Posted by Rick Denney on November 27, 2002 at 14:34:09:
In Reply to: What's the lowest non-pedal you can hit? posted by Tom Eshelman on November 27, 2002 at 11:14:13:
Let's forget the physics for a moment and see if we can figure this out without knowing it.
Leaving the tubes where they belong, all four valves gives you how much? Well, let's think about that. First valve moves you from F to Eb on the same partial, so it adds about 19" (pretty close to the difference between an F and an Eb tuba). The second valve is about half of that. The third valve is about the same as the first two put together. So, the three valves give you about 57 inches. The fourth valve moves you from F to C, and therefore should be about the difference between an F and a C tuba, which is a little over four feet, say 52". The second and fourth valves, added together, total a touch over 60", which is longer than the sum of the first three (this is the valve swindle). Adding them all together, you get about 109", or an inch over 9 feet. If you add that to a BBb tuba, you get a 27-foot tuba. A C fundamental requires about a 16-foot tuba, but playing that C on the second partial theoretically requires twice that--about 32 feet. So, your four valves can't even get you to the theoretical low C. You end up trying to lip it down tremendously, which is why it's so dang hard to play. The typical long-whole-step fifth valve isn't really even enough to fill that gap completely without lipping, though it is long enough to lower a FF to an EEb, which is about three feet.
This arithmetic isn't at all precise, but it uses the notion that your valves convert your BBb bugle into another kind of bugle, which can be compared to the nominal length of that other instrument.
It gets really complicated when you read Fred Young, and discover the possibility that the so-called fundamental isn't even where you think it is. The tuba is not a tube closed on one end--it is open on both ends. The math isn't like a guitar string multiplied by 2. He claims tests that indicate the so-called false tone is the true fundamental of the instrument. On your 24J, you can play the low Eb open as a false tone, then add valves in the normal way (I know that's not what you asked).
Here is what you asked: I can play my four-valve BBb tuba down to a very sharp C-ish. I can play my five-valve F tuba down to a sharp Gb, which is fairly easy to lip into tune.
Rick "finding an excuse for the inability to play well in tune just above the fundamental" Denney