Data-driven measurement of precision of components of pitch curves in Carnatic music

Carnatic music (CM) is characterized by continuous pitch variations called gamakas, which are learned by example. Precision is measured on the points of zero-slope in gamaka- and non-gamaka-segments of the pitch curve as the standard deviation (SD) of the error in their pitch with respect to targets. Two previous techniques are considered to identify targets: the nearest semitone and the most likely mean of a semi-continuous Gaussian mixture model. These targets are employed irrespective of where the points of zero-slope occur in the pitch curve. The authors propose segmenting CM pitch curves into non-overlapping components called constant-pitch notes (CPNs) and stationary points (STAs), i.e., points where the pitch curve outside the CPNs changes direction. Targets are obtained statistically from the histograms of the mean pitch-values of CPNs, anchors (CPNs adjacent to STAs), and STAs. The upper and lower quartiles of SDs of errors in long CPNs (9-15 cents), short CPNs (20-26 cents), and STAs (41-54 cents) are separable, which justifies the component-wise treatment. The CPN-STA model also brings out a hitherto unreported structure in rāgas and explains the precision obtained using the previous techniques.