In my business the scale of a pipe (relationship between diameter and length) directly impact the pitch of the pipe.

For us, reed pipes (they function like a clarinet with a vibrating tongue and resonator), the bigger the scale the longer the resonator has to be to bring the pipe into proper pitch. Does this transfer to brass instruments?

The basic question is; Will the length of the bugle be longer/shorter or the same for a .689" tuba & a .820"?

The physical volume of the pipe has something to do with it; more means shorter. A euphonium and a trombone are the same pitch, but a euph is (I think) about six inches shorter (9 foot trombone versus 8.5 foot euphonium). I may have that backwards, however.

I have measured my BAT and a smaller CC and the smaller CC was a few inches longer that the 6/4 horn.

from my pipemaker's perspective: volume is a factor but the "shading effect" of the taper has more of an influence on length than one might expect. When I used to make Gamba or Gemhorn pipes the final lengths were shorter then a straight pipe due to the pitch flattening influence of the inward sides of the pipe. I made a Dolcan once (for you non-organ types, a reverse tapered pipe like a New Year's Eve noise maker) that ended up being considerably longer than "Normal Mensur" (the sound wasn't very pretty which is probably why they're mercifully rare). My guess would be that the larger bore instrument, presumably with an effectively larger overall taper, would measure longer in length overall.

I've read in the past about the "bell effect". The effective length of the bugle is longer than the physical length by something like 2/3rds of the bell diameter. Since organ pipes are cylindrical, this effect would be visible along the whole length. I suspect, however, that the bell effect is a rule of thumb that works only for conical bugles with wide flares like tubas have.

The narrower the narrow tubing, the more effect on the "velocity factor", I would suspect. In radio frequencies, the velocity factor of the transmission wire affects its electrical length, and the velocity factor is directly related to its conductivity. Friction along the walls of the tubing would drag the traveling pressure fronts back. Because of that, a bugle with narrow tubing would need to be shorter to resonate on the same frequency. This might be the effect that is at least partly described (perhaps incorrectly) by "bell effect".

A lot of what we normally assume about acoustics goes out the window with conical bugles, however. The resonance of the bugle varies with frequency in very significant ways depending on the taper design. It's possible to make a realistic looking bugle that resonates on the odd harmonics, and another that resonates more on the even harmonics. Fletcher and Rossing (The Physics of Musical Instruments) makes really good reading on this topic.

I have this feeling that because of the vagaries of taper design, instrument makers arrive at the correct length by experiment rather than by calculation.

Rick "recalling a story about vinyl tubing from someone in Memfus" Denney

Rick Denney wrote:/snip It's possible to make a realistic looking bugle that resonates on the odd harmonics, and another that resonates more on the even harmonics. Fletcher and Rossing (The Physics of Musical Instruments) makes really good reading on this topic. Rick "recalling a story about vinyl tubing from someone in Memfus" Denney

Rick Denney wrote:I've read in the past about the "bell effect". The effective length of the bugle is longer than the physical length by something like 2/3rds of the bell diameter. Since organ pipes are cylindrical, this effect would be visible along the whole length. I suspect, however, that the bell effect is a rule of thumb that works only for conical bugles with wide flares like tubas have.

Rick "recalling a story about vinyl tubing from someone in Memfus" Denney

Rick, your theory about cylindrical organ pipes is correct. For cylindrical flue pipes (operate like a whistle), the smaller the diameter the longer the pipe must be to produce a given pitch.

But for reed pipes, especially conical ones, the resonator is just that. The 'motor' (vibrating tongue) is what actually produces the pitch, the resonator only amplifies it and gives the tone its body. Now, a resonator of proper length for the vibrating pitch of the motor is essential, but the rule about diameter and length is opposite of flue pipes. The larger diameter the reed pipe resonator, the LONGER it must be to properly amplify a given pitch.

I think tubas (and all brasswinds) would function more like a reed pipe with vibrating motor (embochure) and resonator (tuba).

As usual, Rick is a fount of wisdom, however if you are looking this up in a textbook, it is usually found under "end effect" rather than "bell effect", and the figure usually given for cylindrical organ pipes is to add about 0.6 the diameter to the effective length of the pipe, but is often more for non-cylindrical ends (such as open holes in woodwinds).

The velocity of sound does change when pipes change diameter and the varying impedance of the bell flare affects the higher frequencies differently than the lower ones. The departure of the bell from a conic shape may be an effort by the manufacturer to bring the harmonic resonances into better tune with the fundamental pitch.

"The speed of sound is 343.5 meters per second, assuming relatively normal barometric pressure and a temperature of 20 degrees centigrade. (Higher temperatures require longer wavelengths, and at lower temperatures wavelengths will be somewhat shorter. As can be imagined, when figuring wavelengths for brass instrument construction, one must take into account the warmth of the player's breath. For a temperature of 28 degrees centigrade as compared to 20 degrees C, one must add an additional 1% to the length of the instrument, corresponding to a revised speed of sound of 347 meters per second.) The equal-tempered frequency of FF (F1, or "pedal F") is 43.654 cycles per second, so the length of the wave that produces pedal F is 7.8687 meters long. However, brass instruments act acoustically as "closed pipes", so only half this length is required to produce this note, thus 3.93435 meters. This is further complicated by the fact that a conical pipe contains more air than a comparable cylindrical pipe; it has greater volume. A physicist would say "The pitch produced by a vibrating medium (air!) depends on its weight per unit length." That's why the tubing of a euphonium is shorter than the tubing of a trombone. Yet another factor to consider when planning the correct length of a brass instrument: the diameter of the bell rim. During playing, the acoustical standing waves produced inside a brass instrument actually extend beyond the end of the bell. This effect varies with frequency and the width of the bell. For almost all common purposes, this effect can be expressed thusly:

effective tube length = actual tube length + (0.6 * bell diameter)

In the case of my F tuba, whose bell diameter is 39 centimeters, this means 23.4 centimeters of tubing must be left out of the body of the horn in order for it to come out in the desired pitch. Not an insignificant figure!

By informed guesswork, I determined I needed 92 centimeters (for the 2nd and 3rd branches), flaring from an interior bore diameter of 20.5 mm to 37 mm. Elementary school geometry told me that the following rule applies:

circumference = diameter * 3.1416 "

Boy, I gotta get out more!

Knowledge is knowing a tomato is a fruit. Wisdom is not putting it in a fruit salad.