Coding, Sounds and Colors

The Molecular Music Box in SuperCollider

Via Reaktor tutorials I came across this video. I have already talked about generative systems that create rich patterns (see here, and here), and how simple rules can give rise to emergent complexity.
Watch the video to know what the simple rules are in this case (and to see why it is called “molecular” ), or look at the following SuperCollider code, which, I must say, took me a bit more than I thought

Notice that you can very easily change any of the rules (duration length, scale used, etc.) with a few keyboard strokes: the power of a text based programming language!
I have sent the output of this to the Grand Piano instrument in Ableton Live 9.
Here is the result for 4C3

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and here is the one for 9C14½

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Objects manipulation in SuperCollider and Synths generation

In the last post, I wrote about some object oriented techniques in Processing which simplyfied our code, and gave the possibilty to reason more abstractly. Also SuperCollider is an object oriented programming language, and in this little example below I want to explore a situation where we can really take advantage of this: it somehow belongs to the category of “things one (or I?) can’t really do in Max/Msp, Reaktor, etc.”.
Here’s the simple situation: suppose we want to create 100 different percussive sounds with FM synthesis, with random waveforms as carrier, random harmonics for the modulating signal, etc., and play them randomly. We don’t want to change the sounds later, just play them. So, the first strategy we could adopt is the dirty and cheap no-brainer approach, which works along the following lines: well, what I will do is to create a SynthDef, i.e. an audio graph on the server, which is “big” enough to encompass the various possibilities of sounds, store the various randomly created combinations of waveforms, frequencies, etc. in an array, and poll these data when needed. The SynthDef would look like

Setting the parameter waveform will choose among the waveforms, freq will determine the frequency, etc. A big array (or dictionary, if you prefer) with randomly generated values, and I’m done!
Well, yeah, this approach will work, but it’s quite ugly, and, more importantly, inefficient: indeed, for each Synth created, a copy is kept of the two waveforms, only one of which is heard. So, for each percussion sound, we allocate twice what we need. Remember that there is a difference between not having a sound generator on the audio server, and having one which is muted, since in the second case, the sample rate computations are performed anyways.
Let’s think about this situation from a different angle, which makes more use of the language capabilities of SuperCollider. What we really need are different percussion sounds: they are different enough to be considered not as different instances of the same SynthDefs, but rather as instances of different SynthDefs. Instead of having SuperCollider creating different Synth instances, we can tell it to create different SynthDefs! Indeed, consider the following code (assuming a given choice for the range of the parameters)

First, we are defining names with which we can refer to the SynthDef: this is easily done, since a name for a Synth is a string (or a symbol), and we can obtain each of them by concatenating a string (in this case “perc”) with the counter index. Next, we define different SynthDefs: the beautiful thing that makes this work in a nice way is contained in the part

Remember: SuperCollider is object oriented, and in most cases, even if we don’t think about it, we are dealing with objects. Indeed, when we write something like SinOsc.ar(440), we are actually creating an object of type SinOsc, and sending to it the value 440 via the method .ar (which stands for “audio rate”), which provides the necessary computations to produce audio on scsynth, the audio server. Since SinOsc, Saw, etc are an “extension” of the class UGen (more or less), we can make a list (or Collection) with objects of this type, and use the powerful collection manipulation methods provided by SuperCollider (in this case the method .choose). Since both SinOsc and Saw react in the same way to the method .ar (this is an example of “polymorphism”), we can have it follow the method .choose, and pass everything in the round brackets. In this way the SynthDef itself will only have one copy of the choosen waveform per name.
This way of reasoning might look a bit abstract at the beginning, but it’s based on a simple concept: everything that require repetitive actions is best left to a programming language! Moreover, since SuperCollider is heavily object oriented, it gives really serious manipulations possibilities, as we have seen. We used already an incarnation of this concept when we built graphical interfaces.
Finally, the percussive sounds can be played via something like this

Here’s the complete code

I have added some reverb and delay to taste.
Notice that this code illustrate only the tip of the iceberg concerning what you can achieve with an object oriented approach to structure your code.
No audio this time, since it is not that interesting.

