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I understand how trumpets work - valves open to force the air through crooks, which lengthens the pathway the air must travel, thus decreasing the resonant frequency.
The question is, why are trumpets designed like this? Couldn't they also be designed with all the crooks open by default, such that activating the valve decreases the length of the pathway? Is there a reason they aren't made like this, or is it just a matter of tradition?
The simple answer from a historical perspective is that valves on brass instruments were an addition to simple coiled horns like the bugle and hunting horn. It's kind of counterintuitive to add something in order to take away something; why not add something that adds something? Add the valve, and add its pipe; with the valve not depressed, the instrument is the same as (or as close as possible to) the original instrument. It's when you depress the valve to open that pipe and extend the speaking length of the horn that there's any change.
In addition, from a practical and engineering standpoint, valves add back pressure. The more 90-degree turns a pipe has, the less laminar the flow of air through it becomes, and thus the more resistance the pipe presents to airflow. Modern valves are designed to minimize this by providing as straight a path as possible through the valve tree when all valves are open, only introducing the 90-degree turn into the valve pipe when necessary. This makes the instrument more free-blowing, which gives a more focused tone (though other design elements of the instrument can affect backpressure and tone as much or more, and the amount of backpressure inherent in a design is subject to personal preference).
Lastly, it's just common sense (among wind players at least). Virtually all woodwinds have a series of "main" pads or holes; as each one is pressed or covered in order, the instrument's pitch is lowered because its speaking length is increased. While most modern woodwinds also have keys that raise the pitch when pressed (because they raise a normally-closed pad), these keys were relatively late additions to the instrument, to increase and fill out its range. So, this "key down = lower" mentality was pervasive among wind players before the first valved brass instruments were developed (and in fact, older "keyed brass" such as the serpentine and keyed trumpet used similar mechanisms to adjust their own partial lengths, so even among brass players it was a common way of thinking).
I suppose trumpets have the clarion as a base, and that it feels logical to have a clarion when not pressing any valve.
A reason I can see is that the higher notes of the trumpet do not need the third valve. Above middle Ab, you can play all tones with only two fingers (although the Ab above that is often fingered 23). If you had to press the valve to close to crook, you would have to press the third valve most of the time.
There is a history of ascending valves, which indeed raise the pitch upon being depressed. R. Dale Olson
