Boolean Sequencer Basics

In Uncategorized on July 25, 2011 at 3:27 pm

There are many kinds of sequencers in the world of music creation, each with their own unique set of characteristics.  When I started creating music, however, I knew nothing at all about them not even what a sequencer was.  I could make lots of sounds with ChucK programs and make random notes and such, but I didn’t even know what the word sequencer meant.  All I knew was I wanted to make songs from these sounds.

To this day four years later I still have a limited understanding of all the fascinating variety of sequencers out there but there is one that I know very well:  the Boolean Sequencer.  That’s the name I chose for a technique that I later realized is as old as synthesizers themselves, maybe older.  Possibly a great deal older, historically, but let’s stick to modern day electronics versions.

So not knowing what to do, I got creative.  I remembered Boolean algebra and truth tables and Karnaugh maps and all that jazz from college, and I also remembered programming FPGAs with the Verilog language.  I imagined that there might be some way to take a logic truth table and step through it with a counter, producing a series of on and off signals.  This could tell me when to play notes.

I tried it and it worked, yay \o/ I was making songs – sorta kinda.  But these were one note songs but they had interesting rhythms, patterns of notes that caught my attention.  I was on to something good it seemed.  Then I wondered:  what if that series of ones and zeroes was actually a series of note frequencies?  How could I generate that?

Well long story short, I ended up with a very simple combined digital and analog architecture that I named the Boolean Sequencer, comically producing the acronym BS as a coincidental joke.  That thing is pure BS, I laughed about it!  Well the only real BS was that I thought I was inventing something when I was actually reinventing it, more on that later.

The architecture ended up as follows:  Tempo clock to binary counter to logic network to aggregation network, and out pops a Control Voltage (CV) that can be applied to any music making circuit that responds to an input voltage.  I played around with this BS thingie and learned a lot about it and I will share some of those findings with you shortly, but first let’s examine the stages:

The tempo clock is just an oscillator that produces a digital output.  If you want six notes per second you set the tempo clock frequency to 12 Hz.  Why 12 Hz instead of 6 Hz?  Because the clock will be fed into a binary counter which will divide it by two with the LSB flip flop.  Alternatively if you actually use the clock itself as the LSB you can make it be 6Hz for 6 notes per second timing.

The counter is usually one of the binary counters CD4020, CD4040, or CD4060.  These all count out a binary sequence and make most or all of the bits available on the output pins.  So we clock this counter and this produces a binary count N bits wide.

Next up we have the logic network which accepts the counter output bits as input.  It may be any logic function of the available bits from the counter, and may be any number of bits wide at it’s output.

Finally there is the aggregation network which is often just a set of resistors connected to the logic outputs such as a multiple input voltage divider or an R2R ladder.  I call it an aggregation network because it can be very aggravating!  Just joking!  Actually it aggregates the digital outputs into an analog signal, the CV.

Got all that?  Now let’s discuss some of the properties of Boolean Sequencers.  One is that they can have any sequence length that you like but normally you just set them for a binary whole number of steps like 8 or 256 or 65536 or whatever.  65536 steps?  Holy synthesizers Batman, that’s a lot of steps for a sequencer to have before repeating!  Yep, due to how quickly the power of 2 grows as you add bits, you can get amazingly long sequences.

And those sequences will be completely unpredictable!  Well actually they are very predictable according to boolean algebra and analog circuit theory, but the tendency is not to design for a specific sequence but rather tho just haphazardly hook up logic and aggregation networks until you like what you hear.  You can create by design or by exploration, that’s up to you.

I can say this, however:  AND and NOR gates tend to create sequences with gaps of silence especially at the beginning of the song and get far more active later in the song.  It’s the opposite for NAND and NOR gates, and XOR and XNOR gates tend to be active all the time, with no gaps at all or very few.

One last note about the characteristics of a BS is that it generates fascinating patterns within patterns within patterns.  Just stare at the counter part of the logic netowrk’s truth table (the binary count part) and your eyes will glaze over as you see all these fractal patterns nested at every level of hierarchy.

Well, the same is true of the logic output only in a more entertaining way.  As you listen to the song your mind will latch onto a phrase (pattern) and then hear it again a few times perhaps then again but a little bit different twice, then back to the first one just once, then another new one, and so it goes throughout the song.

I’ll finish up where I started and just mention that the Boolean Sequencer is not really a completely original idea.  In fact it has been created many times before as I have noticed diode arrays in step sequencers and other circuits that effectively implement a BS, and also I have heard what sounds like familiar old tunes in some of the BS programs that I have written.

In fact, I wouldn’t be surprised if the Boolean Sequencer was known well before electronic synthesizers even existed, maybe even centuries old dating back to ancient culture in woven patterns, celtic knots, or tiled art – who knows where binary combinations originally exited?  But that part is strictly conjecture.

Thank you for reading about all this BS stuff, heh, and I hope you enjoy listening to some Boolean Sequenced music or even make some of your own.



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: