In working a great deal with additive synthesis, I have discovered why I believe that additive synthesis is ineffective based on a flawed premise.
First, let me explain that I have the mathematical background to understand the mathematical basis for additive synthesis so this is coming as much from a technical standpoint as a musical one.
The basis of additive synthesis and what is often called the "frequency domain" of sound is based on a mathematical idea called the fourier transform:
The basic idea of this transform is that an periodic waveform can be broken down into two infinite series of sin waves (or as they are called in acoustics) overtones each a multiple higher than the fundamental (the pitch that is heard). Each of the two series are seperated by 90 degrees. Some times this same idea can be expressed as a single series with each sin wave having a different phase. Synthesizers like Absynth use this principle.
There is a variation on this idea in the form of an algorhthm which is easily made into a computer program called the FFT or fast fourier transoform.
Now this idea works fine for a static waveform. However, without going into the boring mathematical detail, it does not work if the timbre changes which makes up just about every sound you find in the natural world. In fact, with a bit of thought, its not difficult to realize that determining the frequency of a waveform and its breakdown into frequencies are tradeoffs. As time periods get shorter either the frequency or the positioning of a sonic event in time become blurry (to use a visual analogy). This is why sonograms are blurry.
So to fix the problem the programer of an additive synthesizer uses what are called windows. These determining a fixed set of harmonics at a given point in time and then, much like connect the dots, the harmonics are joined by a curve that interpolates (guesses) the value between them. No problems right? Well, not really. There is a fine art to this because harmonics come in and drop out. It works well for the sustained part of a sound but not for the transient which is why some synthesizers (one in particular that I can't think of at the moment from Akai I believe) used a form of additive synthesis for the sustained part of a note but samples for the transient.
Tlo avoid making this post any longer than it is, this is the basis of the problem.