TubeNet

I don't recall where I received this information. Every once in a while the subject regarding the length of tubing required for tubas comes up so I thought I would throw this out to the forum. Anyone care to comment on the accuracy of this information?:

F2 = 393.2 cm - 154.8in - 12.9ft
E2 = 416.6 cm - 164in - 13.67ft
Eb2 = 441.4 cm - 173.78in - 14.48ft
D2 = 467.6 cm - 184.1in - 15.34ft
Db2 = 495.4 cm - 195in - 16.25ft
C2 = 524.9 cm - 206.65in - 17.22ft
B1 = 556.1 cm - 218.94in - 18.24ft
Bb1 = 589.2 cm - 231.97in - 19.33ft
A1 = 624.2 cm - 245.74in - 20.48ft
Ab1 = 661.3 cm - 260.35 - 21.7ft
G1 = 700.6 cm - 275.83in - 22.99ft
Gb1 = 742.3 cm - 292.24in - 24.35ft
F1 = 786.4 cm - 309.6in - 25.8ft
E1 = 833.2 cm - 328.03in - 27.34ft
Eb1 = 882.8 cm - 347.56in - 28.96ft
D1 = 935.2 cm - 368.19in - 30.68ft
Db1 = 990.9 cm - 390.12in - 32.51ft
C1 = 1049.8 cm - 413.31in - 34.44ft

BBb Tuba 18 ft. open pipe
CC Tuba 16 ft. open pipe
F Tuba 12 ft. open pipe
Eb Tuba 13.5 ft. open pipe
Bb Euph/Tenor Trombone - 9 ft. open pipe

Matt Higgins wrote: I am wondering how the B-flat tuba is 18ft long yet the length for B-flat1 is 19.33ft???

I questioned that, too! It might have something to do with a major portion of the bore being conical. Maybe someone can enlighten us.

Matt wrote

I am wondering how the B-flat tuba is 18ft long yet the length for B-flat1 is 19.33ft???

The air column does not suddenly stop at the bell. It enlarges gradually, with the result that the region of reflection (which determines pitch) is a few inches (very roughly the radius of the flare) past the end of the bell. This is called, fittingly, "end effect". It also is slightly different for each overtone, contributing to the challenge of playing in tune.

Don S.

DonShirer wrote:The air column does not suddenly stop at the bell. .... with the result that the region of reflection (which determines pitch) is a few inches (very roughly the radius of the flare) past the end of the bell.

And this difference can be as much as one foot four inches as in the case of BBb horn??

few inches (very roughly the radius of the flare) past the end of the bell.

As I understand it this refers to the FLARE, not the BELL. That is, the ratio at which the diameter of the tubing increases as it approaches the bell. This is not a somewhat constant slope as in the rest of the body, but rather resembles the graph of an e^x or x²-function. VERY old German tubas used to have close to no flare at all, increasing that flare radius to infinity. (well, not really infinity because there is SOME flare, but you get the idea).
A sousaphone´s bell will be on the other extreme, the flare radius being much SMALLER than the bell radius.
So, given DonShirer´s information, a sousaphone should have a slightly greater tube length than a tuba. (Could anybody please support / contradict this theory ?)

Maybe this can add to the American vs German sound discussion: from what I´ve seen, American style tubas seem to have much smaller flare radii than German style horns.
(Just compare those pics of a 5/4 Rudolph Meinl in a recent thread to the York or Holton BATs . It´s like comparing German rotaryand American piston flugelhorns. With those bell designs it´s the other way around (German style fl-horns tend to have smaller flare radii), and there is a noticeable difference in sound. (I can tell because I used to play both types at the same time).
Hans

Those numbers appear to be the approximate length of open ended organ pipes for particular pitches. The fundamental frequency of an open ended organ pipe is approximately F=C/2/L where F is the resonance frequency, C is the speed of sound and L is the length of the pipe. Alternatively it could be written L=C/2/F. There is also an end correction added to the lenght, something like 1/3 the diameter of the pipe because the transition of the sound from the pipe to the air outside is not instantaneous. The speed of sound is 13500 inches per second or thereabout, divided by 2 is 6750, and divided by the frequency of A1 (27.5Hz) gives a length of 245.45 inches. Thats close enough to the 245.74 listed in the table for me.

