2 ms·

"The inharmonicity disappears when the strings are bowed, but is more noticeable when they are plucked or struck. Because the bow's stick-slip action is periodi

• boomlinde 8y ago
  That's true by a limited definition of inharmonicity. Maybe it is perfectly harmonic in a musical sense. In reality any audible tone with a slow timbral change will have sub-sound, inharmonic undertones. Depending on the context that could or might not matter in practice. For example, the sub-audio harmonics of a trombone might not matter if I'm just listening, but if you ever record a trumpet you'll know that the pressure at the bell has a low frequency bias that might affect the recording in a significant way, simply because the air entering the system through the mouthpiece largely leaves through the bell. The paper only takes overtones into account. There is also no such thing as a steady-state for a person blowing or bowing. The paper you linked to discusses the ideal conditions for mode locking, but does not assert that these are ever actually satisfied during normal play. It is only for an idealized bow action that the stick-slip is actually perfectly periodic. It is clearly not the intent of the paper to assert that bowed instruments are somehow inherently perfectly harmonic (if nothing else for language like "slightly", "large", "noticeable" and "sufficient" without further specification) but to provide a theoretical framework for discussing this effect and the conditions under which it occurs. This is noted at the end of the discussion section as well.