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How is pitch related to frequency.? If there is a pitch for a fundamental frequency, will that pitch be same for harmonics?

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For a single note (as compared to a chord) there is only one pitch.

The sound typically consists of a fundamental and some harmonics. For example, you play the open A string (note = "A2") on the guitar you will get 110Hz, 220Hz, 330Hz, 440 Hz, 550Hz, etc.

Pitch is mainly determined by the spacing of the harmonics. So if you were to hear the frequencies 220Hz, 330Hz, 440 Hz, 550Hz, etc. you would still perceive the pitch to be an "A2" (corresponding to 110Hz) despite there being no energy at 110Hz.

A different way to think about it is periodicity in the time domain. Pitch is determined by the repetition rate of the time domain waveform, provided the repetitions are "similar enough".

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    $\begingroup$ Strictly speaking, for instruments like a plucked or struck string, or a struck bell, the sound will consist of (possibly) a fundamental, an overtones which are close to, but may not be exactly on, multiples of the fundamental. A single note on a wind instrument such as a clarinet, trumpet, or pipe organ is much more likely to have true harmonics that are exact multiples of the fundamental. $\endgroup$
    – TimWescott
    Jul 10, 2022 at 16:17
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    $\begingroup$ @TimWescott How so? Harmonics of a string are integer multiples of the fundamental since the wavelengths are integer dividers of the string length. In fact, you check the intonation of the guitar by comparing a fretted note to the first harmonic of the open string (by suppressing the fundamental of the open string). The tuning is often temperate (as compared to harmonic) but the overtones of a single note are still harmonic (at least to first order) $\endgroup$
    – Hilmar
    Jul 10, 2022 at 18:29
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    $\begingroup$ Basically, because a guitar string is not suspended from a perfect hinge at the bridge and the nut. Instead, the string acts like a spring on a cantelever mount. This results -- through some physics magic the details of which I have never worked out -- in the overtones being slightly sharper than the harmonics of the string's fundamental note, even though they're close. See this page, especially the section titled "Complications with harmonic tuning". $\endgroup$
    – TimWescott
    Jul 10, 2022 at 22:34

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