Tubas and intonation - why are some better than others?

[poomshanka]

"Input anomalies" notwithstanding, why are some tubas very well in-tune, while others are almost unmanageably out-to-lunch? I'm curious about this as it relates to a design/manufacturing perspective.

Although I don't have the numbers right in front of me, I'm assuming most manufacturers are working off of roughly the same measurements - i.e. XX" bugle and YY" tuning slides for any given key, etc.

Does it have something to do with materials? Brace positioning? Slide wraps? Secret ingredient X? Why, for instance, would two seemingly identical horns that came "off the line" one after the other have different intonation characteristics?

Just something I've been wondering about lately. Thanx in advance for any input...

...Dave

[cjk]

"Bugle" taper.

[MikeMason]

in my opinion, it's strictly luck. despite attempts at science,it seems good ole' trial and error is the only thing that really works(mostly error).luckily,however,as long as a tuba is "close" and the slides are in the right place,it can be played in tune...

[Joe Baker]

Does it have something to do with materials? Brace positioning? Slide wraps? Secret ingredient X?

No expert here, but my limited experience tells me the answer is...

• "yes".

__________________________
Joe Baker, who agrees that bugle taper must surely be the primary influence.

[Dan Schultz]

"Input anomalies" notwithstanding, why are some tubas very well in-tune, while others are almost unmanageably out-to-lunch?

The mechanical lengths of tubing and the development of tapers are pretty much fundamental. My theory is that great playing horns are more-or-less the result of blind luck.

Some manufacturers have spent ages using trial and error to develop new tuba models while others have simply copied the great horns. So... why do the copies sometimes only deliver mediocre horns? I think it is in the quality. Every solder joint, brace, waterkey placement, slide, tube length, and taper plays an important part in making a great horn. Does anyone have a 'magic formula'? I doubt it.

[hbcrandy]

Though I am a tuba player, I worked in the custom French horn field for years.

The writer who said that the taper of the open tuba is critical is correct. Bruce Lawson, son of the great horn maker Walter Lawson has devoted a great deal of time to oscilloscopic spectrum analysis of the horn taper using the complete range of frequencies of the horn. His accoustical analysis has produced a horn that has consistent superior intonation of all open harmonics.

Though this can be done by trial and error, scientific analysis will produce a superior result in much less time.

Randy Harrison
Baltimore, Maryland USA
(Former Proprietor of Brass Arts Unlimited)

[Rick Denney]

"Input anomalies" notwithstanding, why are some tubas very well in-tune, while others are almost unmanageably out-to-lunch? I'm curious about this as it relates to a design/manufacturing perspective.

It's all in the impedance.

Acoustic impedance is the ratio of sound pressure (i.e., loudness) to particle velocity. It describes how the amplitude and phase of a source sound becomes an amplitude and phase of a resulting sound.

The tuba has an impedance that varies by frequency. Some frequencies have a high ratio of sound pressure to particle velocity, and some frequencies are low. Thus, some frequencies are magnified and others diminished. The ones that are magnified are the resonant peaks of the impedance curve. The peaks are sharp, and the peaks generally line up on musically valuable frequencies. How they line up is the result of the taper (which is a broad description that includes anything that upsets the intended taper).

The mouthpiece also has an impedance that varies with frequency. Most tuba mouthpieces peak at similar values. You can hear the peak of the mouthpiece resonance curve by popping the rim on the palm of your hand. But unlike the spiky resonances of the tuba, the mouthpiece resonance is broad and flat, meaning that when you buzz into it, you get a discernable pitch but also quite a lot of noise and a range of frequencies around it. The mouthpiece shapes the sound of the buzz a bit but not much. A tuba mouthpiece impedance curve makes it weaker as you get away from the popping frequency, which is typically in the range of about Ab at the bottom of the staff. Making pitches some distance away requires more energy from the buzz.

The tuba filters out some of the non-resonant noise, and leaves the resonant frequencies. If you overload it with non-resonant noise, that noise will leak into the sound, or it will serve to cancel some of the resonances.

