Volume vs Length

[windshieldbug]

viewtopic.php?f=2&t=59842&p=500590 ?

[Donn]

I have a hunch that you could derive the pitch from some function of the wall profile - i.e., the length down the center line isn't the whole story.

Let's say you measure length W along the side, as well as C down the center line. Tubas with the same pitch will have different length C - and also different length W, but you will see a correlation such that as C gets smaller, W gets larger.

Volume isn't a function of W.

[windshieldbug]

viewtopic.php?f=2&t=23573&p=202001

[Dan Schultz]

viewtopic.php?f=2&t=23573&p=202001

Yeah. But..... what happens when you freeze and thaw it?

[Rick Denney]

Bore affects pitch, and the taper of the bore grossly affects pitch--and overtone tendencies. Length's independence from width is nominal--"in name only"--and is only true at the most simplistic level. The fast taper of tubas gives the characteristic sound in that it emphasizes some overtones and damps others, but it also creates a low resonance quality, which is "Q" to those who study the frequency domain. Low Q does not mean bad sound, and in fact it can mean a colorful sound. That low Q is why it's easy to bend the pitch, and on the most prized instruments without undermining the tone quality. The whole system is subject to a range of non-linear dependencies, which is why trial and error is still used for refining instrument designs.

Physically, the speed of sound, which is assumed to be constant, isn't, because the average density of air in the tuba isn't constant as the tube expands. The speed of sound actually changes in a tapered tube, which makes it impossible to use the straight organ-pipe model.

The notion that volume and length follow some specific (especially linear) relationship is false.

Rick "all models are false, though some are useful" Denney

[Lectron]

The "bell effect" will lower the pitch..
..That's one factor

[timothy42b]

If length isn't the determining factor, then why does pulling a slide get you in tune? hee, hee.

A Helmholtz resonator
http://people.seas.harvard.edu/~jones/c ... holtz.html" target="_blank

is an example of a shape where volume determines pitch. An ocarina is a musical example, as is blowing across a bottle. If you fill the bottle half full, sometimes you can get two pitches: one where you hold the bottle horizontal so it is essentially a long tube, the other vertical making it into a resonator.

I don't think a tuba is ever of sufficiently wide bore to become a Helmholtz resonator though. Well, maybe if you filled it half full of beer????????

[Rick Denney]

Fletcher and Rossing discuss this at some length, and Ken Sloan and I have hashed it out on Tubenet in the deep past. I don't have time to dig it up, but I'm recalling a graph showing an alteration in wavelength in a tapered resonator.

Of course length is a factor, and at the scale (and cylindricity) of tuning-slide movement the organ-pipe model is reasonable. But the tapered bore and bell has a significant effect on the pitch, not just the length.

Rick "whose library has been turned upside down since those discussions" Denney

[timothy42b]

It's just that practical experience with trombones tells me the effect if any is small.

I've played bore sizes from .485 to .562, and the amount of slide motion for a given interval seems to be the same.

There must be a relationship to taper, but the OP asked about volume, and that doesn't seem to be very significant.

[thevillagetuba]

It's just that practical experience with trombones tells me the effect if any is small.

I've played bore sizes from .485 to .562, and the amount of slide motion for a given interval seems to be the same.

There must be a relationship to taper, but the OP asked about volume, and that doesn't seem to be very significant.

Could these instruments have been made to slightly different lengths to account for the change in bore? I seem to remember my bass trombone having a wider difference between the handslide curve than my Holton straight trombone. I do not have a trombone other than my Holton to check this with, but it would make sense that the small amount of added/removed tubing that would/might be required for the differences in bore could easily be done without requiring any obvious alterations to design.

Fletcher and Rossing discuss this at some length, and Ken Sloan and I have hashed it out on Tubenet in the deep past. I don't have time to dig it up, but I'm recalling a graph showing an alteration in wavelength in a tapered resonator.

Of course length is a factor, and at the scale (and cylindricity) of tuning-slide movement the organ-pipe model is reasonable. But the tapered bore and bell has a significant effect on the pitch, not just the length.

Rick "whose library has been turned upside down since those discussions" Denney

This is not the post of which he is referring, but a much older discussion of this same topic in which Rick speaks quite elaborately on the topic:
viewtopic.php?f=2&t=2074" target="_blank" target="_blank" target="_blank

[Rick Denney]

Here's one of those discussions. Search on "Rossing".

viewtopic.php?f=2&t=27854&p=242604&hili ... ng#p242604

Rick "missing the days when there was time for discussions like these" Denney

[timothy42b]

I don't disagree with anything on that link, nor did I mean to rehash an old argument.

However, I note from the original post:

The idea was that the VOLUME of the tubing determines the pitch, not the LENGTH.

and at least to a first approximation that's simply wrong. All my trombones are Bb instruments because they are 9 feet long. An alto in Eb is 6 feet long. The bore size of an alto can be larger or smaller than a tenor. They vary in timbre due to bore dimension as well as contour, ratios of cylinder to cone, etc. Trumpets in Bb are 4.5 feet long. Tubas in CC are shorter than BBb ones. You could not make a CC into a BBb by making it wider.

Not saying volume doesn't have some effect.

But.............only for yellow brass, not for red or gold...............running for cover!

I have suspected that larger volume (meaning larger ID pipe for the same length) decreases Q, allowing easier lipping of pitches, but I don't have any data.

[roweenie]

There is a very well-made (in China) trumpet that a few importers are offering with their names on it.

The bell section (from where it is attached to the valve section, through the crook, and right about to where it is braced to the valve casings) is H-U-G-E.

Being the same length as most all other trumpets, it doesn't quite play up to pitch, and the 5th partial is horribly flat...just about as flat as the 5th partial offered by many models of tubas.

bloke "just an anecdotal observation, but POSSIBLY a HINT as to tuba intonation tendency causes"

Hmmm.....this is very interesting......

[timothy42b]

The bell section (from where it is attached to the valve section, through the crook, and right about to where it is braced to the valve casings) is H-U-G-E.

Being the same length as most all other trumpets, it doesn't quite play up to pitch, and the 5th partial is horribly flat...just about as flat as the 5th partial offered by many models of tubas.

I don't recognize the brand from the description.

That seems like two problems rather than one.

The entire instrument is flat? Could be the end effect. The effective acoustic length of a tube is slightly beyond the physical length. The wider the tube, the less this is true. Seems like they would have noticed after they made the first one, wouldn't you think?

The fifth partial is flat? Yeah, partials never line up with overtones. No horn is a perfect cone or cylinder, but a mix of both plus sharp bends, gentle bends, spit valves, etc. Design compromises make that better or worse, but always at the cost of something. That's an obstacle to intonation but an opportunity for tone control, I think.

[tubanonymous]

For all practical purposes, pitch is determined by length, and width will mostly effect your sound image (that is, what your overtone series looks like). You have to remember that on brass instruments, where partials sit is determined by the overtone characteristics of that instrument. So pitch is basically determined by length--UNTIL YOU LEAVE THE FUNDAMENTAL PARTIAL OF THE HORN. After that, it all comes into play

In other words, length is a uniform change across the instrument. Width is the tuning characteristics within the instrument itself.

Plus, your sound image is going to affect how you perceive your own pitch in relation to other instruments.