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Table 3 Results of fitting a regression line to the scatter plot between log10V and log10L, as \(\log _{10} V =\log _{10} K + \alpha \log _{10}L\) (Heaps’ law), with correlation coefficient ρ. The value of \(\sigma _{c}\) is also shown. Three cases are compared: composers with transposition (our main case of study), composers without transposition (for the sake of comparison), and individual pieces (for which transposition has no effect on L and V)

From: Heaps’ law and vocabulary richness in the history of classical music harmony

Dataset α log10K ρ \(\sigma _{c}\)
authors, transposed 0.35 ± 0.05 1.47 0.64 0.25
authors, no transposed 0.35 ± 0.05 1.53 0.67 0.23
pieces 0.659 ± 0.004 0.31 0.85 0.19