During the first part of a fugue, its initial melody is presented in a slightly altered way each time it is played, because each voice or instrument introduced sings or plays higher or lower notes than those used at the very beginning of the piece.
As the fugue develops, the initial melody and its accompanying ‘counter subjects’ are stretched, shortened, modulated, swapped between voices and instruments and variously combined in new, interesting and stimulating ways. Creative synergies are sort between different and competing musical ideas.
The above aspects of fugue can be applied to many of the more complex problems presented to us.
A characteristic of complex problems is that most of the issues involved can be fairly equal in importance because of the influence they have on each other (just like the melodies and counter subjects within a fugue). Sometimes, therefore, the more we try to break down a problem and address its component parts, the more difficult and challenging it can become; the solutions we propose in one area of the problem begin to cause unforeseen complications elsewhere, perhaps even making things worse.
In these circumstances it is usually best to build up our perception of the problem rather than break it down into compartmentalised chunks. Instead of focusing on each detail separately, look carefully for any new insights created by the counterpoint that exists between them. When different people describe the problem how does it sound, look or feel? What similarities and differences are there between the various descriptions? When two parts of the problem are put side by side how do they look together? Are there any unexpected connections or relationships between them? Add in other related issues or problems. How does the picture evolve as the component parts of the problem are brought together? What patterns or consistent messages emerge when all the diverse issues and problems are considered as an interrelated whole?
The above process of bringing together separate items can also be applied to the generation of solutions to problems. When creating solutions explore what happens when two or more separate ideas are considered side by side. Does trying to identify connections between the ideas lead to even better solutions? Can the best aspects of each idea be integrated into one idea that is even more useful?
Fugues were particularly popular during the Baroque Period of Music (1600 to 1750). J.S. Bach was one of the greatest of fugue writers, as exemplified by his The Art of Fugue BWV 1080.