Posted by Rick Denney on July 16, 2001 at 14:39:12:
In Reply to: Re: Re: Re: Re: Re: Re: Re: Re: Yet another change to The Tuba Sound posted by Carl on July 16, 2001 at 11:30:10:
With all due respect, don't go all passive-aggressive on me. There is no reason for you to remain curious about my assertions--just ask and I'll be happy to explain them.
In my extensive experience in dealing with optimization issues in non-linear environments (I'm a traffic flow theoretician by training), my assumption (not assertion) is always that complex non-linear systems are more easily optimized using heuristic methods than using mathematical programming. "Heuristic" is just the formal term for "expert trial and error." Until someone builds a tuba based on mathematical methods that even approaches what we have now, then a skeptic I will remain. Only the concrete example will move me. Were Anton Meinl to ask me (a laughable concept!), I would advise him that on principle the risk is enormous and the chance of success vanishingly small, unless it is used to round out the expert heuristics they have already built up.
I have no doubt that such an instrument would excel in the factor optimized. If that was intonation, then the horn would provide excellent intonation. If it was a particular mix of overtones, then I'll concede that likelihood. But how do a desirable mix of overtones and intonation interract? Is their relationship with each other linear (answer: almost assuredly no). What about projection? What about response? What about the ability to bend pitches with no loss of tone? What about the tight slotting of notes for security? Note that these last two characteristics oppose each other. What about the ability to play loudly without loss of tone? What about the ability to speak extremely soft notes? Do all these factors relate linearly? I can't imagine how they could. Do not underestimate the complexity of the combination of these factors. Any one or two them can be modeled, perhaps, but all of them together? We don't even know how to quantify or measure some of them.
We have seen the same thing with violins. I'm sure Chuck Jackson can tell you that there are any number of scientists who are sure they understand why a Strad sounds better than any modern violin. Some say it's the glue, some say it's the varnish, others say it's the wood, the thickness and profile of the belly, the tension in the perling, and I'm sure a zillion other factors, each with their fan in academia. I know one highly regarded violin maker who insists that Strads are Strads because of the sloppiness (f holes don't line up, etc.). Each point of view is backed up by extensive measuring and modeling. With all this thinking and modeling, though, the new ones still don't sound like the heirloom violins. If they did, the price gap between new and old would a lot narrower.
Of course, countering my skepticism are other heuristic sticks in the mud who foolishly delayed the implementation of new concepts. I remember a story where Carroll Shelby and Dan Gurney, who had designed an aerodynamic race car for the GT circuit, had their design rendered ineffective by Ferrari builders because the low roofline "didn't look the way a Ferrari should look." So, they built their own car, based on a little British sports car, and called it the AC Cobra. They added the low roofline they wanted based on their aerodynamic testing. The resulting Daytona Coupe killed the competition at LeMans and Daytona and changed race car aerodynamics forever. But it should be said that they also knew what made a good race car other than the body shape, including the right suspension, weight distribution, engine, drivetrain, and driver.
Rick "who is waiting for the model to include the air chambers on the other side of the buzz" Denney