The 1215-Cent Octave: Convergence of Western and Nonwestern Data on Pitch Scaling
W. Jay Dowling · The Journal of the Acoustical Society of America · 1973
Ward [J. Acoust. Soc. Amer. 26, 369–380 (1954)] showed that Western listeners are extremely precise in making octave judgments with pure tones. Ward's listeners adjusted pairs of pure tones to subjective octaves that were slightly larger than a physical 2/1 frequency ratio (12 semitones or 1200 cents). Ward's data between 250 and 2000 Hz showed mean subjective octave sizes of about 1215 cents. The validity of Ward's procedure for establishing a scale of musical pitch was dramatically reinforced by the agreement between scaled octave judgments and absolute judgments by one listener with absolute pitch. Observations made on the tuning of instruments in several nonwestern cultures show good agreement with Ward's result of 15 cents/oct sharpening. For example, reanalysis of Hood's [UCLA Ethnomusicol. Inst. Sel. Rap. 1, No. 1, 28–48 (1966)] data on the tuning of Indonesian gamelans shows a 15.36 cent/oct sharpening. The results of all available precise measurements for widely divergent cultures are summarized. It appears that humans the world over make octave judgments with precision and that these deviate systematically from the 2/1 ratio in ways that must be explained by the structure of the auditory system. The present results enhance the universal applicability of Ward's pitch-scaling methods.