Vietnamese Modal Scales of the Dan Tranh

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Abstract
The dan tranh is a Vietnamese 17-string zither tuned to pentatonic modal scales. Each modal scale, or dieu, encompasses a given tuning and a specific sentiment or modal nuance, and ornamentation using pitch bends is an important embellishment. The dan tranh was tuned entirely by ear, and the repetition rate of the lowest-pitched string varied from G₀ to E₃ in data obtained during a 6-month period from a single highly skilled Vietnamese musician. The modal scales lie in two major systems, bac and nam, and the frequency ratios of the tonal materials comprising the scales were measured. Using a standard categorization experimental paradigm, the musician was unable to categorize intervals in the absence of musical context. In a probe-tone rating experiment, the musician was asked to contemplate the sentiment associated with a particular modal scale, and evidence was found that was suggestive of an internalized hierarchy that differed between the two modal scales used as stimuli. Vietnamese modal scales make extensive use of a 166-cent scale step, which corresponds to $\frac{5}{3}$semitones.