Intonation Relating to the Taper of the Main Bugle

[tylerferris1213]

I have a quick (maybe not so quick) hypothetical question for you guys and gals.

I know that with tubas, the more even the taper through the main bugle, the better intonation said tuba will have. Instruments (like a Jinbao F tuba I mistakenly bought) that have sudden flares or large sections of cylindrical tubing have horrible intonation. First question: is this true in every case?

Secondly, how much does straight tubing hurt intonation? Do instrument makers have to do anything to offset the straight tubing through the valve section? I know the valve section on good horns is graduated with the 4th and 5th valves being bigger. Is there anything else that is normally done?

Also, do alp horns have perfect intonation, being purely conical with no straight valve sections? I know this can depend on the quality of the work and the person making them, but do they generally have better intonation than a tuba on its open partials?

[Ben]

I don't have a bunch of time to comment on this, but the assumption of more taper = more in tune is at least partially not true. Trombones are very in tune, and have comparably short tapered sections. There are text books about the physics of wind instruments (Benade, Fletcher & Rossing), and after reading these, I still struggle to understand the subtleties of intonation deviation in brass instruments.

[iiipopes]

What do you mean by "in tune"? If a person means the Pythagorean partials, yes, a perfectly smooth taper of the right degree will give a perfectly "in tune" Pythagorean partial system. But it can only be used in one key. It can't be used in other keys, because in comparison to equal temperament, the fifths will be slightly sharp, the major thirds significantly flat, and so forth.

But what we really want is not a perfectly "in tune" system. We want some sort of temperament so we can play in multiple keys. Therefore, there is always a compromise. Blakeley compromised the occasional stuffy note to get an almost perfectly evenly tempered scale. Miraphone compromised the 5th partial intonation to get good intonation and response elsewhere. The makers of the 6/4 tuba compromise even intonation for huge tone. King sacrifices tuning in the upper harmonics to provide a good foundation. Yes, these are oversimplified statements, but they illustrate the point that nothing is perfect, and a player must choose a horn based on a determined priority of characteristics.

And that doesn't even address personal ergonomics. I sacrificed some of everything to get the overall tone I prefer with using all four valves in the right hand instead of 3+1, as "tempered" by economic circumstances. So I occasionally have to ride throttle on the 1st valve slide. My tuba may not be preferable to play by many other players, but it works for me. Those who prefer an Alexander seem to value the inimitable tone over everything else.

To be more precise, several large tubas, like Conn 2XJ's and Holton 345's, do seem to have flat third partials due to the large bottom bow.

In the end, it is the balance of cylindrical tubing, which tends to expand the distance between partials, and conical tubing, which tends to compress the distance between partials, which gives the final characteristics of intonation in any given instrument.

[iiipopes]

Interesting discussion. I think the OP's question centered (!) more on the uniformity of taper than the degree of taper. I could be wrong.

It's all tied together. A brass instrument has to have both a fairly uniform taper, with the right combination of cylindrical tubing for flexibility in tuning and conical tubing for the overtones to line up, and it has to be the right degree of taper.

[Dan Schultz]

Intonation on an Alphorn can be a challenge.

[tylerferris1213]

DG, you're right. I'm talking about how consistent the taper is.

The main reason I asked was for food for thought. Also, my crappy Jinbao F tuba is being concerted into a cimbasso, where the purely cylindrical valve section will be perfect. Pictures will come when the project is finished!

[windshieldbug]

Bear in mind that the equal-tempered scale as utilized on modern keyboards such as the piano and electronic tuners is only equally out-of-tune.

No bore profile will play in tune in every key.

[windshieldbug]

I feel like everytime a discussion about intonation, Windshieldbug and I take turns pointing out equal temperament as opposed to physics.

OK, tag, you're it!

[tylerferris1213]

So getting back on topic, when manufacturers are making a new instrument, do they have to keep changing the taper with trial and error until they find something that works, or is there an overlying rule?

One thing that always gets me is the massive bell on my Getzen CB-50. It obviously flares out more than just about any other 4/4 horn, but the intonation on it is very good, in my opinion.

[NCSUSousa]

Read this - http://www.baadsvik.com/the-new-miraphone-e-flats/
Oystein addresses your question about mfrs and taper design in this blog post.

[iiipopes]

The Miraphone method, as with the philosophy of German engineering, is impressive with the proper use of computer modeling.

So getting back on topic, when manufacturers are making a new instrument, do they have to keep changing the taper with trial and error until they find something that works, or is there an overlying rule?

Before widespread use of the personal computer, it was trial and error. Schilke was always experimenting with his trumpets to get the best intonation possible. He understood that to change something in one place for one note or series of notes would affect some other place in the range. He said there was one note he could never get perfect, but wouldn't say what it was (perhaps 5th partial top space e?). He would experiment with thousandths of an inch of taper change at a time, not necessarily making everything smooth and progressive - more like "a snake eating eggs." He made his bows larger than the actual bore at that point might otherwise indicate, which was different than how other trumpet manufacturers at the time made bows, to take into account the effect of the bows on nodes and anti-nodes. In short, the progression of the conical profile was anything but smooth.
http://www.dallasmusic.org/schilke/Quan ... ality.html" target="_blank

[iiipopes]

Organ pipes......- all cylindrical.

Nope, try again.

