# The Study of Counterpoint - J.J.Fux



## Jord

I've bought the English transcription of Fux's Gradus Ad Parnassum. But there's one part i don't understand on page 22 (for anyone who has the book)

I understand perfect and imperfect consonances, dissonances, and direct, contrary and oblique motion, but then it has 4 rules:

_First rule_: From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion
_Second rule_: From a perfect consonance to and imperfect consonance, one may proceed in any of the three motions
_Third rule: From and imperfect consonance to a perfect consonance one must proceed in contrary or oblique motion
Fourth rule: From one imperfect consonance to another imperfect consonance one may proceed in any of the three motions

I'm guessing it's talking about 2 voices but i'm not sure, it doesn't really make any sense to me could anyone help please? _


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## Ramako

Yes, you are right, it is talking about 2 voices.

Basically it translates to: you cannot go to a perfect consonance in direct motion. However I think that it is probably better to think about it in terms of the four rules he suggests because then you are thinking about which motions you are using and thus can consider greater variety than if you were just trying to avoid going to a perfect consonance in direct motion.

It is hard to explain it in any other way that will not obscure it. Perhaps you should read on and it will become clearer to you? I think the first chapter (first species in two parts - note against note) should demonstrate what he is talking about if you take care to examine the examples and read the commentaries, where for the first few particularly he talks about the choices he has made in direct relation to these rules.


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## Jord

Okay thanks


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## ComposerOfAvantGarde

The only progression forbidden is the direct motion into a perfect consonance.


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## paulc

If you are talking about Alfred Mann's translation of Fux, there is only one rule of counterpoint. See the footnote on page 22, referencing Beethoven and Martini:

1. Direct motion to a perfect consonance is forbidden.

As a general rule, learn what the bad progressions and practices are, then avoid them AS FAR AS POSSIBLE. Whenever there is an alternative to a bad progression (especially the above one), use that alternative.

Once you get to the second and third parts of the book (which deal with three and four voices), even this 'direct motion to perf. cons.' rule will be relaxed so that the only forbidden progressions are parallel unisons, fifths and octaves. Even then, you should still limit the bad movements.

The idea is that you are restricted to using only whole notes, half notes, quarter notes and ties for a large number of exercises. Once you adapt to these restrictions, being able to use any number and combination of these notes will allow you to easily avoid the worst voice-leading offences.

Paul.


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## Jord

So say if you have a C and a F in C major a 4th apart with C in the root, and the C goes up and a 5th to G, and the F goes up a 5th to C would that be wrong because it's direct motion with both going to a perfect consonance? 

but if the C went down to a G and the F went up to a G, would that be okay because they're both perfect consonances but they're going in contrary motion?


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## Ramako

Jord said:


> So say if you have a C and a F in C major a 4th apart with C in the root, and the C goes up and a 5th to G, and the F goes up a 5th to C would that be wrong because it's direct motion with both going to a perfect consonance?
> 
> but if the C went down to a G and the F went up to a G, would that be okay because they're both perfect consonances but they're going in contrary motion?


No.

You have the correct idea, but the fourth is a _dissonance_. In two part it is always treated as a dissonance, in three or more parts it can be treated as an imperfect consonance as long as it isn't with the bass.

If you have a D and an F a third apart, with the D in the bass then if:

1) the D goes down to a C and the F goes up to a G then this is correct - an imperfect consonance going to a perfect consonance in _contrary_ motion

2) the D goes up to an F, while the F goes up to a C, then this is an incorrect progression - the imperfect consonance has gone to a perfect consonance by _direct_ motion which is bad.

3) the D stays on a D and the F goes up to an A then this is correct - the imperfect consonance has gone to a perfect consonance by _oblique_ motion

This demonstrates the three motions from an imperfect consonance. Now let us start from a perfect consonance - say a C and a G with the C in the bass.

1) the C goes down to a G and the G goes up to a G then this is correct - a perfect consonance going to a perfect consonance in _contrary_ motion

2) the C goes up to an D, while the G goes way up to a higher D, then this is an incorrect progression - the perfect consonance has gone to a perfect consonance by _direct_ motion.

3) the C stays on a C and the G goes up to an C then this is correct - the perfect consonance has gone to a perfect consonance by _oblique_ motion

The fourth is something of a strange interval, which can act as a perfect consonance, an imperfect consonance and a dissonance. For the purposes of two-part writing, however, it is essentially always a dissonance. This is dealt with in some detail during the course of the book.

Once you have understood the three motions and the ways to use dissonance and the different consonances everything will start to look easier to you. Doing some exercises will help a lot in understanding how it works.


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## Jord

Thanks a lot i totally get it now! I hope :lol:
I've just realised my first idea was wrong, i thought G and C was a 5th somehow
I was thinking say in 2 parts that a C would go to a G so that would be up a 5th and the F would go up a 5th to a C, so it's not the relationship of the notes in their individual voice, but the harmonic relation between both voices so that same idea so according to the second rule 

'Second rule: From a perfect consonance to an imperfect consonance, one may proceed in any of the three motions'

In C major, C and a G with C in the root, going to a imperfect consonance in direct motion, means it would have to go from a 5th, to anything but a Unison, 5th, Octave, 2nd or 4th? so C could go to a E, and the G could go to a C?


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## Ramako

Yes indeed, from a perfect consonance to an imperfect consonance one is permitted to go in direct motion. Your example is correct


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## Jord

Ramako said:


> Yes indeed, from a perfect consonance to an imperfect consonance one is permitted to go in direct motion. Your example is correct


Finally understand it! Thanks guys


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## Kopachris

Ugh. Always liked species counterpoint in theory, but hated it in practice. Good to learn, but afterwards ignore it and your music will sound more interesting.


