An Analog Lowpass Filter Sound

Downloadables from the article:
<Filter1.syx> - 142 bytes
<Filter2.syx> - 142 bytes
<FilterBass.syx> - 142 bytes

Introduction: A Comparison Between Analog And FM

Filters are distinctly an analog technology, so they don't exist in FM synthesis. You may find FM synthesizers with filters in them, like the FS1R and the DX200 groove box, but these are really FM/analog modeling hybrids. The filter part is a completely different type of synthesis than the FM part and they are pretty much independent.

The way frequency spectra are manipulated in FM is in many ways the opposite of analog filters. Analog filters take a very bright sound and remove frequency components while adding to others (resonance). FM takes two simple sounds (like sine waves) and by modulating one with the other creates a brighter sound. So FM is additive rather than subtractive like analog.

In basic analog synthesis, the kind with a single oscillator going through a lowpass filter, the brightness of the sound is determined by the cutoff frequency of the filter. The lower the cutoff frequency is, the more high harmonics are reduced by the filter, making the sound duller and less likely to shatter glass.

The brightness of an FM sound, on the other hand, is determined by what they call a modulation index, and this basically refers to the amount that a modulator operator is modulating a carrier operator. But there is no "modulation index" parameter on the TX81Z. This factor is determined by the overall output level of the modulating operator, and this level is affected by a number of parameters like the output level, the envelope, key velocity, scaling, and the LFO if it is set up for amplitude modulation. The higher the overall output level is, the higher the modulation index is, which means the brighter and more harmonically rich the sound will be.

This difference isn't actually enough to tell us why the brightness of FM sounds different from the brightness of analog. It's theoretically possible that someone could come up with a new type of synthesis which is additive, yet can sound just like analog subtractive. The real difference between analog and FM lies in the fact that analog synthesis is based on natural correlations in electronics and FM synthesis is based on natural correlations in mathematics and the two simply sound different.

Getting Set Up To Make The Filter Sound

Ok, let's make a sound that tries to emulate the sound of an analog filter sweeping up and down, the kind you play real low on the keyboard, shall we? Yes, I think we shall.

Let's start with a clean slate by going into single mode and initializing a voice. This gives us a sine wave sound with operator 1 acting as the carrier set up on algorithm 1. The basic properties of the INIT VOICE sound are encapsulated in these screens:

I'd like to begin this article by restricting our experiments to two operators and I also would like to have feedback available for the modulator, so I'd like to switch to algorithm 7 and just focus on operators 3 and 4. Operator 3 is the carrier which makes the final sound and operator 4 is the modulator that acts on and modifies the frequency content of operator 3. I am going to ignore operators 1 and 2, but they are both carriers that have no modulators. So, change the algorithm to 7 and move the carrier over to operator 3, like so:

The volume will be a little lower but it should sound the same. The volume of an individual carrier gets lower as you increase the number of carriers, which we have done by changing from a single carrier algorithm to a three carrier algorithm. That's probably done to avoid clipping when all the carriers are maxed out.

Now then, we're going to increase the output level of operator 4. Since operator 4 is a modulator, it changes the sound of the carrier it is modulating and the sound it actually makes doesn't get added directly to the final sound. The higher the output level of a modulator, the greater its modulation depth gets, and the more it affects the sound of the carrier. I want to start with a bright sound so that the sweep can be heard easily, but if you increase it too much it's going to get real noisy, so set it to a tolerable level that you can listen to for while.

I'll increase to mine to 85, which ought to be bright enough. It's clearly different from a sine wave, and that's all I'm concerned about. It sounds kind of like a bamboo recorder with a small crack in the mouthpiece being played by monkey sitting on the eave of a Swiss chalet or something.

Alright, now we're ready for some sweeping action. For this, we'll use the envelope generator on operator 4 to do the sweep, since that's a smooth way to do it. Prepare for a mission of EG editing by entering the EG menu.

