I was unhappy with commercially available trumpet mute holders: the clamping screws take forever to attach and to remove.
Solution: design print a trumpet mute holder and fix it to the foldback clamp
The diameter I selected works for my straight mute as well as for the cup mute, the plunger and the Harmon mute.
Slide a 51 mm clip in the slot.
Print the "flexible mute holder"- that includes the lock. The "lock plate" glues to the bottom of the holder.
Print one or more "large mute holder" for Harmon mutes or straight mutes. Print a "smaller mute holder" for mutes wih a thin stem. Slide one to three holders in.
And just for fun: the "cup" will not only be handy for pencils, glasses etc, but by coincidence has exactly the right diameter for beer cans (or bottles :-)
I used https://www.thingiverse.com/thing:2683376 and scaled it to fit the 51 mm foldback clips I use. I slip one padding on the clip for normal stand and two- one on each side- for small stands with thin tubes.
For very large diameter conductors note stands I included a different clip design which requires to insert a spring clamp (with one leg cut a bit shorter), see the images. I used these, https://www.obi.de/spannwerkzeuge/lux-leimklemmen-4-teilig-25-mm-classic/p/5273628