Filter sections

This workshop is about adapting the architecture of some traditional analog synthesizer filter sections for use on the Nord Modular. Some analog synthesizers are taken as example and some patches are named like these synths. However the sounds on the Modular will have their own character and are not meant to be exact copies of original analog synths. Instead they are only meant to be inspirational for the Modular user.

The filter section shapes the sound that is output by the oscillator section. Basically it is a buildingblock that suppressed and exites certain parts of the frequency spectrum. In technical terms this is called the transfer function. The actual form of that function can be drawn as a graph. Synthesizer designers use specific properties of the transfer function to set how the filter will work in practice. Those properties will then be assigned to a few knobs and control inputs. All that you, as a musician, have to do is tweak the knobs and feed control signals to the control inputs to shape the timbre at the filter output to your liking. Tweaking of the knobs can change the sound drastically, making the filter for many the main expressive tool on an analog synthesizer.
This dynamic sound altering property is a powerful feature compared to synthesizers that use e.g. sampling techniques, where the sound is based on a static recording. Some sampler manufacturers have recognized this and added dynamic filters to the better sampling synthesizers. Using the audio input on the Nord Modular enables you to perform very subtle or drastic and expressive filtering operations on samples played by a sampler or a drummachine.

Technically a filter is built up as a series of 'poles'. A pole is set to do either a lowpass function suppressing the higher frequency components, a highpass function suppressing the lower frequency components or an allpass function where no frequency components are suppressed but the higher frequencies are shifted in phase. The point in the soundspectrum where a pole starts to suppress frequencies is called the cutoff frequency. From this point on frequencies are suppressed by 6dB per octave. A suppression of 6dB is equal to halving the actual volume. If the cutoff frequency for a lowpass pole is set to 1000 Hz the volume of a sinewave with the same frequency will pass unaltered. Raising the sinewave frequency to 2000 Hz will halve the volume of the sinewave. At 4000 Hz it will be reduced to a quarter volume and so on. Actually this would be true if perfect poles would exist, however there is some rounding in the curve of the transfer function of the pole at the cutoff frequency. In practice the cutoff frequency is defined as the point where a sinewave is suppressed by 3 dB.
On the Nord Modular there are two 6dB filters, a lowpass and a highpass. When experimenting with these you find out that the filtering action is not very dramatic, although they can be of great use in tone control. Another valuable use of the 6 dB filters is in keeping feedback in certain kind of patches in control. An important property of a digital single pole filter is that it has almost unity gain in the passband and gradually reduces the gain in the suppressed band. This can prevent feedback patches from oscillating in an unwanted way. An important property of the 6dB highpass filter that must be mentioned here, is that it blocks DC-components in audio signals. There will be occasions that adding a 6 dB highpass filter set to 12 Hz to 98 Hz directly after the audio input module wil make your patch behave in a more predictable manner. Sometimes using the 6 dB highpass filter just before the output in the Voice Area, when this output is routed to the Common Area, can prevent overload distortion caused by cumulation of DC-components when several keys are played at the same time.

To obtain a more expressive filter than the 6 dB types a filterdesigner simply adds more poles to the filter. Cascading two similar lowpass poles will increase the cutoff rate to 6 dB + 6dB = 12 dB. Using four poles can increase the cutoff rate to 24 dB. The fact that you can cascade poles, means that you can cascade filters into a single filtering section with increased expressiveness. Musically a 24 dB filter is considered expressive enough for dynamically filtering the output of the oscillator section. When filtering audio material on the audio input of the Nord Modular you may find you need 'sharper' filtering action to isolate a single component from the 'complex' material. If this is the case simply cascade as many filters as you like. A cascade of four 24 dB filters would add up to a gain reduction of 96 dB of a frequency component one octave above or below the cutoff frequency. Such a filter cascade is generally known as a 'brickwall' filter.

When using more than one pole in a filter there are several decisions the filterdesigner can make about which pole should be highpass or lowpass. The individual cutoff frequencies of the individual poles might also differ, this might give subtle differences in how analog filters sound, as analog circuitry has a typical tolerance of 5% when the synth is just build. Aging of analog components can increase that tolerance, the author knows of a Minimoog where, due to aging, the difference in the poles of the filter has become so great that the filter doesn't sound at all like that mythical Moog-filter sound anymore. Digital filters do not possess this tolerance and aging effect, so you can expect your Nord Modular to still sound the same when it is over thirty years old.

When reading technical textbooks about filters you will be confronted with many filter architectures and properties, most of them named after their inventors or mathematicians. If you read names like Chebyshev, Bessel, Butterworth and Cauer, specific properties of the filter curve of a specific multi-pole filter are meant. Names like Sallen-Key or State-Variable refer to specific ways to interconnect the poles. Basically the techniques will be of no interest to a musician, but what is important is to note that there are many ways to design filters, depending of what the designer does with the poles, and these account for the differences in sound between different synthesizer models.