Drones, drones, drones

Who doesn’t like ambient drones? Ok, I guess some people might not like them.
Here’s a little code in SuperCollider to generate a kind of feedbacky ambient atmosphere. It does look involved, but it isn’t. The main thing is using Wavetable synthesis : what the method .sine1Msg does is to fill the buffer b with a sinewave (of 512 sample “period”), and its harmonics, whose number and amplitudes are specified in the array parameter of the method. Then we can “play” the wavetable with Osc.ar, which is a wavetable oscillator. Moreover, for added noisyness and ambience, I have added a bitcrusher with randomly varying samplerate and bit depth, and also a sample player playing the buffer c, which is not too loud, and just contributes to textures. You could modify it easily to load multiple samples, and choose between them. The last part involves a nice trick I learned here : basically, you stack a certain number of short time delays, and use a feedback line to simulate a reverberation effect. In particular, if the feedback parameter is 1, you get an “infinite reverb”. Very cool. Be careful not to keep feeding input in this situation, otherwise you will get the usual feedback headache! 😀

You can listen to the result here

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Tides on the Sea of Tranquillity

A quick post, since it is a while I’m not updating this.
Here’s a short track, “Tides on the Sea of Tranquillity”, built around one of my favourite UGens in SuperCollider: GrainBuf. GrainBuf is a buffer granulizer which is very flexible.
The idea for the track is quite simple: there are four granulizers, which get activated at a certain point, whose parameters are controlled by the loops in the Task. In particular, the position parameter for each of them is “lagged”, so that at each change it will start from the middle of the buffer, and reach the new value in a given time. Also, the spread, pitch, and pan are jittered, to give a spacey feeling. The other important part is that the rate for the grains are controlled via the .midiratio method, which allows to vary the pitch according to a temperate scale, hence giving some harmonic consistency. To end, everything is passed to a feedback delay line with a simple compressor.
One technical point: make sure you load buffers which are mono in GrainBuf, otherwise it will fail silently! Some times ago it took me ages to figure this out (I know, the documentation says so…).
Enjoy. 😉

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A sequenced fx machine

Ever wondered how to make a sequenced fx machine, where the effects cut each other out (like dbGlitch, say)? Here’s a very simple example

which uses the Ugen Select.ar, which functions as a “one-to-many” audio switch*. The delay part works as a simple beat repeater, and the other effect is a bit-crusher. After instantiating an audio bus, you can then delegate the sequencing to a Pmono

Whatever you send to ~rep will be processed by the fx SynthDef (be careful with the order of execution, or use Group to be on the safe side). If you have already SynthDefs for the single effects you would like to use, it is more convenient to send the audio to single busses, and then add a SynthDef at the tail of the synth chain containing a Select.ar Ugen which will choose among the different effects. You will have to run additional Pmonos to control the various parameters, though.
Notice that this approach to sequenced fx machines is quite expensive, since the various effects will run constantly on the server.
Anyway, in this simple case it sounds like

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*You can use a similar approach in Max/Msp, Reaktor, etc.

Finite fields and musical phrasings

In this post I want to talk about musical phrasings in algorithmic composition and algebra over finite fields. Yep, algebra, so brace yourself  :-).
I am pretty sure you have been exposed to clock arithmetic: basically, you consider integer numbers modulo a natural number p. Now, in the case p is a prime, the commutative ring is actually a field with finite elements. There is a name for that, and it is finite field, or Galois* field.
Now consider a pxp-matrix A with entries in : A will give us a map from to itself via

where are the entries of A. Now, consider a function f from to a finite set S, and consider the subgroup P of the group of permutations of p objects given by elements satifying

If the function f is not injective, this subgroup will be not empty. Notice that for any function f of the type above, the matrix A gives us another function defined as**

Now we can ask ourselves: given a function f, can we find a matrix A such that

for some natural number k? What this means is that we want to find a matrix such that applied k-times to the function f returns the function itself. This problem is equivalent to finding a matrix A such that