A conical pipe closed at the small end resonates at the same frequency as an equal length open ended cylindrical tube, but a tuba is neither of these and its resonance frequency is just a little different.

-Eric

Matt Higgins wrote:I have no idea about the accuracy, the the information looks very interesting. I am wondering how the B-flat tuba is 18ft long yet the length for B-flat1 is 19.33ft???

It's the bell effect. The shape of the bell creates a variation in the length of reflection for each frequency, such that the effective length of the instrument is generally thought to be about two-thirds of the effective bell diameter beyond the actual opening. The shape of the bell flare will affect this significantly. My Miraphone, for example, is about 17" shorter than the 19.33 "official" length of a resonating BBb tube.

But the effect of the bell is only part of the story. The problem is that these numbers are based on a formula that applies to closed-end straight tubes of constant diameter. The shape of the bell departs from that assumption, but so do many other things.

The numbers derive from the speed of sound. When you make a pulse, the pressure front travels through the instrument at roughly the speed of sound, run into a zero-pressure "wall" at the bell opening, and then reflecting back a vacuum pulse. That vacuum pulse helps pull the next pressure pulse through the lips, to sustain the buzz. This is resonance--when the pressure and vacuum pulses are in synch and don't cancel each other out. The speed of sound is about 1115 feet/second, which means that the pressure front from a pulse will reach the end of the tube in 1/58th of a second on a BB tuba (1115/19.3). The vacuum pulse returns to the lips in another 58th of a second to help pull the next pulse from the lips. Then, THAT pulse reaches the bell yet another 58th of a second later. So, you have two pulses exiting the bell 2/58ths of a second apart, the first one being 1/58th of a second after the player's lips first parted. That's a pulse every 26th of a second, or 26 pulses per second, or 26 Hz, which is a pedal Bb.

But lots of things affect the reflection and the speed of the pulse. The wall of the tubing pulls at the air, slowing down the pulse for the air right up against the wall. The more twists and turns you have, the more the pulse is affected by this friction. The expanding taper causes some harmonics of the pulse to escape without reflection, and others to be reinforced, changing both the character of the sound and the alignment of the partials for when you are buzzing at a rate higher than the pedal. All that friction means that the air gets to the opening a little later than we would expect at the speed of sound in free air, with the result that the end of the tube has to come a bit sooner or the pulses will be too far apart.

Rick "who thinks the 'bell effect' is really a general correction for that particular instrument configuration that includes the effect of the bell" Denney

tubeast wrote:As I understand it this refers to the FLARE, not the BELL.

It's actually the taper design, which includes everthing about the conicity between the mouthpiece and the opening at the bell.

A couple of good books on the subject are Benade's Horns, Strings, and Harmony and Fletcher and Rossing's Fundamentals of Musical Acoustics. In those books, you'll find that the taper design is a modification (reached by empirical refinement rather than by calculation) of a Bessel function, with particular constants.

Rick "think that it's both the flare and the bell" Denney

UF_pedal_tones wrote:

tubeast wrote:(I can tell because I used to play both types at the same time).
Hans

YOU CAN PLAY TWO TUBAS AT THE SAME TIME?? WOW!

i really need to get in the practice room....

hey....I can play two trumpets at the same time!! It sounds terrible but is possible. Two tubas....you'd have to have a REALLY big mouth to do that!!

