Low-Frequency Characterization of Music Sounds -- Ultra-Bass Richness from the Sound Wave Beats

Abstract: The orchestra performance is full of sublime rich sounds. In particular, the unison of violins sounds different from the solo violin. We try to clarify this difference and similarity of unison and solo numerically analyzing the beat of violins with timbre, vibrato, melody, and resonance. Characteristic properties appear in the very low-frequency part in the power spectrum of the wave amplitude squared. This ultra-buss richness (UBR) can be a new characteristic of sound on top of the well-known pitch, loudness, and timbre, although being inaudible directly. We find this UBR is always characterized by a power-law at low-frequency with the index around -1 and appears everywhere in music and thus being universal. Furthermore, we explore this power-law property towards much smaller frequency regions and suggest possible relation to the 1/f noise often found in music and many other fields in nature.