On page 39 of Alfred Mann's The Study of Counterpoint there is a passage concerning justification of using accidentals in first species counterpoint.

Here is the passage:

Aloys: [...]but why did you put a sharp in the eleventh bar? This is generally not used in the diatonic system.

Joseph: I wanted to write a sixth here. But when I studied singing, I learned that fa leads down and mi leads up. Since the progression moves upward from the sixth into a third I have used a sharp in order to emphasize the tendency to ascend. Besides, the "F" in bar eleven would result in a harsh relation with the "F#" in bar thirteen.

What does Joseph mean by "fa leads down while mi leads up"? What is his reasoning for changing the "F" to a "F#"?

Also, what does Joseph mean when she says that "the progression moves upward from the sixth into a third"?

2 Answers 2


In the older hexachordal system, mi refers to a note below a half step (like E below F or B below C) and fa refers to a note above a half step (like F or C in a white note system). So by changing F (which is a Fa) to F# he is temporarily making it a Mi. Think of Mi as like a leading tone with a tendency to move upwards. Fa had a tendency to move down, particularly when the Fa was created by putting a flat on a B. Since he wants to make an ascending cadence to G then the temporary Mi of F# is warranted.

I don't understand his argument that leaving out the # on the last F would create a harsh relationship (semitonal motion) with the previous F# since the only reason why that F# would have added in the first place was to prevent a harsh relationship with the following F#. :-)

The calling of any note below a half step Mi and any note above the half step Fa is where the definition of a tritone as "Mi contra Fa" comes from. Because this usage is foreign to modern music theory, it is often misquoted as "Ti contra Fa." (an aside: the second half of the rhyme, "Mi contra Fa est diabolus in musica" is not a medieval or Renaissance expression; the idea of the tritone as the devil's interval cannot be traced back earlier than the 18th century. Fux himself in fact seems to be the creator of the rhyme. see F.J. Smith, "Some aspects of the tritone and the semitritone in the Speculum Musicae: the non-emergence of the diabolus in musica," Journal of Musicological Research 3 (1979), p. 68.)

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    So by changing F (which is a Mi) to F# he is temporarily making it a Fa. You mean the opposite I think. That is not right what you wrote. He is changing it from a Fa to a Mi because Mi has a tendency to ascend May 19, 2013 at 16:39
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    Also, Michael Scott Cuthbert, why does f# have a tendency to ascend to g and not descend to f since both g and f are one semitone away from f#. f# can be interpreted as either a mi or fa right? May 19, 2013 at 17:00
  • I am in agreement with Cuthbert here. @ Chris - "Mi" and "Fa" refer to the motion of the voice and not the actual individual pitches themselves. You are incorrect in saying that the F# is temporarily "Fa" because the voice-motion indicates ascension and on downward motion. To answer your other question, in this case, F# has the tendency to ascend because the tonal center of the exercise is pitched in "G" and F# serves as a leading tone to G major. By raising the seventh degree at the end of the exercise, the student is ensuring a greater sense of finality and completion. May 19, 2013 at 17:40
  • 'You are incorrect in saying that the F# is temporarily "Fa" because the voice-motion indicates ascension and on downward motion' I never said that jjmusicnotes. This is the mistake Michael Scott Cuthbert made. I was pointing it out. May 19, 2013 at 18:03
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    @ChrisOlszewski - you would be better off continuing the conversation in Music: Practice & Theory Chat. Comments here are not forextended discussions.
    – Doktor Mayhem
    May 20, 2013 at 6:32

Chris - you have many questions in a row, so I thought it easier to submit an answer rather than post several comments. To moderators, I apologize if this is cluttersome.

Here we go:

1.) You are correct, you did not in fact make that statement - I did not realize that you were quoting Cuthbert. I will expand upon this answer momentarily.

2.) The term "diatonic" refers to what naturally occurs in the scale. In major keys, each degree of the scale corresponds to a different mode - even the root pitch. The exercises are in modes that are for the most part diatonic. The exception includes use of Musica Ficta.

During this time period, modal counterpoint dominates the contrapuntal landscape - if not the entire musical landscape. Much music of this period is referred to as "motor music" because of the constant rhythms and motion of independent voices.

3.) Ascension cannot be on downward motion. Your confusion stems from a typographical error on my part. The sentence should read "You are incorrect in saying that the F# is temporarily "Fa" because the voice-motion indicates ascension and not downward motion."

That said, I would like to redact that sentence as it is incorrect.

