 Last but not least today we have Very nice talk here to present to you. His name is Jadz Greenway and He worked in some fields not really related to music up till now But he will show us What how you can? Yeah, make the continuous discreet and the discreet continuous so Please Welcome Jadz with a big hand of applause on this cold night Actually, my watch says we've got three minutes to go. Shall we wait or not? Yeah, I want to get out here before I get lynched. Okay, so my background is Polymer physicist without portfolio The title Indiscreet music is of course a troll on Brian Eno's discreet music and is itself a follow-up to Oblique strategies against humanity, which I presented at EMF This is about nearly half new material after which I shall So to say Shut up and play the hits and repeat some of the stuff at EMF that at least I know people liked So I'm August on Twitter the links to my slide share will be on every Slide little that's the housekeeping and here we go. So the prologue Back in the day. I was a child of the eighties and I was raised on the sorts of mathematical recreation books you could buy particularly those of Cliff pickover and The compendiums of the Scientific American computer recreations column and And they were different from what you can get today you were sort of there were pseudocodes You were encouraged to actually mess around with things and to code things up an experiment for yourself And not wishing to be all soggy with nostalgia because it was terrible because all you had to play with if you were lucky Was a sort of eight megahertz Atari ST and the thought of the thought of playing with the signal processing in real time Was it was just a dream? I could I could play MP3's on my Atari Falcon in mono if I kept the mouse still These days, of course, you you know the you don't see tomes like that and apparently what the kids want is scorched pieces of laser-cut plywood with LEDs on them and that's that's what they want to do So a little bit more of background. I first became aware that Computers and pictures and mathematics and sounds went together because of all things Jeff Minter and his his light synthesizers tripletron color space psychedelia, etc. And later much later I Became aware of the the power electronics and the noise scene now this didn't impress me Well, I liked it, but it didn't impress on put upon me in terms of sounds I wanted to make myself But it did real and make me realize what I could get away with I'm a really good description of The noise scene can be had from Jennifer Wallace's fight your own war on headpress and my own particular introduction to the noise scene was the Hinoyma Club in Finsbury Park in London anyway without further ado Let's start with something simple very simple elementary one-dimensional cellular automata, so we have a set of in fact an array of Cells which can be in in this instance two states on or off and as is fairly traditional We shall start with a single on state a single defect in the center and If you imagine an image the image will evolve Down the page with the y-axis representing time So a cell's future depends on its past and the pasts of its neighbors. There are eight possible arrangements of Live or or dead cells Thus there are two cubed equals eight previous configurations for each cell For each of those Configurations, there's a single choice of will the cell be on or off So there are two to the eight is 256 possible 1d cellular automata Some of which will be inverses or reflections However, and that is that is attributed to that that name that numbering scheme is attributed to one Stephen Wolfram of Mathematica fame now. I'm gonna briefly No, I'm not actually I'm gonna go back to the Go back to the slides and So rule 30 You can make a sort of tolerably not very good random number generator out of that Rule 110 more of the the uses and abuses of that later as well So that's what these that's what these things look like in a nice fetching green And I just wanted to know what they could potentially sound like admittedly so did Stephen Wolfram So you can you can find online his Wolfram tones It's an attempt to sonify these these these very simple rules And what's what's happened is that a narrow strip of cellular automata is taken and if a cell is on or off That corresponds to a note or at least a percussion part so different different Columns of cells will correspond to different Notes or rather. Yeah different notes This is tricky Where's I That probably says Wolfram tones Well, that was nice So much for the support act Let's try something a little more fundamental and simpler faster yet slower Now the problem with that was that well if it's you've only got that strip of of Cells each one corresponding to a particular note Well, that's not very many notes. You could have a wider strip of cells and much as I'm a fan of the genre known as black midi Do you really want all 88 keys on a piano mashed down by these these cells all at once? So possibly not so could we get a bigger range of notes with with this small strip of cells? So first thing we can actually have more than one cellular automata going not at a time But we can have something almost approaching verses. So rule 75 45 30 etc You'll notice that coming in The two rules on the left are the mirror of the two rules on the right In fact, the three rules on the left are the mirror of the three rules on the right and the two in the middle are Symmetrical there's something bordering on on structure there. So eight rules each gets 64 beats and this time now the The five cells in the center are dealt with in the sort of traditional manner Again, there's some symmetry there though. So we'll