For many years the physics of trumpet design have been known. Just about every trumpet made today has the right formula. So why do trumpets range from $75 to $75,000?
Materials and workmanship are 80% of the process. The other 20% is an artistic ear and a flare for creativity.
A very skilled workman can make even a student model ring and play in tune, but that is not enough. There is the quality of the timbre, and the projection of sound. Of the millions of choices in materials you can expect that there are as many possibilities for Sound and projection.
Then there is the matter of "feel". If you pick up an instrument and it just feels wrong chances are it is wrong. Suppose you have 2 trumpets separated by a single serial number. One feels right and one doesn't. Why?
The ideal is to have the many pieces function as one. A well tempered trumpet will be perceived as heavier and solid in the hand, whereas a similar trumpet with a few loose solder joints and some thousandths of an inch difference in brass thickness will feel light loose and sloppy.
What I look for in the timbre is an even distribution across the overtone series featuring 2nd through 5 partials with a mean frequency of the actual note sounded maintaining at least 60% of the peak volume of the overtones 2-5.
With a bright timbre I want to see a very even slope from the 3rd harmonic on up. Producing a darker or more fundamental 2nd and 3rd harmonic is not simply a matter of killing the highs. It means that the spectrum has to have enough variety of peaks to excite the sound. A warm or dark horn still has to sing.
Developing an ear for tone colour is essential for fine craftsmen. Unfortunately with mass produced instruments it is seldom you find workers with the ability to "build" the overtones as they assemble.
Every horn must be different to lesser or greater degree. It is impossible to match all of the millions of tolerances, thickness's and connections. So with the very high quality trumpets you have very killed workmen with good sense of the harmonic spectrum and the time it takes to get it right.
Top line custom instruments may take months to complete. Compare that to the assembly line that turns out multiple horns each day.
Remember the design of the trumpet is not a secret, although each has their own take on materials and colour balance so even the assembly line student models can play pretty well.
High end trumpets are put through a break-in period prior to shipping. For example Mr. Schilke had a very simple little device that worked the valves thousands of times before sale. He play tested the horns and tweaked them until they sang.
The valve body is the sounding board for the trumpet. This is where the sound can be hijacked by any of a hundred things. The valve caps on a quality horn are critical to tone colour and the feel of the back pressure. An the average a diameter of .200" is the size for the vent holes in the caps.
The bore and bell size demand the need for properly balanced valve caps. The 1st cap has much to do with the attack and colour of the sound. The 2nd effects how the sound is perceived by the player and how the articulation pops or snaps between slurred notes. The 3rd adds or subtracts highs in the colour and is the rudder for the projection of the sound out into the hall.
The 3rd valve slide is the longest and the easiest place to "mess" with the playability of the horn. Simple adjustments of the saddle or ring - spit valve and even the compression of the slide will cause very perceptible change.
Most of these subtleties are not heard by the listener but are felt in the fingers lips and air column of the player. This is why a trumpet that is set up properly can extend endurance, range, power, and projection. Cuffed notes can be eliminated by balancing the response of the valve combinations. Bob Reeves has made a science of Positive Valve Alignment.
Valve alignment does not mean that each valve matches each port perfectly in both up and down positions. It means the balance of each fingering matches the next. i.e. playing an arpeggio on 1st valve should be even from bottom to top in resistance tone and feel. Then the 2nd valve should give the same feel as well as the 3rd.
When this is achieved the settings both vertical and horizontal are noted and stored. when things begin to shift it is a simple matter of going back to the numbers and re-setting.
Use of felts gives by far the most pleasing sounds, but the synthetic ones hold the settings much longer. I find it helpful to measure the felt thickness and or corks and then purchase my own felt and cork to cut to size within the many different thickness's available on the market.
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