfer's Chaos Patch and got it to work? Are there any other interesting equations that might be used in an analogue generative patch?"

I just patched up the logistic map - not precisely as in the doepfer example, but pretty close to the formula - I wrote a thesis on chaotic maps a long time ago, dammit. I'm pretty sure you can also use wavefolders to do this, would probably be much easier...

In any case, after the logistic circuit was working (O'tool helped a lot),
I basically send the cv out from the SH to a uscale, and let braids do the sound generation (+ some filtering and echophone for ambience, peg for
more interesting triggers, the usual)

Had NOT expected it to generate such cool sequences. In the soundcloud file below, I first slowly ramp up the amplicification (the constant in the equation that determines what patterns, if any, the equation spits out). You haer the pitch going up, and then going ABABABABA - that's called a period doubling. Cranking the amplification up further it gets chaotic. For example, I do not touch anything from 2-4 minutes, and the whole melody is just generated by this simple logistic circuit. After that I do change the settings every minute or so, to generate different melodies. At the 1.30 mark, the thing gets stuck in a variation for 30 secs before bouncing back to its earlier type melodies. Chaos...

[s]http://soundcloud.com/oskies/logistic[/s]

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Post by wellurban » Sun Oct 27, 2013 5:37 pm

kindredlost wrote:
thermionicjunky wrote:Have you visited the chaos section of Ian's website?

http://home.comcast.net/~ijfritz/Chaos/ch_over.htm

Apparently, one can also modify a CGS gated comparator to turn it into a drunkard's walk module.

Yeah, dis' is it man.

Ian Fritz and Ken Stone have been at this for quite some time. A lot of DIY but worth it. The 5U world have had the Fritz modules available for some time and I'm sure many Euro projects have incorporated them as well. I use the ChaQuO quite a bit in my setup. I also have the MFOS quantizer in quad on a panel. The variable input attenuator helps to escape the ordinary 12tET tuning.

Another diversion from the straight-up analogue simulation (which is the point of this topic) are the Ardcore modules from 20Objects.com has some of this type of thing in scripts. Cheating, but the modules in your system is pretty cool.
Thanks for the links, the chaos page in particular. I have a Dreamboat, which is useful for noisy audio and quick modulations, but not really slow enough for chaotic sequences. I think I need to look more closely at Chaos Brother, ChaQuO and the like.

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Post by wellurban » Sun Oct 27, 2013 5:42 pm

oskies wrote:Wellurban wrote: "Has anyone tried Doepfer's Chaos Patch and got it to work? Are there any other interesting equations that might be used in an analogue generative patch?"

I just patched up the logistic map - not precisely as in the doepfer example, but pretty close to the formula - I wrote a thesis on chaotic maps a long time ago, dammit. I'm pretty sure you can also use wavefolders to do this, would probably be much easier...

In any case, after the logistic circuit was working (O'tool helped a lot),
I basically send the cv out from the SH to a uscale, and let braids do the sound generation (+ some filtering and echophone for ambience, peg for
more interesting triggers, the usual)

Had NOT expected it to generate such cool sequences. In the soundcloud file below, I first slowly ramp up the amplicification (the constant in the equation that determines what patterns, if any, the equation spits out). You haer the pitch going up, and then going ABABABABA - that's called a period doubling. Cranking the amplification up further it gets chaotic. For example, I do not touch anything from 2-4 minutes, and the whole melody is just generated by this simple logistic circuit. After that I do change the settings every minute or so, to generate different melodies. At the 1.30 mark, the thing gets stuck in a variation for 30 secs before bouncing back to its earlier type melodies. Chaos...

http://soundcloud.com/oskies/logistic
Oh my, that is gorgeous! I really ought to try harder to implement that Logistic patch: at first glace I thought that I couldn't do it without a waveshaper, but on further inspection Doepfer's just using it to get a high amplification factor, and I can do that with the Gain sections on my PTG. It probably will be tricky without a decent oscilloscope (my iPhone apps won't help with slow CV), though maybe I can dust off my multimeter and that would help with amplification factors.