have open and closed hat on the outside High tom and low tom further in and then in the middle we'll have the kick drum But the melody the melody if you want to call it that what we'll do is look at the history of the cells in fact the Previous six generations and we'll consider those as binary values will have most significant bit In the present and the least significant bit in the future and that'll have a little more variation in in the notes played So three notes polyphony for the three cells in the middle zero to 63 so three lots of 64 potential notes corresponding to the lower register of the zero to 127 possible midi notes the middle and the top end All done nicely with the with the python mido library to which for which I'm reasonably eternally grateful We'll have a vulca Beats doing the drums and not the vulca keys as pictured will have a vulca fm, which is a digital device playing the melody if I'd have got over my analog obsession earlier I could have had a nice Navation circuit and had five note polyphony one for each finger so Let's see what this sounds like find the mouse elementary ca dot flak Righty clicky. Oh, come on On that one. Do you think oh, thank you too kind There are still problems there for me in that I chose the drum sounds and Chose the sort of electric bass of the of the of my vulca fm until it sounded nice That's yielding too much of the sound To me and not enough to the to the mathematics to the algorithm He got to give the you got to give the algorithm a fair chance at sounding terrible so could why possibly yield Control of the very timbre of the sound in fact do away with notes all together yield control of over the number of even Oscillators or whether we even had any sort of identified Identifiable oscillators to the system. Well, maybe however brief digression That's a gauss map What should it sound like more to the point? What even is a gauss map? so Interestingly the the image On this t-shirt. Yes. I am wearing the man's t-shirt at the gig and the image on the first slide when I did some of this at emf Though I was actually surprised how that you know, there were people who didn't recognize it So if I'm preaching to the converted about five and down diagrams and bifurcation, I apologize, but recurrence relation take a value exit time t plus one Is a function of exit time t And two parameters alpha and beta so for any alpha and beta We create a sequence of x values and we chuck away the transients and we keep going and various things can happen It can collapse to zero. It can reach a steady state two steady states oscillation between the two for period four implies chaos, etc. etc. Michael Feigenbaum And we do that And we build up this series and what we can do with this this series of values is to build a histogram So each of those slices through the bifurcation diagram through the gauss map Is a histogram so bright means that point was visited lots that value of that that range of x values was visited Lots of times the black means the system never went there So we scan beta across the horizontal axis and we can scan alpha through time And watch the thing evolve And I thought to myself well, how could I make the how could I get this to make sounds? I'm going to imagine that those slices those histograms are in fact spectra So if you imagine your amusing t-shirt with your Equalizer bar graph led display We're going to do that backwards problem number one Is that my histogram is full of real values and the inverse Fourier transform Required to turn it back into signal Has requires complex values. Well, there's I've got no imaginary part. Am I bothered? Actually, no if I have zero or constant imaginary part. I have zero or constant phase And all that the only constraint is that my signal will be symmetrical about the middle. So what? I'm really not explaining the coulis-tukey fast Fourier transform algorithm at this time of night to you lot at this time of night, but do look it up It's quite nice so problem the second the idea of a Fourier transform is that A periodic signal or one that you've at least repeatedly copied till it looks periodic produces a spectrum therefore a spectrum should produce a periodic signal. We've already decided that our Our histogram our spectra are going to be varying through time So you cheat slightly so you have the short time inverse Fourier transform. So you Take your chunk of spectrum for that slice of the bifurcation diagram Inverse Fourier transform it multiply it by What is called a window function, which isn't Gaussian, but looks a bit like one I believe blackman harris is the name of the function I used and I'm I've got a horrible feeling I've left out a convolution here somewhere, but never mind. I don't care at this time of night so We take our chunks of signal we multiply it by these window functions and we overlap them and we Add them together and eventually we get noises thinking about it The only sort of sense of time here was in the recurrence relation But when we've got that histogram all that's all over so we're going to vary This beta Parameter back and forth as we scan up and down our diagram whilst alpha is Increasing in time Well, if beta is going backwards and forwards, why shouldn't why shouldn't alpha so in the Right channel will have the whole rigmarole only played backwards I got that idea by reading my kick-started copy of Of daffy orams individual notes in a place of ultimate Vitreous china seclusion But you can read of daffy oram on uberweb And while we're at it if you imagine the The bifurcation diagram Splitting recombining becoming noise will take the We'll take its center of mass if you like and use that to pan between the left