Object in context

Progression of objects

Let us have a progression of objects A,B,C..., having certain natural
properties (states) defined with help of vectors a,b,c,... 

Objects are adaptable. Under influence of his predecessor the object X change its state to x'.
In our example it comes on a,b',c',....


If the object has plenty of time, it converges back to its natural state.
E.g. a,b',c' -> c.

We assume, 2 processes exist:


    
·          Influences of objects: c'= c * T(b,c), where T is transformation matrix.
·         
·          Convergence of object: c = c' * N^i, where N is convergence matrix  and i number
·         of steps. (After time interval dt we always multiply vector c'(i) again by matrix N.)
·         
The aim is to find for each object x such convergence matrix, that

 lim(x'*N^i)=x, for a finite integer n, i->n.


Characteristic equation

If object accomplish its natural state, than convergence does not change him:

 N * c = 1 * c.

This equation is a special case of characteristic equation:

  N*c = b *c, where c is characteristic vector

and b characteristic number (b=1).


Musical stream

Let us apply the mentioned draft to musical stream.

Every chord has elementary characteristics (potentials of tones, continuity, impulse, ...),

and in consequence also certain real characteristics (sonance, genus, ...).

In context all this characteristics change.

E.g. chord G by himself sounds unlike the chord G in sequence F-F#-G.

We acquire the perception of pure G only after certain time of convergence.


    

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