Sonic Frequencies

[Chuck(G)]

Actually, I am one of those slower tuba players, but on Roger Bobo's website, he talks about using a G tuba to better match the "sonic frequencies" of a modern orchestra for Berlioz' Symphonie Fantastique.

Ya got me! "Sonic Frequencies" as opposed to "Radio Frequencies"?

Maybe he means the spectral distribution of sound in a modern orchestra, as opposed to the spectrum of an orchestra from Berlioz' time...

[Chuck(G)]

Yes, but that's were I stop following. If a BBb and a CC tuba play the same note, wouldn't it have the same frequency?

The same fundamental frequency, true. But it's the harmonic content that gives the sound its character. (We talk about "bright" or "dark" sounds, etc.). Same goes for the physical size of a tuba. A big 6/4 BBb doesn't have the same harmonic content (i.e. relative strength of the various harmonics) that a little 3/4 BBb does. And it's very important--a tuba playing in the lower register has more harmonic content than fundamental. "Pedal tones", for example, have almost no fundamental in them.

Not wanting to put words in Mr. Bobo's mouth, I'd still venture that what he meant to say was "spectral distribution" or that less-understood word, "timbre".

[Allen]

"Pedal tones", for example, have almost no fundamental in them.
quote]

Now how is that possible? A CC tuba, playing a "pedal C", is producing a 16' C. It is playing in the fundamental of the harmonic overtone series of the horn. Anything above that is playing in harmonics. So I don't follow how a 16' C, played on a full length resonator (a tuba is only a resonator), has almost no fundamental.

It is true: A tuba playing pedal C will produce a note that has almost no fundamental at all; the note is just about all harmonics. A tuba playing pedal C is playing the same note that an organist would call "16' C," 32Hz. We need to keep in mind that, for low notes, our pitch perception is entirely determined by the overtones (harmonics). A pure sine wave at 32Hz would only have a perceivable pitch when played against other notes, or with harmonics.

Different types of organ pipes have different proportions of fundamental to harmonics. An organ builder who wants to build a 16' C pipe that will have plenty of fundamental will use several hundred pounds of lead to make the pipe, or will make it of wood at least two inches thick.

The point is to have the resonator acoustically opaque at the frequencies you want the pipe to create. A thin-wall brass resonator is certainly acoustically transparent at 32Hz, and thus would not create any 32Hz wave. Harmonics consisting of various multiples of 32Hz will be created.

Of course, if you don't mind having several hundred pounds of metal or wood in your lap, you could be making those fundamentals we dream of!

Allen Walker

[Chuck(G)]

I'm not taking any sides on the organ pipe thing, but if you have a good MIDI synth, here's something to try.

Take a voice that's fairly bald of overtones like GM 74 (Recorder) and play a scale at ff down from the pedal C. Note that you can see the speaker cones vibrating, but you don't hear much of anything and the effect increases to almost complete silence by the time you're down an octave past that.

Now take an overtone-rich voice like GM 43 (Contrabass) and repeat the experiment. You can hear it loud and clear all the way down--but what you're hearing is harmonics.

The organ builders are certainly familiar with the ear's ability to infer a low pitch from harmonics. There's the very old trick of faking a 32' voice by combining a 16' voice with a 10 2/3' quint. The 32' fundamental isn't present, but you certainly can hear it.

If you've got access to a good audio spectrometer and a mic, record yourself playing a pedal CC. You'll find almost no energy in the fundamental.

In fact, the pedal doesn't occur at a resonance point of the horn--but its overtones do. See the following (a good online resource for brass acoustics) for an explanation:

http://www.phys.unsw.edu.au/~jw/brassac ... html#pedal

[Chuck(G)]

Without going too much further off the site topic, I will say comparing a wind driven organ pipe to a synth or any other digital tone producing device is comparing apples to cows.

Agreed. The synth is capable of producing pure tones. That's probably why they don't give hearing tests using pipe organs or air-raid sirens.

OTOH, didn't Helmholtz observe the effect using an air-operated siren?

(just joshin' )

[Allen]

Different types of organ pipes have different proportions of fundamental to harmonics. An organ builder who wants to build a 16' C pipe that will have plenty of fundamental will use several hundred pounds of lead to make the pipe, or will make it of wood at least two inches thick.

I totally disagree. In my years as an organbuilder, I can count on one hand the number of times I've encountered a wooden pipe with anywhere near the thickness of lumber you talk about. And those were for 32' stops, not 16'. <...SNIP...>

OK, OK, I was being a bit extreme in my wood thicknesses and metal weights, although a few very large-scale theatre organ ranks certainly can have dimensions in that ball park. It isn't typical in the classical organ field.

Still, my point was that, if you want to produce a low frequency, you need a resonator that can hold in that frequency, that is, a resonator that does not itself vibrate at that frequency, letting the low frequency leak out instead of confining it inside the tube. A thin brass walled resonator, such as a tuba, allows the low frequencies to pass out directly through the tubing wall, and there is no effective resonator for the low frequency. The thin brass does a fine job of keeping in the harmonics, so the tuba does a good job of producing those.

There was a topic a little earlier that had posts about enjoying the tuba vibrating in one's arms. I enjoy it too. However, I know that if I ever had a tuba that could produce a real fundamental pedal tone, it would not vibrate in my arms: all of the energy in the horn would go into producing a low frequency out of the bell, not in vibrating the walls of the horn.

Cheers,
Allen