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Gregory Taylor

 (translation/annotation by Ada Lovelace), London, R. and J.E. Taylor, 1843)

Algorithmic composition is a rich and deep and subtle endeavor, and one of those things that probably every Max audio person out there has opinions about. If you're curious or a beginner, it's hard to know how to translate your curiosity or interest into action.

The multiplicity of opinions aren't so much a comment on the ability of persons to disagree on a big idea, but rather it suggests that there are a whole lot of different approaches to using computers to generate music or audio thought up by a whole lot of people over a very long time (The bad news? There's no single best answer about how to do things. The good news? There's no single best answer about how to do things, so you might as well take a crack at it yourself and join the party!).

There are great collections of Max externals available through the Package Manager to assist you in exploring algorithmic composition - 

 collections of Max externals, the ml.star and 

 packages for exploring machine learning, and the recent 

But there are other, quieter and humbler places where you can start exploring your own solutions. That’s what I’d like to introduce in this tutorial: some places to start from the ground up.

Algorithmic_Composition_for Beginners.zip

In this tutorial, I’d like to encourage you to take those first steps and investigate how you can use algorithms to generate and organize musical variety. We’re going to be using Vizzie modules to do that.

Yeah. You read that right. I’ve got two reasons for doing this:

: There's an update to Vizzie available using the Package Manager. You should install it.

One of the ways that Max uses “meaningless numbers” involves the formatting of MIDI messages that generate note events. That activity has its own rules. To play a MIDI note in Max, you need three values between 0 and 127 (as specified by the MIDI standard):

Although you probably usually think of MIDI events as being the result of your action, there’s no reason that that list of three numbers need come from you (or your DAW); they’re just three values. Anything that can generate numbers in the range of 0 - 127 will work just fine.

For this tutorial, we’re going to generate MIDI notes, and use the default AU DLS synth that all of you have as output.

 file is a recreation of the first and second Max patches I ever saw (in a lecture at the Academy of the Arts in Utrecht in 1989. Max was called “Patcher” back then). It’s a little hard to express just how revolutionary these two little bits of patching seemed to me back in the day.

image.png

While you may not be as excited as I was by these two patches, you can try them yourself by clicking on the title bars of the 

 modules to turn them on. In the first case, the immediacy of grabbing a fader and generating a stream of notes by wiggling it was astounding.

 objects do the heavy lifting when it came to turning that fader output into MIDI notes on the synth. With each change of a fader value, it sends a MIDI note message (they all had the same velocity and duration) to a 

 object that handles adding a note-off (velocity 0) message after the time specified by the duration in milliseconds.

The second patch was my first look at “algorithmic composition in Max.” A simple random number generator (in this case, the Vizzie 

 module which can be found in the Vizzie Generate browser tab) kicks out numbers in the range of standard MIDI note numbers. It did exactly the same thing with one crucial variation: a random number generator was doing that my fader used to do. It feels a little funny to write this now after so many years, but I was absolutely transfixed by this… for the first minute or two, anyway. While it was pretty cool to listen to the random number generator tick away, it sounded, well… 

So I wondered about I could do to change that. I tried two simple things to start with - I took 2 random sources and averaged their outputs, and also tried multiplying to random numbers together. At first I thought that I was getting the same output until I started really listening to each one (in these patches, I’ve added a multislider object that lets you visualize the random numbers as well as to listen).

I learned my very first lesson in algorithmic composition that day: 

. There are people out there who create arbitrary formal systems and then just turn them on and go with whatever comes out. What I learned is that - deep down - I 

 one of those people. I’ve spent the intervening years finding my way by listening and deciding at every point along the way whether what I’ve got is what I’d like to listen to. So I started thinking about what other sources for generating variety were out there for me to explore and listen to.

By the way - here’s a Max patch that helps you visualize the frequency of the output of note values over a long period of time for each of the three ways of working with randomness. With each button press, you generate a thousand random outputs, and then create a histogram that shows you the frequency of output for each value. The interesting results will confirm what you might have heard: adding and averaging the outputs tends to skew the results toward the center of the total output range, and multiplying them means that the single most commonly occurring result is zero (that higher number clinging to the left side of the rightmost 

Before I move on, I want to make something clear: My move away from randomness in terms of algorithmic composition was a strictly 

I sometimes have gone back and thought again about using randomly created raw materials to achieve results I found pleasing

). The history of algorithmic composition is full of extraordinary examples of stochastic processes to create wonderful music, from Lejaren Hillier’s groundbreaking Iliac Suite to the work of Iannis Xenakis’ stochastic synthesis, Barry Truax’s POD composition system, and so on. They’re well worth your attention, and great stochastic work is still being done.

The sort of naïve explanation of my turn from strict randomness in the early days was simple: Since I'm not random myself, the second I handed some part of my stochastic program over to a random number generator, it was completely obvious that I’d done so. I found myself wondering about ways that I could live somewhere between the wide jumps of randomness and something a little, well… 

. In doing so, I found myself venturing into that second part of what I think of when I think of algorithmic work - 

 the material I’d generated. My patient and longsuffering teachers aimed me at one of my life’s happier algorithmic discoveries: the drunkard’s walk.

