certain number of pieces, the image appears. In that precise moment we say that "we can see" the puzzle, even though it is still incomplete. In the same way, while we are doing the puzzle it seems very difficult, but once we have fitted in the final piece it seems to us to be easy. I am afraid that something similar occurs with the understanding of a paradigm.
In this brief chapter I will try to explain clearly the theoretical basics behind the Intervalic System and its most outstanding consequences for Music up to the present day. Without doubt, and taking into account what has been said up to here about changes of paradigm, this sounds like madness. I will avoid descriptions in mathematical language as much as possible. I will feel satisfied if, after reading this essay, the reader becomes convinced that the music composed up to the present day is but a mere drop of water in a huge sonorous ocean, and that the tonal system -in comparison to the vast vibrant Universe that is opening up before our eyes- is rather like a handful of insignificant folklore songs belonging to a primitive tribe called Homo Sapiens who live in an obscure corner of the spaceship "Earth".
The tonal system is capable of organizing sound quite accurately if and when the composition adapts itself previously to very specific organization criteria. Outside its limited domain the tonal theory generally loses effect, and proves insufficient in the organization and allocation of the sonorous spectrum. Any chord that surpasses half a dozen notes is on the limit of the analytical capacity of this theory.
Tonality consists of 12 notes, that are repeated in order forming what is known as a cyclic group of 12, (that is, it has 12 elements or notes). The rule for the order of the group is established by the place which a note occupies within the twelve, and its position in a determined cycle. For example, taking C4 as the first note of the group, a G4 means that it is the seventh note of the group (from C to G there are seven notes), belonging to cycle no. 4, which according to normal notation takes the following form:
The study of combinations of notes according to this method is the subject of Tonal or Classical Harmony. Throughout its development a series of relationship-types were created (scales) that led to a collection of tonal functions and the emergence of what today is called functionality. It is important not to confuse functionality with tonality. All functional music is tonal, but not all tonal music is functional (for example, dodecaphonic and avant-garde music is not functional but it is tonal since it uses the cyclic group of 12 notes taken from the tonal system).