How many sounds are there to describe?
The question above is of course impossible to answer. But, it is clear that the space Schaeffer gave to unbalanced sounds doesn’t match the space he gave for balanced sounds. A common intuition, at least among electroacoustic composers, would be that there are many more unbalanced than balanced sounds in nature. After all, people have felt it necessary to construct elaborate instruments just in order to produce the balanced sounds. And, as any beginning musician would know, there is many more ways to make noise on an instrument than beautiful sounds (all sounds are beautiful in their own right, but you get the picture). Scraping bows, rattling guitar strings, and breathy flutes all need at least as much space for detailed description as the balanced sounds. And, now they do – in the sections for stratified, vacillating, composite, and accumulated sound-objects!
When making a stratified sign the bottom symbol can be of three kinds, and so can the top one, add to that four different symbols for describing amplitude and frequency gait and we have 3×3 × 4×4 = 144 ways to make a symbol.
For even more possibilities to describe the inner life of a sound, the vacillating category offers an additional position for a mass sign, thereby giving the opportunity to simultaneously render combinations of all of the three mass types. In the signs for vacillating and stratified sound-objects the closed symbol at the bottom and the open symbols on top are a notational convention. Filled symbols in the upper positions, would be used to describe something sounding like a chord.
Combining the mass type with the spectral gait of the partial components we can make as many as 33 × 43 = 1728 different symbols.
That’s a lot of descriptive power emanating from only a few kinds of symbols combined in different positions. Now, this really starts to resemble an alphabet capable of making words!
The standard way of writing the composite category starts out with a mere 6×6 = 36 combinations.
After taking into account that either of the two symbols can have a glissando up or down the number of combinations rises to 6×3 × 6×3 = 324. But in fact this category is even more versatile than that; consider that the slur can be written in the opposite direction and the number of small mass symbols is not limited to two. In fact, I will not even try to calculate how many variations are possible, it is easy to see that there is room for a huge amount of variation here.
If continuing to add ever more mass signs, this could be the category that has the most combination possibilities. But if we were to do that, it would soon start to look a lot like an accumulation. So we should be careful not to overdo the details in the composite category.
In terms of basic combination possibilities, the category accumulation really surpasses them all. Consider that it has 9 “positions” to put a symbol. We still only use 6 different masses (3 open and 3 closed symbols), but each of these could have a glissando up or down as well.
That makes it possible to put 6×3 variants in each of the 9 positions and (6×3)9 gives an astounding 198,359,290,368 combinations!
Would it even be possible, by ear, to distinguish between sounds notated as e.g., and ?
Well, at least we won’t run out of notational options should the need arise. Until then we can settle with the more limited, but practical, use of the pre-assembled symbols at each height.
If we take into account that each of these height placements can have corresponding glissando signs, we still end up with (6×3)3 = 5832 symbols to express what we hear.
And Then There is Morphology…
We already have a very large number of ways to describe all possible sounds, but it doesn’t end here. Factor in the signs for onset, onset brightness, grain, and gait, then the number of possible combinations to describe a sound is huge.
In fact, you could say that the possibilities are unlimited also in the formal sense. As each static symbol can be described as transforming into another statically described sound, a dynamical development of the sound can be described in arbitrary detail and length.
This is akin to an alphabet making words that combine into sentences!