and the right So the idea is we'll start off with a single tone chirped becoming too And having beat frequencies And eventually turning into skronk to use the technical term and then coming back again now. I hasten to add This work should not at all be compared to that of elaine redeague But if you're prepared as I am to listen to hours of a slowly evolving Modular analog tones and and studies on a plane Then you will be prepared for the desolation you are about to hear it lasts for four minutes not four hours at least So this will be a little bit meditative. Maybe it's what you need on this on this Barmy evening And tell a lie this this this of course has pictures to go with it. So I'll just Enable the slightly cheesy tape echo on my digital Effects unit And I'll play this and then I'll shut up. Oh, thank you. I'll get rid of that Yeah with regards to the the function the the role of time in that I forgot to get a get a decent in-joke in And that's that's equation wise. We should consider time as officially ended That in fact is culled from sundar's space and the place Sorry space is the place at which well as a as a polymer physicist I recommend you go and see space is the place by sundar on uberweb, but your earliest convenience That was a public service announcement. So All of a sudden the inverse short time Fourier transform becomes my favorite new toy and let's think back to those Those cellular automata and can we really have 88 Cells acting as keys on the piano. Well, no, we can't have that but what we shall have instead is individual bits of array in an inverse Fourier transform so 512 cells this time Oh, I left out the zero padding You're gonna have to zero pad your arrays otherwise You'll end up sounding like a dog whistle and your housemate will not be impressed Somebody remembers that. I haven't got it quite right. What's that? Is there a mosquito? It's very loud. Ow Oh My hearings long been destroyed by mersbos. I was oblivious So single defect will take the six previous States of all the cells interpret them as binary values treat those binary values that array of binary values as a spectrum Will go for rule 30 on the left channel rule 86, which is the reflection of rule 30 as the right channel The results are going to be a little bit uncompromising. I like them. There is no one No one has heard these sounds except for people wearing this t-shirt Um None of us and and we too have not heard these at sufficient volume now Again, I'm not going to compare my work to elaine redeague I'm not going to compare my work to that of mersbo either But if you can stand an entire mersbo gig, then you'll be all right with this otherwise That there are no guarantees. I must say Do read do read fight your own war by By miss Wallace if you can I must say though, I'm no longer particularly interested in the some of the nihilistic Aspects of the power electronics or the other or the paranoia scenes So I I have I feel no particular urge to acquire a balaclava Get a silly name like a duodenal abuse unit And sit with my arms folded glaring at a row of guitar effect guitar effects pedals Which I refuse to touch or alter because hey harsh noise wall progression is for losers um, yeah, do look up harsh noise wally uh a A satire on the harsh noise wall scene an actual legitimate use of scott adam's cartoons it can happen All right brace yourself. No don't want to do that. No, I will do that now Thanks for the thanks to the av people by the way for getting audio and video that worked pretty quickly um Have you got gaffer tape? Have you got a fire extinguisher most have you got a digit on them on a On a slider somewhere This is going to last three minutes and ten seconds and I'm not going to stop it I'm probably not going to start it either until looking to find my mouse Ah, yes rule 30 86 dot flak It's a catchy tune catchy title or rather brace yourselves Oh, no, he just teasing you Earplugs brace yourselves That to me is what rule 30 sounds like and that to me is what rule 30 looks like it doesn't look like a piddling little column of uh Five or maybe a dozen a dozen cells. Um How are you missing me? I forgot to be nasty to steven wolf from Before we before we leave the cellular automata. I did say rule 110 was interesting It's been proven that rule 110 is universal That is to say if you can find a suitable way of encoding any uh Any computational problem and you have a large enough Array of cells you can encode a problem and interpret the answer in terms of an initial state Of rule 110 and you can run rule 110 and get the answer And that was a proof That i'm not going to explain cyclic tag systems at this time of night Frankly, I couldn't explain cyclic tag systems at 10 in the morning with a big strong cup of you know part of coffee either to be honest, but that proof was um Not developed by steven wolfram, but wolfram research said that its existence was a trade secret If you go on my slideshare the url will be uh, there is a url which is a link to um A review of wolfram's rather immodest tome a new kind of science also Some wag has gone and implemented rule 110 in pure css not one nasty line of javascript. So Officially css is turing complete That wasn't me. You don't have to clap that I said i'd shut up and play the hits. So again people I I saw people emf. I'm about 50 50 good. Oh, is that listed juice? No, it's a larence attractor already. So back in 1963 This is like the sort of uh apocryphal newton apple on on head moment Edward larence deterministic non periodic flow you can find a pdf somewhere set of three differential equations simplified models of convection currents and what he does is apocryphally possibly true He stops