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Referring back to Figure 5-1, you’ll notice that there’s a point on the lowpass filter response curve where the curve starts to dip downward. We can define this point in terms of where it falls on the X axis — that is, in terms of its frequency. This is the cutoff frequency of the filter. Scrutinize the panel of almost any modern synth and you’ll see a knob labelled “cutoff” (or, if panel space is tight, simply “cut”). The cutoff frequency of a filter is perhaps its most important characteristic, and changing the cutoff frequency, as we’ll see, is one of the most musically useful things you can do to alter the sound of the synth. Before delving deeper into this area, though, we need to talk about some other characteristics of the response curve.

The amount of boost or cut introduced by the filter at a given frequency is expressed in decibels (dB), a unit of measurement defined in Chapter Two. (For most listeners, a signal has to change amplitude by between 0.2dB and 0.4dB before the change can be perceived. These figures define the just noticeable difference for amplitude changes. A decrease of 6dB reduces the amplitude of a sound by 50%.)

You’ll notice that the filter response curve shown in Figure 5-1 doesn’t jump from zero down to infinite attenuation at one specific frequency. It looks more like a hillside than a cliff. The sloping part of the curve is called the rolloff slope, because it describes the part of the spectrum in which sound energy is rolled off (attenuated) by the filter.

The cutoff frequency is usually defined as the point on the rolloff slope where the signal is attenuated by 3dB. In the case of a bandpass filter, which has rolloff slopes on both sides of the pass-band, the bandwidth of the filter is the distance between the -3dB points on both sides of the center frequency.

Figure 5-6. Lowpass filter response with rolloff slopes of 6dB, 12dB, 18dB, and 24dB per octave.

Depending on how the filter is designed and, in some cases, how its parameters are set, its rolloff slope can be steep or gradual. The steepness or gradualness — that is, the angle of the rolloff slope — is expressed in decibels per octave. A rolloff slope of 6dB per octave is fairly gentle, 12dB per octave is more pronounced, and 18dB or 24dB per octave qualifies as a steep rolloff slope. Lowpass filter response curves with these slopes are shown in Figure 5-6. Because the rolloff slope is defined in terms of octaves, when the X axis of the graph is marked in octave units, as mentioned above, we can draw the filter’s response curve in the stop-band as a straight line. If the X axis used linear units, the response curve would indeed be displayed as a curve.

JARGON BUSTER: A filter’s rolloff slope is sometimes described in terms of poles rather than in

dB per octave. Each pole (a pole is simply one of the elements in the design of the filter) introduces 3dB per octave of rolloff. So a 2-pole filter has a rolloff of 6dB per octave, a 4-pole filter has a rolloff of 12dB per octave, and so on.

To explain cutoff frequency and rolloff slope in musical terms, let’s assume you’re sending a signal that’s rich in high harmonics, such as a sawtooth wave or, better still, white noise, through a lowpass filter. If the cutoff frequency is extremely high (20kHz or so), the filter won’t do much of anything. All of the harmonic components of the incoming signal will be passed through without attenuation. In this case, the filter’s pass-band is the entire audible frequency spectrum.

As you begin to lower the cutoff frequency of the lowpass filter, perhaps by turning the cutoff knob on the front panel, the amount of energy in the high overtones will begin to diminish. The amount of attenuation at any given point in the frequency spectrum will depend on two factors: the cutoff frequency and the rolloff slope. As noted above, the energy of the signal at the cutoff frequency will be reduced by 3dB. Frequencies above the cutoff (assuming the filter is in lowpass mode) will be attenuated more sharply. For example, if the rolloff slope is 6dB per octave, frequencies one octave above the cutoff will be attenuated by 9dB. Those two octaves above the cutoff will be attenuated by 15dB, and so on. If the rolloff slope is 24dB per octave, on the other hand, frequencies one octave above the cutoff will be attenuated by 27dB, those two octaves above the cutoff by 51dB, and so on — a much more significant attenuation.

Figure 5-7. The response curves of a bandpass filter (top) and a notch filter (bottom) with a wide bandwidth (a) and a narrower bandwidth (b).

As we continue to lower the cutoff frequency, the higher components of the signal will be more and more attenuated. Eventually the signal will become quite dull and muted in tone. Depending on the filter’s characteristics and the nature of the input signal, it’s even possible to lower the cutoff of a lowpass filter so far that the entire signal is filtered out, so that the filter’s output will be silence.

TIP: If you’re editing a synth patch and suddenly you don’t hear anything when you play the

keyboard, the first thing to check is the filter cutoff frequency. Quite likely, raising it (in the case of a

lowpass filter) will allow you to hear the signal.

In the case of bandpass and notch filters, the term “cutoff” isn’t quite applicable. Instead, you’ll be dealing with the center frequency of the filter. In the case of a bandpass, the center frequency is the frequency at which incoming signals are not attenuated. In the case of a notch filter, the center frequency is the frequency at which incoming signals are most attenuated. While it’s possible to talk about the rolloff slope of a bandpass or notch filter, you’ll more often encounter the term width or bandwidth. A bandpass or notch filter with a high bandwidth has a shallow rolloff slope, and one with a low (narrow) bandwidth has a steep rolloff slope. This relationship is shown in Figure 5-7.

