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Is the 2.73 mm measurement the O.D. of the rod ? Or the major diameter of the thread ?

It's probably some kind of a US inch based screw thread since Holton was a USA company - 2.73 mm = 0.107 inch.
 

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It's hard for me to see exactly what you are measuring in the bottom two photos, but I 'think' that you are measuring the major diameter of the threads and the length of the threads ?

Later today I'll take a screw out of a Holton Tenor Sax that I have and see if I can figure out the thread pitch.

And yes, as Holton was made in the USA, I 'think' that the threads would be US inch series...
 

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Get a thread pitch gauge.

If the threads are too short to tell, take the mating part to a hardware store and try screws (or nuts) till you find what fits, then that's the size you need.

Machinery's Handbook will have the thread pitch and OD data you need.
 

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Holton will be American thread.
If the outside ("major") diameter of the thread is 2.66mm, that suggests the thread size is "4"
So it could be 4-36 ("Special") or 4-40 (UNC) or 4-48 (UNF).
You now need a thread gauge.
 

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Holton will be American thread.
If the outside ("major") diameter of the thread is 2.66mm, that suggests the thread size is "4"
So it could be 4-36 ("Special") or 4-40 (UNC) or 4-48 (UNF).
You now need a thread gauge in order to determine which one.
 

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A-ha ! I was just looking through my Machinery's Handbook and was going to post, but I see that others have helped with the answer...
 

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I'd recommend a GOOD thread gauge. I bought a cheap one off of ebay and the thing is almost impossible to read.
 

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Starrett is the standard.

Also, in my experience it can be really tough to discriminate between short thread lengths of tiny little threads, even with good lighting and a powerful magnifier. Sometimes I have to end up using nuts of known dimension to size screw threads because I just can't tell. And wtih real short threads, sometimes even two different nuts appear to fit, and you have to make a decision based on what seems most likely (for example, it's most likely to the be same thread as another elsewhere in the machine, than to be the only screw of that thread on the machine, and so on).
 
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