How do you play quarter-notes on a trumpet?

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I am trying to compose music in the Arabic scale. Now for those familiar with Middle-Eastern music, it uses a 24-note system. This is the regular Western 12-tone system but with exactly 12 other notes exactly in between each Western tone.

If D-flat is the 1st and 2nd valves fully depressed on the trumpet, then would D-flat-flat (quarter tone between C and D-flat) be the 1st and 2nd valves halfway depressed? Or is it not that simple?

Also, if I rig my guitar with extra struts to affect the 24-tone system, where would those struts need to be constructed? Not exactly half-way between the two main struts, I imagine. Perhaps 2/3 of the way?

Thank you.

I don't know how trumpets work, so I can't answer that one

On the guitar, my best guess would be the square root of two, minus one, which would be about four tenths of the way (0.4142 should be accurate enough). Not completely sure though

Thank you. Is that the square root of two minus one of-the-way to the next fret working toward the center of the guitar or out from the center of the guitar?

What is the trumpet tuned to? Are you writing for C trumpet?

Hey

Just wanted to say I've been doing the math and... Now I don't know. Sorry for the misinformation. May have an answer later, but the problem is more complex than I initially thought

Well, it's the principle I'm worried about. Whatever the trumpet is tuned to, if a certain tone is played 1/d-u, 2/d-u, 3/d-u (where 1, 2, 3 denote the 1st, 2nd, and 3rd valves respectively, and "d" and "u" represent whether that valve is depressed or undepressed), then can a quarter note be played 1/d(.5)-u(.5), 2/d(.5)-u(.5), 3/d(.5)-u(.5) [where the ".5" denotes halfway depressed/halfway undepressed]?

Whatever the answer to that question is, I found an easier way to Arabically tune the guitar. Say, for example, that 4 revolutions of the D-screw clockwise render the D-string a C-string. If the relationship between the tautness of the strings and the pitch of the strings is simply arithmetic (which is precisely what I'm trying to find out), then 2 revolutions of the screw render it a D-flat string and 3 revolutions turn it into the D-ffllaatt string (where "ffllaatt" stands for that quarter note which is between C natural and D-flat).

I imagine this would be easier than similarly tuning the E, A, B, or E strings, since those would involve more difficult finger work.

it is not that simple, if only becouse you can't 'half-press' the valves on a brass instrument; this will block the airflow, preventing any tone from forming.

to play in a 24-tone scale, you will need either a fully chromatic instrument, like a trombone, or instruments that are specifically built with the valves being build on quarter-tone distances, western brass indeed only has half-tones (1/2, 2/2 and 3/2 tones, to be exact, some have a 5/2 tone valve added, but that's it)