Simply put, the drunkard’s walk is also a 

, but one with a twist. At each point, a random number is generated within a set range, and the result is then added or subtracted from the current value. If the range is very small, the result is a kind of wandering path which, though randomly generated, looks like it has some kind of “goal.” If the range is large, the results look (and sound) random. The 

 file shows an example of the drunkard’s walk in action. Turn on the 

 Vizzie module (which can be found in the Vizzie Generate browser tab) to produce output data by using a drunkard’s walk algorithm by clicking on the title bar and watch/listen to the results. If you turn the 

 dial, you’ll see the output change dramatically. I was particularly taken with the ability to change the “feel” of the output by altering the step size alone.

 file contains a tool I built to simplify the process of working between floating-point values and MIDI values. The 

 handles the input data scaling and formatting to pass along to the Max 

 will display its floating-point input properly scaled and labeled, and you can also type in values to test your MIDI synth. Its insides are simple, but tools like this make it a lot easier to work quickly.

The other technique for managing random output I explored was good old averaging using the 

 module (which can be found in the Vizzie Control browser tab). Like the drunkard’s walk, it offered that similar ability to switch between the rough and the smooth. The results look and sound quite different, as you’ll probably notice by experimentation. But they both shared that ability to adjust from randomness to something smooth and destinations between. Which method do you prefer? Try them and find out.

As I kept on patiently trying new sources and listening to the results, I slowly began to produce some little tools that more closely resembled how I worked. One of those tools is memorialized as a Vizzie module: The 

 module (which can be found in the Vizzie Generate browser tab).

 module’s ability to introduce a controllable amount of randomness to each step in an input. This patch uses a new Vizzie module - the 

, which functions as floating-point data output source whose outputs will be recognizable as the kinds of waveforms you use all the time.

Here’s a simple version of that patch that uses the Vizzie 

 module to introduce subtle to unsubtle degrees of departure from a triangle waveform output:

pasted image

 may look a little more complicated, but don’t be fooled: I’ve replaced the single 

 Vizzie generator module with its big sister 

, which combines four synchronized output waveforms as data output sources. In the name of averaging, I’m using a pair of 

 objects (we need the 0. to indicate we’re working with floating-point numbers) and a 

 Max object to sum and average the first/second/third and similarly summing/averaging the fourth/fifth outputs of the 

 module to create more exotic output shapes, Those are fed to a Vizzie controller module I’ve not used yet in this tutorial - The 

 (which can be found in the Vizzie Control browser tab) lets you set an upper and lower bound for data output, and then scales any input you give it in the 0. - 1.0 output range to the new range.

Since I want to use this module to set the MIDI note number output, that means I can scale the notes I output to a specific pitch range. Of course, I need to know which floating point value corresponds to a given MIDI key. While you and I are completely comfortable with the idea of adding or subtracting numbers to transpose MIDI notes (12 for octaves, 7 for fifths, etc.), doing that with floating-point numbers is um… not at all easy or obvious. So I built myself a little tool to make the task easier.

The insides of the patch are very simple - see? You don’t need a degree in rocket surgery to do this stuff!

 attached to the low and high output range inputs to handle that. Despite the apparent simplicity of the patch, what’s coming out is starting to sound somewhat less random. Maybe evening interesting. Try setting the values for the 

 modules parameters and listen to the results!

Here are a few other Vizzie modules that you can use to control and organize your algorithm's outputs.

 module (which can be found in the Vizzie Control browser tab) is a cousin to the 

, with a crucial difference - you can not only set the high and low ranges of the output data, but you can select the behavior for any input data that falls outside of the input range. You can fold, wrap, or clip the results, and there's the additional ability to take that output and rescale it to the full 0. - 1.0 data output range (shown in the center example)

 modue (another Vizzie Generate browser tab resident) lets you divide your output into specific regions, and route any data falling in that range to one of four outputs - think of it as four RANGR modules hooked together!

 control module, though somewhat exotic, provides an interesting way to deal with two simultaneous streams of output data. While you can use the module to perform standard averaging (in 

 also lets you alternately select from one of the two inlets (in 

 mode) or randomly select an outlet at every step along the way (in 

 mode). This module is perfect for more fragmented data sources (We'll look at another Vizzie module that you can use to sum and average multiple outputs next).

 is a great source of linked and synched waveforms. While it's a great source of raw output all by itself, there are a few other neat tricks you can make use of when it comes to providing new sources for your algorithms.

 module (which can be found in the Vizzie Control browser tab) provides a simple and elegant way to sum and average a number of data inputs to produce new forms and shapes. When combined with the synched output of 

 module, you can create some interesting outputs which keep time with each other while producing more exotic output that you can further process.

Explore the Online Tutorials

Algorithmic Composition: An Introduction for the Curious, Terrified, or Perplexed Beginner

gen~ for Beginners, Part 1: A Place to Start

A Brief Introduction to Vizzie

A Few Minutes with BEAP, Part 1