The player's lips also have an impedance, and that impedance also varies with frequency. It is controllable based on the tension of the lips as balanced against the air flowing through them. If the peak resonance of the lips matches the peak resonance of the tuba, there will be no attenuation in the sound. But the impedance curve of the lips is even broader and flatter than with the mouthpiece. If the noise produced by the buzz contains enough energy and tonal variety, it will excite all the resonant frequencies of the tuba. That's why a noisy buzz with lots of energy ends up making better sound than a buzz that seems to ring a single pitch more clearly, especially if it does so weakly. More air is the secret to a bigger buzz, assuming there are no fundamental faults in the structure of the embouchure. I was quite surprised to discover that great players have a fairly noisy, but loud, buzz. Listen to Jacobs's buzz on the recording of his TUBA lecture from 1973--it's quite noisy but it is also very loud and filled with energy.

If the buzz lacks energy or the impedance curve does not match the instrument (i.e., buzzing the wrong pitch), then you'll get noise and attenuation as the sound is reflected back into the instrument rather than out the bell. Also, a buzz that is off pitch will not get reinforced by returning pulses reflecting back from the bell opening, making it harder to maintain the buzz.

So, the sound that comes out is the sum of the impedance curves of the tuba, the mouthpiece, and the lips.

The resonance peaks in the impedance curve of the tuba are controlled by the length of the tubing and the shape of the taper. The shape of the taper can be affected significantly by disturbances in the tubing (i.e., leaks, edges where parts don't fit well, solder blobs, curves in the branches, and even blobs of grease). It might be subtly affected by the vibration and impedance of the brass itself, but I think this effect is very subtle indeed. The player might, however, hear the ring of the brass and mistake that for acoustic energy that is in the sound coming from the bell and getting "out front".

A straight tube has a well-defined set of resonance peaks, but a tapered tube is all over the place. It's quite possible to have tapers that kill upper overtones, and others that amplify them. If the overtones are not well-tuned, they will affect the apparent pitch of the sound. As the player forces the tuba into different modes of vibration by buzzing the higher partials, those overtones are mixed differently. Dominant but poorly tuned overtones will therefore make some notes worse than others.

Since the objective is an instrument that plays an equally tempered scale accurately, and then provides the flexibility to line up the pitches to the more resonant natural pythagoran scale when playing in an ensemble, the instrument has to be designed to counter the natural resonance harmonics to some extent. Figuring this out ain't easy. There is a computer program used by the German makers that will optimize a taper design for a particular intonation objective, but it does not optimize the taper for a particular sound objective. There is no indication that these objectives are always the same.

So a tuba that sounds great, responds well, and plays in tune is a dynamic balance between competing objectives, each of which can be affected by the taper design, the location of bends and curves in the tubing, production faults that disturb the propagation of sound waves, the match of the impedance curve of the mouthpiece, and the match of the impedance curve of the player's lips.

Thus, Dan is right. Great tubas mostly result from experimentation, because modeling all these effects in a design process is just about impossible. That's why we keep copying the great instruments of the past, making incremental changes to correct or improve this aspect while not doing too much damage to that aspect, and hoping that the production techniques are adequate not to negate those little design tweaks. Very occasionally, someone makes a breakthrough, and creates a new archetype to be copied in the future.

Rick "who can describe it but not model it" Denney

[Rick Denney]

Though this can be done by trial and error, scientific analysis will produce a superior result in much less time.

With all due respect, the process you described is not analysis, but rather the use of sophisticated measurement techniques in support of experimentation. Using spectrum analysis is a more precise way to measure the sound than one's ears, but it is still only a measure of the result. It doesn't give advice on what to change, and that has to be done based on the intuition and experimentation of the designer.

Modeling all the things that affect the impedance of the instrument is another matter. There are computer models that will take a measured spectrum and its taper design and suggest improvements to repair intonation faults, but they do not repair faults in the resulting sound, which most tuba players seem to value above intonation (within obvious limits, and as long as the intonation is controllable). Getting the balance between sound and intonation correct, and then executing that balance consistently in production, is not easier now than it was 100 years ago, even though we can more accurately measure the result.

Rick "noting the difference between simulation and measurement, and between empirical and analytical optimization" Denney

[MaryAnn]

Though this can be done by trial and error, scientific analysis will produce a superior result in much less time.

