The vibrating air mass is ONE variable and a major variable, not
the variable that completely describes the behavior of a tuba. OK, now you've made me do it, cite the concrete math, physics and philosophy in the matter. Go read the treatise, "On the Sensation of Tone," by Hemholtz. All three plus inches thick of it. I have.
Who is Hemholtz?
http://www.ilt.columbia.edu/projects/bl ... holtz.html
The treatise addresses all aspects of musical tone, and explores not only the physical aspects of sound waves, but the psychoacoustic phenoma associated with music, such as how we perceive pitch, overtones, non-harmonic transients (of which the alloy in a tuba contributes to), difference and summation tones, masking, and a plethora of other issues.
And in regard to this issue and other physical issues, everyone on the TubeNet needs to read this:
http://www.rosslg.com/works/WebNotes/Sy ... stems.html
Because the bottom line (pun intended) is that 99% of the people "dereference," as this thesis puts it. To put that in everyday English, it's like the witch-duck scene in Holy Grail, where the loudest guy yells "witch" or "duck" and everyone else goes along, instead of analyzing what is really there to determine the real question.
Granted, it is easy to say, "I see no difference, I hear no difference, I feel no difference, therefore, there must not be a difference." But this does not take into account limitations in human senses. It is not that far removed from the next statement in that vein that a deaf person might say watching a person who is speaking at a far enough distance away that they cannot see their lips move: "I see no difference, I hear no difference, I feel no difference, therefore there is no such thing as sound." The precepts are the same, the conclusion, though different, is of a similar dereferenced conclusion, instead of the true scientific method, which can be expressed thus: "I see no difference, I hear no difference, I feel no difference. There are multiple inferences here: 1) There actually is no difference, but that is inconsistent with data (in this case, the alloy), which has at least one variable of measurable difference, 2) There is a difference or differences, but not measurable with the current reference, or 3) some other factor(s) is(are) either overriding the differences or truncating their effect, or 4) some combination of 2 & 3."
Inference #1 is not viable as it does not take into account all the data, and #s 2 & 3 must be explored further in order to discover what has not been quantified or qualified as yet, and further to see if the question is actually more complex, as is usually the case, or #4. Ironically, even the best scientists and logicians do not always keep #4 open. This is either because of insufficient data, or not enough dots to draw the correct line, so that several lines and shapes will all go through the same dots, which only causes argument based on 1st tier observation, and is counterproductive to further research, and which is accounted for by an alternative inference, or by the natural urge to focus on a particular inference, which can transform the objective into the subjective, nullifying the quality of further research as the encroachment of subjectivity self-actuates conclusions. Just look at any pharmaceutical company "study" on one of their products for proof of that.
In other words,
everything makes a difference. The real question is objectively how much difference, so a determination may be made as to whether or not that difference is noticable, and then if it is noticable, then whether or not it is significant or not as evaluated by even another layer of subjective criteria, a second step removed from the actual process.
I have at this point blown enough through my brass.