TubaTinker wrote:iiipopes wrote:(Sigh!)... And it is not 25%. Do the math: it is the difference, for example of trying to get the combination of 4+2 to be in tune, between 2^(5/12) + 2^(1/12) of the open bugle length, which is all the tubing that is available without slide pulling on a conventional non-comp instrument, which this one is, and the added length of the comp tubes that bring it all the way to the necessary length of 2^(6/12) of the open bugle length [twelve semitones to the octave, each semitone being exponentially related by the function 2^(n/12), where "n" is the number of semitones down from open].....
Never mind the 'big sigh'!
YOU do the math! I'm talking about the difference between the fundamental Eb and BBb tuba.... it's roughly 13.5 feet as opposed to 18 feet. I think that equates to 25% off of the BBb open bugle.
Mashing that 4th button down has absolutely NOTHING to do with a compensating system. Even with a compensating tuba... that 4th valve is still a 1-3 combination. Get as technical as you want but it's still just a 4th valve.
Like Peter Birch mentioned... the question posed here is really not a sensible way to look at tubas (or any other valved instrument for that matter).
Dan,
That was my whole point - no, the 4th valve by itself and its own circuit not fed back through the block has nothing to do with the compensating system. But a 4th valve does add the extra tubing to get notes played by a 4th valve in tune, which are not in tune when played 1+3 without pulling either the 1st or 3rd slide to get them there.
I'm agreeing with you. We are just saying it different ways.
Sorry I ruffled your feathers. I didn't mean to. It's a complex issue. Here's the math:
Let's see: if an Eb tuba is about 13 1/2 feet long, or 162 inches long, then theoretically:
2nd valve circuit would be [162 * 2^1/12] - 162, or about 9.63 inches.
1st valve circuit would be [162 * 2^2/12] - 162, or about 19.84 inches, which is a little longer than twice the length of the 2nd valve circuit.
3rd valve circuit would be [162 * 2^3/12] - 162, or about 30.65 inches, which is longer than the 1st valve circuit and 2nd valve circuit together, which is only about 29.47 inches, so a pull of about 1/2 or so, totaling the difference of a hair more than an inch, is necessary to get 1 + 2 in tune if not using the 3rd valve alone, but keeping it pulled so 2+3 is in tune, which is what most players do, and how many older tubas were constructed. As a result of 3 being long, then 1+3 needed less lipping or pulling than on instruments where the 3rd circuit is of "dead" length, so you use 3rd alone, instead of 1+2. This is/was the case with 3-valve comp system instruments, including tubas, euphs, and baritones, which add the required tubing when 3rd is pressed in combination with either 2, 1 or both, since there is no 4th, so that 2+3 and 1+3 have the additional tubing through the comp circuit to be in tune.
4th valve circuit would be [162 * 2^5/12] - 162, or about 54.24 inches. Yes, 162 + 54.24 is 216.24 inches, which is about what the open bugle of a BBb tuba is.
This is where our misunderstanding may have occurred: of course, 54.24 is about 26% of 216.24. You were expressing it in relation to what an open BBb bugle would be, and I was expressing the individual valve slide lengths as combined in relation to the Eb open bugle.
I was also trying to say that the length of the 4th valve circuit, by itself, is the same, whether or not on a non-comp or on a comp tuba, because on a 4-valve comp, the comp loops only come into the circuit, of course, when one or more of the other valves are pressed in addition to the 4th valve.
Here's where my real point was: 1 + 3, without extra pulling, is about 162 + 19.84 + 30.65, which is only 212.49 inches of tubing engaged, which is significantly shorter than the full 216.24 inches necessary to get the note in tune, requiring not quite a 2-inch pull, on either 1 or 3, or some combination thereof, to get the full almost 4 additional inches necessary to get the note down to pitch and not be sharp without pulling or lipping.
Finally, to restate what I thought I was trying to explain, however inartfully, was that the lower notes below 4th valve need exponentially even much more tubing than that:
My example was that simply pressing 2+4 would be 162 + 9.63 + 54.24 inches, or about 225.87 inches of tubing engaged on a non-comp horn, but the pitch needs [162 * 2^6/12] or about 229.1 inches of tubing to get all the way down to pitch. So either 2 or 4 or some combination of each also needs to be pulled a significant amount on a non-compensating horn to bring the note down to pitch without lipping, and which, again, as we all know, is the purpose of the comp loops: to add this extra tubing by running the circuit back through the valve block.
Epilogue: all these are, of course, theoretical values, modified by the taper of the branches and everything else that goes into just how much tubing and in what progression of diameter and placement is required to get to the pitch. But hopefully this demonstrates my point.