# Calculation of 1/f Fluctuation from Sound Signal and Comfort Evaluation
## 2 Calculation Method for Fluctuation Coefficient of the Sound Signal
### Music Selection for the Experiment  
We needed to select the most suitable music to consider the influence of the difference in fluctuation coefficients for human comfort. Therefore, we focused on classical music with many samples for the same melody and recordings by various performers. We selected unaccompanied classical music by playing one instrument that did not exist in various music parts, such as an orchestra and accompanying music, to clarify the factors that affect \(1/f\) fluctuation. In addition, we selected music playing only the cello, which is a stringed instrument. Using this instrument, it is structurally difficult to generate three or more notes simultaneously, in contrast to using a piano. We selected Johann [PERSON]: Cello Suites in this study considering the experimental condition above. The selected Johann [PERSON]: Cello Suites does not have existing original music notes. Therefore, tempo, volume, bowing, and accidentals are entrusted to the player's interpretation. Furthermore, we used the prelude of BWV1007, which is used as background music in movies, television shows, and commercials. Figure 7 shows the fluctuation coefficients for 15 players who played the prelude of BWV1007 from the Johann Sebastian Bach: Cello Suites. The results showed that all fluctuation coefficients were different for the same music depending on the players. On the basis of this result, we selected music A, which had the frequency fluctuation farthest from \(-1\), and music B, which had frequency fluctuations closest to \(-1\). In this experiment, we investigated the comfort that music with different fluctuation coefficients gave to a human using the sound signal of the same melody. In addition, the \(\lambda_{\text{f}}\) values of music A and B were \(0.0068\) and \(-0.982\). Figure 7: The \(1/f\) fluctuation coefficient \(\lambda\) of each fluctuation for each player. Experimental Consideration of Subjective Evaluation by Listening to Music including Different 1/f Fluctuation Coefficients  
Using the previous consideration of this study, we described the calculation method used for the fluctuation coefficient of the sound signal. Therefore, we experimented with the effects of sound signals with fluctuation coefficients close to \(-1\) on humans. In the experiment, we selected music A, with the frequency fluctuation farthest from \(-1\), and music B, with frequency fluctuations close to \(-1\). In addition, we conducted a subjective comfort evaluation using a questionnaire after playing music A and B to clarify the effects of sound signals with a fluctuation coefficient close to \(-1\) on humans. In this paper, we focused on the difference fluctuation coefficients of frequency, which represent the characteristics of the sound signal to assess the relationship between the calculated fluctuation coefficient value from music and human comfort [19]. We studied the fluctuations, including sound signals. Therefore, it was not the purpose of our study to clarify whether the slope of the spectrum of the sound signal was close to \(-1\). Figure 8 shows the experimental flow. First, the participants listened to music A and B. After listening to two pieces of music, the participant selected the most applicable option, as shown in Figure 9. In this experiment, the participant could listen to music A and B many times until the participant understood that music A and B were clearly different. We considered that this question could prove that music B, which had a coefficient of frequency fluctuation close to \(-1\), made the participant feel comfortable. (Listen to music A and B, and intuitively choose the one that best fits your mind.) (I felt that A was more comfortable than B.) (I felt that B was more comfortable than A.) (I felt that both A and B were comfortable or did not understand.) Participant selected the most applicable option  
Figure 8: Experimental flow. Figure 9: Question on comfort.