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It is a fact in classical physics that high frequency sound has more energy than low frequency at the same amplitude.

However, my horn clearly requires more energy (air mass flow) to produce acceptable sound as frequency decreases. As I go below FF into the 5th valve range, I need a lungful of air for one or two notes per breath. Does anyone have an analytical reason why this is so, or have a reference which could be checked out?

In the very low register, I find if I am not careful, the embouchure opens up way too wide, and yes I seem to dump a lung full for just a quarter note. (Resistance is the key factor) I have to work on it, but forming the embouchure with a bit more focus, makes for a bit more resistance behind the lips. The feed of wind then is regulated a bit more and the air is conserved. Practicing longer phrases or simple melodies (sort of like singing) down there, while imagining blowing through a paper straw helps teach my muscles to perform in this manner. The last thing I want to do is to be over thinking what I am doing, so some conditioning and imaging is helpful. When I need more volume I simply feed more air, but keep the focus on the embouchure. For me it works nicely and is something that is included in my daily warm-up. In my case the problem began when I overdid the 'open jaw for low notes thing' and went way too far open.

By way of partial explanation, see Equal-loudness contour.


The red lines are the sound pressure required to achieve a certain loudness, at various frequencies. Loudness as perceived by a young person with no hearing damage. You can see how at the right edge, very high frequencies shoot up to the sky - i.e., they're inaudible to humans. And likewise, as you go down the scale, lower frequencies are also less loud, given the same sound pressure. To make a low frequency loud, you need a relatively high sound pressure, in decibels.

Now what I'm not looking up, is the relationship between sound pressure and amplitude. That could add to the fun, if the nature of the relationship to energy is not the same between the two, but I'm guessing the above is adequate to explain the phenomenon.

Thanks for 2 perspectives on that.
The equal loudness approach is particularly helpful because the change in energy "content" of any mass has to equal the amount of work added. . . modulated by transduction efficiency. The upshot is that most of that energy is in the low low note, it's just not perceived efficiently.

Oh, and thanks for the embouchure advice. I'll work on that!

Neat instruments. The output confirms my OP.