Monofilament metal saw wire for a wire saw, wherein the saw wire being provided with a plurality of crimps. The crimps are arranged in at least two different planes, such that, when measured, between measuring rods of a micrometer, over a length comprising crimps in at least two different planes, a circumscribed enveloping D diameter of the saw wire is between 1.05 and 1.50 times a diameter d of the saw wire itself.