One thought that comes to mind is that a finer thread might be more resistant to loosening under vibration and impact loads. A fine thread on  high strength alloy hardware tends to be able to withstand higher tightening torques and loading. As for lampshade hardware, appliance manufacturers were and are notorious for deliberately creating and using odd hardware to force the owner to obtain it only from their "Local factory authorized and certifer dealer and service center".

    Bruce Gentry, KA2IVY

On 11/25/22 14:21, Nick England wrote:
Well, Teletype is kind of weird in using 5-40 and 6-40 where most folks would use 6-32. 
And using 1/4-32 instead of 1/4-28. 
But who in the world decided on 1/4-27 for lampshade finials? Where did *that* come from?
--
Nick England K4NYW
www.navy-radio.com

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