BTW, what's the pluck sound in that piece? It sounds Braids-ish to me, but I'm sure there are analogue ways of making that sound.
[Edit: damn, should've read you post more closely! Nice Braids plucks there :-)]

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Post by wellurban » Mon Oct 28, 2013 2:44 am

I got it to work! :bananaguitar:

http://soundcloud.com/and-per-se-and/cascade

It took a bit of gain adjustment to get k into the proper chaotic range, rather than running above or below the quantiser range too quickly, and I don't think that the riffs it produces are as "human" as yours. But it definitely creates some pleasing complexities that sound more interesting than plain old random melodies.

I also added a bassline, by using a VCBEND to scale and fold the CV and modulate it with a slow triangle. This creates a sequence that is related to the original, but not too obviously so, and it brings in some more traditional approaches to analogue "generative" sequencing.

I also ended up tweaking the k factor manually a few times, but I think this could also be automated. This could be done with a sequencer, to create a more structured composition based on several "movements" with different types of chaos. Or it could conceivably be achieved with a different sort of algorithm: some combination of logic and comparators tracking the amount of variation being generated by the chaotic sub-patch, and giving it a nudge when it needs it. All sorts of possibilities!

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Post by oskies » Mon Oct 28, 2013 2:50 am

That's great! Did you make the nonlinear function with a vca or wavefolder?

I also used the PTG for gain - very handy module.

Another thing worth exploring is to use analog shiftregisters. A single SH circuit with a nonlinearity can be written as x(n+1)=F(x(n)), where
x(n) is the voltage at time n, F is the nonlinear function, and x(n+1) is the next voltage. If you use ASRs, you can get x(n+4)=F(x(n+3)*G(x(n)), or many more of some complex forms, many of which are chaotic. Will try tonight.

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Post by wellurban » Mon Oct 28, 2013 3:33 am

oskies wrote:That's great! Did you make the nonlinear function with a vca or wavefolder?

I also used the PTG for gain - very handy module.

Another thing worth exploring is to use analog shiftregisters. A single SH circuit with a nonlinearity can be written as x(n+1)=F(x(n)), where
x(n) is the voltage at time n, F is the nonlinear function, and x(n+1) is the next voltage. If you use ASRs, you can get x(n+4)=F(x(n+3)*G(x(n)), or many more of some complex forms, many of which are chaotic. Will try tonight.
Thanks! I just implemented the X^2 term with a Pittsburgh Dual Index: mult X to both input and CV in, as in the Doepfer patch. A function-based waveshaper would be a very handy module, though.

I have a Doepfer A152 on the way, and I was about to point you towards the thread with the amazing ASR-alike patches using that modules...until I realised it was your post :hail: Looks like ASRs, and in general lots of S&H-like modules, will be crucial for creating self-reflexive generative patches with a "memory".

I've currently left my modular running with a variation on my earlier patch, using a sequencer to vary the k factor every few minutes, and it's just hit a run that's more like yours: lovely shifting arpeggios reminiscent of Philip Glass or early Kraftwerk. Before that it was doing something much sparser and Enoesque. The trouble with this sort of patch is that I could just lie here for hours listening to it rather than carrying on patching :ripbanana:

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Post by oskies » Mon Oct 28, 2013 4:53 am

Yeah its great - after I had the patch going last night, I could not get to bed as it was surprisingly pleasant to listen too. I had been playing with the logistic map generating midi data on an atari in the 90s, but it never sounded so good! Ok, let's see if we can get something going with ASRs or other maps also...

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Post by Tombola » Mon Oct 28, 2013 5:16 am

Here's the PDF reading list I put together while designing the Turing Machine - has a bit of this stuff http://musicthing.co.uk/modular/wp-cont ... g-List.pdf

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Post by strettara » Mon Oct 28, 2013 5:33 am

wellurban wrote:The trouble with this sort of patch is that I could just lie here for hours listening to it rather than carrying on patching :ripbanana:
Slightly off topic, but I think this is actually an important part of learning the instrument. Why hurry to do more patching? I often let patches run on for a long time in the background while working, because I think you can learn a lot this way, get used to the variety of sounds and structures produced by a patch, for more disciplined use later. It is especially valuable for chaotic systems - whether the blippoo box or some recursive modular patch.
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