I admit it, I started out as a skeptic . . . sizes just didn’t look right . . . but now I believe our mouthpieces come close to completing the conic shape formed by our horns. I say “come close” because of the assumptions made along the way.

• We made the assumption that the horn is an un-interrupted frustum from the bell to the end of the neck. We ignored the cylindrical section formed by the neck socket.
• We made the assumption that we could unbend the neck, average out the sides and that the volume of the neck didn’t change.

What I’d really like to do is take a defunct horn and saw it into 1cm rings along its length and measure the inside diameters of the rings. You could then plot these and see if the horn is actually a right circular cone (point directly over the center of the base like the diagram on the first page of the tome), whether there are diameter variations along the length of the horn, or even if the horn is something exotic like a parabolic cone.

As it stands, with the assumptions we made here, I can push in my mouthpiece just a bit and it completes the theoretical cone of my horn. Well, fancy that!!

But wait! There is one more thing we can do: Check please!!