With certain filters, if the resonance parameter is pushed past a certain limit, the filter enters self-oscillation. In self oscillation, the filter will output audio all by itself, even when there is no input being fed into the filter (i.e. it behaves like an oscillator).
The audio the filter outputs in this state is a sine wave, whose tuning is roughly the same as the filter cutoff. As an example, if the filter cutoff is set to 100Hz, the sine wave produced when in self oscillation will generally be playing at about 100Hz. Other filter parameters such as the resonance amount can affect the sines tuning, but this effect is often minimal.
The pure sine wave out is only really the case when the input into the filter has been removed, or at very low levels. In cases where the audio into the filter is at normal levels, it is common for the output of the filter to be a sort of mix between the filtered signal and the sine wave. Which of these is more prominent can differ depending on the filters settings.
A common feature found in synthesisers is the ability to “Key-track” the filter. When you enable this, the filters cutoff will change its value depending on what note on the keyboard you are pressing.
With most synthesisers, the different keys on the keyboard are associated with a different frequency. As an example, pressing a middle C will make the oscillator for some voice currently playing back (provided you haven’t applied any kind of tuning offset) run at about 261.625 Hertz, pressing the key which is the next semitone up makes the oscillator play back one semitone higher (in this case at a rate of about 277.18 Hz).
The cutoff of a filter is also a value set in Hertz. As an example, with a lowpass filter if you have a cutoff of 100Hz, then different frequencies contained within your sound that are above 100Hz will be attenuated in amplitude by some amount. What key-tracking does is apply an offset (or scaling) to the filter cutoff frequency that is in some way proportional to the value of the note you are pressing. As an example, the most common key tracking set up is that the by playing gradually higher notes on the keyboard, the filter cutoff value will steadily increase. For a lowpass this means the sound gets “brighter” the higher up you play.
A useful property that this style of key-tracking enables is that if you have a filter in self oscillation, you can use the filter as a standalone sine wave oscillator, that will (mostly) track the note you are pressing on the keyboard.
Roll Off/ Slope
Another way that filters are characterised is in terms of their roll-off (also called slope). The roll-off of a filter gives you a general indication of how sharply the filter attenuates different frequencies. The roll-off is given in dB per Octave. For synthesisers the most common roll-offs are 6dB, 12dB and 24dB. In general, the higher the dB per octave roll-off, the faster the rate at which frequencies are attenuated.
Deciphering what this means, if we have a lowpass filter with a 6dB per octave roll off, we can take a frequency that is currently being attenuated by the filter, say 100Hz, and then look at how much more a frequency of 200Hz (i.e. the frequency an octave above 100Hz) is being attenuated by.
If you do this, you will find that the frequency of 200Hz comes out of the filter roughly 6dB lower in amplitude than that of a 100Hz frequency. If you were then to look at a frequency of 400Hz (which is an octave above 200Hz) you would find that that comes out of the filter about 6dB quieter than the 200Hz signal.
As a more practical example if a frequency of 100Hz comes out of the filter reduced in amplitude by about 3dB, then a frequency of 200Hz will come out of the filter reduced by about 9dB (i.e. has an extra 6dB of attenuation applied).
More generally with this set up you would find that
- Freq of 200Hz (+1 octave from 100Hz) is 6dB quieter than 100Hz
- Freq of 400Hz (+1 octave from 200Hz) is 6dB quieter than 200Hz
- Freq of 800Hz (+1 octave from 400Hz) is 6dB quieter than 400Hz
And so on. So, each octave higher we look at (provided it is a frequency being attenuated by the filter), will generally come out of the filter 6dB quieter than the last.
If the roll-off was instead 12dB, with the same setup, you would find that
- Freq of 200Hz (+1 octave from 100Hz) is 12dB quieter than 100Hz
- Freq of 400Hz (+1 octave from 200Hz) is 12dB quieter than 200Hz
- Freq of 800Hz (+1 octave from 400Hz) is 12dB quieter than 400Hz
Other Roll-off signifiers
Other terms are also used to signify how sharp the filter roll off is. The common two are order and pole count. The term order stems from the fact that most filters found in synthesisers are constructed out of simpler structures or elements chained together in some configuration. The order of the filter commonly relates to the number of simpler elements / stages used to create the final filter.