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Stompboxes illustrated: Octaver

I've always had a soft spot in my heart for audio effects. Stompboxes were one of the main reasons I became interested in designing music gear because I just had to know how they worked. I decided to post this thread because I figured a few other people may be interested too. The octaver is one of my favorites and it's also one of the more easy to understand effects. If there is any interest here, I may put up more effects simulations, possibly by request because I like a good simulation challenge. First, a little bit of background...

Most everyone who plays bass knows that the pickup generates a voltage because of the strings vibrating over pickups. We're going to call this a signal. Amplifiers make this signal large enough and strong enough to drive speakers. Obviously, stompboxes are inserted in the chain somewhere. Stompboxes change or modify the signal. The technical name for a stompbox is a signal processor. Many stompbox types came from circuits originally designed for radios, telephones, and computers by engineers and technicians screwing around trying to make weird sci-fi noises.

An octaver is based around an electronic device called a flip flop. These are usually packaged in chips. Flip flops are used for all kinds of stuff. There are the foundation of computer memory for example because they are capable of storing digital bits. One other thing they are used for is processing clock signals, and that's where they come in handy for octavers.

First pic is an example of what a clock signal may look like:

clock pulse.JPG

This is just a stream of pulses that makes a type of square wave. We are switching back and forth between 0 volts (off) and 5 volts (on)--those are the horizontal sections of the wave. The vertical lines that connect the horizontal sections are called transition points. If you think about it, some of the transition points go up, and some go down. When passed through a flip flop, we get this on the output:

divided clock.JPG


Now, I'm going to plot both and zoom in a little to show what's happening:

clock layered.JPG


The green wave is input and the blue wave is the output. If you notice, the flip flop output changes direction only when the input wave is going up (on). We have 4 upward clock pulses going in, and we have 2 upward going clock pulses out.

So how can a clock divider process a bass guitar signal? Well, first, let's look at a simulated bass guitar signal:

input audio.JPG


This wave is not squared off--it's said to be sinusoidal in shape. This is a mix of more than one sine wave because your bass signal is full of harmonics. When you play a note, the note itself has a defined frequency called a fundamental that determines the pitch. The harmonics are the part that when you hear them mixed in just the right way, you know you are listening to a bass guitar and not a tuba. The harmonics in your voice are what makes you sound like you when you are talking or singing.

Now, let's plug our bass guitar into the octaver...the first bit of processing is to clean up the signal by filtering out the harmonics a little. This is done with a low pass filter, which passes lows and blocks the highs somewhat. This leaves mostly just the fundamental:

filtered input audio.JPG


The next step is to amplify the signal, except that we are going to use a whole lot of gain. There is so much gain, we are going to cause clipping:

clipped audio.JPG

If we listened to what we have so far, it'd sound like a jacked up fuzz box. We have converted our sinusoidal wave into a square wave. Hopefully, I've done a good job explaining so far and you can already see where this is going...

I'll continue with a new post.
 
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Next, we will pass our bass guitar square wave through a flip flop. This divides the frequency by two. The output looks like this:

divided clipped audio.JPG

After that, we need to convert this signal back into a sine wave because we want smooth sub bass quality to our octaver, not fuzzy harsh bass. Actually, some FX junkies may love the sound of what we have so far....Anyway, if you filter a square wave with a low pass filter, it changes shape into a sine wave. Here is our square wave process by a low pass filter:

wet output.JPG

This is called the "wet" signal. The "dry" signal is the pure bass guitar signal we started with. We need to mix the wet and dry signals together. 50 / 50 is the standard mix ratio. Some stompboxes have a mix knob to control this ratio. Anyway, here is our stompbox output after mixing:

mixed output.JPG

If you compare this signal to what we started with, you will notice that we have changed the shape with processing. This is analog processing.

Just for recap, here is a plot of input bass guitar signal to wet, step by step:

step by step.JPG

1. Raw bass guitar (pink)
2. Filter harmonics (light blue)
3. Provide enough gain to clip signal (red)
4. Pass through flip-flop to divide frequency (blue)
5. Filter square wave to change to sine wave (green)

Some octaver pedals have a second octave down. This is done the same way, except two flip flops are used to divide the signal twice.
 
