Ancient Chinese believed that change is the true essence of being, and in particular they believed in the never-ending exchanges between the “Two Polarities,” i.e., the Yin and the Yang, or good and bad, white and black, day and night, etc., etc. Each and every phenomenon in this universe is understood as the result of a confluence of “currents” which are in a state of toggling between Yin and Yang, or constantly going from one end of the spectrum toward the other and back. This is considered the true law of Nature, the Tao, and this law is laid out in the ancient Oracle of the I Ching, hence the I Ching is also known as the Book of Change.

The I Ching is the Head of the Five Classics, the only book that escaped the book burning of Emperor Chin Shih Huang. In addition to enveloping Taoist thinking, the I Ching has prompted the likes of Confucius to write commentaries on its contents. Thus, the I Ching has emerged over the years as a fossil record of the two major indigenous school of thoughts in Chinese culture, namely Taoism and Confucianism.

Chou Wen-chung was no stranger to the I Ching, his father was such an adroit practitioner in the art of I Chingprognostication [sic] he was called “Chou the Iron Mouth.” More startling is Chou’s discovery in recent years that his family tree can actually be traced back to that of the great Song dynasty Confucius scholar Chou Tun-i, who re-invigorated Confucianism by injecting the concept of Yin/Yang and the Taichi diagram into its canon.

Nevertheless Chou never studied the I Ching from his father — he didn’t study the I Ching while he was in China. It was Chou’s teacher at the New England Conservatory of Music, Nicolas Slonimsky, who had initiated Chou on a journey of self-discovery and a course of re-examination of his own cultural roots.

Chou likes to tell stories of how he, for an extended period in the 1950s, practically lived in the basement of the Columbia University Library where the East Asian Collection was housed, reading every available primary source of Chinese culture (be it music, philosophy, cosmetology, etc.) he could lay his hands on — Chou had in fact learnt about the East in the West!

As a result of this extensive amount of research, Chou has, since the 1960s, been working with a system of variable (“pien”) modes based on his study of the modal systems in the world (e.g., the Indian Raga, etc.), the concept of the Chinese pien tone, and his interpretation of the I Ching and its Taoist principle of Yin/Yang exchange.

Chou has always maintained that the three characteristics of Chinese aesthetics are 1) affinity to Nature in conception, 2) allusiveness in expression, and 3) terseness in realization. The application of the I Ching in the derivation of a compositional system is perhaps the most vivid evidence of the “Chinese-ness” of Chou’s music: whether the “sound” is immediately close to nature is a subjective call, but the internal logic of the music is based on a simple premise of continuous minute changes not unlike that of the holistic working of an organic structure, or, Nature itself. After all, Tao is the working of Nature, or the universe. Chou’s compositions are perhaps manifestations of an “affinity to Nature in conception” on the most fundamental, structural level. In any case, how does one go about translating the abstract content of the I Ching into concrete idea of expression?

The universe, according to the I Ching and traditional Taoist teachings, originates in Wuchi (“nothingness”), from which Taichi (“somethingness” or more literally, “ultimate being”) is born — one can almost envision this as the Big Bang and the beginning of the universe as we know it. Taichi is then divided into “Two Polarities,” the Yin and the Yang. The Two Polarities then become the “Four Phenomena,” from which the “Eight Trigrams” of the I Ching are derived. In addition to this, Lao Tsu commented that “From One, Two is born; from Two Three is born; from Three the myriad of things” — from this derived the simple ratio of 1:2:3 which plays an important part in Chou’s musical thinking.

Chou has obviously made a conscious choice to root his modal system in the equal tempered 12-tone universe of Western music. Not that he was unaware of the pentatonic tradition in Chinese music—compositions from what critics say is Chou’s “first stylistic” period derive materials from the pentatonic. It seems that right at the point when Chou had to make decision concerning the Taichi — the basis or background for his system — he chose to espouse an all-encompassing attitude toward music, not limiting himself to any one stylistic influence. And he has been consistent about this — Chou calls himself the “Four No Old Man” — he considers himself neither East nor West, New nor Old, but closer examination suggests that Chou is and has always been East, West, New, Old, and more.

