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 |