Rules of motion within Counterpoint!? HELP.

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Josephfarrar

Rules of motion within Counterpoint!? HELP.

Post by Josephfarrar » Wed Jul 31, 2013 8:29 am

I have recently started trying to improve my counterpoint although i have come across the same problem again and again. Hopefuly the composers on this site might be able to enlighten me and help me with my problem. The rules of motion are as followed.



First Rule
Only proceed from perfect consonance to perfect consonance in contrary or oblique motion.

Second Rule
Any of the three motions is permitted if moving from a perfect consonance to an imperfect consonance.

Third Rule
Only proceed from imperfect consonance to perfect consonance in contrary or oblique motion.

Fourth Rule
Any of the three motions is permitted if moving from an imperfect consonance to an imperfect consonance.

What i do not understand is that what happens when you move from the 1st note of say the major scale in C to the 4th (G)? Is that not movement from a perfect consonance to a dissonant one? Because of course melodies can utilize all notes from within a scale how can the rules only be applied to perfect and imperfect?

I think perhaps this is not talking about horizontal movement.. But i can't see how else it could apply.

If the melody is for example. D F E F G F A G F E D, or in scale degrees (Dorian mode), 1 3 2 1 4 3 5 4 3 2 1. The seconds and the 4th should be classed as dissonant intervals and should not be used (Or rather the rules can't be applied to this movement) according to Fux's rules. But this melody is taken from a cantus firmus and so is obviously used within this setting.

What is it that i am failing to understand about the rules?

If someone can help me with this i would be hugely appreciated as this has caused a difficulty for years.
Thank you for any help you can give.

- Joe :)

Rich

Re: Rules of motion within Counterpoint!? HELP.

Post by Rich » Wed Jul 31, 2013 11:01 am

I am not sure I understand the question. The rules of motion apply to the intervals that are formed between the Cantus Firmus and the Counterpoint. A melodic motion from D to G in Dorian is permitted. But if you had a G in the Cantus Firmus in a two voice, first species setting, you would not be permitted to set a D below the G as a counterpoint because the interval of a Perfect Fourth is dissonant in that circumstance. And you mentioned that all notes in the scale can be used in melodies. But some melodic motion is prohibited in strict counterpoint. For example, if I remember correctly, no Augmented, Diminished, or chromatic intervals; no intervals larger than the 5th – except for octave & min 6th, the minor 6th only in upward direction and so on. I hope this is helpful.

Josephfarrar

Re: Rules of motion within Counterpoint!? HELP.

Post by Josephfarrar » Wed Jul 31, 2013 11:17 am

thanks for your help :) Its the word MOVING that confuses me. By placing a counterpoint against the cantus firmus there is there is no movement. Movement seems to suggest movement along the horizontal (melody line) to me. Would you be able to give me an example of how the rules of motion apply? You cant move from an imperfect to a perfect consonance in an interval.. it is simple one or the other i thought?

Although... I think you have just made sense of it for me...

Is this right?

Is it that you look at the intervals and compare them to the next one in line.
So if you were to have a F in the Cantus firmis (in the key of F) and a C in the counterpoint.. then the next note was a G in the Cantus Firmis and there was a B in the counterpoint. It would be a PERFECT consonance moving to an IMPERFECT one? (The fifth relationship between the first note's and a third relationship between the second). And Then moving back to an F in the cantus Firmis and a F (octave) in the counterpoint would then again be moving from an IMPERFECT to a PERFECT?

Is this correct?!
IF SO! IT FINALLY MAKES SENSE :D

Rich

Re: Rules of motion within Counterpoint!? HELP.

Post by Rich » Wed Jul 31, 2013 1:16 pm

Yes as far as moving from an imperfect to a perfect consonance. But the move from a B natural, if that is what you mean, to an F natural would be prohibited in strict counterpoint because it is a Diminished Fifth. And you must also account for whether you are approaching a perfect consonance in direct, contrary or oblique motion. If you have an F natural in the CF and an A natural set above it in counterpoint and then the A moves up to a D natural and below it the F moves up to a G natural the move is prohibited because you have approached the Perfect fifth between G and D by direct motion. ie. the F moved up to a G and the A moved up to a D, both voices moved in the same direction.

Josephfarrar

Re: Rules of motion within Counterpoint!? HELP.

Post by Josephfarrar » Thu Aug 01, 2013 5:46 am

Thank you so much, I understand now. I can go on to continue my studies in counterpoint. This has been an eye opener for me.
Thanks for your time to explain to me how this works!

Max Karios

Re: Rules of motion within Counterpoint!? HELP.

Post by Max Karios » Fri Aug 09, 2013 2:39 pm

Josephfarrar wrote: First Rule
Only proceed from perfect consonance to perfect consonance in contrary or oblique motion.

Second Rule
Any of the three motions is permitted if moving from a perfect consonance to an imperfect consonance.

Third Rule
Only proceed from imperfect consonance to perfect consonance in contrary or oblique motion.

