Very simple: Fourier found out that every arbitrary sound phenomenon can be explained as a sum of sine waves.
Every oscillator generates sine waves and numerous software helps to mix up whole the waves.
Even the different velocities and pitches (amplitudes and frequencies) can be handled easily as well as the phases (locations of the waves zero amplitudes).
A measure for the subtlety of the sound surely is the amount of the overtones adding to the basic sound, the pitch.
There you are!
To build a sound one has to add overtones (integer multiples of the basic sound´s frequency), each one with it´s own amplitude, so long till the desired sound is reached. A lot of work:
The deepest piano pitch (55 Hz) needs more than 360 Harmonics! A pity that the utter mass of the processed sound components is no guarantee to get a “real” (living, animated) sound. A sound rich of overtones must not lead to a natural outcome!
The reason is based in the “time”.
Music not only is an art of pitches and sounds but also an art in time. Already in the macrocosm of music you have to play the right tone right in the time. All the more you have to take care in the microcosm of sounds, the “atoms”, the sine waves.
It is not sufficient to accumulate a wast number of partials, you must define exactly their beginnings and ends of each and the separate courses of their dynamics.
Envelope generators (> ADSR) design the loudness process of each of the sound componentes thus giving it more aliveness.
This means to process several more bits and bytes.
Most of interest is the beginning of the sound, the “attack” (the “A” of ADSR): It is here where there the classical instruments get their sound energy; it is also the part of the sound with the most noise and here you can get the sounds most characteristic information and this is sometimes not that easy!
Indeed is the numerical description of this phase of the very beginning completely different from the “S”, the sustain part, the calmed part of the sound. A special importance have the > “formants”
By forming the attack one needs non-harmonic overtones which are components having non integer multiples of the basic frequency. The energy building up the sound is initially of chaotic behaviour (with noise and peaks of energy).
Later on the classical instruments (as analogue filters) leave the typical base frequency with overtones formed by their individual envelopes.
The amount of parameters as described above should be o.k., but how about to work with?
How looks hard- and software with their GUIs, what time does it need to “feed“ with numbers or respective signs? E.g. my “Dino” - K5 (KAWAI), one oft the very seldom Synthies made for Additive Synthesis, has a little window on its surface to type in the parameter’s values. This window easily could be covered by my mobile phone! There was for the K5 on a ftp server a GUI (Graphical User Interface) which needed fully spread out 2 (TWO!) 19 - inches monitors!
So there are synthies dealing with the addition of partials a very seldom species.