With all due respect, the process you described is not analysis, but rather the use of sophisticated measurement techniques in support of experimentation. Using spectrum analysis is a more precise way to measure the sound than one's ears, but it is still only a measure of the result. It doesn't give advice on what to change, and that has to be done based on the intuition and experimentation of the designer.

Modeling all the things that affect the impedance of the instrument is another matter. There are computer models that will take a measured spectrum and its taper design and suggest improvements to repair intonation faults, but they do not repair faults in the resulting sound, which most tuba players seem to value above intonation (within obvious limits, and as long as the intonation is controllable). Getting the balance between sound and intonation correct, and then executing that balance consistently in production, is not easier now than it was 100 years ago, even though we can more accurately measure the result.

Rick "noting the difference between simulation and measurement, and between empirical and analytical optimization" Denney

Due respect or not, Walter Lawson has designed horns, bells, and mouthpieces that are spectacularly good. I use a Lawson mouthpiece and a Lawson bell on my German horn, which I bought because of its light weight and ergonomics to fit my small hand. Lawson horns do play a little like tanks, but they are in-tune and wonderful-sounding tanks.

I first bought the Lawson mouthpiece; it did not dramatically improve my tone but it did dramatically help me lock in the notes in the right place. That was followed by the Lawson bell, which both noticibly improved the tone and made the instrument easier to play. You may be right, Rick, that the equipment makes it easier to experiment, but that equipment has to be in the hands of someone who has the intellect to use it.

MA

[TubaRay]

In regards to the two above posts by Mr. Denney: "What he said!"

I was going to say: "Some tubas seem to play better than others."

[Rick Denney]

Due respect or not, Walter Lawson has designed horns, bells, and mouthpieces that are spectacularly good.

That's why the respect was due.

I do not believe that the experimental approach, however supported with scientific measurement methods, is wrong. In fact, I think it's the only approach. Good measurement helps with basic understanding, and that helps direct the trials. But it's not the same thing as a model that can be optimized or deterministically designed.

Rick "who did not intend to disparage Lawson's results in any way" Denney

[Donn]

Due respect or not, Walter Lawson has designed horns, bells, and mouthpieces that are spectacularly good.

Was Walter Lawson using that oscilloscope spectrum analysis for his designs? From what I am reading here, that was Bruce Lawson. Not to be unduly picky.

One of the violinmaker types around these parts used to practice a sort of instrumented analysis to make the most out of a violin (viola etc.) top. The results didn't always satisfy everyone, but of course that doesn't prove anything one way or the other; just mentioned it in case anyone's interested in such things.

[imperialbari]

There are lots of elements in tuba designs, which are influential. Economy being maybe the most important one. The more tooling, which can be reused for more models, the better for the maker.

Yamaha has its 621 series, where the 4-pistons' block is identical (aside from the slide lengths) on the models in F, CC, and BBb. As are the bell, the bottom bow, and one or two of the large branches. These tubas aren't considered especially bad, even if the CC and BBb versions are relatively small for their pitches. The same bell even can be found in the small student BBb models also.

At least since WWII B&H/Besson have had 4 Eb tuba variants: the 15" bell and the 19" bell both with small receiver leadpipes, and the 19" inch bells with slow leadpipe bore expansion, the 982, and with fast leadpipe bore expansion, the 981. My personal preference has not been kept a secret, but for their time all must be considered relevant instruments. And from valve block through bottom bow, they all were/are identical.

Wenzel Meinl has a CC series (2145, 2155, 2165) sharing many elements but for the bell diameters. The 2000 is made after the same template. All variants appear to have a following.

The new Conn CC and King BBb were constructed around one fixed element: the bottom bow of the preceding King BBb model. Aside from some production inconsistencies both models appear to have been well received among tubists.

RD has mentioned a number of production problems. In my opinion two factors are especially important: proper valve alignment and precise cum smooth alignment of all branches.

There are several more aspects, most of them escaping me, only one mentioned: the mouthpiece. Personally I don't go for well slotting mouthpieces. I prefer mouthpieces putting me in command of the intonation.

Klaus, who even didn't mention the "recycling" of parts within the GDR era B&S tubas