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My current understanding is that if a sound has a pitch it must be periodic, i.e. it is composed of sound waves that have frequencies. So I assume that means there must be a fundamental frequency.

Also, I assume that no sound which is not periodic will have a pitch or a fundamental frequency.

Please let me know if I'm wrong about any of this.

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    $\begingroup$ You will perceive a distinct "pitch," and a spectrogram will show distinct peaks, if you listen to a mix of some pure musical tone with white noise, but because of the noise component, the waveform will not be a periodic function. $\endgroup$ Aug 6 '20 at 18:05
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I'm not aware of any purely physical notion of "pitch". Pitch has something to do with physical frequencies but also how your brain perceives the sound. The overtones accompanying a fundamental frequency, if any, may influence the perceived pitch in a way similar to how a given color (say, a single frequency of light) may appear different depending on what colors are around it. You can also get cases where two pure frequencies played together are perceived as more than two pitches, which I think gets at your question more directly.

Pipe organs might be a particularly interesting instrument to check out for this type of question. For a single pipe, pitch is primarily determined by length, but the organ is usually designed with stops that allow multiple pipes to be played together on the press of single key. There are different schemes for choosing the stops to alter the subjective qualities of the music played, including but not limit to dealing with pitch.

The so-called "missing fundamental" is a more precise example, which is used among other places in organ design to extend the range of pitches that a listener experiences without including longer and longer pipes. When the overtones are present, the mind will fill in the fundamental even though it is not physically produced.

Some more information here: https://en.wikipedia.org/wiki/Pitch_(music)

And here: https://en.wikipedia.org/wiki/Missing_fundamental

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All sounds are composed of periodic waves, but if there are too many frequencies and not a single one prevails , you will not hear it as a sound, but as noise . So you are right, to have a pitch you have to have a prevailing frequency .

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  • $\begingroup$ You seem to say that audible noise is not sound. I'm not sure that many people would agree with that. $\endgroup$ Aug 6 '20 at 18:08
  • $\begingroup$ should I have said a musical sound? $\endgroup$
    – trula
    Aug 6 '20 at 18:14
  • $\begingroup$ For a "musical sound" you don't always need to have the fundamental at all. The brain will fill it in in some cases: en.wikipedia.org/wiki/Missing_fundamental $\endgroup$
    – Brick
    Aug 6 '20 at 18:49
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    $\begingroup$ Real musical sounds often do not have constant amplitude (e.g. an acoustic guitar) so the idea that "sounds are composed of periodic waves" is probably too simple. Also, the sound of a bell for example will contain frequencies that are not simple multiples of each other, but the combination does not sound like "noise". $\endgroup$
    – alephzero
    Aug 6 '20 at 18:53
  • $\begingroup$ On an equal-tempered scale, the frequencies of the notes do not differ by ratios that are rational numbers and the waveform of the sum of two notes will not be periodic. So this is not even true for musical sounds. $\endgroup$
    – user137289
    Aug 6 '20 at 21:57

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