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Anyone who has used an octaver effect knows that it can take an adjustment in playing technique for best results, otherwise, what you get out sounds like rumbling garbage or nothing at all. Many people will talk about the "tracking" of an octaver. Tracking refers to the response of the flip flop stage. The flip flop stage can become confused by harmonics. Above, I mentioned that the first stage in the octaver is a filter that strips harmonics leaving mostly fundamental signal. The tracking performance of an octaver depends on the design of that filter. When you adjust technique to make an octaver track better, whether you realize it or not, what you are doing is playing in such a way as to reduce harmonics from the bass.

This is also why you will find octavers meant for bass and some for guitar, because it's best for tracking performance if the filtering is optimized for a range of notes.
 
It's great to see this visually - makes the concept much clearer.

One thing I'd add is that octavers like the OC2 take the squarewave and uses it to periodically invert the original bass signal - when the square wave is high, the bass signal is normal, when it's low, the signal is inverted. The higher harmonics of the squarewave are then filtered out as per your description, so the result is not as bright same as the original bass signal.

The result is something that has the characteristics of the original bass signal, but with an added octave down component. This also allows the octaver to follow the volume of your playing - otherwise, the output would be a full volume square/sinewave all the time.

This would be great to see reflected in one of your waveform plots - would make how these octavers work much clearer.
 
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It's great to see this visually - makes the concept much clearer.

One thing I'd add is that octavers like the OC2 take the squarewave and uses it to periodically invert the original bass signal - when the square wave is high, the bass signal is normal, when it's low, the signal is inverted. The higher harmonics of the squarewave are then filtered out as per your description, so the result is not as bright same as the original bass signal.

The result is something that has the characteristics of the original bass signal, but with an added octave down component. This also allows the octaver to follow the volume of your playing - otherwise, the output would be a full volume square/sinewave all the time.

This would be great to see reflected in one of your waveform plots - would make how these octavers work much clearer.

I'm glad you brought that up, because it's something I should have mentioned...

The octave down signal that gets added in has a fixed output level when you are talking about traditional octaver stompboxes. That's because once the flip flop is tracking, you are dealing with a square wave at a fixed level. In other words, the wet signal is extremely compressed. One of the cool things to me about effects is that they can have a funky sound quality that makes some particular boxes must haves for producing a certain sound. Some people prefer that low fi type of effect, but What Phagor is describing is an improvement on the design that allows the effect to also track playing dynamics. If I'm remembering correctly, DBX patented that way of producing the octave effect a long time ago, and was used in rack gear as bass enhancement for PA systems and recording. I believe that EBS also borrowed that idea for their octaver pedal. I'll try to modify my octave stompbox model and plug in a virtual plucked bass guitar to see if I can demo that part. Coming soon...
 
As promised, here is a simulated OC-2 style octaver. This type of octaver basically works the same way as described, except the flip flop output is not filtered back into a sine wave and mixed with the audio directly, it's used to control the phase of the input audio by switching it back and forth to in phase / out of phase. This is kind of a pseudo octave, and certainly has a characteristic sound. The OC-2 has controls for one and two octaves down, but I only modeled the first octave part. It's too bad there's not an easy way to add sound clips, because I used my spice models to generate wave files so I could hear the difference.

First, here is a virtual plucked bass guitar note that I let sustain out a little. This is called an amplitude envelope. If you've familiar with envelope filters, this is what the name is referring to:

bass envelope.JPG

Let's say that we play this note through the traditional octaver. As was described earlier, the octave tone amplitude (in green) is constant because of how it's synthesized:

traditional envelope.JPG


You can see the tracking starting up once the note is plucked, and you can see the tracking die out once the note fades out. Here's what happens when I used the same bass signal with the OC-2 style octaver:

oc2 envelope.JPG

You can see that the synthesized tone envelope in green matches the input bass envelope in blue. Because the octave tone is developed by screwing with the phase shift, here is what it looks like zoomed in (green) plotted with the input audio (red):

oc2 waveform.JPG


If you look back at the output of the original posts, the output of the traditional octaver is almost a pure sine wave. It seems there is a little bit of a trade off between the two types of octavers depending on what you are looking for.
 
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So, theoretically if I could find that octaved or double-octaved square wave signal and connect that to the output I might end up with that slow growlly rattly-fuzz sound I hear in my head that I cant find a pedal for?