Of the various filters used in subtractive synthesis, the low pass filter is by far the most commonly used. Accordingly it is useful to examine how this filter alters sound. To that end, I’ve made a couple of videos that demonstrate three different filters in Logic Pro’s Retro Synth instrument.
Before getting too deep in the process, I’ll start with some basic information. A low pass filter attenuates frequencies above a set center frequency. Filters are often described in terms of their slope, that is the amount that higher frequencies are attenuated. Slope can be described in terms of decibels per octave. Thus, a 24dB filter dampens frequency content by 24 decibels per octave. To put it another way if the center frequency is set at 100 Hz, audio at 200 Hz should be attenuated by 24 decibels, while audio at 400 Hz should be attenuated by 48 decibels. Thus, the higher the slope, the more effective the filter is at attenuating filtered frequency content. Slope can also be described in terms of poles, which translates out to 6dB. Accordingly, a 24dB filter is also called a 4 pole filter, while a 12dB filter is called a 2 pole filter.
The three filters demonstrated in these videos are a 24dB low pass (described as being Lush), a 12 dB low pass (described as being Creamy for some unknown reason), and a 6dB low pass (described as being Lush). Each is demonstrated with a 4 second, 55 Hz sawtooth wave (A1, where C4 is middle C). In each pass, the center frequency is swept up from the lowest to the highest frequency setting for the filter. Thus, we hear harmonics add in over the course of four seconds.
Additionally, these videos also demonstrate how the filters in question respond to difference resonance settings, which begs the question, what on God’s green earth is resonance? Resonance feeds the audio at the center frequency of the filter back through the filter. At moderate settings this can allow harmonics to be accentuated when the center frequency matches the frequency of a sound’s harmonic. At very high settings quality analog filters self resonate, which means they produce a sine wave at the center frequency even when no sound is patched into the filter. Because resonance creates a peak at the center frequency, it can increase the perceived slope of a filter. Each video features nine passes, three for each filter (24dB, 12dB, and 6dB respectively). The first pass of each group features no resonance, while the second has the resonance set at 50%, and the final has the resonance set at 100%.
What do we learn from these videos? While it would be technically incorrect to say that these filters all self resonate, we can say that they are coded to emulate self resonating filters, so for all intents and purposes, these filters are functionally self resonating. Thus, when the resonance is turned up to 100% we hear a sine tone sweep up the entire frequency range of the filter in addition to the filtered 55Hz sawtooth wave. Furthermore, we can see that sweep in a linear fashion in Logic’s graphic equalizer, confirming it responds in a linear fashion in pitch space, or exponentially in frequency space. The resulting wave form is basically a sine wave laid out over the structural form of a longer period sawtooth waveform. One odd thing we notice is that the 12dB (Creamy) filter peaks severely when the resonance is turned up to 100%. I found this to be true at every key velocity.
We also hear that the filters effectively accentuate harmonics when the resonance is set at 50%. This allows us to hear the exponential curve of the filter. As the center frequency moves up linearly in terms of octave pitch space, it accentuates increasing numbers of harmonics as the more harmonics are grouped within an octave as you sweep up the frequency range.
We can also hear and see how much more effective the higher slope filters are than the lower slope filters. We can see how the higher slope filters effectively squelch higher frequencies when the center frequency is low. Likewise, we can see how much more curved the output waveform is when the center frequency is low.
Here we can see the waveforms as each filter is tested . . .
Here we see the spectral analysis of each tone as evolves in Logic Pro . . .