Resonance Synthesis

Natural Grandeur
Copyright Dr Alexander J Turner all rights reserved.
According to the literature there are many different forms of audio synthesis. However, one key behind many great sounds is resonance which is not considered a form of synthesis its by itself. Maybe it should be.

At the bottom of this post is a list of synthesis types from Wikipedia. It does not mention resonance. One could argue that it is part of physical modelling synthesis; but I would say this is incorrect and that wave guid synthesis and similar techniques are a subset of resonance synthesis. The perfect example of why this is incorrect comes from the Mini Moog. Its resonant ladder filter allows this amazing machine to play notes generated from white noise. This is not traditional additive synthesis because it is not being generated from oscillators or their digital equivalent. It is not (as one might mistakenly think) a form of subtractive synthesis either. Resonant filters do not just remove frequencies but they add tone as well. To demonstrate this here are two generated sounds; the first is band filtered white noise without resonance and the second is filtered with the same IIR Butterworth filter but with resonance added.

White Noise Filtered
White Noise Resonance Filtered

White noise filtered by a third order Butterworth band pass filter between 600 and 1050Hz.

The same noise with the same filter but this time with a filtered feed back resonance of 800Hz.
The spectrogram of the above resonant filtered signal showing peaks symmetrically either side
of the 800Hz resonant frequency at 635 and 980 approximately.
Here we can see the very strong peaks created by resonance. These are not filtered to be there via subtraction of the signal around them; these are generated by positive feed back in the filter. To create this two peak effect I used a Butterworth order 3 filter. If I use a 2 or 4 order filter three peaks are created. The resonance here is at 800 Hz and the peaks are either side of that. Again. for an even order filter the centre peak is at the resonant frequency with two side bands. Other, more complex side band structures can be produced by filtering at a higher frequency than the resonant frequency of the filter (see below). In the above the filter was set to shoulder at 600 and 1050 Hz using this code:

(600,1050,3)CreateDirectBandPass !filter

To go even further was can use resonant filtering on a 1Hz square wave. The same filter as above, with a very small amount more resonance produces the following metallic sound and spectrogram:

Spectrogram of resonant synthesis driven from a 1Hz square wave.
Which is nothing at all like the simple clicks which come from band pass filtering the square wave. It is unambiguous that resonance is synthesising audio rather than just filtering it.

Here is the spectrum of the same system but with the resonant frequency set to 50Hz but the filters the same:

Inharmonic resonance generated by resonating below the pass band of the filter.
The above was generated using this filter:

(600,1050,2)CreateDirectBandPass !filter
(?signal,0.995,0.15,50 Period,?filter)FilteredResonantFilter Normalise dbs-1 !signal  

The sound is something like a "Jew's Harp" which I think you will agree is not much like the square wave driving it!

Why Resonance Sounds So Good:
Well - that it my view- resonance is a very powerful and great sounding tool. Adding resonance (originally from simpler methods than the above) has consistently given a great deal of depth, interest and realism to my syntheses. In Romance, which was one of my earliest successful renders, adding sympathetic resonance from all the strings to the sound of the plucked string for an electric guitar made the difference between a sterile digital sound and something approaching a real guitar. Similarly, in Sound Of Four, the key ingredient to the sound of the drums is set of resonances for the circular and radial modes of the drum skin.

I believe these sounds are 'good' because real things resonate. We learn to hear the world in terms of the resonance of real world objects. Hence, when we synthesise sounds, resonance makes the result appeal to our learned and innate sensory systems. It does not need to be a physical modelling type of resonance either. Completely artificial resonance effects still have the ability to produce some interesting sounds. Modulator is done almost completely with resonant filtering of white noise as is Secret Interiors. Neither of these two renderings could be accused of being physical modelling synthesis!

Where Else Do We Find Resonance:
So far I have chatted about the timbre of resonance. It has other very important temporal characteristics. These can be heard in the Resonance Filtered Square Wave above. The clicks of the wave are converted into much longer sounds. The envelop of such sounds often has a very natural, organic shape to it because, as I mentioned before, we hear resonance in the real world so it sounds natural. That long decay of highly resonant systems is also a key factor in reverberation and ambience.

Deliberately over emphasised reflections during reverberation at the end of Anticipation.
If we consider reverberation as a form of very low frequency resonance it starts to make more sense in the way it behaves. It has a progressive filtering out of higher frequencies and enhancement of particular modes which are characteristics of resonance with filtering in the feedback. The 'reflector' effect in Bells Of Time (and many other renderings) makes use of these aspects of reverberation. It functions by repeated, filtered delays laid on top of one another so that they start to feed back with one another to produce a gradually decaying reverberation with an indefinite length. The effect is striking because one can start to model reverberation of spaces which are hard to imagine or physically impossible in the real world.

So - Resonant Synthesis - Does It Exist?
I am in two minds as to the answer. In one way the answer is completely and utterly YES! If one considers that nearly all analogue oscillators use resonance to produce their frequencies then an analogue synth' like the Mini Moog is actually a resonant synthesiser. It uses resonance to create wave forms and then resonance (in the filter) to shape the result. It is as much, if not more, a resonance machine than an additive/subtractive synthesiser.

If one considers resonance to be a non generative effect; it does not create tones but it does alter them, then it might be reasonable to say it is not a form of synthesis but rather a form of processing. However, that argument would apply to distortion and frequency modulation, both of which are in the Wikipedia list.

So, in my view, Resonance Synthesis does exist as its own category and is indeed one of the most important forms of synthesis with enormous potential to be used and expanded even more.