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In Fux's Gradus ad Parnassum, when in the F mode (lydian), the B is always flat, at least in the first and second species examples. The cantus firmus proposed by master Aloys avoids the note altogether, and in the counterpoint done by the pulpil Joseph, whenever a B appears, it is always B flat and it doesn't seem to be avoiding any tritones that I am aware of.

Is there something I'm missing? When working out the exercises myself, should I always use B flat instead of B natural?

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The reason why a Bb is used instead of a B has to do with the key aspects of the Lydian mode itself which is the #4 and how it acts.

The only difference between the Ionian mode and the Lydian is the 4th which is perfect in the Ionian mode and augmented in the Lydian mode. In Fux's counterpoint whatever mode you were in, you would want your cantus firmus and its counterpoint to reflect that. That's why you'll see a D# in E Phrygian, C# in D Dorian, ect. They are not natural to the mode, but emphasise and lead to there respected home note. While the E in F Lydian does this nicely, because of the way the scale is laid out the B (the augmented 4th) can also lead to the C very easily and makes it seem like the home note.

To counter this, the B is typically avoided and when introduced it is flattened to avoid this.There are a few sources that talk about this in depth and are worth a read. Here an excerpt from two that explain it pretty well:

Counterpoint in Composition: The Study of Voice Leading

In writing a modal cantus firmi, the students should bear the following in mind:

  1. In relation to voice leadin the Ionian and Aeolian modes (on C and A) can be considered equivalent to major and minor.
  2. The distinction between authentic and plagal modes becomes problematic in polyphonic music; the student, therefore, can disregard this distinction.
  3. In polyphonic textures the Lydian mode (on F) regularly employs B flat; this mode, therefore, becomes equivalent to transposed Ionian.

Source

Music from the Middle Ages Through the Twentieth Century

Despite the fact the b flat in lydian mode gives the appearance of the modern "major" mode which was an anomaly in medieval theory, one must take into account the evolution of modal theory that, in Adam's day, readily accepted b flats in lydian mode. Moreover, the use of b flats in refrains "He! Robechon" and "Vous l'orres" may be justified on the basis of the understood principle of fa supra la or modal commixtures.

Source

  • Thanks a lot. The link to the second source was very helpful. It's a shame The first source's link provided no text to read. I was hoping it could give me a more direct answer to my second question: to be consistent with the rules of counterpoint followed at the time the book was written, when working out it's exercises myself, must I treat the F mode as if it were transposed Ionian? In which cases could I use B natural? – Gustavo Jul 6 '15 at 0:02
  • @Gustavo for simplicities sake, you would treat it like F Ionian which has the notes F - G - A - Bb - C - D - E. The Lyian part of this counterpoint is the fact it starts on F. – Dom Jul 6 '15 at 0:40
  • I undersstand you would do so for simplicity's sake. It's just a little disappointing that the characteristic B natural which is what gives the Lydian mode it's characteristic sound is actually not very present. I took a look at a score of Machaut's Sanctus and found it was very consistent with the rule explained in your second source according to which "if there is a more rapid descent to F than there is a an ascent to C, it is sung uniformly by soft b", although there are a few B flats that are sung B natural by the Hilliard Ensemble so I guess some situations are open to interpretation... – Gustavo Jul 6 '15 at 15:18
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    Back then, modes were simply not seen as the rigid pattern of whole-and-half steps that we see them as today. There's good reason why, when Heinrich Glarean first introduced the Ionian mode in 1547, he claimed that it was already the most-used mode. – Caleb Hines Jul 10 '15 at 12:49

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