'Ello, folks! I'm currently studying Johann Joseph Fux's Gradus Ad Parnassum and I've run into a wee bit of a snag. In his book, Fux says, and I quote "... the cantus firmus is in D (la, sol, re) 4, as the beginning and conclusion show, and you started with G (sol, re, ut), you have obviously forced the beginning out of the mode." I'm slowly beginning to get a grip on what this means, but I think I need a deeper explanation.
Also, down below in a footnote, it says "4 This quadruple denomination of the same tone derives from the old distribution of the tones into three hexachords", and then proceeds to give three examples, the hard hexachord, the soft hexachord, and the natural hexachord.
As far as I can tell, the la, sol, re of the cantus firmus (D), as the footnote goes on to explain, ut, re, mi, fa, sol, and la was the customary way to indicate the degrees of a tone in the hexachords.