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"Pimping the BS" is my little joke because of my history with the Boolean Sequencer (BS). I'm the one who chose the name for the thing and I really did reInvent it, only to discover later that it had existed for probably 40 years prior to my reInvention! That was a real slice of humble pie, but it wasn't the first time I reInvented something and the ice cream on the humble pie is that I sort of described it in engineering terms and defined what it is and what it isn't (see block diagram).
Checking out the block diagram here, we see that the BS is composed of a clocked binary counter, a logic section, and an aggregator. This produces a control voltage (CV) which is a stepped analog signal that you can use to drive a voltage controlled oscillator (VCO) or other audio output circuit such as a Karplus Strong circuit. Rather than make a big dedicated expensive board with a whole BS on it, the emSynth solution is to sell the pieces and let you build your BS the way you want it to be at minimal cost to you.
So why would you want to build a BS? For the awesome sequences, of course! A BS produces short, medium, or amazingly long sequences depending on the number of bits in your binary counter and these sequences can be quite captivating. The reason for that is that the logic section will often produce phrases of musical sequences that repeat with subtle changes over time, evolving into a familiar yet different set of phrases that keeps you interested in what's coming up next. Even better is that these phrases exist on multiple levels from the short to the medium to the long, all within the same song!
In my experience with the BS, using digital AND gates in the logic section is one good way to go because you tend to get those repeated phrases with pauses in between them and/or interspersed within them, leading to a fun listening experience. To hear what I'm talking about, listen to this audio sample. It contains synthesized guitar and drums driven by separate boolean sequencers. In fact there are two guitars and one drum instrument. The guitars have similar but different logic sections so they compliment each other well.
So yeah, AND gates are good. Another good one is the XOR gate which produces a more continuous sequence of notes due to the nature of the XOR logic table which has roughly an equal number of ones and zeroes. The AND gate by comparison has mostly zeroes and only a single one bit in it's logic table (use 3-input AND gates for this BTW for best results). - OR gates are like the opposite of AND gates because they have all ones and just a single zero in their logic tables so they produce tons of notes with no pauses and in my experience the OR gate sequences are less interesting.
Some critics of the BS say that the sequences are essentially unpredictable so you can't really control what your output is. This is largely correct but I don't see it as an issue because there are tendencies that you can use to imagineer your sequence such as the ones I mentioned with the AND, XOR, and OR gates. Another great gate to use with the Boolean Sequencer is the ANY gate because you can wire a few of them up to form your logic section then just throw the switches on the ANY gate modules to form your truth tables. IF you want more pauses, add more zeroes and such like that.
OK, so you've got a clocked counter counting at song tempo rate and a logic section producing a few logic outputs, what's next? The aggregation network of course! I normally use equal valued fixed resistors, one in series with each digital output (usually 100k) and tie them together to form the CV output. To go one step further you can make them be 100k pots in series with 10k resistors, or use an R2R ladder network, or even get fancy and make a pot variable R2R ladder or similar creation of your own. Regardless of what network you use, the goal is to combine the digital signals into a single analog CV output signal for use by an instrument-type module such as a VCO or Karplus Strong or VCO / Sine Wave Thing combination or whatever you dream up to be your instrument. That's what makes the actual musical tones.
In my explorations of the boolean sequencer, I have discovered a lot of BS, haha! Some variations on the theme include Linear CMOS as part of or all of the logic network, using three or more counters to make sequences as long as 100 years or more, clocking the counters at audio rates so that the CV output is the musical signal (no instrument following the aggregator), capacitors in the aggregator, feedback in the logic section which causes state information to exist there, and whatever else you may dream up. And I promise not to write a longer run-on sentence than that one, lol!
So that's the deal on the boolean sequencer - I hope you consider creating your own masterpiece of BS, heh, and create some awesome tunes!