Indeed - Gemshorns, Spitzflutes, Spitzprincipals, Bell Gambas, Trumpet, Tuba, Oboe, Bassoon and similar reed resonators, Spillflutes, Koppelflutes, Nacthorns, Erzhalers, Dolcans (outward taper) and many others have either the entire body of the pipe or at least the tuning cap tapered to some degree or another, depending on the tone desired. Only the English "classical" era school of organ building from roughly the Restoration to the Accession of Queen Victoria insisted on the tone of cylindrical pipes, and even then there were exceptions and experiments, including the aforementioned reeds, Bernard Smith's tapered ranks in the Temple Organ, Snetler's original configuration of the Dulciana, Jordan's experiments with a French Horn stop, Green's experimentation with pipe scalings, especially in the bass, and the infamous "Pyramidon," among others.

And then there is the French "flute a biberon," or "baby-bottle shaped flute," and other strangeness, not often made anymore.

[GC]

@Tuben: aren't some diapasons long rectangular wooden boxes?

[Rick Denney]

One thing I have learned reading books by Benade and the definitive text by Fletcher and Rossing, by reviewing experiments conducted by people such as Fred Young, and by conducting my own experiments, is that there is no generalization that can be made between intonation and taper that works at enough detail to do any real good. The speed of sound is subject to variations as the profile changes, and thus the wavelength of the sound also changes, so all simple models that assume those are constant just don't work. Computer models can predict it, but they struggle to incorporate all the factors, including subtle differences in manufacturing execution, and including all the various curves in the bugle, valves, and valve branches.

And the profile that works best for intonation does not necessarily provide the best sound, though it seems to me that intonation is more affected further up the instrument and sound is more affected in the bell stack.

So, yes, trial and error. And that process is still used today, even for computer-designed profiles. One hopes the computer assistance would give them a better starting point, but it doesn't always work out that way.

Another thing: All the mythology around the difference between conical and cylindrical tapers is mostly gross over-simplification (if it isn't outright wrong). All supposedly cylindrical instruments are conical in any case, just a bit less conical than some others.

In looking at resonance (or impedance), one will see that it is not a smooth curve for a resonant bugle. It is a series of peaks that emphasize or depress harmonic partials, or that do or don't damp non-harmonic noise. That suggests to me that the evenness of the bugle (either cylindrical or conical) has little to do with those peaks--it's a highly nonlinear system. I suspect that the quality of the signal has more to do with intonation than the resonance of the instrument--a poor signal can't find good intonation in a perfect instrument, and a good signal can overcome the problems with an instrument that has poor intonation. Signal=buzz, both pitch and quality. Smooth resonance curves generally illustrate non-harmonic systems. A mouthpiece by itself has a smooth resonance/impedance curve, for example, but it makes a noisy buzz instead of a clear tone. We want an instrument with clear resonant peaks that occur at frequencies and in magnitudes that add up to both a good sound and workable pitch. The sense of pitch that we hear is also highly influence by those upper harmonics in the sound, which can create misleading difference tones.

The newest instruments have better intonation than instruments did even 50 years ago, by a healthy margin. But the instruments from 50 years ago occasionally have a sound unmatched by those newer instruments, and their intonation is still workable. The instruments from a hundred years ago were worse, and the first tubas were, well, really challenging. Trial-and-error is a slow process.

Rick "thinking this a good topic for a drive-by posting from a past pontificator" Denney

[tbn.al]

Rick "thinking this a good topic for a drive-by posting from a past pontificator" Denney

I'm thinking that pontification is a good thing, at least in this instance.

[tylerferris1213]

Thanks for all the information and links to information. I've learned a lot about my original question in a very short amount of time!

[roweenie]

This topic is very interesting.

I'm no scientist, but if an even taper is critical to intonation, how could any of those "BBb cut to CC" horns ever hope to play in tune? I've got to imagine the taper is all shot to hell in those cases....

[iiipopes]

Yes, but then all major chords would be so bright as to be irritating, as they are on equally tempered electronic keyboards, rather than lipping or pulling down the major third to "lock" from a Pythagorean alignment.

[iiipopes]

Buzard uses a Flute a Biberon in their Choir organs. (not worth the effort to my ears)

I agree. It is functionally no different than a rohrflute or chimney flute with a very wide short chimney, the only real structural difference being the rounded shoulder and unitary construction, necessitating tuning by the ears or the foot, or coning the top. As a 4' flute in the choir organ, I would rather see an Elliot opened flute that will blend with just about anything, or a koppelflute, again, with the opened top to let some octave harmonic give some definition and blend.

[PaulMaybery]

So then, when we talk about intonation in a closed pipe, and how the harmonics distribute themselves with regard to flat or sharp to whatever temperament - what then are the influencing factors that determine the "slotting" characteristics that we hear of so much these days? Some horns are said to have a "narrow" others a "wide" slot and therefore varying issues in dealing with the ability to lip pitches up or down.

For example: I remember an old 1940 CC King rotary that I had for about 40 years. Sound was incredible, pitch was a problem - though workable, but I remember the slots seemed very wide and I needed to be at the very "top of my game" when it came to centering pitches. It seemed like a note could go almost 30 cents or so in either direction.

Other horns I have played seemed to slot rather tightly and lock right on a center but would not have anywhere near the ambience of sound that the old King did.

Can anyone explain the physics of "slotting"?

Paul (who is trying to find out these things - because he thinks he can find or develop the "utopophone" ) Maybery