Length versus Volume?

[Alex Reeder]

This has me slightly confused here. Is the only thing that affects the pitch of a tuba the length of the tubing? Remembering high school physics class, doesn't volume come into play? When you blow into a bottle to make a note, it is the volume that causes a certain pitch. What is the difference between this example and a tuba?

This is confusing because if volume did determine pitch, instruments with larger bores would have to be shorter.

6/4 tubas, I am assuming, have the same length as a 4/4 but more volume. What does this added volume do for the sound?

Does volume of air = volume of sound?

[Rick Denney]

This has me slightly confused here. Is the only thing that affects the pitch of a tuba the length of the tubing? Remembering high school physics class, doesn't volume come into play? When you blow into a bottle to make a note, it is the volume that causes a certain pitch. What is the difference between this example and a tuba?

This is confusing because if volume did determine pitch, instruments with larger bores would have to be shorter.

6/4 tubas, I am assuming, have the same length as a 4/4 but more volume. What does this added volume do for the sound?

Does volume of air = volume of sound?

To properly answer your question, I'd need pages and pages. Instead, I would recommend the book Horns, Strings, and Harmony and Fundamentals of Musical Acoustics by Arthur Benade. Both are available from Amazon.

The distance between nodes--pressure peaks--of a pressure wave define how often those nodes will strike the human eardrum at the speed of sound. The frequency of those impacts determines the pitch. The speed of sound is fixed by the nature of air. So, what affects pitch? Pitch is controlled by how often your lips blow apart as you buzz, which is what creates those pressure nodes in the first place. But try to buzz a pitch different than what the instrument will resonate, and you'll have real problems. Why is that? It is because the instrument naturally resonates at a given frequency.

When you send that pulse of pressure into the mouthpiece, it travels at approximately the speed of sound through the instrument. When it gets to the end, the pressure is brought to zero, because the opening of the pipe allows the pressure to dissipate. This sends a reflection back up the instrument, also at the speed of sound, which creates a vacuum in front of your lips just at the time they part again. Thus, if those vacuum pulses are timed to arrive at the beginning of the next pressure pulse, it will help you produce that pulse. This is why it is easier to buzz the note that the instrument is tuned to than any other note. The only thing controlling when that vacuum pulse gets back to your lips is how far it had to go back from the bell. That's why length is the only thing that determines basic pitch.

The volume of the instrument, taper design, bell diameter, moutnpiece design, and even how you hold your lips will all affect that resonance a little, which is why you can bend pitches. To put it even more technically, the final pitch is what remains of the noise of your buzz after it has been filtered by the impedance of your lips, the impedance of the mouthpiece, and the impedance of the tuba. Each has its effect, but they vary around the pitch controlled by the length of the bugle.

Each instrument design results in different filtration of overtones. Some instruments allow a mix of higher overtones, and others do not. The size and taper design of a tuba affects these results, and perhaps even the material and construction. Some really big tubas produce a dark sound (lots of emphasis in lower harmonics) and some produce a bright sound with lots of upper harmonics. Some of them sound deeper but still have all that upper harmonic information--these have a wide range of very well-tuned harmonics that suggest the fundamental to the listener through the differences in those harmonics. Tuba players describe these instruments as having a lot of "color". This is, I think, what most are seeking when they play the big instruments.

I'm not sure a big tuba is louder than a smaller tuba, depending on the design, but when played louder it avoids too much edge more effectively. I'm not sure my Holton is louder than my Miraphone, for example, but it surely has a deeper and fuller sound at the limit of my ability to push air through it. So, I would say that a bigger tuba creates a bigger sound, all else equal. (Of course, all else is never equal.)

Because of the ease with which some tubas resonate, even some big tubas, they can play more softly than other instruments. I can play my big Holton more softly than my Miraphone with a good tone, which is counter to expectations because of its size.

I'll bet that a narrow bottle of the same height as a wide bottle will ring at the same pitch. (I don't have any bottles on hand to test my bet.)

Rick "who thinks the dynamic balance of resonance can be strongly influenced by subtle changes in that balance" Denney

[Rick Denney]

With apologies I believe you're off the mark a bit on the bottle analysis....

Well, I'm glad nobody took my bet!

Rick "appreciating new information" Denney

[Rick Denney]

while I'm not expert on tuba construction, I can state that "volume" DOES impact the length of an organ pipe. Take middle C, a smaller scale (diameter) pipe will be longer than a larger scaled pipe to produce the exact same pitch. If anyone really wants proof and math, I can break out my Rensch slide rule and figure it out, but I'm tired right now.
Point is, if volume (see scale) impacts the length of an organ pipe, seems logical that it would also impact the length of a tuba "pipe".


Robert Coulter
AIO

While I have no doubt of what you say, I would warn that you cannot too closely compare straight organ pipes and tapered tuba bugles, especially with a bell flare on one end which attains some aspects of a bessel horn. The acoustics are remarkably different, particularly concerning the spacing and strength of overtones.

I did mention the bell effect, which, as a rule of thumb, is taken to be about 2/3rds the bell diameter. That's an estimate only because the shape of the affects it. The official length of a closed-end tube resonating BBb is 19.2 feet, but mot BBb tubas measure about 18 feet because of the bell effect.

My Holton has at much more volume than my Miraphone--at least a third more and maybe two thirds more--but it's basically the same length. And it plays the same pitches, even with me playing it, heh, heh.

Rick "wondering what the difference is in organ-pipe lengths with changes in diameter" Denney