Wooden Instrument Body Filters

Wooden Instrument Body Filters

Up until now, the model hasn’t sounded much like a violin, or a cello, or anything else. The reason is that we’ve only modeled the bow and string. That’s just not enough. The resonances in the wooden body are what make these instruments so interesting.

Resonances in instruments

Most instruments have some kind of unique and characteristic frequency response. Brass instruments, for example, have a kind of bandpass response, where the size of the bell determines the cutoff frequencies: larger bells = lower frequencies.

Wooden instruments such as violins, cellos, and acoustic guitars, have among the most complicated resonance patterns of all. The frequency response of a violin body, for example, may have hundreds of peaks and troughs. And, no two violins are identical.

Below is the frequency response of a particular violin.

What are our options?

Sheesh! How are we ever gonna model that?

The only way to precisely match a response like that is to use a finite-impulse-response filter, or FIR filter. It’s like a convolution circuit: a long series of multiply-by-a-constant-and-accumulate-the-results kind of thing. We’ll need thousands of stages to successfully model something like this.

But the G2 doesn’t have one of these, and probably never will. Unfortunately, that means we won’t be able to precisely model that response. Instead, we’ll have to settle for an approximation. So then, what options are available to us, given the modules we’ve got? Three possibilities jump out:

A large number of parametric filters, arranged in series.

A large number of bandpass filters, arranged in parallel.

A large number of comb filters.

In theory, all three can approximate the above response. In a decision that may be surprising, we’re going to choose the bandpass filters.

Why not use parametric filters?

The parametric filters on the G2 have one omission that’s going to disqualify them: their center frequencies are not voltage-controlled.

Why is that a big deal? Because we want to do more than mimic just a violin; we also want to mimic violas, cellos, and contrabasses. And maybe guitars and mandolins. We’re going to end up with close to 50 filters in this patch, and it would be really nice to be able to move one knob and just “dial” the frequency of all the filters up or down. After all, what’s a cello, but a bigger violin?

Yes, a morph group could tie a bunch of filters together. But only 25 parameters per patch can be controlled by a morph group, and we’re going to have a lot more than 25 filters in our patch.

Why not use comb filters?

Because they’re difficult to precisely control. Also, their peaks tend to be harmonically related, and we want to avoid that.

Which type of bandpass filter?

OK, so we’ve settled on a parallel array of bandpass filters. But which kind? The G2 has three different ones:

The 2-pole/4-pole Nord filter.
The 2-pole multi-output filter.
The 2-pole fixed-frequency static filter.

The third one is disqualified for the same reason we disqualified the parametric filters: the center frequency is not voltage-controlled. The remaining choice is tough. Do we need the first filter’s 4-pole response, or its voltage-controlled resonance?

Well, we’ll bite the bullet and choose the first one, the Nord filter, even though it uses more DSP cycles. Why? Because voltage-controlled resonance is cool. If we tie all of the resonance inputs together and wire them to a single Constant module, and then assign the Constant module to the front panel, we can control the “peaky-ness” of the entire patch with a single knob.

Our strategy

We’re going to make an array of 48 parallel bandpass filters. This array will have the following features.

The first filter will be tuned to G3, or 196 Hz, which is the lowest note that a violin can play. We’ll call this the Starting Frequency. The entire array will be tunable, either up or down in frequency. Hopefully, we can convert a violin into a cello by simply tuning the entire thing down.

We’ll initially space them apart by one semitone, so that they’ll cover four octaves, up to F#7, or about 3 kHz. We’ll add a Spacing knob, which will let us stretch-tune the entire thing, up to the point where the filters are spaced apart by three semitones.

The resonances of all the filters will be tied together and controlled with a single Resonance knob.

The amplitude of each filter will be separately controllable, via a front panel knob. That will be 48 knobs. Using these knobs, we’ll attempt to mimic the violin’s most prominent resonances.

The entire array will be contained in a single patch. We’ll use both the VA and FX sections, so we have up to 2 DSPs available. We’ll have 24 filters in the VA section, and 24 more in the FX section.

The array will accept input from any source (analog input or internal bus). In practice, we’ll combine it with the bowed string model, and save the two together as a performance. We’ll connect the bowed string model to the filter array using one of the G2’s internal busses.

Observing the patch’s output

This patch will have a lot of adjustable parameters: Starting Frequency, Resonance, Spacing, and 48 Levels. If our initial goal is to match the frequency response of that top picture, what’s the easiest way to proceed?

One way to feed white noise into the patch, and study the patch’s output with a spectrum analyzer. Below is a performance that contains two patches: Slot A contains a white noise generator, and slot B contains the filter array. The filter gets its input from the white noise generator, so the filter’s output is filtered noise. The picture contains a fragment of the filter patch. Below the picture is a spectrum analyzer’s view of the filtered output. Notice the 48 evenly-spaced peaks.

<patch>

Tweaking the patch

Now we can begin adjusting the knobs and try to approximate the top picture. There are four basic settings:

Starting Frequency: This is the frequency of the lowest bandpass filter. Initially, it’s tuned to 196 Hz, which is G3, the lowest note that a violin can play. We’re looking to duplicate a violin, so we won’t change this setting.

Spacing: This is the spacing between adjacent filters. This can be adjusted from 1 to 3 semitones. We’re going to increase this value until the frequency of the highest bandpass filter is about 12 kHz, the highest frequency we’re interested in adjusting.

Resonance: This is the sharpness of the resonance peaks. We’ll adjust this until the dips between adjacent filters are between 10 and 20 decibels.

Levels: These are 48 separate level controls, one for each filter. We’ll adjust these in an attempt to mimic the top picture. For example, the peaks in the picture are pretty high between 2 and 3 kHz, so we’ll set the levels for those filters pretty high.

The modified patch is <here>. Below is the spectrum analyzer’s view of the filtered output.

Let’s listen to it

Now, let’s listen to it. <Here> is a performance that includes two patches: slot A contains the bowed instrument model. Variation 1 is controlled by the mod wheel, and variation 2 by a breath controller. Slot B contains the filter (all variations are identical).

Customizing the violin

As mentioned above, no two violins sound exactly alike. We can mimic this behavior by simply changing the body size slightly. For example, just tuning the filter up or down a half semitone will produce quite a different sound. This is useful when laying down multiple violin tracks. Each track can have its own character, even when playing the same notes.

Simulating other instruments

We can use these patches as springboards to simulate other instruments, such as violas, cellos, or contrabasses. Some guidelines are:

Violas: A viola is strung about a half an octave below a violin, and can play down to C3. But the body isn’t that much bigger. Try simulating a viola by moving the starting frequency down from -4 to -8 semitones.

Cellos: A cello is strung about an octave and a half below a violin, and can play down to C2. Once again, the body isn’t that much bigger. Try simulating a cello by moving the starting frequency down from -8 to -16 semitones. Also, it would be a good time to re-tune the string to play between C1 and C6. Feel free to add more bow noise, as cellos can be quite noisy instruments.

Contrabasses: A contrabass can play down to E1 (the same as a bass guitar). Try simulating a contrabass by moving the starting frequency down from -16 to -28 semitones.

Some other hints:

It may be helpful to shorten the bow velocity attack time on the bigger instruments.

The bow model has a three-band equalizer in it.

The performance <here> is designed with a string quartet in mind. Variations 1 through 4 are designed to mimic violins, violas, cellos, and contrabasses, respectively, and are controlled with the mod wheel. Variations 5 through 8 mimic the same instruments, but use a breath controller. Note: both the bow model and the filter should be set to the same variation.