Modeling of piano string and analysis of piano tone using non-harmonic analysis

Previous studies have shown that piano string motion exhibits changes not only in the horizontal direction but also in the vertical direction, that this motion has different frequencies in each direction, and that the frequency difference between the two directions causes a beat tone. It is difficult to precisely analyze signals such as a beat tone signal that have imperceptible frequency changes using a traditional spectrum analyzer, for example, Discrete Fourier Transform (DFT). DFT does not have high frequency resolution and is influenced by a window function. We have studied non-harmonic analysis (NHA) as a timefrequency analysis method. NHA has a high frequency resolution without the influence of a window function. In this paper, we construct a model of the orbit of piano string motion displacement. Then, we verify the piano string motion using a high-speed camera (8000 frame per second). Finally, we analyze a piano tone of A4 to observe the characteristic of time-frequency changes using NHA. From the results, we assume that the piano string motion combines a large and small oval orbit in the cross-sectional direction, and this orbit transforms as time advances. Distribution of piano tone by DFT is unable to analyze timefrequency changes accurately enough, as some frequency spectrums appear around 440 Hz. Therefore, it was difficult to extract imperceptible frequency changes such as beat tone. In contrast, distribution by NHA analyzes imperceptible frequency changes correctly. We verified that the frequency changes slightly like a very small vibrato tone. We assume that this phenomenon is caused by piano string motion, and that the oval orbit is transforming as time advances.