The two-pole State-Variable or multimode filter

This type of filter is found on many analog synthesizers, especially the ones with a simple architecture. Internally it is based on the principle that when you have a lowpass pole you can create a highpass characteristic by simply subtracting the output of the pole from the input signal. This behaviour is demonstarted in the next patch example.

In the State-Variable filter design two poles are cascaded internally. By using an input mixer and use of inverted feedback from the end of the two-pole cascade, a highpass signal (HP), a lowpass signal (LP) and a bandpass signal (BP) become available at different points in the cascade. Adding the highpass signal to the lowpass signal creates a bandreject output (BR). Feedback from the bandpass output to the input mixer creates a resonating effect. This means that the frequency at the cutoff point is 'excited' and a strong resonant peak results. Having all four basic filtering modes and the controllable resonance makes this a particular expressive filter type.
The cutoff slopes are 12 dB for the highpass and lowpass outputs and 6dB for the bandpass and bandreject outputs.

In the example patch you can switch between the four filter modes LP, BP, HP and BR. Note that raising the resonance on the BR mode does not introduce a frequency peak as it does in the other modes, instead it 'narrows' the bandwidth of the rejection band. The BR mode sounds like a phasing sound when swept through the frequency range.
With a somewhat higher resonance setting the BR mode can be used to selectively suppress a specific frequency component, if well tuned. This can be useful in suppressing a strong resonant frequency in complex audio material from the audio input on the Nord Modular, e.g. a beat sample.

Crossfading between the lowpass output and the highpass output creates a new filter mode called a Cauer or ellipse mode. When the signals from both LP and HP are mixed there will always be a small rejection band or frequency dip in the mixed output. This dip can be used to increase the LP effect. The higher the cutoff frequency the more HP signal can be added to increase the perceived sharpness of the LP mode.

By turning the knob on the X-Fade1 module you can hear this effect.

The recommended way to use the multimode filter is by adding a 3-input mixer module to the patch, mixing the signals from the three filter outputs. This will make possible any filter mode a Stave-Varible filter is capable of by mixing the three mixerknobs.

The fun really starts when cascading two multimode filters. Example of synths that use this configuration are the MS20 and the Chroma Polaris.

Morphs can be used to control the basic cutoff and resonance settings of both filters to make them track each other. Setting both filters to different settings however, gives much more control range over the timbre.

A popular effect is to use one of the filters to boost the fundamental frequency of the sound. To do this one of the filters is set to HP mode and the resonance is raised to a value around 100 to 120. This filter must(!) track the pitch of the oscillator section, so don't feed it other modulation signals. As the resonance frequency of the HP mode is equal to the fundamental of the oscillator pitch that fundamental will be boosted considerably, the HP mode makes sure that the rest of the signal is still passed, although slightly suppressed. Controlling the resonance setting controls the amount of bassboost you want. The other filter is then used to modulate the sound.

Analog filters use circuits called 'transconductance amplifiers' to actually control the cutoff frequency. These circuits start to distort when their inputs are overloaded giving a subtle overdrive effect within the filter. This happens when the resonance is raised. On some synths, especially the cheaper ones, this is stronger than on others. This overdrive has become a much wanted feature on basslines, etc. as it makes the sound more expressive or 'phat', as some like to call it. Digital filters do not have this overdrive as a 'built in' function, so we have to emulate it. Entering a distortion function between the two filters gives a satisfactory effect. You can choose between the overdrive module or the clipper module. Both these modules can give much more distortion than the analog filters did, so try not to overdo it. Experiment with the effects, used subtly they can enhance the sound without becoming an effect by themselves. Or use them extremely to get a very bright and raw 'gritty' sound.

 Here is another example where both filters receive their own, differing modulation signals.

The first filter is used as a 'sweeping EQ' with a very high resonance setting. The following clipper adds grit to the sound. A clipper is used instead of an overdrive module as the clipper creates more high frequency components if the EQ filter excites the lower frequencies. This results in the very bright sound. The second filter is set to standard LP mode, but the basic cutoff is resonably high, as is the resonance setting with a moderately low envelope cutoff modulation. The combination of the EQ, clipper and LP accounts for the bright and expressive distorted filter sound.
The WaveWrap1 module is used to 'scramble' the LFO waveform used to play the notes.

Instead of cascading the two filters they can also be patched in parallel. This is particular useful if one of the filters is set to LP mode with a resonably low cutoff setting and the other is set to BP mode sweeping through the higher frequencies.

