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I am doing a physics experiment researching the effect of temperature inside the clarinet pipe on the quality of its sound. I know that the speed of sound is directly proportional to temperature of the medium it propagates in, I can measure decibels, frequencies, air pressure, and have theoretical knowledge on the production of resonance in open pipes. But how can the perceived quality of sound be measured and analyzed?

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What do you mean by quality? A single frequency? Or steady amplitude? – user1717828 Jan 11 at 5:53
That comment made things more confusing. Before, I would have said the words you are looking for are "timbre" and "spectrum." But how does an instrument getting sharp as the temperature changes make it "worse"? Is it worse because it is no longer in tune with whatever reference you have? – Chris White Jan 11 at 8:43
I think this is more related to psychological than physics... consider researching about psychoacoustics. Otherwise, I agree with current answer that your approach is "going backward". – Andrew T. Jan 11 at 9:44
There's no physical quantity that defines "quality" of sound (well, except perhaps the price of the concert ticket). The usual way we do this in engineering is double blind trials of users followed by double blind trials of known/respected audiophiles (because audiophiles keep insisting that "regular" people can't appreciate how musical instruments are supposed to sound like and keep insisting on buying stuff like gold wire ethernet cables). – slebetman Jan 11 at 10:08
One example of such "user testing" is the trials involved in the development of the mp3 codec by Fraunhofer Institute. Basically, they figured out the transfer function of human hearing of songs by asking lots of people "does this sound good?" on various encodings of songs. – slebetman Jan 11 at 10:12
up vote 6 down vote accepted

This question is "turned upside down". The proper direction of research is:

$$ I \ can \ describe \ the \ percieved \ quality \rightarrow \ Let's \ seek \ for \ its \ physical \ (objective) \ description $$

not the other way.

At this point the question suddenly becomes very broad and will be closed probably. Generally: any measurements of intensity, pressure etc. will not provide you any "quality" as a physical quantity, at least without listening tests and a great deal of psychoacoustics.

There are some phenomena that would certainly lower the quality as unwanted impedance discontinuities in the clarinet tube, but you should study some literature first. This is, of course, a studied phenomenon. Try The Physics of Musical Instruments by Fletcher and Rossing and maybe Signals, Sound and Sensation by Hartmann.

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Thank you for the suggestions Victor Pira and your insight. It will certainly prove to be very useful. – Arthur Alex Karapetov Jan 28 at 21:06

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