I see, cool trick. Question is, when you start calling it distortion. I'm no physicist, but yeah, in the case of trumpets, they're built in a way, so their "natural" overtone series gets distorted. The reason being they want to play equal temperated system.
BTW What they do with church bells, in terms of "harmonic distortion", blew my mind. The bells are "tuned", meaning built, so that the 5th overtone, which is the *major* third (10th an octave lower), becomes close to a *minor* third. At least in my part of the world. (-: In other words, "naturally", when the * bell would begin to chime*, it would do so with a note that contains its major third upper harmonic. Which would not sound like a church bell at all anymore probably. But the form of the bell is specifically built so that its fundamental resonates with a *minor* 3rd harmonic, which gives the tone of the bell its seriousness. If you train your ears a bit, you can hear it. Quite clever, those old church hoshis.