In this case a suboctave squarewave is used to drive one filter to provide the bass and the other filter is driven by a sawtooth for the expressive modulation in the higher frequencies.

Korg MS20 filter section

The MS20 features a cascade of two 12dB State-Variable multimode filters, however the first is fixed to HP mode and the other is fixed to LP mode. Limiting the filters to these two modes only, is a bit a pity. Still the HP filter is very useful to boost the bass.
The next MS20-lookalike patch was already presented in the Oscillator Section workshop. This time play with the two filters, add the LP|BP|HP mixers to the filters and maybe insert your favourite distortion circuit in between to enhance and personalize the MS20-model.

A resonant filterbank

Another interesting use of the State-Variable multimode filter is in a multiband resonant filterbank. Such a filterbank could be build for the modular DIY Formant synthesizerkit, designed by C. Chapman in 1979. This was a very popular kit in the UK, the Netherlands and Germany. The name Formant referred to a great extend to this resonant filterbank.

The design is based on three State-Variable filters in BP mode. Cutof frequency, or in this case it is better to speak of centerfrequency, and resonance are by knobcontrol. There are no control signal inputs to control the center frequency or resonance. The OnOff1 module can be used to switch the resonances on or off.

As the resonant frequencies are independent of the pitch that is played, the resonant filter bank can conveniently be placed in the Common Voice Area of a polyphonic patch. Using a resonant filterbank can greatly enhance e.g. pad- and orchestral sounds. Adding a Chorus module after the resonant filterbank completes the padsound setup.

Take care of signal levels in polyphonic patches. The resonant peaks are added to the original signal, a sudden loud resonance on a particular note can overload the output of the Nord Modular, resulting in an unpleasant crackling noise.

A few patches using the resonant filterbank.

As the resonant frequencies are fixed, patches using a resonant filterbank are mostly limited to a two to three octave range, outside this range the effect of the resonant filterbank decreases.

Another interesting use of the resonant filter bank is in synthesizing electronic percussion sounds. The next patch is a simple double bassdrum pattern.
The trigger for the filterbank is a processed gatepulse. The gatepulse is derived from a downslope sawtooth LFO fed into a compare module. Setting the compare module to a value close to 0 gives a slightly asymmetrical pulse on its output. The transients, the raising edge and the falling edge, are isolated with a 6 dB highpass filter, resulting in a swinging spiky pulsetrain twice the rate of the LFO. The raising edge will create a small positive spike and the falling edge a negative spike. Using a diode module isolates the raising spike only. A crossfade module controlled by an event sequencer module switches between the positive pulse only and the positive and negative spike. Then an AD module is used to decrease the level of the negative spike. The output of the AD triggers the resonant filterbank, which creates a percussive sound.
Changing the center frequencies and resonance controls on the filters controls the type and decaytime of the percussive instrument sound. Changing the frequency of the 6 dB highpass filter influences the sound as well.

Replacing one or more filters to multimode filters with a control input for the cutoff frequency adds even more possibilities.

Summary

Hopefully it has become clear that the 12 dB State-Variable multimode filter is a very expressive and subtle filter. The sound is distinctly different to 24 dB filters, don't limit yourself with the thought the 12 dB multimode filter is inferior to 24 dB filters. Many still popular vintage synthesizer sounds make use of the particular characteristics of this filtertype. Added bonus is that it is DSP-cheap as well. And on the Nord Modular you can of course use lots of them at once with complex interconnections to create deep filter modulation patterns.
Mixing of the outputs of the filter gives extended timbre shaping possibilities, but requires subtle tweaking. Best procedure to tweak the mixer is to first add the LP output signal. Then add some HP signal to introduce the dip in the high and listen carefully to the effect. On low cutoff frequencies almost no high is necessary, with high cutoff frequencies the amount of HP can be increased. The last tweak can be adding some BP signal to increase the level of the frequencies around the cutoff peak.
As the amount of HP that can be added to enhance the dip is depending on the cutoff value, the HP mixerknob can be assigned to a morph group. Assign the morphgroup to the Keyboard->Note value in the righthand morph popup menu. Set the HP mixerknob morphrange to 40-127. This will enable the dip to more or less follow the pitch when the filter is set to track the keyboard. Experiment to get your own personal favourite settings.
The resonant filterbank can give sounds more body and character. The fixed multimode filters can be used to introduce formantpeaks. Assigning the centerfrequency controls to a morph which is assigned to the Note parameter can make the formants shift when lower or higher notes are played. The resonant filterbank is also a very nice tool to synthesize all sorts of percussive sounds. Replacing the fixed frequency multimode filters by the type with the control signal inputs and adding ringmodulation can be used for all sorts of blippy percussive sounds.

The 24 dB filters.