this simulation Restarts it after lunch or whatever having made a couple of little rounding errors in the uh when Entering back the into the the state of the entering back the state of the system because you can't solve these Analystically you have to have you have to have you know use numerical methods and it Behaves in a completely different fashion so two very very slightly Differing initial conditions and the system diverges and stops looping around the complete op-me other lobe Butterflies yadda yadda yadda. I'm sure well maybe more than half. You know, you know, this is this is not news And I wanted to make some noises again a sort of Manifesto of mine as many parameters of the mathematical system should be as possible should be Making the decisions about what this about what the the sounds are minimize your own influence It wasn't me give the give the system a fair chance to sound terrible and it should sound the way it looks so quite quite pedestrian compared to the abuse of Fourier transforms we'll just have the the three variables Modifying the frequencies of a bunch of in this in this first instance actually sinusoid Oscillators and we'll have other oscillators oscillators modulating those themselves Controlled by the variables of the stranger tractor etc And just for a laugh we'll have stereo panning on the x variable Now how to implement this I did not use chuck. I did not use super collider at first I did not use arda I did not use pure data I only had to go Wrong slide actually Before I resigned myself to doing this in software I must I'm actually actually stress. I never wanted a modular synth. Please believe me When you're at evil physicist school you get taught how to model Analog circuits in terms of differential equations therefore a differential equation can be turned back into an analog circuit and this is Mr. Horowitz of Horowitz and Hill art of electronics fame and his Lorenz attractor circuit You want to build one at home The analog for quadrant multipliers he specifies are 20 quid a pop I paid six quid for mine Just if you want to build one yourself Can be cheaper It's almost too simple, isn't it? It does work So that there are problems if you want to the weight is at the moment if you want to change the speed of the thing big nasty rotary switch and Three sets of four caps to change the the speed of the integration I need to mess around with dual trans conductance amplifiers to get the To get the chaoticness of the system controlled by control voltage as well So that that was taking time So back to software again, not chuck not pure data anybody guess javascript Web audio api Heard about this in fact because of I'm completely not seeing the how are we doing okay for time How long left? 10 minutes of the original 45. Okay. Well speedrun then. Where's my browser? Now this is going to be a game Uh, can we have the laptop order you're back? Oh dear hang on Belt and braces Let's just see if it's me or you So what sorry? I wonder if it's chrome chromium being foolish Didn't want to advertise google sound card All right improvisation I can't believe I'm doing this Yeah, I'm using my ruddy phone Let's try something a bit different Oh, of course. I actually need to change the bloody buttons on the mobile browser, don't I? Let's have a tura tractor instead if we want to talk about fail. Um, I ought to completely fail to build a a tura circuit at camp Never mind So that was a nice little stopgap at least Don't know why this ruddy DAC has stopped playing ball. I really don't Maybe it's the Can we turn that down, please? Because that'll be helpful for later uh Cambridge audio DAC magic don't buy one So that was a nice little stopgap next thing I tried closure of all things so I didn't want to use superglider directly so I tried to Uh Well, just domain specific language heard rather not so closure has a project called overtone Which I believe in looking looking at git. It's just acquired a new maintainer, which is nice and I'd hope to get um hope to get uh My larenza tractor implement implementation controlling controlling uh supergliders oscillators and Try as I might I just couldn't Get it happening in real time. It was all horrible and and steppy worse than the javascript. So I ended up Ended up just building a buffer full of larenz signal and using that it was It was a little more, I guess continuous and non-steppy than the than the javascript But not much and so in the end I relented Oh, all right, I do slightly want a modular synth So I've finished messing around with my uh With my larenz circuit normalize the voltages from 0 to 5 with op amps 5 minutes. Thank you So so so things didn't get fried And we'll have a little mini modular synth called a nano synth the patching is all done by uh By a pcb headers, which are perhaps not very durable But at least you don't need to sell a kidney to have one So we'll have one variable controlling pitch one variable controlling the pulse width of Your square wave will have something approaching Not not so much panning, but we'll have the the vca's on two synths being turned up and down according to the uh the exposition and mogverkstatt variables controlling pitch lfo rate and filter cutoff as is traditional A little snippet of that. I tried to this was recorded at EMF But of course it wasn't played live at EMF and I wasted quite a bit of time Staring at the circuit board in disbelief and swearing Now all I've got to do Is work out Yeah, I've worked at nano synth there's also a bit of noise here to Get a nice whooshing effect as the thing winds from side to side Uh, didn't open that Come on Oh, I hope get me bloody amarok No So turning it faster and slower on the Little