Spectrographic Portamento Gradient Analysis: A Quantitative Method for Historical Cello Recordings with Application to Beethoven's Piano and Cello Sonatas, 1930--2012

Abstract

Portamento in string performance has been studied primarily as a binary presence-or-absence phenomenon, with existing research measuring frequency of occurrence and, less commonly, duration in milliseconds. This paper introduces a third quantitative descriptor; the spectrographic gradient of the portamento slide, measured in Hz/second, and demonstrates its measurement using a protocol combining Sonic Visualizer's melodic spectrogram layer, GIMP pixel analysis, and metric calibration against the spectrogram's known frequency axis. The gradient captures what duration alone cannot: the steepness of the pitch trajectory, which encodes the expressive character of the slide independently of its length. Applied to the opening measures of. Specifically because their monophonic texture permits reliable spectrographic pitch tracking. The method yields gradient values ranging from approximately 600~Hz/s in late-period recordings to over 4,000~Hz/s in early twentieth-century performances. The paper further documents a gain-recovery protocol that extends the analysable corpus to analogue recordings from the 1930s where portamento traces are faint in digital transfer. Applying the method to a corpus of 22 recordings spanning 1930--2012, the paper tests the hypothesis that gradient steepness correlates negatively with tempo: that slower performances produce steeper, longer slides while faster performances produce shallower slides or none at all. The results support this hypothesis, suggesting that the widely documented decline of portamento across the twentieth century is not a binary transition from presence to absence but a continuou