Treble boost from trumpet bells may not actually make high frequencies louder

Evidence

The second effect of the bell is supposedly to enhance the strength of the upper harmonics by letting them out with little reflection (so-called treble boost), thus contributing to the brilliant timbre of the trumpet. Although it is noncontroversial that the bell flare allows higher frequencies to escape more efficiently, the net effect of this is subtle. Whether or not letting out the high frequencies actually makes them louder depends on several factors. — Eric J. Heller, Why You Hear What You Hear- An…, 1505

Categorization

• QUESTION: The author flags the accepted ‘treble boost’ explanation as subtle and possibly wrong — worth chasing which factors decide whether letting highs out makes them louder.
• SEED: An article on how textbook explanations of musical instruments persist even when their underlying physics is questionable.