4 ms·

Your statement is incorrect, which your provided source clearly acknowledges. Only idealized waveguides produce perfectly harmonic timbres. Idealized waveguide

Your statement is incorrect, which your provided source clearly acknowledges. Only idealized waveguides produce perfectly harmonic timbres. Idealized waveguides do not exist in nature. The closest thing we have to the sound produced by ideal waveguides is digital oscillators driven by a highly accurate clock playing back a single-cycle waveform. The result is close enough and is often described as an organ like sound.

mrob 7y ago
"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 periodic, it drives all of the resonances of the string at exactly harmonic ratios, even if it has to drive them slightly off their natural frequency." See: https://newt.phys.unsw.edu.au/music/people/publications/Fletcher1978.pdf https://newt.phys.unsw.edu.au/music/people/publications/Flet...
- boomlinde 7y 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.
ncmncm 7y ago
"Criteria" is plural. The singular is "criterion". I shall assume by the above that you will welcome the correction.

mrob 7y ago

"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 periodic, it drives all of the resonances of the string at exactly harmonic ratios, even if it has to drive them slightly off their natural frequency." See: https://newt.phys.unsw.edu.au/music/people/publications/Fletcher1978.pdf https://newt.phys.unsw.edu.au/music/people/publications/Flet...

boomlinde 7y 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.

ncmncm 7y ago

"Criteria" is plural. The singular is "criterion". I shall assume by the above that you will welcome the correction.