The basic unit of the I Ching is the trigram, and the trigram is made up of three yao — three lines that can either be Yin or Yang, broken or unbroken, as shown in Example. 1. In terms of the proper ordering of construction (or procedure for divination) for a trigram, the lowest line, the one representing Earth, is always decided upon first. Next comes the middle line representing Man and the last or top line is Heaven.

Example 1. An I Ching Trigram.

There are altogether eight possible trigrams — three lines each having two possible modalities (Yin or Yang): 2 × 2 × 2 = 8. The eight trigrams are 1) Chien <111> (“1” and “0” are used to denote Yang and Yin yao respectively, and the three yao inside the bracket are arranged in the correct order of Earth, Man, and Heaven), 2) Tui <110>, 3) Li <101>, 4) Zhan <100>, 5) Sun <011>, 6) Gan <010>, 7) Kan <001>, and 8) Kun <000>, as shown in Ex. 2.

Example 2. The Eight I Ching Trigrams

Translating this into musical terms, Chou began with the equal division of the octave (12 semitones) into three conjunct major 3rds, i.e., each major 3rd is built on the upper note of the previous, or lower major 3rd.

Example 3. Three conjunct major 3rds, ascending and descending.

The interesting thing about Ex. 3 is that we realize the octave is being carved up in a “directional” manner. Ex. 3a is an octave carved up in an ascending manner, while that for 3b is descending. But no matter which direction the octave, or the resulting scale/mode is being drawn, the order of the three major 3rds will never change — Earth will always come ahead of Man, followed by Heaven.

The fact that three conjunct major 3rds trisect the octave may interest those who realize the importance of the number “3” in Western civilization, e.g., Holy Trinity, Golden Triangle, etc. At the same time, “3” forms part of the 1:2:3 ratio mentioned earlier with the quote from Lao Tsu. Nonetheless, the division of the octave into three conjunct major 3rds only prescribes and defines the places (or ranges) on a chromatic scale in which one can find the musical equivalences of the three yao in an I Ching trigram. The crucial thing is to figure out a way to somehow show the modality (whether it’s Yin or Yang) of the particular ranges (intervals of major 3rd on the chromatic scale) thus prescribed. It is therefore important to add a second element, another note, within each of the three major 3rds to help differentiate their modalities.

A major 3rd comprises four half-steps. Suppose a line is being equally divided into four units ( _ _ _ _ ), and one is allowed to break the line once (a second note is added) at any one of the three points that separate the four units. There are three ways (i.e., three different combinations of units) this line can be divided into two parts:

1. one plus three units: _ x _ _ _
2. two plus two units: _ _ x _ _
3. three plus one units: _ _ _ x _

(“x” marks the breaking point)

It is interesting to note, when one looks at the two “columns” of different number units in the above illustration, that the 1:2:3 ratio presents itself vertically across the three possible distributions. Nevertheless, Chou Wen-chung chooses 2) and 3) above to represent the Yin and Yang lines, respectively. That is, the musical equivalence of a Yin yao comprises two whole-steps, while the Yang yao is represented by a minor 3rd followed by a half-step. Ex. 4 is a representation of a Li trigram <100> as Chou’s Thunder mode. A <100> structure is therefore translated into a minor 3, half-step, whole-step, whole-step, whole-step, whole-step (or 312222 if one is to count the number of half-steps).

Example 4. Li Trigram, Thunder Mode

The two small-cap letters represent two different versions of the mode, t (for Thunder) for the ascending version and t’ for the descending. Note that the ascending mode and the descending one have different pitch contents: while they both share the three conjunct major 3rds, C, E, and G (A), and the F(G) that is part of the Man (middle) line for both modes, the ascending mode also has E and A, while the descending mode has D and A. The fact that the ascending and descending versions of the same mode are different indicates that the notion of Yin-Yang affects not only the “intervallic structure” of the mode (or scale), but also the “contour” (or direction). This is only intuitive: ascending and descending are the Yin and Yang of contour. In addition, the two pairs of notes that are unique of the different contour modes, E/A and D/A are half-steps apart.

