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Post new topic Odd Harmonics Are Flat on Plucked Strings
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Author Topic:  Odd Harmonics Are Flat on Plucked Strings
b0b


From:
Cloverdale, CA
Post  Posted 30 Jun 2019 9:50 am    
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https://newt.phys.unsw.edu.au/jw/harmonics.html



Very interesting...

Quote:
Strings and pipes are not inherently harmonic. An ideal, homogeneous, infinitely thin or infinitely flexible string has exactly harmonic modes of vibration. So does an ideal, homogeneous, infinitely thin pipe. Real strings and pipes do not. We saw in the experiment that adding a mass - making the string inhomogeneous - makes the string inharmonic. (By the way, worn or dirty strings are also inharmonic and harder to tune. Washing them can help.) For wind instruments, variations in bore diameter, the presence of tone holes and other perturbations mean that their resonances are inharmonic as well.

Real strings are also inharmonic because they are not infinitely thin or flexible, and so do not bend perfectly easily at the bridge and the nut. This bending stiffness affects the higher modes more than the lower, so the harmonics are stretched. Solid strings are worse than wound strings, steel strings are worse than others, pianos - especially little pianos - are worse than harps. 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. Thus the operating mode of a bowed string playing a steady note is a compromise among the tunings of all of the (slightly inharmonic) string resonances. (For the technically minded, this phenomenon is due to the strong non-linearity of the stick-slip action. It is called mode locking.)

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Earnest Bovine


From:
Los Angeles CA USA
Post  Posted 30 Jun 2019 10:21 am    
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Inharmonicity accounts for much of my irreverence to just intonation.
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b0b


From:
Cloverdale, CA
Post  Posted 30 Jun 2019 12:53 pm    
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Earnest Bovine wrote:
Inharmonicity accounts for much of my irreverence to just intonation.


Good point. When you're tuning your 3rds 14 cents flat (theoretically in tune as JI), odd harmonics flat of that are likely to be hard on the ears. It's a good argument for a less radical meantone temperament.
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Paul McEvoy


From:
Baltimore, USA
Post  Posted 30 Jun 2019 3:03 pm    
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Earnest Bovine wrote:
Inharmonicity accounts for much of my irreverence to just intonation.


Doesn't Paul Franklin change his strings every gig or something like that?
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Ian Rae


From:
Redditch, England
Post  Posted 30 Jun 2019 3:41 pm    
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Many players change their strings frequently, and a clean string is less imperfect than a dirty old one. But in the end there's no getting away from the science.
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Tucker Jackson


From:
Portland, Oregon, USA
Post  Posted 30 Jun 2019 4:10 pm    
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Also, don't wrap tape around the midpoint of the string like the scientist did in the article. Boom! Instant improvement in harmonicity.
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Charlie McDonald


From:
out of the blue
Post  Posted 1 Jul 2019 2:06 am     Re: Odd Harmonics Are Flat on Plucked Strings
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Quote:
Washing them can help.

I can't go out tonight; have to wash my strings.
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Donny Hinson


From:
Glen Burnie, Md. U.S.A.
Post  Posted 3 Jul 2019 7:09 am    
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I think it's probably safe to say that we cannot blame all the "clams", poor (improper?) intonation, and tuning problems/methods on "odd harmonics being flat on plucked strings".

Winking
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Ian Rae


From:
Redditch, England
Post  Posted 3 Jul 2019 8:35 am    
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All instruments have imperfections and it is our duty as artists to overcome them. If it sounds right, it is right.

[moderator please move to Philosophy section if desired]
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