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isn't a mixte the type of step-through that has a pair of stay-sized tubes instead of a top tube, which run all the way from the head tube past the seat tube down between the seatstays and chainstays?
Yes.
Which makes me wonder, is there a name for the half marathon step through which has a single tube from headtube to seat tube supported by a pair of stays from that junction to the dropouts?
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Point of order - isn't a mixte the type of step-through that has a pair of stay-sized tubes instead of a top tube, which run all the way from the head tube past the seat tube down between the seatstays and chainstays? A more rigid design which addresses the flex normally associated with a much lower top tube at the cost of a little weight.