In the case in which the function f is injective, this coincides with the problem of finding idempotents matrices in a finite field: the fantastic thing is that they are known to exist***, and even better their number is known in many situations!
“Ok, now, what all of this has to do with musical phrasing?! No, seriously, I’m getting annoyed, what really? ”
I hear your concern, but as with almost everything in life, it’s just a matter of perspective. So, consider the set S as a set of pairs (pitch, duration) for a note. A function f above will tell us in which order we play a note and what is the duration of each note: in other words, it is a musical phrasing. By picking a matrix A, we can generate from f a new phrasing, given by the function , and we can reiterate the process. If A is such that it satisfies the condition above, after a finite number of steps, the phrasing will repeat. Hence, the following Supercollider code

represents a “sonification” of the probability distribution of finding a matrix A with the properties above, for p=7. We are assuming that the various matrices have equal probability to be generated in the code above.
So, how does this sound?
Like this

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*By the way, you should check out the life of Galois, just to crush all your stereotypes about mathematicians. 😉
**Mathematicians love these “dual” definitions.
***Apart from the identity matrix and elements of P themselves, clearly.

On L-systems, dictionaries and all that

It’s quite a while I have not written anything here: Python, ChucK and functional programming are keeping me quite busy. 😉
Here I want to tell you about Lindenmayer systems (or L-systems) and how to use dictionaries in SuperCollider to sonify them. So, first of all, what is an L-system? An L-system is a recursive system which is obtained from an alphabet, an axiom word in the alphabet, and a set of production rules. Starting from the axiom word, one applies iteratively the production rules to each character in the word at the same time, obtaining a new word which allows the procedure to be repeated.
A classical example is the following: consider the alphabet L={A,B}, the set of rules {A -> AB, B -> A}, and axiom word W=A. This will give the following words by iteration

A
AB
ABA
ABAAB
ABAABABA

and so on.
You are probably thinking “Wait a minute: alphabets, words, formation rules? Has this all anything to do with languages?” And the answer is: “Yes! But…”, the main difference with (formal) languages being that the production rules in a formal grammar don’t need to be applied all at the same time.
Ok, all well and good, but you may ask “What is this all for?! I mean, why?!?”, and I suspect the fact that, for instance, the sequence of the length of the words in the above example gives you the Fibonacci sequence is not an appropriate answer. The point is that Lindenmayer came to realize that these iterative systems can describe nicely the growth of many types of plants and their branching structures. For instance, the example above describes the growth of algae. The truly surprising thing, also, is that L-systems can be used to generate all* the types of known fractals, like Mandelbrot, Koch curve, the Sierpinski triangle, etc., when the alphabet is appropriately geometrized. So. in a nutshell, L-systems are very cool things. 😉
What about dictionaries, then? Dictionaries are powerful objects in many programming languages, and are sort of arrays in which elements can be indexed with keys which are different from the index position of the element itself. They can be, for instance, strings or symbols**. Basically, they are perfect to work as mappings.
So, let’s look at the code

The code above is in a certain sense a “universal L-systems generator”, in the sense that you can change the alphabet, the production rules and the axiom and get your own system. A generalisation of L-systems are “probabilistic L-systems”, in which the production rules are weighted with a certain probability to happen. This is maybe the topic for another post, though. 😉
While listening to this, notice how the melodies and the beats tend to self replicate, but with “mutations”.

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*I don’t know any mathematical proof of this statement.
**I have used Identity Dictionaries here, where keys are symbols.