Regarding your confusion concerning "Mi" and "Fa", I would like to direct your attention to page 35. Read the footnotes carefully, particularly #8, and refer to the bottom of page 31 for further clarification.

According to the text, the Mi / Fa relationship in this instance is not as Cuthbart describes in his answer, but regards relationships within different hexachords.

As as aside to Cuthbert - the popular phrase mentioned in your answer appears in Fux's text, which was published in 1725, the early part of the 18th-century. It may be understood that this phrase does not actually hold a religious connotation as some may ascribe, but rather that the interval is a "devil" to work with because it offers no readily available diatonic solutions.

4.) Joseph's comment about "harsh relation with the F# in the thirteenth bar" is an apt one. Here Joseph is pointing out tendencies of aural memory. Since it is toward the end of the exercise, listeners would have perceived that non-diatonic semitone relationship between the "F" in bar 11 and the "F#" in bar 13 as jarring dissonance and therefore unsatisfying. Composers during this time period were extremely cautious (as you will read in further species of counterpoint) about approaching and resolving dissonances. Aural palettes were simultaneously refined and immature.

In order for the relationship not to see too jarring, Joseph would have needed more time in between each occurrence. Due to the brevity of remaining measures after bar 11, Joseph astutely concludes that he does not have the space necessary to facilitate appropriate pacing to leave the "F" as natural.

5.) Also: How does the progression move upward from a sixth to a third? What does that mean?

If you look on pg. 39 of the book, you will see that the line for counterpoint contains a treble clef with an "8" below it. This indicates that all written pitches sound 1 octave lower. By comparison, the "D" in bar 11 on the top staff would sound as the fourth line from the bottom on the lower staff in the same measure. The numbers above the lower staff indicate the interval between the two pitches, but do not qualify the type of interval (such as major or minor.) In this case, it is a minor-sixth.

In the following measure, the voices move by contrary motion to another consonant interval: a major third. Since the exercise involves counterpoint below the cantus firmus, the progression may be aurally perceived as moving upwards.

6.) By the way: c and c# are used in a previous example so does Johann Fux contradict himself for using a good example (as his teacher Aloy. calls it) with a c and c# and then avoiding the use of f and f# in the invention that I wrote out above?

My understanding is that you are referring to the exercise on page 31. Here the context is different which is why it may seem contradictory and therefore incorrect. Before I answer, you should know that Fux was a master of counterpoint. He was very, very famous during his lifetime and regarded as one of if not the foremost counterpoint pedagogue. The Fux text has not remained the authority on counterpoint for almost 300 years because it is full of mistakes. Any mistakes in the text are more likely the result of translation, copying, or editing. That said, Mann provides a wonderful translation.

As the book states on page 32:

"...put a minor third in the next to the last bar since the cantus firmus is in the upper voice..."

From then on, the exercise resolves to a unison. If the counterpoint was left as "C" then it would have been incorrect. Moreover, if the "C" in bar 8 were written with as a "C#" instead, two worse issues would have occurred: the interval between the two voices would have been a tritone, which is bad news for everyone, and the counterpoint motion from bar 7-8 would have been the interval of an augmented fifth - another big no-no. In this instance, any jarring dissonance experienced by a listener between the "C" and "C#" would pale in comparison to the dissonance of a tritone or voice movement of a augmented fifth. Sometimes you need to break small rules to avoid breaking larger ones.

  • Isn't there only an enharmonic distinction between augmented fifths and minor sixths? Why if a minor sixth is allowed an augmented fifth isn't? May 20, 2013 at 1:32
  • What do you mean jjmusicnotes that by "the counterpoint motion from bar 7-8 would have been the interval of an augmented fifth"? If the interval between the two notes in bar 8 is a tritone? May 20, 2013 at 1:35
  • Don't worry, the limit's 30 000 characters, almost six times the length of the answer. :P
    – Luke_0
    May 20, 2013 at 1:43
  • @ Chris - I check this site occasionally, so I cannot guarantee a time frame for responses. To answer your questions, I was referring to motion within an individual voice, not the interval between voices. This is a very important distinction. @ Luke - thank you for letting me know, that is good to keep in mind. May 20, 2013 at 6:01
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    Hi folks, just a reminder that to summon other users in comments, you type @username at the beginning of a comment with no space after the @ sign. However, the post owner as well as the OP will always be notified of comments whether they are explicitly referenced or not, so there is never a reason to repost a comment--it will just be removed. See more information about comments here.
    – NReilingh
    May 21, 2013 at 5:19

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