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(I'm the OP here.)

My source for the statement that "instruments were being tuned to this scale well before the invention of logarithms" is an article by Edward Dunne and Mark McConnell, "Pianos and Continued Fractions," Mathematics Magazine, Vol. 72, No. 2 (Apr., 1999), pp. 104-115. They write: "Guitars in Spain were evenly tempered at least as early as the fiftheenth century, two hundred years before Bach. And Hermanus Contractus, born 18 July 1013, invented a system of intervalic notation that anticipated equal temperatment."

My source on Simon Stevin's work is a Rudolf Rasch, "Tuning and Temperament," published as Chapter 7 in The Cambridge History of Western Music Theory." Rasch gives an interesting account of the state of root extraction before the advent of logarithms. He attributes the errors to "Stevin’s sometimes rather reckless rounding of digits after the decimal period, which are often truncated rather than rounded."