Tubular bell fabrication and tuning - Discussions with Jim
-----Original Message----- From: Jim Sent: 01 February 2010 To: firstname.lastname@example.org Subject: Tubular bell fabrication and tuningCan good quality German long case clock movement has fallen into my hands, but its sound work is unmusical to me: tempered rods set in a cast iron block; the striking tone achieved by ganging four rods to produce by their frequency interference an apparent low fundamental tone. The overtones are disagreeable and, being mounted in a common block, all the rods vibrate when one is struck.
I am setting out to make tubular bells to replace them. Could you please tell me the proper lengths for major third, perfect fourth, and perfect fifth above the fundamental tone for cylinders of equal diameter and wall thickness throughout their length? Only these tones are needed as the movement chimes only Westminster. I intend to strike the hours on a bell as long as the case permits, which would be most pleasant tuned to some perfect interval of the quarter hour bells.
My intention is to cut the tubes from soft brass thin wall tubing of 1-1/2" outer diameter, cap them at their tops with braised discs, and suspend them by cords run through small holes within about 1/4" of their tops, to be struck by leather hammers about 3/4" below their tops. Are these dimensions likely to produce pure tones? It is normal to make the walls of tubular bells thicker where they are suspended and struck?
MAKE AND TUNE YOUR OWN WINDCHIMES!
Well I'm not a super expert on tubular bells, but I have played around with tuning these sorts of things before, and whilst there is some math that may help you, I FIRMLY believe it is to get you in the ball park only - you are still likely to need to fine tune by gradually cutting down or grinding to sharpen the pitch until correct.
One certainly cannot simply specify a length universally - that wall thickness and diameter as well as the exact tube alloy will all play a big part in determining the final length. There is some info available in the articles at www.percussionclinic.com - if you visit the articles page there is a separate section with 5 tubular bells articles - in particular this one: http://www.percussionclinic.com/art_tubbells05.htm has some dimension charts which may be helpful.
Your basic plan sounds not too bad - braising the caps on the top sounds perfect and pretty much exactly as a set of orchestral tubular bells would be made. If you look at a set of these however you will notice that the suspension point is usually quite high - higher than 1/4 length from the top - sometimes even right at the top. It depends on the mode of vibration the tube is being set up for, but the orchestral instrument has the tubes suspended from the very top, and that is also where they are struck. Usually with a hammer made from coiled hardened rawhide at about 45 degrees to the tube at the junction of tube and end cap. I suspect you would find the primary vibrational mode is not a transverse mode as the idea of 1/4 or 2/9th node points would suggest, but in fact a longitudinal mode. Certainly I have never heard of tubes being reinforced or constructed with extra thickness at any point in the tube - this would make the lengths even more difficult to calculate.
You may also find that you can get less of the upper overtones and a more mellow, "fundamental rich" sound by simply changing the striking tool - something softer than metal. Even on a beautiful sounding tube, striking it with a metal implement will make a harsh clang -that is why coiled rawhide or leather topped cork/timber is more usually used - certainly worth some experimentation anyway.
Sorry I cannot help more than this Jim, but hopefully there are some useful bits here.
You are absolutely correct about fine tuning by ear instead of formulae. --which would be analogous to the mechanized wine "tasting" by chromospectrograph attempted by some Japanese researchers several years ago.
I have reviewed your links and tables for standard tuning frequencies, and find them very useful if I cut the tubes somewhat longer then they indicate, to ream the mouths to 60 degree flares from there. Especially, a second order like cited Euler's equations, which are outstanding, especially concerning the modulus of elasticity and density of the tubes. From them I have decided that rather than using brass as I had planned, it will be better to use slightly denser and much softer pure copper. That is, it is better to use plumbing pipe!
I initially asked you an odd question about perfect fourth and fifths as my application is non-orchestral. As the clock will need to sound in only one key, I can tune it to perfect harmony. It will never need to play with other instruments; it can stand in the corner and play with itself.
Maybe 40 year ago I built a single manual, two choir Burton kit harpsichord to playability (though never to visual case aesthetics-- thereby hangs a tale) and tuned it to perfect intervals to my ear by beats--that is, similar to bringing a principal or octave tone into consony with a standard, but with a longer auditory test interval.
The effect on hearers was striking: they described the music as sweet, clear, and more gushy adjectives, though they could not identify why --certainly, it was not because my playing was sweet or clear: if I listened carefully, I could hear Couperin shifting in his grave. I believe the reason was their natural recognition of perfect harmony, even though they heard it rarely, and never by name.
As the harpsichord is single-strung in each voice, it was easy for me to adjust string tension back and forth to achiever that. Tubular bells are tougher, as i can't stretch them for a second try. But I hope to evoke that same sensation in those hearing the clock. And if they attribute it to the irreplicably sensitive expertise of some long-dead clock maker, I will be silently amused.
(The case maker, Randall Mathias, is an expert joiner, but the case will be of local high-altitude pinnate wood, chosen for its visually interesting grain patterns rather than its acoustical properties. Thus, suspension of the tubes on cords to minimize sound transmission through the case rather than directly to the air is very desirable.)
BTW, the wood Stradivarius used was floated and most was kept for use in brackish pools. But also, he benefitted climatologically from lumber with thin growth rings from low annual growth conditions. His were more from water deprivation, but the same slow growth occurs today in Montana in trees growing on North slopes at high altitude. Only very small, individual wood crafters such as Mr. Mathias separate out such wood and specifically quarter saw it for its acoustical properties.
(That is, most often the scars, gnarls. knots, etc., which are visually interesting, occur to a tree some while after it started to grow, leaving it early grain clear, with beautiful musical properties. They are of no commercial interest to corporations concerned with building construction; indeed, gnarls & knots are considered defects for construction purposes, while thin, clear grain is considered of no especial value, and so is made into plywood.)
Hello again Jim
You sound like an interesting guy Jim, and perhaps there's even a chance that we could chat about stuff over a coffee if the opportunity comes up. Anyway - sounds like you have a good handle on the project - good luck with it, and if you think of it drop me a note to let me know how it turns out - I'm always interested in such things.
All the best again.
MAKE AND TUNE YOUR OWN WINDCHIMES!
For more help on instrument building you can email Jim.