# Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

For fans of synths, pianos or keyboard instruments of any sort.

### Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

A strange confluence of the last Genesis documentary (Sum of the Parts), the documentary on Peter Gabriel's fourth album, and my recent patch teardown led me down a very interesting, and very deep, rabbit hole that started with the idea, I wonder if you can apply Euclidean patterns to melodies ...

The fact is, you can, and there are two ways to go about it. The way I am doing it is the simpler of the two, merely using Euclidean patterns to source a melody, but with a traditional quantizer, not one based on Euclidean maths.

Whilst it needs actual work now, I am sufficiently chuffed from my initial experiment and proof of concept that I thought I would share it here for anyone else interested in generative composition:

It started with the idea of using Euclidean patterns to create melodic patterns instead of rhythmic ones. I sketched it out first and then started patching. The core elements are:
Euclidean trigger generators (in my case, Euclidean Circles)
Sequencers with randomization (Pittsburgh Modular, 2hp Turing Machine)
Quantizers (Disting Mk4)
Synth voices

The concept is this: The Euclidean pattern generator's output is multed to both an envelope generator and the clock input of a sequencer. The output of the sequencer goes to a quantizer and then into a synth voice. Every time the Euclidean pattern fires a pulse, it advances the sequencer 1 step.

To add randomization to the Pittsburgh sequencer, I also took a mult out to a Make Noise Function generator. I patched the EOR trigger to a Mutable Instruments Branches. By adjusting the Rise and Fall of the Function, I can introduce a delay into the coin toss from Branches. The pulse outputs from Branches go to the Reset and Hold inputs on the Pittsburgh.

The real fun begins when you add a second voice, however! This is where you start getting long, evolving patterns that drift in and out of unison to various harmonies.

My proof of concept video is here, https://photos.app.goo.gl/sDqWVFDv2GUgqy8E6

With 6 trigger outputs, the sky's the limit in terms of melodic or rhythmic variation. Simply shortening one of the circles and rotating it's orientation created countless variations and the sequencers were also playing randomly determined notes.

It's funny because, until now, I had never really got on with the Turing Machine. I now have a newfound respect for it and can see how important it can be to improvised, generative music composition.

The other thing this has shown me is that I definitely want another Euclidean pattern generator that I can run off a clock division for even more variations! Perhaps the new Super Disting is in my future lol ...
Ben Asaro
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Don't tease us like this. ;)

blinddrew
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Don't tease us like this. ;)
Whoops! :)

https://photos.app.goo.gl/eKENKHT9CiowQDrY7
Ben Asaro
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Ah, no, my bad. I've just seem the little play symbol in the top right.
Sorry! :oops:

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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Sounding good!

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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Interesting idea. I was a little 'hmmm' at first but when the second part started to develop I see what you mean. I'd agree on the 'needs more work' part but as a generative pseudo-composer to get some good ideas going I think it's a great approach.

I can see I should have a proper play with the euclidian pattern generator in my Squarp Pyramid!

Nice one :thumbup:

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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Eddy Deegan wrote:Interesting idea. I was a little 'hmmm' at first but when the second part started to develop I see what you mean.
Yup, just like with a single percussion voice going, it's a bit like, 'yeah, so?' until the second pattern comes in, and then it's more like, 'aaaah, I get it'.

I'd agree on the 'needs more work' part
Oh dear, yes! This is just my first shot across the bow, as it were. The kernel is there, but that's about it at this point. I just spent the last 2-3 hours trying to keep everything in sync just in case I want to incorporate MIDI, and it was an absolute nightmare without using the NerdSeq -- but I figured it out in the end! Using Pamela's Workout as the master clock, into the Erica Synths MIDI <-> CLK and using MIDI out, I can start everything at the same time. I had to set up one of the outputs from Pam's as a reset pulse for Euclidean Circles, but it works great now, and I retained 75% of my hair in the process lol

but as a generative pseudo-composer to get some good ideas going I think it's a great approach.
I have yet to muster up the discipline required to really knuckle down with something like this and give it a serious attempt. Whilst I'm working on a mega prog thing at the same time, (songwriting demo here of what I have thus far, https://soundcloud.com/asfollowswriting ... apr-20-v10), this is proving to be a great antidote to all of that structure lol.

I can see I should have a proper play with the euclidian pattern generator in my Squarp Pyramid!
The Pyramid is a real beast, you should definitely have a play and let us hear the results!

Nice one :thumbup:
bows :)
Ben Asaro
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

blinddrew wrote:Sounding good!
Thanks for listening! There's really not much to hear just yet, it's just the basic idea, but I appreciate the encouragement!
Ben Asaro
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

My default position is to think of hardware rather than software solutions for making music, but I must admit, when it comes to making mathematically-generated music, haven’t computers got this aspect covered? I couldn’t name any, but I know there have been many such applications over the years, on every platform.