Once inside this shadowy cave, we're going to slow the attack and decay rates of the sound to make a simple peak for the big sweep. Modulator attack rates between about 8 and 13 make a good wah sound. When the rate gets over 13 it gets more subtle and hard to hear. It kind of turns into a brass sound at that point. Below 8 is more of a fading-in sound, and that's what I'm shooting for right now, so I'm going to set my attack rate to 5.

I also want a slow decay rate, about the same speed as the attack rate. Since I'm just looking to make a simple sweep up and down at a constant rate, I'm going to leave D1R and D1L alone at 31 and 15 and change the D2R. This will make the envelope act like a simple ADR envelope with no sustain.

You could just use the same value as the attack rate, but a given decay rate on the TX81Z is a little slower than that same value for the attack rate, so I'm going to bump it up a little from the attack rate to 7 to compensate.

Alright, we have a sweeping effect now. When a key is pressed, the sound starts off as a simple sine wave and the envelope causes the modulator's output level to slowly increase, which makes the sound get brighter and more harmonically complex. When the envelope peaks, the modulator reaches its maximum output level and it will then start to decay and the sound will start getting simpler until the modulator level reaches zero and we're left with a sine wave again.

Using Feedback To Sound More Analogish

Ok, it sweeps, but it doesn't sound very analog, does it. The easiest and most effective thing to do is to add some feedback to operator 4. FM synthesis tends to create humps in the frequency space. Feedback not only increases the complexity of the sound, but it flattens out these humps to some degree, which makes it sound more like an analog sawtooth wave or square wave. Let's turn up the feedback to 7 and listen to what it sounds like:

Hmmm. It starts off good, but it makes a weird buzzing sound when it reaches the peak. What do you think is wrong? Well, since I can't hear you I'm just going to tell you: it's aliasing now and we need to turn down the output level of operator 4 to compensate for the high feedback level. 77 sounds good to me.

Not too bad, eh? It's pretty sawish in its character. We can change it to squarish pretty easily by changing the frequency ratio of operator 4 to 2.00.

You can almost hear that the sound is on the threshold of aliasing now. It might even already be aliasing just a touch. By setting the modulator to 2.00 we've increased the width of the frequency spectrum being produced and sent the sound closer to the edge.

Square Waves In FM

A square wave is unusual in that it consists of only odd-numbered harmonics, and this configuration we currently have with a 2.00 ratio operator modulating a 1.00 operator generates only odd-numbered harmonics. The way FM generates its harmonics creates them in multiples of the modulator ratio which are added to the carrier ratio, so the harmonics created start at 1.00, the next one is 3.00, the one after that is 5.00, etc. When operator 4 had a ratio of 1.00, the harmonics went from 1.00 to 2.00 to 3.00, and if it was set to 1.50 they would go from 1.00 to 2.50 to 4.00. They are also created in the negative direction and they reflect back around zero, but I'll spare you the in-depth analysis for now. Just remember that 2.00 modulating 1.00 produces a squarelike wave.

Let's change the frequency back to 1.00 so have a sawtooth-type wave again.

Simulating Resonant Filters

Remember how I said that feedback flattens out the humps in the frequency spectrum? Well, resonance is a hump in the frequency spectrum. So we're caught in the middle between the fact that feedback makes FM sound more analog and the fact that we need a hump in the spectrum to simulate resonance. As you may have guessed, FM is not very good at simulating a resonant lowpass filter, but we can try and see what we can come up with. Much of the time when trying to simulate a certain sound, you get a different sound that's just as great, only it might serve a different purpose. It's always good to keep your ears open for good sounds when programming synths.

To make this attempt, this first thing that crosses my mind is to lower the feedback level, so that the feedback is still creating an analogish sound, but so that the spectrum isn't so flat. I'll lower my feedback to 6.

That kind of cut the peak short, didn't it. Let's turn the output level back up so the sound peaks at the same place as before. 82 sounds about right.

Well, it's resonating a bit. It's closer then what we had, anyway. Another thing to try is to change the operator waveforms. I'll just try changing the operator 4 waveform to the triangle.

