The principle of scale length is actually quite simple. The narrower the instrument remains after the mouthpiece, the brighter and brighter the tone. The tube opens up considerably just before the bell. If the wind instrument opens quite wide after the mouthpiece, it is called a cylindrical opening. This means that there is no strong projection before the bell and the tones become darker and softer.
The trumpet has a conical (narrow) mouthpipe, which gives it its radiant and incisive sound. So the narrower the bore, the greater the proportion of harmonic partials (overtones). If you want to play an instrument that has a sharp, bright sound, the bore of the brass instrument must be narrow. If the instrument has a wider bore, you will hear darker and warmer tones.