With all due respect …
The concept that intonation is, “The #1 overriding factor in volume” is hogwash.
Volume is determined by the transfer of power (see note below) from the source to the receiver. In this case, from a horn to an ear using air as the medium of transfer. The more power the source can put into the air, the more power will be presented to the receiver. Given multiple sources, the total power put into the air is the sum of the power of each source. It doesn’t matter if the two hours are playing the same note, the same note but not in tune, or different notes. It’s the sum of the power across all sources.
The “perceived” volume argument is similarly a canard. Most often the physics cited is the additive effect of in-phase waveforms. Believe me, no horn player short of Gabriel can control the phase of a horn. Even if they could and even if the waveforms were in phase at one ear of a listener, they would be out of phase at the other ear.
The only answer to this argument is to measure the power output of G and Bb instruments. I’ve not performed that experiment and know of no papers on the subject.
Can we please end this discussion?
Thank you, Mr. Wizard
Note: Power is the rate at which work is done or energy is transmitted. Energy is the capacity to do work. Energy is power delivered over time. For this discussion, either power or energy is acceptable.