This reveals that the “trigger” (or at least one of the triggers) for a Yin-Yang exchange may very well be the half-step, i.e., the pien tone. A Yin line of C-D can change its modality by raising the second note (D) by a half-step and turn it into a C-E Yang line. By applying the pien tone (the raising or lowering by a half-step) a Yin line can turn into a Yang line and vice versa. This is also the way one pien mode is changed into another. This convenient and economic gesture of transformation reflects the “terseness in realization” aspect of Chou’s music/system.

Just as there are Eight Trigrams there are eight pien modes in Chou’s system:

Legend has it that the Eight Trigrams were invented by Fuxi, one of the fabled leaders of ancient Chinese civilization. But it was the founder of the Chou dynasty, Emperor Wen, who devised the sixty-four hexagrams and their accompanying aphorisms which made up the original I Ching (hence the I Ching is also known as Chou I).

Chou’s answer for the hexagrams is his sixty-four Modal Complexes. Just as the hexagram is a stacking of two trigrams one on top of the other, Chou’s Modal Complex is a succession of two pien modes which satisfies the following three conditions.

1. The two modes must have opposite contours, i.e., an ascending mode followed by a descending one, or vice versa.
2. The principal notes upon which the two modes are built must be a half-step apart. For example, a C ascending mode is to be followed by a C descending mode, or a C descending mode to be followed by a B ascending mode.
3. The two modes are related in terms of their intervallic structures. There are at least three different ways the two modes can be related but the most interesting and probably most often used relation is that of symmetry — that is, a <100> Thunder mode is to pair with a <001> Mountain mode — the first line of the first mode is the same as the last line of the second; the middle line of the first mode is the same as the middle line of the second; and the last line of the first mode is the same as the first line of the second, as shown in Ex. 5.

Example 5. The lw (Lake <110> Water <011>) Modal Complex.

The most interesting thing about this combination of modes as Modal Complex is that the resulting ascending and descending collection of pitches just happens to exhaust all twelve notes on the chromatic scale, as shown in Ex. 6.

Example 6. lw’/C

The lw’/C stands for an ascending Lake mode on C followed by a descending Water mode on C. The other Modal Complexes that satisfy all three of the above conditions are tm or mt (Thunder-Mountain), ss (Sun-Sun), rr (Rain-Rain), hh (Heaven-Heaven), ee (Earth-Earth), and of course the reverse of lw, wl.

The above is merely a simplistic exposition of the fundamentals of Chou’s modal system: how the sixty-four hexagrams find their ways into Chou’s system for musical composition. The simple, elegant, and intuitive way in which abstract, metaphysical constructs become concrete musical reality is only characteristic of how Chou Wen-chung works. From these simple materials and operations come elaborate structures and tightly controlled designs. Chou’s modal system governs every aspect of the composition, from rhythm to pitch to timbre, from background to surface, and from the tiniest details to the broadest gestures.

However, one should not come away with the misconception that this is just one other compositional system that minimize efforts by the composer. The three yao of an I Ching trigram puts the biggest importance on the middle yao, Man. There may be fixed natural laws governing Heaven and Earth, but Man makes the decision of what course of action among many to take.

In another light, Chou’s endeavor is in fact very close in spirit to what Johann Joseph Fux had done with his definitive textbook on species counterpoint: Fux’s effort was to explore the simplest, most fundamental ways each single-tone in counterpoint would proceed; Chou seeks the same, except that the scope is much broader. His is an effort that, with the help of the I Ching, gets at the most innate nature of each musical note, in a sense, the Tao of music.

By Kenneth Kwan, Ph.D.; from lecture delivered at the Chou Wen-chung Music Festival, Taipei, 2003