That's A Keeper, I Think

I think that's a little better. That definitely sounds like a filter to me, so I think it's a keeper. I'll save this patch in a file and put it on the site for reference. The file is Filter1.syx and it contains a voice edit buffer, so it won't wipe out anything you have stored.

Speaking of storing, it will be useful to store the sound in the voice bank at this point so that we can use the TX81Z's comparison function to compare the sounds we come up with later with this sound to see if we've made any actual improvement to it, but that's only a suggestion. I'm personally going to store mine and use it for atmosphere in a wedding march I'll be playing later.

Making The Sound Wowier

There is a lot of experimental potential in this sound as it is just sticking with operators 3 and 4 and playing with the output levels, the waveforms, the frequencies, and the envelopes. But I'd like to leave that to your own ears and venture into some different territory and see what we can do by adding another operator to the mix. What I'm after here is a sound with a very pronounced "wow" effect that makes you want to pucker your lips. What we have now wows a little bit, but I want to show you a technique that can make this sound even wowier. Maybe even wowie zowie.

What I want to do is keep using operator 4 as the basis for the filter effect, but add a little more complexity to the base sound that it's modulating. The carrier in this sound is working out alright, so I would like to keep it the same and insert a modulator between operator 4 and operator 3. Let's look at the reference card:

Evidently, the unit doesn't have any algorithm like that, so it looks like we're going to have to use algorithm 2 or 4 and copy operator 3 to operator 1. Luckily, we've only changed one parameter in operator 3 the whole time, so it won't be a big deal. Let's change the algorithm to 4,

and move operator 3's output level setting of 90 over to operator 1.

Now all we have to do is connect operator 4 to operator 1 by turning up the output level of operator 3. Let's turn it up real slow like and listen to how the operator is changing the sound...

The harmonic spectrum is getting more complex as the level of operator 3 increases, but it's real subtle until it gets to about 80, where it starts to develop kind of a growling in the background...a couple of different growlings. It turns into FM mayhem at about 90. I'm going to try and keep it in the analog realm and set it to 75.

Ok, if you stored the previous version of this patch, hit the EDIT/COMPARE button to kick in the comparison mode and see how we did.

Well, it's louder, that's something. I think it does sound a little more resonant, I'm not really sure. Let's try experimenting with the waveforms again...

Ok, I'm done. Here's what I came up with:

I wound up changing operators 3 and 4 to the half-sine wave.

Well, I think we're getting pretty close here! There's something very analog sounding about this W3->W3->W1 cascade. There might be a better combination lurking in there somewhere, though. Who knows?

The interesting thing about this technique is that although operator 3 has a flat, gated type of envelope, this actually gives the sound a wowier effect than it would by copying the envelope of operator 4 over to 3 and having them both rise and fall together. You would think the opposite would be the case since if they both sweep together the amount of complexity at the peak in proportion to the trough would be greater than it is when operator 3 is sounding the whole time. But when they sweep together, it diminishes the impact of the wah effect because operator 3 acts like a carrier for operator 4 before modulating operator 1 and sweeping it makes the volume of the wah sound fade in and out. It's kind of weird how that works and it's hard to explain.

But Why Stop There?

Indeed, why? Let's take the next obvious step and move up to the dangerous, the deadly, algorithm 1.

Let's bump up operator 2 to connect operator 3 with operator 1. I'm trying to keep this page nice and clean (for the children, of course), so I'm only going to go up to 65.

Operators 1, 2 and 3 are creating a lot of complexity for operator 4 to modulate, so it's really wowing good right now. Too bad we've run out of operators. I don't think it sounds too bad like this, though, if I do say so myself, so I'm going to save it as Filter2.syx and call it a day.


Well, we succeeded in making a resonant filter sound with the TX81Z. It might not be the fattest thing you ever heard, but still I think it's a small testament to the power of the TX81Z and FM synthesis. To celebrate I'm going to take this sound and turn it into a bass sound. Just make sure the children are out of the room before you play with it!

Until next time,
Matt Gregory

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