Tag Archives: The Art of War

Five Notes

Jonathan L. Friedmann, Ph.D.

Cultural evolution greatly outpaces biological evolution. The excruciatingly slow pace of natural selection is eclipsed by the rapid and localized intellectual, behavioral, and technological transformations that take place within human societies. Moreover, whereas the mutations and adaptations of genetic evolution typically lead in a single direction, cultural changes can be linear, cyclical, conservative, progressive, or all of these at once. Such variety is a result of human-directedness. Unlike the non-sentient forces of nature, which spawn diversity through gradual descent with modification, cultural advancements and retrenchments are conscious choices, and thus prone to splinter off in multiple directions.

In this sense, the use of the term “evolution” in discussions of culture, while commonplace, is somewhat misleading. Rather than progressing unidirectionally, human culture is the fickle and multidimensional product of a capricious species. This is obvious when examining music. If musical styles were placed on an evolutionary continuum organized from simple to complex, actual timelines would be demolished. Minimalism would predate Romanticism, blues would precede madrigals, and the Beatles would come before Bach. The absurdity is exacerbated when world musics are thrown into the mix.

Beneath the false premise that fewer notes indicates an earlier period is a bias regarding what constitutes complexity. Just as each style has its own history, each style is complex in its own way. Where harmonic density is lacking, rhythms may be more intricate. Where counterpoint is highly cultivated, modal choices may be limited. Where orchestration is refined, emotional content may be restricted. More often than not, these scenarios are the product of preferences: the relative absence or abundance of a musical element is dictated by taste, not chronology.

A good example is the Chinese predilection for the pentatonic (a five-note non-semitone scale). Chinese musicians are aware of “bigger and better” scales, but five is a sacred and symbolic number. The five notes of the scale—gong, shang, jue, zhi, and yu (usually equated with do, re, mi, sol, and la)—correspond with a variety of other fives. Among these are the cardinal directions (center, west, east, south, north), elements (wood, fire, earth, metal, water), colors (yellow, white, blue, red, black), tastes (sweet, pungent, sour, bitter, salty), and political structure (king, minister, people, national affairs, natural world). Far from being a “primitive” stage in musical development, the Chinese pentatonic is a conscious conservation of socio-historical meaning.

What’s more, while the pentatonic may exclude notes present in the Western heptatonic (not to mention chromatic and microtonal scales), it is similarly capable of generating endless melodies. This point is made in The Art of War, which observes that the five colors combine to “produce more hues than can ever be seen,” the five tastes “yield more flavors than can ever be tasted,” and the five notes “give rise to more melodies than can ever be heard.” Indeed, the value ascribed to discovering new combinations has ensured the preservation of the scale, despite many cultural changes that could have swept it away. This, in itself, goes against any hypothetical theory of musical evolution.

Visit Jonathan’s website to keep up on his latest endeavors, browse his book and article archives, and listen to sample compositions.

The Art of Tune

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.