Method of and apparatus for computer-aided generation of variations of a sequence of symbols, such as a musical piece, and other data, character or image sequences

A method of producing variations of an original sequence of successive symbols, comprising, generating in a computer a reference chaotic trajectory representing dynamic time-changing states in x, y, and z space;

• developing a list of successive x-components for the trajectory and pairing the same with corresponding successive symbols or characteristics thereof in similar time sequence;
• plotting each such symbol or characteristic at its x-component location to produce successive symbol domains creating a landscape of the original along the x axis;
• generating a second chaotic trajectory initially displaced from the reference chaotic trajectory in x, y and z space;
• developing a further list of successive x'-components for the second trajectory;
• seeking for each such x'-component a corresponding x-component that is close thereto;
• pairing each x'-component with the symbol as characteristic that was paired with the corresponding close x-component;
• pairing each suchx'-component with the symbol or characteristic that was paired with the corresponding close x-component to create a corresponding symbol or characteristic in a resulting modified sequence that is a variation upon the original sequence.

Apparatus for producing variations of an original musical composition, constituted of a sequence of successive musical pitches p occurring one after another in such original piece and including, where desired, one or more chord events, said apparatus having, in combination, means for generating in a computer a reference chaotic trajectory representing dynamic time-changing states in x, y, and z space;

• means for developing a list of successive x-components for the trajectory and pairing the same with corresponding successive pitches p in similar time sequence;
• means for plotting each such pitch p at its x-component location to produce successive pitch domains creating a musical landscape of the original piece along the x axis;
• means for generating a second chaotic trajectory initially displaced from the reference chaotic trajectory in z, y, and z space;
• means for developing a further list of successive x'-components for the second trajectory;
• means for seeking for each such x'-component a corresponding x-component that is close thereto;
• means for pairing each such x'-component with the pitch p that was paired with the corresponding close z-component to create a corresponding pitch p' in a resulting sequence of pitches that is modified and represents a variation upon the original piece.

Apparatus for producing variations of an original sequence of successive symbols, comprising, means for generating in a computer a reference chaotic trajectory representing dynamic time-changing states in x, y, and z space;

• means for developing a list of successive x-components for the trajectory and pairing the same with corresponding successive symbols or characteristics thereof in similar time sequence;
• means for plotting each such symbol or characteristic at its x-component location to produce successive symbol domains creating a landscape of the original along the x axis;
• means for generating a second chaotic trajectory initially displaced from the reference chaotic trajectory in x, y and z space;
• means for developing a further list of successive x'-components for the second trajectory;
• means for seeking for each such x'-component a corresponding z-component that is close thereto;
• means for pairing each such x'-component with the symbol or characteristic that was paired with the corresponding close x-component to create corresponding symbol or characteristic in a resulting modified sequence that is a variation upon the original sequence.