Research->Music & Fluctuation->Issues in Analyzing Frequency Component
 Provides information about issues in analyzing frequency component.
Accuracy of Fourier Transform
Fourier transform is used as an analyzing method for fluctuation. Fourier transform is the algorithm that transforms any wave into combination of sine and cosine waves. However, it does not mean that a wave is precisely resolved into each frequency. For example, I have prepared a WAV file including only a sine wave such as the bottom figure.
Bottom left figure is the result by using the analyzing software.
 Result by analyzing software Ideal result
Regarding the result by analyzing software, the part where the mountain in the vicinity of the left end has risen is a frequency of the sine wave. If Fourier transform were able to resolve precisely, only the part of frequency of the sine wave would rise and the rest would be zero like the above figure of ideal result. Bottom figures are the result of analyzing the same WAV file by Audacity. Bottom left figure is displayed by the rectangular window mode and you can see that the graph is similar to the above figure on the left. Bottom right figure is displayed by the [Hanning] widow mode. Although the shape of the graph is different from the ideal result, the part distant from the frequency of sine wave indicates zero.  I could not  find the explanation of "Hanning" in the help of Audacity, but it seems that "Hanning" is a name of filter and is used for revising  the result.
Problems with Sample Number
As for the same WAV data, when the number of samples given to the calculation is changed for the Fourier transform, the data that have more sample numbers might be displayed in the shape that is close to "1/f Fluctuation". This is understandable, but on the contrary, there can be some cases that the data that have less sample numbers might be displayed in the shape that is close to "1/f Fluctuation".
(Following figures are not logarithmic graphs, they are the graphs in normal form.)
 Javanese Court Gamelan    Ketawang Puspåwårnå (Sample Number　2048) Javanese Court Gamelan    Ketawang Puspåwårnå (Sample Number　8192)
 Bulgarian Voice    夜の集会　 (Sample Number　2048) Bulgarian Voice    夜の集会　 (Sample Number　8192)
 Chopin    Etude (Sample Number　2048) Chopin    Etude　 (Sample Number　8192)
Does Fluctuation Reflect the Good and Bad of Music?
It is difficult for us to judge the good and bad of the music from just looking the graph of frequency component and its shape. The graph of frequency component indicates no more than degree of fluctuation. For instance, If you compare the result of analyzing frequency component of a certain music and the result of analyzing the frequency component of the same music when reversely played, you will get the same result. If fluctuation is something that grasps the good and bad of the music, every music should be ear-pleasing and relaxing regardless of playing reversely. But it is clear that fluctuation does not have such a role.