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Interesting instrument.....

Very imaginative. The artist has seen some tubas but has no idea how they work. Fun picture anyway, though.

Vienna valve saxhorn....

For many years, I too thought this was an approximate rendition of a tuba, however last year I saw a real version of the instrument in the painting. It was pitched in CC like a modern C tuba and tuned to A450Hz, consistent with what one would expect from Austrian windbands from around the late 1800s. I believe the correct name for this instrument is: Ornaphone/Ornaphon/Ornafon etc. Unfortunately I didn't manage to take a photo of that particular instrument, however here is a photo of a very similar instrument, but with rotary valves.
Best regards from Berlin,
TheBerlinerTuba

That valve setup was also called "box valves" IIRC. There was a thread on here not long ago regarding it, and it was supposed to be incredibly fast compared to rotary or piston valves. But I can't seen to find it now.........................

I remember the thread. viewtopic.php?t=70662&p=577336" target="_blank
The link to the box valves is there, but here it is if you can't be troubled;
Scroll down to the second tuba (Jacob Löw/Münster Kastenventil)
https://brassandpipes.wordpress.com/aut ... linertuba/" target="_blank" target="_blank

Don't assume box valves from the flat surface.
Looks to me like Vienna valves with a cover protector.
1890 would be VERY late for box valves in any event.