what is the best way to build the upper register for trumpet players??

One of the most desired assets for a trumpeter is the ability to play in the upper register, also known as the extreme register. Upper-register playing is required in most genres of music, and it is considered one of the most difficult mental and physical challenges of trumpet performance. This paper aims to critically analyze and discuss upper-register playing, thereby serving as a guide enabling trumpet players to more effortlessly master this task. To achieve this, there will be an in-depth analysis of the Baroque approach to the upper register, which will then be compared to the modern approach. The assessment will differentiate among embouchures used, jaw and facial structures (i.e. overbite or under bite, straight teeth, or gaps in teeth), diet, breathing techniques, tongue placement, and equipment or combinations thereof (i.e., different mouthpiece and trumpet combinations). Additionally, a study of past and present professional upper-register masters, as well as myths of upper-register playing, will be presented. This paper is intended to serve as a methodology to upper-register trumpet playing and will offer trumpet performers simple, yet proven, practical methods which can improve proficiency in this critical arena.