Resonance

If you’ve been around synthesizers for more than about two days, doubtless you’ve heard the term

“resonant filter” or “filter resonance.” Resonance has been used on synthesizers since the 1960s to make the sounds produced by filters more colorful and musically expressive. Resonance is referred to by some manufacturers as emphasis or Q. Technically, Q is a way of measuring the bandwidth of a bandpass filter, so it’s a bit of a misnomer when applied to lowpass or highpass filter resonance. But the term is sometimes used as a synonym for resonance.

When you turn up the resonance amount on a highpass or lowpass filter, frequencies in the part of the spectrum nearest the cutoff frequency are boosted rather than being cut. As the amount of resonance is increased, the boost becomes more pronounced. Resonance introduces a peak into the filter’s frequency response, as shown in Figure 5-8. Overtones that fall within the resonant peak will be amplified.

Q TIP: The Q (which stands for “quality factor,” though no one ever uses the term) of a bandpass filter is defined as the center frequency divided by the bandwidth. For instance, let’s suppose the center frequency is 100Hz and the bandwidth is 50Hz. The Q of the filter it then 2. If the center frequency is 1kHz and the bandwidth is 500Hz, the Q is again 2. A narrower bandwidth results in a higher Q.

In many analog filters and some digital models, the resonance can be boosted to such an extent that the filter begins to self-oscillate. That is, it will emit a sine wave at the cutoff frequency even when no signal is present at the input stage. This is sometimes useful: If the filter is programmed to track the keyboard, for instance (see below), you may be able to use it as an extra oscillator. But it’s also something to watch out for: Cranking the resonance up at the wrong moment could damage your speakers or even your eardrums. Even if the filter isn’t self-oscillating, a prominent overtone in the signal at the filter’s input can be boosted to a very high level by turning up the resonance.

When the filter’s cutoff frequency remains static, adding resonance imposes a formant on the signal (see above). Modulating the cutoff when the resonance is high does a variety of interesting things to the tone, as discussed below under “Filter Modulation.”

Depending on the distribution of energy in the signal being sent to the filter, cranking up the resonance can drastically increase the level of the signal emerging from the filter. Because of this, some filters provide automatic gain compensation: As the resonance increases, the overall output level is attenuated by a corresponding amount. As a result, gain compensation lowers the level of frequency components in the pass-band. Gain compensation is illustrated in Figure 5-9. Gain compensation can be good or bad, depending on the nature of the input signal and what you’re trying to do musically. If you’re using a lowpass filter to create a bass tone for pop music, gain compensation can work against you, because as you increase the resonance the bottom will tend to drop out of the tone. Gain compensation is not a user-programmable feature on most resonant filters, but it’s something you may run into from time to time.

Figure 5-8. The response curve of a lowpass filter with no resonance (a), some resonance (b), and a lot of resonance (c). Note that the resonant peaks rise above 0dB.

Figure 5-9. Two response curves of a heavily resonant lowpass filter: with gain compensation (a) and without gain compensation (b).

Early digital filters, such as those on Korg’s popular M 1 synth (built in the late ‘80s), didn’t have resonance. This was because the extra computation required to build a resonant filter would have required a faster processor, which would have made the instrument prohibitively expensive. Today, fast processors have become cheap enough that the bottleneck has disappeared. Very good simulations of resonant analog filters are found on most digital synths. Even so, purists maintain they can tell the difference between a real analog filter and a digital simulation.

In some synths, when a multimode filter is set to bandpass or notch mode, the resonance control usually turns into a bandwidth control. A few synths, however, have independent controls for filter resonance and filter bandwidth. If only one knob does double duty for resonance and bandwidth, increasing the

“resonance” of a bandpass or notch filter will usually narrow the bandwidth (that is, it will increase the filter’s Q). It’s worth noting that narrowing the bandwidth of a notch filter will cause it to have less audible effect, because fewer partials will be filtered out. A notch filter produces the most striking effect when the bandwidth is at a maximum. In other words, adding more “resonance” with a notch filter (the knob being labelled with that word, although notch filters aren’t usually resonant) will reduce the character of the filtering rather than increasing it. At high “resonance” settings, the notch filter may have no audible effect at all.

Overdrive

In order to make the sounds coming from their filters fatter and more satisfying, some manufacturers include an overdrive knob in the filter section. While this control adds new harmonics, which is not what filters do, filter overdrive is worth mentioning in this chapter simply because it’s found in the filter section of the synth. The idea is that in real analog circuits, overloading the filter’s input can produce a pleasing type of harmonic distortion. This effect can be simulated digitally. Unfortunately, manufacturers sometimes neglect to provide automatic gain compensation for the overdrive knob, so when you turn up the overdrive you have to turn down the volume parameter for the patch (or the instrument’s volume knob). In some instruments, filter overdrive is achieved by turning up the inputs in the oscillator mixer past 8 or so. Between 8 and 10, increasing amounts of overdrive will be heard.