The cutoff is one of the main parameters for a filter, it provides the user control over which frequencies the filter affects. The cutoff is usually a specific frequency value given in Hertz.
Whilst the purpose of a lot of filters is to attenuate the amplitude of various frequencies, the resonance control commonly does the opposite, in that it boosts (or emphasises) the amplitude of certain frequencies around the filter cutoff. The way that resonance is commonly implemented is by feeding the output of the filter back into its input. Increasing the resonance means increasing the amount of feedback applied.
Lowpass And Highpass
With Lowpass and Highpass filters, increasing the resonance parameter has the effect that frequencies close to and at the filter cutoff are boosted in amplitude. Making them more prominent in the sound.
With Bandpass filters, in most cases increasing the resonance has the same effect as Lowpass and Highpass filters, in that frequencies around and at the cutoff are boosted in amplitude. In some applications Bandpass filters can be configured so that the resonance control instead only affects the filters overall bandwidth.
In these cases, at low resonance values, the bandwidth is relatively wide. At higher values this bandwidth becomes narrower. This approach is more common with EQ’s than it is with synthesiser filters.
Resonance applied to notch filters tends to work differently than other filter types. When the resonance is increased the width of the notch shrinks, meaning less frequencies are muted or attenuated. At low resonance values the width is relatively wide. At higher values the notch width shrinks. This happens to the point that at very high settings the notch can completely close, meaning that all frequencies pass through (essentially becoming an Allpass filter)
Please also see our blog post on 2 pole vs 4 pole filters here.