In this study, the Fourier transform is used as the core method to systematically compare the mathematical properties of the Eastern pentatonic scale with the Western purely melodic pitch system and the differences in their vocal performances. The SWIPE algorithm is optimized by improving the Fourier transform to estimate the pitch of pentatonic scale. Based on the differentiated interval segmentation characteristics, the calculation method of the pitch score value of the pure law is deduced. Combining audio signal preprocessing and FFT algorithm, the harmonic structure and note recognition efficiency of the two types of meters are quantitatively analyzed. The study shows that the harmonic energy of the Eastern pentatonic scale is concentrated in the low-frequency band (50- 200Hz) due to the mathematical characteristics of the five-degree phasing law, and the note intervals are concentrated in the interval of 0.6s~0.9s, and the note recognition accuracy reaches 99%. On the other hand, the western pure melody is based on the frequency proportionality of the natural overtone column, and the peak boundaries of the envelope are not obvious, which leads to significant high-frequency harmonic interference, and the note misdetection rate rises to 2.5%. This study reveals the deeper correlation between the mathematical properties of the metrical system and vocal performance through Fourier transforms, providing a quantitative analytical framework for cross-cultural music theory.
