Yesterday afternoon I got excited about a new design for a brass instrument. Conical bore instruments have the problem that you can't combine valves (or slides) with having the tubing consistently expand over the length of the instrument. The valves force you to have a cylindrical bore segment in the center, and while you can design the tubing to minimize the cylindrical segment, you do have to have some.
Or do you? Imagine you have seven bells, with a single rotary valve that has seven positions, one for each bell. You use the standard fingering, with keys to rotate the valve 1/7, 2/7, and 3/7. This gets you approximately the same options for tubing length as a standard brass instrument, except that you no longer need to make compromises: pushing in all three keys brings you down exactly six half steps and you don't need a tuning slide to compensate. You can play chromatically, and you play it just like a trumpet, baritone, or tuba.
It looks like Adolphe Sax tried something like this, but with six two-position piston valves instead of a seven-position rotary valve, and he was just trying to solve the tuning problem and not the bore problem:
It turns out there's a somewhat successful instrument along these lines, but for totally different reasons. Instead of being optimized for tone, it's optimized for being easy to play. Each instrument has one horn per note, typically eight, so a range of just eight notes. The base of each horn has a reed, so you don't need any sort of embouchure, you just blow. See this video where someone takes one apart to demonstrate. They seem to be German; to find more videos search for "Schalmeien", while if you want to buy one (please don't) search for "Schalmei".
I do think a rotary trumpet, played chromatically with trumpet fingering, could work well though, and I'm curious whether anyone has explored this.
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