Differences with wave sequences
While wave sequencing can produce similar results to wavetables, the underlying architecture is actually quite different. Firstly, rather than using single-cycle waveforms, it's based on looped PCM samples--in some cases this includes multi-cycle waveforms with separate attack transients. Secondly, the sequence is entirely user-definable: rather than using modulation to cycle sequentially through waveforms one can define arbitrary steps, with each step having its own duration, level, and cross-fade time. (To use an another analogy, think of a DJ cross-fading one track into another into another etc. etc. )
As with wavetable synthesis one can typically route this complex "oscillator" through traditional subtractive synth architecture.
Wave sequencing was introduced by Korg's Wavestation and has since made its way into their OASYS and Kronos synths. It can also be found on Arturia's Origin. If you're looking for a software option, Korg has released a VST version of the Wavestation as part of their Legacy collection: http://www.korg.com/LegacyWAVESTATION
Here's an example of a "motion pad" consisting of 3 separate wave sequences (Korg Wavestation):
In some ways vector synthesis is very much the same as wave sequencing: the ability to cross-fade between multiple sound sources (usually 4). Typically this is done with a joystick but in some cases it can also be done with an LFO or envelope.
Korg's Wavestation implementation of "Vector Synthesis" is even more elaborate, however: each "vector" is a tone generated using a wave sequencer, each with its own envelope generators, LFOs, filters, etc.
Vector synthesis was first introduced by Sequential Circuits' Prophet VS in the 80s, and subsequently appears on Yamaha' SY series, Korg's Wavestation and OASYS, and Arturia's Origin.
Linear Arithmetic Synthesis (LAS) and Realtime Convolution and Modulation Synthesis (RCM)
Linear Arithmetic Synthesis was introduced by Roland's D-50 and D-550 synths in the late 80s. It can be viewed as a combination of virtual-analog synthesis and PCM wave sequencing. A sound consists of three parts: a PCM-based attack transient, a single-cycle PCM "body", and a traditional virtual analog synth waveform (saw or pulse).
(I have to give a shout-out to the talented producer ASC who cites the D-50 as one of his favourite synths: http://theasc.blogspot.ca/2013/07/gear-talk-1-asc-and-his-roland-d-50.html )
Along the same lines, Yamaha's SY77/TG77 and SY99 allowed for the playback of PCM-based "attack transient" waveforms alongside FM synthesized sounds. They called this "Realtime Convolution and Modulation Synthesis", but it essentially boiled down to the Yamaha/FM equivalent of Roland's LAS.
Where to go from here?
Why should you bother with this type of synthesis, you ask? Well for one thing, there's a limit to what can be done with traditional analog or virtual analog synthesis. While subtle variations in oscillators and filters can create some sonic variation, the base architectures between analog synths are typically quite similar. FM synthesis, on the other hand, can often be difficult to tame and tends to get into "metallic" and "bell-like" territory far too easily.
Wavetable, wave sequence, and vector synthesis sit somewhere in the middle: a nice melding of digital and analog principles.
If you're looking for a starting point I would recommend NI's Massive VST for wavetable synthesis, and Korg's Wavestation VST for wave sequencing and vector synthesis. While the latter has a much steeper learning curve it can be used to synthesize some very complex sounds, such as the one heard above. The downside of the Wavesatation is that the UI can be at times awkward and unintuitive, and it only offers two types of filters (-24 dB/octave resonant low-pass, exciter)
Prior to our full review, we take a listen you ask the questions