MA

Rick Denney wrote: The shape of the bell creates a variation in the length of reflection for each frequency,
Rick "who thinks the 'bell effect' is really a general correction for that particular instrument configuration that includes the effect of the bell" Denney

more on bell shapes....since I have a cut bell (french) horn, I've had opportunity to try various bell flares on it. The horn manufacturer sells a variety of flares for it, of different metals (which do seem to change the sound) in medium, wide, and extra wide, with or without garland. The medium flare produces a bit of a tinny sound but the high notes lock a little better than the wide. The wide bell produces a more focused sound, however. And I tried a flare from a different manufacturer that happened to have the right screw ring on it....and it locked in the notes far better than either of the other flare shapes, although the sound was slightly less focused than the wide flare. In January someone tried my flare (I bought the other manufacturer's, a Lawson) against his wide flare, and he was amazed. It was noticible how much easier it was for him to hit the notes in the high range (the clams were far fewer on a piece he knew well, switching back and forth.)

A friend also changed out the bell on his recalcitrant F tuba and found that the low range worked better.

There must be a lot of math to bell flares.

MA

Rick Denney wrote:
The numbers derive from the speed of sound. When you make a pulse, the pressure front travels through the instrument at roughly the speed of sound, run into a zero-pressure "wall" at the bell opening, and then reflecting back a vacuum pulse. That vacuum pulse helps pull the next pressure pulse through the lips, to sustain the buzz. This is resonance--when the pressure and vacuum pulses are in synch and don't cancel each other out.

Positive and negative pressure pulses do cancel each other out, though. A positive puff from the lips needs to coincide with a positive wave returning from the horn so that they add together and a stronger positive wave shoots back into the horn. When the negative wave returns from the horn the lips need to be closed.


-Eric

TubaSTL wrote:

MaryAnn wrote:In January someone tried my flare ... against his wide flare, and he was amazed.

This one caught me a little funny. I know, I know, it's out of context ... which tells you exactly where my mind is.

Maybe the two flares will produce more Baby Bells??

MA

Shockwave wrote:Positive and negative pressure pulses do cancel each other out, though. A positive puff from the lips needs to coincide with a positive wave returning from the horn so that they add together and a stronger positive wave shoots back into the horn. When the negative wave returns from the horn the lips need to be closed.

We are both right, really, but describing different things. The returning vacuum pulse (what I was describing) helps pull open the lips, so that the pulse that issues forth lines up with the returning pressure pulse (as you describe). Without the effect of the returning vacuum pulse, it is very difficult to sustain a buzz or make the instrument speak.

The timing of the assistance provided by the returning vacuum pulse and the immediately subsequent stacking of the new pressure pulse on top of the returning pressure pulse is controlled by the impedance of the mouthpiece and lips. That's why tubas have big mouthpieces and trumpets have small mouthpieces. If the mouthpiece (or embouchure) encourages the new pulse to come just a little early after the vacuum boost, it will drive the pitch up. If the mouthpiece and embouchure don't respond quite quickly enough, the pitch will sag. That's why big mouthpieces tend flat and small mouthpiece tend sharp even on the same instrument.

Rick "thinking that there's nothing completely predictable about pitch on a tuba" Denney

Rick Denney wrote:"thinking that there's nothing completely predictable about pitch on a tuba"

In trying to be witty, I think you've hit the nail square on the head with that comment

All this stuff about positive and negative pulses....reminds me of last January watching a performance with a bunch of horns and tuba at a workshop. The tuba was on a low D or something like that, and he was moving the valve slide in and out several inches...the pitch stayed the same, and I presume he was trying to make it "feel" better, resonate better, through changing the length of the tubing.

MA

bloke wrote:... If it was indeed low D, and he was playing a C tuba while (typically) moving the 1st valve slide, that makes perfect sense.The fingering for low D is "everything but 1st valve".

"Everything but 1st valve" would work for the low D on a 5-valve CC (i.e., 5-2-3-4) ... on a 4-valve (like mine) it's "everything plus pull the 1st valve slide almost out of the horn"! It might also have been a BBb -- 2-3-4 on one of those would give you a low D.