We had a similar conversation back in February and, among the topic
discussed was, why 3X1 instead of 1X3? Bill pointed out that commercially
available 3 speed fws of good quality with huge tooth gaps are hard to
find, whereas anyone can find a triple crank.

But I keep coming back to theoretical efficiencies: IIRC, the gearing
effect of tooth jumps in back are more or less double what they are in
front. So the question is, how to get just 2 or 3 big jumps in back without
a IGH.

Question: I've never followed BMX, but IIRC I've read of 2-speed BMX
freehubs; was that really a thing? If so, perhaps that would be the ideal
low-cog-count/big-ratio-jump system. And then there are those packages of
spacers and ss HG-freehub-compatible kits that allow you to use just 1 --
or a few -- cogs on your 7-8-9-etc.-speed freehub.

Long ago I asked Phil Wood & Co. if they'd build me a fixed hub that would
accept 3 sprockets. They replied, "Sure! Figure on about $400" -- this in
circa 2000 dollars which per the DoL Inflation Calculator is ~$740 in 2024
monopoly money. With horizontals or track ends and a good steel internal
cam QR you could have yourself a very good time without the need for a
lousy (and FWIW considerably less that I paid for my TF hub). A  44 X
17/20/24 would give you 70", 60", and 50", a good spread with relatively
unobtrusive hardware and bulk.

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