Modal scales of the Dan Tranh

The Dan Tranh is a Vietnamese 17‐string zither tuned to pentatonic modal scales. Each mode encompasses a given tuning and a specific mental expression 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 G3 to E4 in data obtained over a 6‐month period from a single artist (P.N.). The octave stretch was approximately 13 cents over 3 octaves with most of the increase in the upper octave, and was subtracted out to define a mean modal tuning. The intervallic distances and standard deviations in cents relative to the tonic of each mode are: Bac = [0, 188 ± 7, 500 ± 9, 698 ± 7, 891 ± 4], Ho Mai Nhi = [0, 166 ± 10, 513 ± 5, 695 ± 9, 859 ± 9], Oan = [0, 338 ± 9, 503 ± 6, 699 ± 6, 1026 ± 15], and Vong Co = [0, 375 ± 13, 519 ± 8, 704 ± 10, 866 ± 6]. The octave stretch and tuning variability are smaller than comparable data obtained in Western and other music cultures. The Vong Co ...