Jonathan L. Friedmann, Ph.D.
“In battle, there are not more than two methods of attack—the direct and indirect; yet these two in combination give rise to an endless series of maneuvers.” This truism, taken from the classic tome The Art of War, speaks to the almost inexhaustible possibilities that can arise from limited choices. Like much of the treatise, attributed to Chinese general Sun Tzu (c. 544–496 B.C.E.), this aphorism has been applied to areas outside of warfare where slight tactical changes can have an enormous impact. It is especially apt for competitive entities like sports teams and marketing firms, which are constrained by conventions and regulations, yet find sometimes-subtle ways to out-smart and out-play their opponents.
Sun Tzu (or whoever wrote The Art of War) was aware of the book’s multiple applications, as he frequently used non-military examples to illustrate battlefield insights. In the sentences leading to the words quoted above, several comparisons are made to non-combative life pursuits. The possibilities arising from direct and indirect attacks are likened to the five primary colors (blue, yellow, white, red, black), which in combination “produce more hues than can ever be seen,” and to the five tastes (sour, acrid, salt, sweet, bitter), which in combination “yield more flavors than can ever be tasted.” The author cites a musical analogy as well, explaining that the five tones of his native pentatonic scale “give rise to more melodies than can ever be heard.”
The inclusion of these examples in The Art of War shows the diversity of painting, food and music known in China at the time. When we add the rest of the world and the centuries that have passed since the treatise was written, the amount of creations made from finite raw materials is staggering. And new mixtures are being concocted each day.
This becomes apparent when we consider the variety of potential melodic phrases. A widely cited article posted at the collaborative website Everything2 computes the number of one-measure melodies possible within a Western octave. Assembling the twelve notes in their various values (whole, half, quarter, eighth, sixteenth and thirty-second) gives us a figure thirty-six digits long—a theoretical integer far exceeding our comprehension. Actual melodies are much less numerous, partly because they are subject to restrictive forces like taste and cultural expectation. Even so, music that has and will be composed borders on endless.
Similar observations could be made about visual, culinary and other art forms. The drive to invent through combination is a peculiar trademark of our species. It may, in fact, be the only type of creativity we are actually capable of. Whether the activity is battle, artistic expression or something else, minor gradations and small manipulations can make a significant difference.
Visit Jonathan’s website to keep up on his latest endeavors, browse his book and article archives, and listen to sample compositions.
THINKING ON MUSIC 