Chou Wen-chung
Chou Wen-chung’s modal system: the Basics
[continued]
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:
- one plus three units: _ x _ _ _
- two plus two units: _ _ x _ _
- 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.