rotary switch to switch in out the three banks of capacitors. Not what I wanted at all really Enough of that nearly that I'm going to play you out fairly shortly With well in when I abused Fourier Fourier transforms and the 1d cellular automata that was a continuous system abused and Sorry a discrete system abused and made continuous So now as threatened I finally threw in the towel and did what I thought would be awful All right, so I quite haven't quite got the definitive analog larynx sounds I wanted so I threw in the towel and said, oh, all right. I'm just going to have to quantize the Quantize the system to the 120 or 227 midi notes. So x variable Playing an archeria micro brute y and z variable playing the notes on a vulca keys x variable however also controlling the filter on the vulca itself also quantized to 127 Every time the x-axis Or rather the the z-axis is crossed by the x variable will have a kick drum triggered on the vulca beats And Yeah, it's going to be all quantized and steppy and not very good. So we'll just turn up the portamento and hope for the best my uh My expectations were not high all gone quiet Well, what do I know? I thought that was going to be horrible. Um, it turns out that Real live musicians who I who I respect and are Have been sadly rent from their homes because of the actions of our prime minister when she was home secretary actually quite liked it As to why I keep using Um external gear rather than software since I did that just just because I did all right Also, obviously hell is other people's software. Um, I do appreciate that Music hardware isn't always cheap but one One trick around the you know the the cost of of musical hardware is not to Um Try not to detonate your currency because uh straight bananas and energy saving light bulbs give you a bad feel Thank you Any questions or abuse or runaway screaming? There's still an audience here Thank you very much for this amazing talk. Is this was definitely something different? Uh, oh, it's that all right No, the music was really, um It's my favorite talk today definitely I love that So do we have any more questions or do we have any questions regarding? I don't know the music Uh as a math perhaps a little late for that, but do we have any questions here? What you can do is if you want to find me later I'll be in the vicinity of milliways and if you've been partaking of its entertainment hospitality and libations you better go and Buy a buy a milliways challenge coin That's the commercial break So We don't want them to fly wasting away Oh, everyone's stunned. Oh, there's someone actually approaching a mic. No, that's just the sound guy Getting his earplugs Oh, he has a question So go on Yeah, um I'm actually studying physics and I just had a course on digital signal processing You know more than me and what we did there was we did a Fourier transform of some sound and afterwards Sorry, I'm just trying to turn this off into me. Well Um afterwards, uh, we had to do certain things here like first thing we did was we, um Normalized it so we threw away all the amplitude information And we noticed that that way the sound was still recognizable. You could still understand what was being said on the recording Um, but when you threw away all the phase information and made it completely real It turned into like a blur of noise So have you tried experimenting with actually generating complex? Not yet. I mean the if you can think of a way, I mean it trouble It troubled me for a while and I'm resisted doing that just because I thought well, where's the where's the phase gonna come from? um Well, you describe the the results as just sort of sludgy noise Like I care about if I get sludgy noise. I mean that was a it's a good point though I mean if I I'm looking around trying to if you can think of a physical system that obligingly produces arrays of you know streams of Streams of arrays of complex values That could be uh visualized and uh sonified at the same time that would be that would be good so I'm I'm looking out for one. I mean make could you I'm where I'm wary of messing around with complex iteration maps because um the one thing about cellular automata and those Byfication maps is a natural sense of time for the thing. So I guess if you could take slices and scans through Through a Julia set or something well, which direction I mean I suppose yeah, you could go on axis uh, but is that really how um How you perceive the thing when looking at it and that sort of Violates somebody I'm stupid self-imposed rule of the thing needs to look like the way it sounds I mean it's it sounds like you If I don't if I've got that Silly self-imposed mental block and you haven't then you go away and do it with my with my blessing, of course I should Maybe I should start looking at real oblique strategies cars instead of my own my own pistakes, but yeah quite right good point Does that answer your question or? Yes, it does. Thank you. Well, you just said it. I thought of an answer. Couldn't you walk through one? For example some complex fractal and choose your sampling point based on the result of the Lorenz equation You could I mean for me that's sort of uh Again, it's my own mental block about these uh These things sort of exist in their own eschetic isolated universes. Um So you have go go and do it. I mean I might get around to it, but you were you ignore the sort of restricted old old get and Do your own please Maybe I will maybe I'll get over myself and my my escheticism, but possibly not So it seems to be don't have any more questions in a moment So I would like to thank you again for this amazing talk and uh, please give a big round of applause for giles