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I am building an old Rivendell road bike (2005). It has a Rivendell Silver 38x24 crankset.

Would this be compatible with a Dura-Ace 11-28 cassette? If not, which cassette would you recommend?

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Your cassette doesn't care what size your chainrings are, although those are remarkably small chainrings for a road bike. Is that possibly a triple missing its big ring?

The number of sprockets on your cassette will determine your chain width, and that in turn will determine how thick the chainrings should be. In my experience, there's a lot more latitude in this regard than component manufacturers would like us to believe (I've used chainrings for an 8-speed system with an 11-speed chain). Still, something to be aware of.

Because those rings are so small, you may also have some trouble with some front derailleurs: the outer cage of the derailleur hugs the circumference of the big ring it was intended to be used with (typically 50 to 53 teeth); with a much smaller big ring, there will be an unavoidable gap between the derailleur and chainrings, so that the chain hits the cage differently. It may not shift as well, and you may get rubbing in extreme cases.

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