p. 31 of The Study of Counterpoint by Johann Joseph Fux (translated by Alfred Mann) says:

page 31

I don't understand what this page is telling us. I understand what a hexachord is. However, why note is G not a correct note in D Dorian mode? D Dorian mode is: D, E, F, G, A, B, C, and G is the 4th note in Dorian mode, right? So why is this note wrong?

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    Sorry, I do not understand what your reference is. Is "p.31" referring to a page number? Of what book? Maybe the book "The study of counterpoint" by whom? – nath Jan 26 '18 at 21:28
  • In order that this question receives some answers, you need to be a lot clearer with its wording. Thanks. – Tim Jan 27 '18 at 9:28
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    Hi sorry for the confusion, it's the page 31 from the book 'the study of counterpoint' by Johann Joseph Fux (Author),‎ Alfred Mann (Translator), many thanks – Stephen Crabb Jan 27 '18 at 10:32
  • @Tim and nath, does this edit meet your approval? – jdjazz Jan 27 '18 at 13:15

The problem in that particular part of Fux's The Study of Counterpoint is not that G doesn't belong to the mode at all, but that the student is putting the G below D in the first measure. The first measure of a species counterpoint exercise must make the modality completely clear, but a G on the bottom would cause the exercise to sound initially as if it was in G Mixolydian instead of D Dorian. This is a problem in this context because the exercise will clearly end in D, and species counterpoint exercises don't modulate.

The upshot of this is that, although the initial consonance can be a P5th when a student is writing an upper counterpoint to a cantus firmus, it is not an option when writing a lower counterpoint. That's why the teacher says it wasn't the student's fault, he just hadn't told him about the rule yet.

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