Multidimensional acoustical and psychoacoustical aspects of inharmonic plate and bar tones of real and resynthesized instruments
Edward C. Carterette, Roger A. Kendall · The Journal of the Acoustical Society of America · 1999
Following a brief review of the mathematics of inharmonic plates and bars, the acoustics and comparative psychoacoustics of the tones of Indonesian bars and plates are considered. Tones were derived from real instruments of the UCLA Department of Ethnomusicology’s Javanese and Balinese gamelans, and from resynthesis of spectral analyses of instrumental tones. The comparative psychoacoustics of the tones was assessed by a number of methods, including JNDs, ratings by MDS similarity-scaling, and verbal-attribute magnitude estimation. Several methods were used to converge on the general perceptual and cognitive properties of the tones. Illustrative findings are: It was shown (1) that Indonesian gamelan makers can and do tune their metallophones in stretched octaves. Their stretchings (1.02 to 1.05 times the normal octave) were fit by a mathematical model which was derived from the data of many gamelans. (2) That the perceptual dimensions of Indonesian and Balinese gongs were interpreted as pitch, ombak (beating), and volume. These dimensions can be mapped to frequency, amplitude modulation, and spectral envelope. It was concluded that gong makers can modify the plates to achieve desired physical properties and correlated perceptual dimensions. One important finding is that the relative positions of two close axially symmetrical modes control the ombak rate.