Table 1.
The information of composers and their compositions.
Table 2.
Frequencies (Hz) of notes, each named by a scientific pitch notation with a letter-name and a number identifying the pitch's octave.
Figure 1.
Mozart-Eline Kleine Nachtmusik K.525.
Extracted from .
Figure 2.
The mean value of pitches for the five composers: 343.658 Hz (Bach), 435.448 Hz (Mozart), 416.332 Hz (Beethoven), 406.961 Hz (Mendelsohn), and 314.037 Hz (Chopin).
Table 3.
Statistical Analysis of the pitch fluctuations.
Figure 3.
CDF of pitch fluctuations in the log-log plot: (a) the positive tails and (b) the negative tails.
All the tails have a part in the power-law (or scale-free) distribution as indicated by the straight lines.
Table 4.
The parameters of power-law fits for cumulative distribution functions shown in Fig. 3.
Figure 4.
The power-law exponent for both the (a) positive and (b) negative tail.
decreases from Bach to Mendelsohn/Chopin [Note the horizontal coordinates corresponding to the five symbols in either (a) or (b) denote the birth years of the five composers from Bach to Chopin, respectively]. The lines are just a guide to the eye.
Figure 5.
The autocorrelation function of the absolute values of pitch fluctuations.
The horizontal coordinate indicates the time lag, , from 1 note to 50 notes, while the vertical coordinate indicates the value of
. It is worth noting that
is always positive. In this log-log plot, the five panels respectively show a straight line, suggesting a long-range correlation of notes for each of the five composers.
Figure 6.
The power-law exponent of autocorrelation function.
The five composers have different 's. Chopin has the smallest value while Mendelsohn has the largest although they were of the same era.
Table 5.
The parameters of power-law fits for autocorrelation functions shown in Fig. 5.