Fun with additive synthesis and interfaces

When I started learning SuperCollider, I was motivated more by algorithmic and generative music. I was (and still am) fascinated by bits of code that can go on forever, and create weird soundscapes. Because of this, I never payed attention to build graphical interfaces. Another reason why I stayed away from interfaces was that I was using Pure Data before, which is an environment in which building the interfaces and coding are, from the user’s perspective, essentially the same thing. While it was fun for a while, I always got frustrated when, after spending some time building a patch, I wanted to scale it up: in most of the cases, I ended up with the infamous spaghetti monster. Studying additive synthesis was such a situation: once you understand the concept of a partial, and how to build a patch say with 4 of them, then extending it is only a matter of repeating the same job*. It’s almost a monkey job: enter the computer!
The code here shows exactly this paradigm: yes, you’ll have to learn a bunch of new classes, like Window, to even be able to see a slider. But after that, it’ll scale up easy peasy, i.e. in this case via the variable ~partials. So, as a sort of rule of thumb: if you think you will need to scale up your patch/code, then go for a text oriented programming language as opposed to a graphical environment. The learning curve is higher, but it’ll pay off.

If everything went according to plan, you should get this window

*Yes, I know the objections: you should have used encapsulations, macros, etc., but this didn’t do for me, because I rarely know what I’m going to obtain. “An LFO here? Sure I want it! Oh, wait, I have to connect again all these lines, for ALL partials?! Damn!”

Ambient soundscapes – A variation on theme

It’s always a good practice to take a simple idea, and look at it from a different perspective. So, I went back to the ambient code of my last post, and built a little variation. If you check that code, you’ll see that the various synths are allocated via a routine in a scheduled way, and it would go on forever. The little variation I came up with is the following: instead of allocating a synth via an iterative procedure which is independent of the synths playing, we will allocate new synths provided the amplitude of the playing synth exceeds a certain value. In plain English: “Yo, synth, every time your amplitude is greater than x, do me a favor darling, allocate a new synth instance. Thanks a lot!”. But how do we measure the amplitude of a synth? Is that possible? Yes, it is: the UGen Amplitude does exactly this job, being an amplitude follower. Now we are faced with a conceptual point, which I think it’s quite important, and often overlooked. SuperCollider consists a two “sides”: a language side, where everything related to the programming language itself takes place, and a server side, where everything concerning audio happens, and in particular UGens live. So, when you allocate a synth, the client side is sending a message to the audio server with instructions about the synth graph (i.e. how the various UGens interact with each others) to create. Since Amplitude lives on the server side, we need to find a way to send a message from the server side to the client side. Since in this case the condition we have, i.e. amplitude > x, is a boolean condition*, and we want to allocate a single synth every time the condition holds, we can use the UGen SendTrig, which will send an OSC message to the client side, which in turn will trigger the allocation of a new synth via an OSC function. We have almost solved the problem: indeed, SendTrig will send triggers continuosly (either at control rate or audio rate), while we need only 1 trigger per condition. For this, we can use a classic “debouncing” technique: we measure the time from a trigger to the previous one via the Timer UGen, check if “enough” time has passed, and only then allow a new trigger. The value chosen here is such that only one trigger per synth should happen. I say should, because in this case I end up getting two triggers per synth, which is not what I want… I don’t know really why this happens, but in the code you find a shortcut to solve this problem: simply “mark” the two triggers, and choose only the second one, which is accomplished by the “if” conditional in the OSC function. Of course, this little example opens the way to all cool ideas, like controlling part of synths or generate events via a contact microphone, etc. etc.

Here’s how it sounds. Notice that the audio finished on itself, there was no interaction on my side.

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*Technically speaking, it’s not a boolean condition, since there are no boolean entities at server side. Indeed, amplitude > amp is a Binary Operator UGen… For this type of things, the Supercollider Book is your dearest friend.

Wind Chimes

It has been a while, but I have been busy with a new work to be released in July, and recently I have spent some time fiddleing with Reaktor, which I have to say is quite good fun.
So, here’s something very simple and a classic in generative music, i.e. a wind chimes generator. I have decided to use only one graph synth in Supercollider (everything happens at “server side”), using a geiger generator (Dust) with varying density as a master clock, and a Demand Ugen as pitch selector. There is also a bit of FM synthesis, which is a nice way to get “tubular” type of sounds in this case. Finally, some delay and reverb.

Here’s how it sounds

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