The accepted textbook claim of bell treble boost fails once loudness differences are normalized

Evidence

Figure 16.21 compares sonograms for a plain tube buzzed with a trumpet mouthpiece, and the same tube with a funnel-shaped bell added. The sound file (found on the CD for the Springer Acoustics Handbook) is intended to demonstrate treble boost on addition of a bell. However, once differences in overall loudness are accounted for, the bell has subtracted from the relative strength of the higher upper partials, as we have predicted. — Eric J. Heller, Why You Hear What You Hear- An…, 1528