There is a strange phenomenon in music: a solo violin sounds beautiful, and three violins playing in unison sound sophisticated. However, if two violins play the same note, the sound can become unbearably grating. This isn't limited to violins; it can happen with any instrument playing the same melody simultaneously. My professor always advised never to have two oboes or two violins play the exact same melody; they should either be offset or play chords. Why is the duo the most problematic? Because it's impossible for two instruments to have identical pitch. For example, if one is at 440Hz and the other at 441Hz, they mathematically create a 'beat frequency' (F1-F2). That 'wobbling' sound you hear is this beat frequency. Even if their frequencies are identical, it can still sound bad due to the phase (φ). In reality, tiny variations like hand tremors, bowing speed, or breathing cause the phase to drift constantly, making it random. When two violins overlap, if the phase fluctuations fall within the range sensitive to human hearing (1-10Hz), we hear a pulsing, wavering, and unstable sound. The volume is constantly being cancelled out and reinforced by these random variables, leading to a thin, hollow, and plastic-like tone due to comb filtering on the overtones. However, with three or more instruments, the problem disappears. By adding a third violin, we have multiple phase differences (φ1-φ2, φ1-φ3, φ2-φ3). According to the Central Limit Theorem in statistics, as the number of these independent random variables increases, the fluctuations average out, making the sound distribution smoother and the system more stable. Thus, when three or more instruments play the same melody, the random fluctuations cancel each other out, resulting in a stable and pleasant sound.
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