Pentatonic Transformations

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Pentatonic Signature Transformations in Chinese Music


The pentatonic scale (CDEGA) is fundamental to Chinese music theory, and so are the transformations from one pentatonic scale to another (Du 2019). Yet, the largely pragmatic labels for these techniques are as diverse as the musical contexts they appear in. Similar moves can be described using from a multitude of different perspectives, resulting in overlapping and sometimes confusing terminology.

The theory of pentatonic signature transformations uses the precise language of mathematical music theory to enrich, complement, and shed light on existing Chinese terminologies. The theory does so by making explicit the general principles that guide musicians and contextualizing pentatonic transformations in the entirety of possibilities.

Pentatonic signature transformations expand on the original (diatonic) signature transformations based on actual key signatures (Hook 2008). Despite the subsequent generalization from diatonic scales to other scales (Tymoczko 2013), specific cases differ widely in their application.

For the pentatonic scale, there are 60 different transformations (12 notes × 5 scale positions), four of which are basic:

chromatic Tn (CDEGA → GABDE),
pentatonic tn (CDEGA → GACDE),
bian bn (CDEGA → BDEGA), and
qing qn (CDEGA → CDFGA).

The bian and qing transformations are generalized sharps or flats adapted from classical terminology. Successive applications of them can generate all pentatonic forms under enharmonic equivalence. This paper showcases four applications of the theory. First, the theory of pentatonic transformations provides fresh ways of understanding and listening to well-known songs. Second, it disambiguates key relations in debates on key names (weidiao and zhidiao) and modulations (xuangong fandiao). Third, it clarifies qupai modulations, especially the complex thirty-five-key cycle (chaoyuan) in Northeastern Shawm-and-Percussion Music (Dongbei Guchuiyue) (Li 1985). Four, it sheds light on the highly chromatic music of Li Yinghai and Bright Sheng that use pentatonic transformations as an organizing principle.