ASSESSMENT OF MUSICAL QUALITY OF TANPURA BY FRACTAL-DIMENSIONAL ANALYSIS
R. Sengupta, Nilanjan Dey, Asoke Kumar Datta, Devlina Ghosh · Fractals · 2005
Tanpura is a multi-stringed accompanying drone instrument extensively used in classical music in India. The instrument is plucked by finger. We know that jitter, shimmer and complexity perturbations (CP) are found also in tanpura signals. The source of origin of these perturbations was reported to be related to some sort of nonlinearity associated with the strings and their mode of attachment. The objective of the present study is to see in what way fractal-dimensional analysis may be helpful to relate the apparent nonlinearity and also if there is any relation of these dimensions with different part of the signals like attack time, quasi-steady state and the decay. In the paper fractal dimension, D0 and generalized dimensions, D2 to D10 and their dynamic behavior over time are studied for 15 tanpuras having four strings each, tuned to Pa (5th note), Sa (tonic), Sa (tonic) and Sa′ (lower octave tonic). The obeying of power law indicates nonlinearity in the production source system. The presence of multifractality is studied through an examination of relationship between q and Dq and the functional relationship between Dqs.