Or would that miss the point that it doesn’t fit in a rack or have physical knobs?
BillB
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

BillB wrote:My default position is to think of hardware rather than software solutions for making music, but I must admit, when it comes to making mathematically-generated music, haven’t computers got this aspect covered?
A valid question, for sure. The answer is yes, computers can do this type of generation with ease. From my perspective, there are two parts to the question of, 'why hardware':

Part 1: The hardware/modular approach seems to encourage exploration on a tactile level. You could argue about range of control and nuance, I suppose, but for me it's about not having any sort of tablet or computer interface to deal with. I find it to be a lot less distracting than when I am sat in front of a device that's connected to the Internet.

Part 2: In my opinion, one of the reasons "ambient" and "generative" are such watch words among modular enthusiasts is because no actual musical theoretical knowledge is required. Your role as 'composer' is, in fact, more that of 'curator'. From a performative stance, it's a lot more interesting to see someone turning a knob, of course, as apposed to just being stood in front of a laptop...

I couldn’t name any, but I know there have been many such applications over the years, on every platform.
Oh, definitely. Even Brian Eno has a couple of 'generative' music apps, and there are apps that specifically apply Euclidean geometry to melodies as well as rhythms.

My favorite computer-based generative program is Nodal, https://nodalmusic.com/

I have found that Nodal + a CS80 plugin = endless hours of soundscape fun. :)

Or would that miss the point that it doesn’t fit in a rack or have physical knobs?
It would miss the point for my purposes, but I don't knock hybrid systems. I think that the hardware/modular mindset has swung along both sides of the extremes and has now settled somewhere in the middle. A few years ago there was a big push for 'DAWless' systems, but now most systems are a hybrid mix using a computer, Ableton, or something like Push or Circuit along with a hardware based system. I also definitely count a sequencer as a 'computer' in this context.

This is, in fact, my first 'serious' attempt at generative music composition. I personally prefer much more structure in my music, so it will be interesting to see, if/when this rabbit hole either dies on the operating table or produces fruit, what will be the take away from all this? Will it somehow inform my musical worldview? I guess that's what I'm ultimately more interested in, expanding my limits as a music listener more than a music maker, if that makes any sense.
Ben Asaro
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Too many new/recent hardware and software acquisitions for me to learn. But I have bookmarked that Nodal link. Just having that appear on my screen would have people thinking I'm some kind of genius! They already think I'm mad, so that would complete the package.

Andy :beamup:

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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

zenguitar wrote:Too many new/recent hardware and software acquisitions for me to learn. But I have bookmarked that Nodal link. Just having that appear on my screen would have people thinking I'm some kind of genius! They already think I'm mad, so that would complete the package.

Andy :beamup:

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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

I haven't come across Nodal before, will check that out. I'm interested in generative music but haven't done much with it beyond downloading a few apps like Wotja.

Back in 2008 Benge put out an album called Twenty Systems which was his one-man answer to One Synth Challenge. I thought it would be interesting to revisit the concept with an album of generative music created in a dozen different languages, with pieces that reflected the nature of the paradigm.

...yeah, one day...

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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

BJG145 wrote:I haven't come across Nodal before, will check that out. I'm interested in generative music but haven't done much with it beyond downloading a few apps like Wotja.

Back in 2008 Benge put out an album called Twenty Systems which was his one-man answer to One Synth Challenge. I thought it would be interesting to revisit the concept with an album of generative music created in a dozen different languages, with pieces that reflected the nature of the paradigm.

...yeah, one day...
LOL that does sound like a monster project!
Ben Asaro
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### Re: Euclid, Turing, and Boole walk into a bar ... (modular synth/generative composition content)

Today's stab at the process led me towards something a bit more cinematic sounding. This is 4 voices of Euclidean patterns playing, 3 percussive and 1 melodic. I wanted to spend time getting a good looping melody and then focused on the actual sound. I ended up taking the square wave output from the Mother-32 and feeding it into a subharmonic generator and then fed that back into the M-32 and mixed them to taste.

The rhythm is deceptive in that the "1" is not really the 1; it actually occurs an 8th note beforehand. That creates this cool shift-register style melody, which is comprised of 8 notes, but played in triplets so it "lands" in a different spot each time depending on how you perceive the 1. I focused in on the Euclidean Circles this time so you can get a visual as to what's going on.

Proof of concept: https://photos.app.goo.gl/RmRjoTbN5gnwYgp56

Still have miles to go!
Ben Asaro
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