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?
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.