Boolean Sequencer Tutorial
by Les Hall
www.electro-music.com Lunetta Forum

One way to get some really cool sounds from a Lunetta circuit is to build a Boolean Sequencer.  I created the concept of the Boolean Sequencer myself and people tell me that it is a new concept, however I like to say that I reinvented it rather than invented it because it has existed in various forms for many years.  Here's how it works.  

First, make an LFO clock signal of your choice.  This clock is usually of a constant frequency, though you could vary the frequency over time if you like.  The notes produced by the Boolean Sequencer will normally occur once per clock cycle, so if you like 4/4 timing then make the clock be 4Hz.  

Second, send your clock into a CD4040 binary counter chip.  You'll want to use a pulldown resistor of any value from 20k to 1Meg on the reset input so that the counter will actually count.  

Third, add some logic chips like AND gates or XOR gates and connect the inputs of the logic gates to the output bits of the CD4040 chip.  You can use any type of logic you prefer and you can add as many layers of logic as you like.  This is where the creativity of the Boolean Sequencer comes into play because the logic that you set up will determine the sequence of notes that you get.  

Fourth, use a passive component network such as an R2R ladder or a voltage summation circuit to combine the outputs of the logic that you created into an analog signal.  

Fifth, buffer the signal with a voltage follower using an op-amp chip such as a TL074.  Drive this into a VCO made from a CD40106 oscillator, then buffer the VCO output with another voltage follower and send it out to a jack with a DC blocking cap and a 1k resistor in series.  This will enable you to drive the output signal into a pair of amplified speakers or into the line-in jack of a computer for example.  

OK that's a lot to understand, so I'll explain some more about the Boolean Sequencer.  Unlike many other sequencers, the Boolean Sequencer can produce very long sequences of notes.  Normally you have 8 or 10 or 16 steps in a step sequencer, however a Boolean Sequencer can produce a huge number of steps.  You can create any binary number of steps such as 256 steps or 4096 steps or whatever, though you can make the sequence be any number of steps by playing a little reset trick.  

The CD4040 has a 12 bit output count, which is 4096 unique output states.  If you were to make use of all 12 bits as input to your logic, then you would get a 4096 step sequence.  To put that into context, at four quarter timing (four notes per second) a 4096 step sequence will last for 1024 seconds.  That's 17 minutes of continuous music before the pattern repeats.  

In addition to the long sequences, a Boolean Sequencer will often produce repeating patterns of notes, or phrases, that change a little bit as they occur.  These phrases are typically a binary number of steps as well.  Yet another curious aspect of the Boolean Sequencer is that it will often produce moments of silence mixed in with the notes.  This occasional silence can add a dramatic element to your music.  In practice I have found that using a sum of products logic network causes lots of dramatic gaps, while using XOR gates generally produces no gaps at all.  

As an example I will describe one Boolean Sequencer that makes nice sequences and great sounds.  Start with a LMC555 timer or a CD40106 inverter and send that into a CD4040 binary counter.  Then add a CD4030 quad two-input XOR chip and connect the inputs of the CD4040 chip to the inputs of the XOR gates.  Next connect the four outputs of the CD4030 chip to four resistors and connect the other end of the resistors together.  Send the combined signal into a TL074 quad op-amp or any suitable op-amp to buffer the signal.  This buffers the signal so that you can do the next step, which is create a CD40106 oscillator and connect the output of the op-amp to the power supply pin of the CD40106 chip.  Use another one of the op-amps on the TL074 chip to buffer the CD40106 oscillator's output and you're done.  

In summary you do this:  LMC555 LFO => CD4040 binary counter => CD4030 XOR => resistor summation network => TL074 op-amp => CD40106 oscillator => another TL074 op-amp => listening device.  

This is a little bit complicated as it involves five chips, but that's OK because it produces really cool sounds.  Here is what is happening in the circuit:  The LFO clocks the CD4040 at the desired note rate, the CD4040 produces a binary count, The CD4030 establishes the sequence of notes, the resistor network creates a stepped analog control voltage (CV) signal, and the TL074 along with the CD40106 serve as a voltage controlled oscillator (VCO).  Clear as mud?  Good!  Now go build one for yourself!