We look at three examples of Chinese folk songs. They illustrate that hierarchical structure and dialectical development are found in the music of non- Western cultures.
Example 1
This example illustrates that the Multiresolution Principle of hierarchical structure of time-frequency patterns applies to non-Western music. First, play this clip of a Chinese folk song (it is a bit noisy):
Here is the spectrogram of the Chinese folk song:
We have drawn rectangles around several similar structures that are repeated at multiple time scales (by sliding your mouse cursor over these rectangles, starting with the smallest one at lower left), you can read our commentary on the roles played by these structures in the musical passage). The structure at the lower left is the smallest time-frequency structure (P1), a brief pitch excursion. The next enclosed structure, to its upper right, is a larger scale version of a rotation of P1, we call it P2. Finally, most importantly, the largest rectangle on the lower right side of the spectrogram, is a hierarchical structure (P3) composed of multiple repetitions of P1 and P2. The structures P1 are repeated in an ascending linear arc, topped off by (a slightly smaller scale) repetition of P2, and then followed by a faintly discernable (but clearly audible) descending linear arc of repetitions of brief single pitches (repetitions of the structure that precedes P2). The combined pattern of these two linear arcs (or contours) is a large scale version of the two linear arcs that make up P2. The structure ends with a repetition of P2, almost as if to emphasize this last point. Please choose one of the options below to play a video, and see if it confirms our analysis of the passage.
AVI (best quality, but large size) RAR archive (decompress to view the AVI) MPEG (most compatible, lower quality)
A second part of the song, reveals a similar spectrogram structure:
We again have the hierarchical patterning of the triangular shaped structures, but this time the inversion that follows the largest scale triangular structure is more fully developed.
Example 2
For this folk song, we show a spectrogram from a passage in the figure below:
We have marked several hierarchies of triangular shaped structures, at multiple time scales. There is also an inversion of the triangular structure at the conclusion of a prominent one (marked by the arrow). The structure on the far right is a longer time-scale version of this type of triangular structure, with some embellishments.
Example 3
For this folk song, we show a spectrogram from a passage in the figure below:
In the two rectangular boxes we
have enclosed triangular structures: in the left rectangle, the notes
are played by a chiming instrument, while in the second they are repeated
(with some embellishment and at a lower pitch) by a flute. Within the
ovals we have enclosed two structures that are repeated (with variation)
at different time-scales. The prominent vibrato of the flute
playing is also clearly displayed in this spectrogram.
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