Brass Tubing Lenght

[haydenlance]

Earlier today i was wondering how instrument makers determine the right lenght for the tubing in their instruments to make sure they play right and are in-tune? Can anyone recommend any books about this (And instrument making) because this is really interesting! Thanks!

[Posaunus]

Physics.
Experience.

[brassmedic]

Don't know books, but there's a thread here that shows how to calculate it. You have to scroll down to the reply.

viewtopic.php?p=65701

[Sesquitone]

Earlier today i was wondering how instrument makers determine the right lenght for the tubing in their instruments to make sure they play right and are in-tune? Can anyone recommend any books about this (And instrument making) because this is really interesting! Thanks!

The following refers to some reverse engineering on this topic. Full article is available.


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[elmsandr]

Speed of sound is known, can calculate wavelength based on the frequency you want. Heck, you probably did all the math you need for this in high school. Some bell effects complicate it a little…. But it isn’t that hard.

Heck, do it yourself, figure out the length of a Bb trombone based on a frequency of ~466 Hz. Then take a tape measure and check it against your horn. (Remember you need to adjust to the fundamental AND the half wavelength)

Then, for equal temperament, multiply by the 12th root of 2 for each half step; figure out the length of your F attchment and compare to the real thing.

For the differences, figure out if the errors are elements of the physics (like where exactly the wave ends at the bell) or your measurement methods.

Cheers,
Andy

[ghmerrill]

It's relatively easy with trombones (and similarly trumpets) since they're cylindrical instruments. With (conical) horns in the tuba family (tubas, Sousaphones, helicons, euphoniums, .. even flugelhorns) it is more complex and somewhat more of an art -- which becomes entangled in "nodes" and where these occur in the tubing (in cylindrical or conical sections). It's complicated. By comparison, a trombone is pretty much like an adjustable straight piece of garden hose with a mouthpiece on one end and a funnel on the other.

[JWHartley]

For the physics: see Arthur Benade. He wrote several books, one is:
Fundamentals of Musical Acoustics. 2nd edition. Dover
For a newer, more mathematical discussion see:
N. H Fletcher & T. D. Rossing, The Physics of Musical Instruments, 2nd edition. Springer-Verlag

The Benade book will be more readable, the Fletcher & Rossing is more math.

[ghmerrill]

Acoustics is not a simple science. Like special relativity (which I think is clearly much simpler than acoustics), it needs the math to understand it. Otherwise the closest you can get is via some pictures, some analogies, and maybe a vague but coherent picture of "sort of" what's happening. I'd love to understand it, but at my age don't want to devote the necessary effort and have to settle for my vague grasp of the major concepts.

[Olofson]

The lenght of a trombone (in first position) is 274 cm. A conically tub with the same lenght blown at one ende like a trombone (or rather a didgerido) will sound a B one major seventh lower than the tromone pedal BBb. The partials line up with odd multiples of the frequency of lowest frequency, the B. (Just like a stopped organpipe). An open pipe would be wery difficult to play, but if you stop the open end, not absolutely tight, you can get a "stop horn effect".
On a french horn fully stoped you get tones a semitone higher, a F horn will sound like F# horn. On the cylindrically tube you can get the low B, now one octave higher, and the the partials line up like on a horn.

[jonathanharker]

The Science of Brass Instruments¹ is a great book that goes into a bunch of detail, how the length of the tubing works, something called the "Horn function" which can be used to calculate where in the bell (or beyond the bell!) the effective length can be taken, how cylindrical vs. conical bores work and measuring "brassiness" of sound, and all sorts of other interesting stuff. Like the Reynolds number, which relates to air flow and resistance, which in brass instruments is so low that fussing about tight kinks in rotary valves can sometimes be "overblown"... or like why drilling holes in brass instrument tubing and playing them with woodwind fingering doesn't work as well as you'd think - especially for cylindrical instruments, which was why keyed trumpets were harder to play than keyed bugles (and ophicleides, which are basically bass keyed bugles)...
Anyway, a mine of information.

1. Campbell, Murray; Gilbert, Joël; Myers, Arnold (2021). The Science of Brass Instruments. Cham: ASA Press. ISBN 978-3-030-55684-6. (DOI, WorldCat)