Wavetable synthesis - (truth unveiled)

[salina]

've found many people really don't have a firm understanding of various synthesis methods. One of these has been "Wavetable Synthesis". What follows is a small write on the history of Wavetable Synthesis and it's basic workings.

This write is based on writings I had previously done on the subject (edited and condensed into one body) which were partially historical and partially theoretical. I recently obtained some info from an associate with ties to Waldorf regarding details on how their "Wavetable Synthesis" system worked, and so that information has now been infused with my initial writings.

Before I begin with any of this, there is a larger lesson embedded in this. In particular, it is that I have found that where electronic instrumentation is concerned, it is quite worth while to actually truly learn the instruments one is working with. This places one in a position to not only get the most out of that instrument, but also to pull more from instruments they may work with in the future.

In any regard......

WAVETABLE SYNTHESIS:

"Wavetable Synthesis" can be a bit of a confusing term in the synth world, as you have basic Wavetable synthesis, and in this regard, there are quite a few wavetable synths out there actually. And then you have what the synth company Waldorf called "Wavetable Synthesis". Now the Waldorf term did something that included Wavetable Synthesis in it's original sense, but used it in conjunction with an interpolation process they had come up with to shift through mulitiple wavetables......they then called their own process "Wavetable Synthesis" as well. Further, Waldorf (to the best of my knowledge) has never publicly detailed how their system worked. This has led to quite a bit of confusion at times.

Why Waldorf called their process "Wavetable Synthesis" when "Wavetable Synthesis" was already a term in use I have no idea.

But in any regard, this creates a situation where one needs to be weary of when they hear the term "Wavetable Synthesis", as there truly are two different things that may be being discussed.

The origins of Wavetable Synthesis can be traced back to Max Mathews and Bell Labs circa 1958 (yes, wavetable synthesis has been around that long).
A wavetable is a description of a wave shape, represented as a series of samples. The wavetable capitalizes on the fact that pitched sounds are created from periodic waves, waves that repeat regularly. Thus, musical material contains a high degree of redundancy. Since music has a high degree of redundancy, it is not necessary to produce samples representing the entire duration of a piece. One description of the wave is all that is needed. A table is made up of a number of address locations, each of which contains an amplitude value for the wave. An incrementer reads through the table and sends sample values to a digital to audio converter. That is, the wavetable oscillator has a phase value and a current address in memory. It reads the value stored at the current address, then skips a number of addresses, the number determined by the phase value. When the end of the table is reached, the incrementer "wraps around" to the beginning of a table. Thus, addresses are read in a circular fashion. The sampling increment, the number of samples that are skipped from output to output, affects how quickly the table is iterated, and, correspondingly, which pitch is produced. The sampling rate determines how many samples per second are sent to the digital to analog converter.
In short, a wavetable is nothing short of a looped sample of a single cycle waveform.
Further, this actually means that the majority of synthesizers that have been created up to the present day are actually Wavetable Synthesizers. Though a synth based on PCM sample playback is not necessarily a wavetable synth, it can be a wavetable synth.
To this end, I've actually made quite a large number of Wavetables myself. (As have many)

Now, jumping forward almost two decades, we come across Wolfgang Palm. Palm had began working on synths around 1975, and actually did quite a bit of work with Tangerine Dream.
Around 1977 Palm began working with digital synthesizer concepts, particularly he was dealing with using Wavetables as oscillator sources.
By the early 80s Palm had developed the first commercial Wavetable based synthesizers.
Palm's implementation of wavetable synthesis employed an array containing 64 pointers. At least 2 of these pointers would point to actual wavetables, though more than two could capably be used. The empty slots would be filled through a Fourier Transform/Morph method based upon the wavetables that had initially been set in the array. Palm referred to this array as a "Wavetable".

The table could then be swept through via an EG (Envelope Generator) or other methods. What was interesting about his implementation is that the original wavetables of reference could be related or totally unrelated....and thus the interpolation process pretty much allowed one to deal with a tonal source that could change subtly or greatly over time.
The process of creating the (Palm) Wavetable coupled with the ability to sweep through it Palm would come to call "Wavetable Synthesis".

I've long theorized that a FFT (Fast Fourier Transform) Morph, as used with Palm's system, would ultimately yield results that bore little difference from crossfading. And to put what was going on simply, I've actually referred to the Waldorf/Palm process as being akin to a digital crossfade.
I've not endeavored to personally explore this area, but I have an associate that is currently playing with it (he expects the same results I do)....and I'm pretty interested in seeing if his results bare much audible difference from the results of crossfading.

So now, there's a number of things we can postulate here.
1. Wavetable Synthesis, in it's most true sense, is nothing more than a means of digital oscillation and is based around the looping of a sampled single cycle waveform (though technically, there is no reason why a wavetable can not do things like contain things more complex than an analog single cycle waveform).

2. Wavetable Synthesis as it is known to the majority of the synth world is not Wavetable Synthesis in it's most true sense but is dependent on true Wavetable Synthesis in order to function.

3. A Fourier Transform/Morph between waves will probably yield results similar to those yielded by crossfading between two waves. One thing that is certain is that if the crossfading between to waves sounds bad, a morph between the same two waves will in all probability also sound bad. Further, due to the nature of how a FFT Morph works, a digital crossfade can be expected to come off sounding more "natural" the majority of the time. (I'll just ask you take my word for this)

4. In the current age, many synths and samplers are capable of crossfading between multiple waves in some way.

Now I was able to obtain details just recently (yesterday in fact) from a Waldorf person in regard to how exactly their system of "Wavetable Synthesis" works.
In essence, with their system (which was derived from Palm), it is more like there are only 61 pointers actually available. The other 3 pointers in the Array are taken up by standard waveforms (Saw, Square, and a Sine or Triangle I believe). When a (Waldorf) Wavetable is called up, any open slots are filled with new waves generated via an FFT Morph process.
The (Waldorf) Wavetable from that point on is static and can merely be swept through.

So, there is the mystery of the"Wavetable Synthesis" unveiled.

In any regard, going back to our postulates, I think postulates 3 and 4 bear extremely interesting implications. For one, it shatters the idea that functions of things like the PPG Wave and/or Waldorf Wave and Microwaves are extremely unique in regard to what they can achieve. Granted, I'm speaking merely of the (Waldorf) "Wavetable Synthesis" action, as there are still be other aspects of a synths architecture that can make it stand out from other things.
Further, if what they are achieving is akin to little more than crossfading.....











Well.....I'm not going to give the entire story away.....like I said, it can do one good to know their instruments and how they work well. I'll just note that take heed to postulates 3 and 4, and then ask yourself how (Waldorf) Wavetable Synthesis might relate to tools you are already using. =)


(as you may guess 23 helped with this, in fact wrote this)