Many early scientists as well as humanists investigated those aspects of music which had traditionally been dealt with by music theory in the medieval quadrivium. Their agenda included a reckoning of tempered scales and to a lesser extent vocal intonation. The main challenge in the 1500's was to overcome certain old precepts, e.g.: that the major third (theditonus) naturally had the monochord ratio (9:8)2= (81:64); that the comma was some kind of “ultimate” interval; that “superparticular” intervals (n:n − 1) could not be divided into equal parts (because music theory must reckon with rational “multitudes” and not “magnitudes,” music being “sonorous number”). In the 1600's, regular temperament and various equal divisions of the octave containing nicely tempered consonances (19, 31, 43,…, as well as 12) were sorted out, often with logarithms; but then keyboard musicians took up irregular temperament, and for some time the sophisticated French‐speaking scientists were so off the track that less urbane German organists outstripped them in developing an adequate account of the contemporary scale.