Harmonics Question: How Can Harmonics Be Present?

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The discussion centers on the concept of harmonics in relation to a string instrument's fundamental frequency. It clarifies that while the fundamental frequency defines the note being played, real instruments produce a combination of frequencies, including harmonics. The presence of harmonics arises because strings are not ideal, meaning they can vibrate in multiple modes simultaneously. This results in a complex sound, where even a note like middle C (261.6 Hz) can include higher harmonics (523.2 Hz). Ultimately, pure notes are theoretical, as actual instruments always generate a mix of frequencies.
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I have a question about the following text:
upload_2015-3-1_9-41-20.png

In the red section, if I understand correctly, they're saying that if on a string, there is a musical note being played, the frequency that the note is being played at is called the fundamental frequency. But, if it's at its fundamental frequency, how can there be other harmonics present?
 
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I think two elements play a role: the string is not ideal, you are not able to excite ONLY the fundamental mode (when you apply a force to the string, that force has Fourier components also at higher harmonics).
 
ThatDude said:
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In the red section, if I understand correctly, they're saying that if on a string, there is a musical note being played, the frequency that the note is being played at is called the fundamental frequency. But, if it's at its fundamental frequency, how can there be other harmonics present?
No, they say that the note being played is considered to be the one corresponding to the fundamental frequency. If you have a combination of 261.6 Hz and 523.2 Hz, you consider it to be middle C.

As matteo137 said, a pure note is never played on a real instrument.
 
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