Fourth Rule
Any of the three motions is permitted if moving from an imperfect consonance to an imperfect consonance.
This is how Fux wrote it in his book "Gradus ad Parnassum", but it is actually quite redundant. You can sum up all of this in one single rule: When going to a perfect consonance, do not use direct motion. That is all. If there are no restrictions then why make a rule (#2 and #4)? If the interval that you come from does not have any impact on the result then why mention it at all (#1 and #3)?

Gene

Re: Rules of motion within Counterpoint!? HELP.

Post by Gene » Tue Aug 13, 2013 11:00 pm

Download Zarlino's book on counterpoint he is much better .

jack_cat
Posts: 88
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Re: Rules of motion within Counterpoint!? HELP.

Post by jack_cat » Mon Jul 30, 2018 5:56 am

Josephfarrar wrote:
Wed Jul 31, 2013 8:29 am
What i do not understand is that what happens when you move from the 1st note of say the major scale in C to the 4th (G)? Is that not movement from a perfect consonance to a dissonant one? Because of course melodies can utilize all notes from within a scale how can the rules only be applied to perfect and imperfect?

I think perhaps this is not talking about horizontal movement.. But i can't see how else it could apply.

If the melody is for example. D F E F G F A G F E D, or in scale degrees (Dorian mode), 1 3 2 1 4 3 5 4 3 2 1. The seconds and the 4th should be classed as dissonant intervals and should not be used (Or rather the rules can't be applied to this movement) according to Fux's rules. But this melody is taken from a cantus firmus and so is obviously used within this setting.

What is it that i am failing to understand about the rules?
Joe is confusing melodic motion, in which a single voice moves by intervals, with harmonic relationship, in which intervals are created between two or more voices sounding simultaneously. When one of the voices moves, it must take into account the interval to be produced between it and the other voices or voices. In beginning exercises, the first voice, called the cantus firmus, is given in a fixed form, and is NOT subject to these rules, and it is the second melody (which accompanies this first melody and which the student is supposed to compose) which must obey the rules.

The Dorian melody quoted by Joe is similar to the Dorian cantus firmus given by Fux. It contains, by itself, only melodic intervals. A second melody is required in order to produce harmonic intervals by harmonizing with this first one, and the student is supposed to compose this second melody. What the first melody is doing is not subject to the rules; it has already been composed. The job is to stack another melody on top of the cantus firmus (or below it), to create a note-against-note counterpoint, and this second voice is the one which must follow the rules, using the three motions appropriately according to what interval will be created between the notes which the two voices simultaneously sing together at each step. The interval used in the melodic motion of each individual voice is a different issue; there what's important is the type of motion, contrary, parallel or oblique, and whether the interval by which the counterpoint moves in relationship to itself, is a perfect or imperfect interval, is not relevant. (Note that there is no oblique motion in the following counterpoint, as this would require one voice to repeat a note. Oblique motion usually occurs with one voice moving in faster notes than the other.) It is whether the interval produced by the simultaneous sounding of the two voices is perfect or imperfect that is relevant to the direction of movement made to get to this point. There are, in this counterpoint, four perfect intervals and seven imperfect intervals.

P---I---I---I---I---P---P---I---I---I---P
D4 A3 C4 D4 E4 F4 E4 B3 D4 C#4 D4 (added melody, i.e. counterpoint)
D3 F3 E3 F3 G3 F3 A3 G3 F3 E3 - D3 (cantus firmus)

As the counterpoint moves to each new intervalic relationship with the cantus firmus, it must do so by the correct movement. Thus at the sixth note, there is an octave F4 above the cantus firmus's F3, and this is approached in contrary motion. However, it is the second voice which must choose this motion in relationship to the pre-existing shape of the cantus firmus, because the cantus firmus has already been composed.

PeteJ
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Joined: Fri Jul 08, 2016 12:52 pm

Re: Rules of motion within Counterpoint!? HELP.

Post by PeteJ » Tue Sep 18, 2018 4:32 pm

Max Karios wrote:
Fri Aug 09, 2013 2:39 pm
This is how Fux wrote it in his book "Gradus ad Parnassum", but it is actually quite redundant. You can sum up all of this in one single rule: When going to a perfect consonance, do not use direct motion. That is all. If there are no restrictions then why make a rule (#2 and #4)? If the interval that you come from does not have any impact on the result then why mention it at all (#1 and #3)?
What an incredibly useful post. Your point is obvious once seen but I imagine it would be frighteningly easy to miss for a struggling student of Fux.

I wonder if it can be further simplified. It seems to me that most of these rules are about not losing the independence of the voices. I'll say more and risk talking nonsense in public, as usual.

If we listen to what happens when we break the rules we often create the same effect as parallel octaves and fifths. It seems fine to have an octave between the two voices where one is heard as a passing note but not where the voices seem to land on the octave as a downbeat and a harmony. This creates the need for rules designed to maintain the melodic independence of the voices and avoid jarring full-stops in the flow of the music.

Would it makes sense to say that the single rule you give above together with the rules for parallel fifths and octaves could be subsumed within a general rule stating 'Maintain the melodic independence of the voices'?

Or, are there further reasons for these rules?

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