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## Ramako

Kopachris said:


> Ugh. Always liked species counterpoint in theory, but hated it in practice. Good to learn, but afterwards ignore it and your music will sound more interesting.


Blasphemy! 

:lol:


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## Jord

Kopachris said:


> Ugh. Always liked species counterpoint in theory, but hated it in practice. Good to learn, but afterwards ignore it and your music will sound more interesting.


Not too sure what species counterpoint is yet, i think first species is when the notes are the same length, but from what i know so far, I love counterpoint and can't wait too get into composing it properly!


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## Ramako

Jord said:


> Not too sure what species counterpoint is yet, i think first species is when the notes are the same length, but from what i know so far, I love counterpoint and can't wait too get into composing it properly!


That's the spirit!


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## KenOC

Jord said:


> Not too sure what species counterpoint is yet, i think first species is when the notes are the same length, but from what i know so far, I love counterpoint and can't wait too get into composing it properly!


Don't know if this will help, but Wiki sez, "In species counterpoint, as given in Fux, the student is to master writing counterpoint in each species before moving on to the next. The species are, in order, note against note; two notes against one; four notes against one; ligature or suspensions (one note against one, but offset by half of the note value); and florid counterpoint, in which the other species are combined freely. Once all the species are mastered in two voices, the species are gone through again in three voices, and then in four voices."


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## Kopachris

Jord said:


> Not too sure what species counterpoint is yet, i think first species is when the notes are the same length, but from what i know so far, I love counterpoint and can't wait too get into composing it properly!


Species counterpoint is what you're studying.  You're right in that the first species of species counterpoint is when the notes are the same length. Second species is when the notes are a 1:2 duration (e.g. half-notes against whole-notes). I think (correct me if I'm wrong--it's been a while) third species is the same as second, but 1:4 duration (e.g. quarter-notes against whole-notes), fourth species introduces suspensions, and fifth species combines the other four. All five species are considered sections of species counterpoint, and species counterpoint is simply a method by which you learn how to handle counterpoint.


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## paulc

Counterpoint sucks!






1:23 -> 4:13


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## Kopachris

paulc said:


> Counterpoint sucks!
> 
> 
> 
> 
> 
> 
> 1:23 -> 4:13


When I realize Vivaldi added a fugue in the middle of a concerto like it was nothing:


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## clavichorder

Hey! I love that Vivaldi piece he linked, but I haven't heard it in quite a while...


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## ComposerOfAvantGarde

Does anyone know any text books on atonal counterpoint? I've just been applying everything I know about [species] counterpoint to atonality (basically getting rid of rules of consonance, dissonance and the four rules of motion but still keeping in mind that contrary and oblique motion sound most interesting) but I'd like to see how I could improve in this area of composition.


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## paulc

> "Does anyone know any text books on atonal counterpoint?"


The only one I know of :lol: is Basic Atonal Counterpoint by Stanley Funicelli.

I can't say if it's any good, or if there are others.


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## millionrainbows

Jord said:


> I've bought the English transcription of Fux's Gradus Ad Parnassum. But there's one part i don't understand on page 22 (for anyone who has the book)
> 
> I understand perfect and imperfect consonances, dissonances, and direct, contrary and oblique motion, but then it has 4 rules:
> 
> _First rule_: From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion
> _Second rule_: From a perfect consonance to and imperfect consonance, one may proceed in any of the three motions
> _Third rule: From and imperfect consonance to a perfect consonance one must proceed in contrary or oblique motion
> Fourth rule: From one imperfect consonance to another imperfect consonance one may proceed in any of the three motions
> 
> I'm guessing it's talking about 2 voices but i'm not sure, it doesn't really make any sense to me could anyone help please? _


_

Rule 1: A "perfect consonance" is a fourth or a fifth. If you went in similar motion, you'd have parallel fourths or parallel fifths. Makes sense, unless you're writing Gregorian chant, Japanese, or heavy metal.

I guess rule three, which ends on a perfect consonance, is to avoid even the *appearance* of parallels. God forbid!_


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## Renaissance

I thought that perfect 4th are forbidden (dissonances) in first species counterpoint. They are allowed only when supported by a 3rd below when you have more than 2 voices. (the same pattern used by chords in first inversion for example.) Maybe I am wrong...


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## millionrainbows

Renaissance said:


> I thought that perfect 4th are forbidden (dissonances) in first species counterpoint. They are allowed only when supported by a 3rd below when you have more than 2 voices. (the same pattern used by chords in first inversion for example.) Maybe I am wrong...


*Consonances *are termed thusly, as *perfect or imperfect:*

*Perfect consonances:*
unisons and octaves
perfect fourths* and perfect fifths

*Imperfect consonances:*
major thirds and minor sixths
minor thirds and major sixths

...and the Fux rule (in the opening post) reads: [First rule:* From one perfect consonance to another perfect consonance *one must proceed in contrary or oblique motion]

You must mean this rule of first species counterpoint:

Avoid dissonant intervals between any two parts: major or minor 2nd, major or minor 7th, any augmented or diminished interval, *and perfect fourth (in many contexts)....*

*The perfect fourth is considered a dissonance in most classical music when its function is contrapuntal. In the Western Middle Ages, only the octave and perfect fifth were considered consonant harmonically.


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## Renaissance

Sorry I haven't looked more carefully. You wrote perfect consonances with quotation marks.  That's OK.


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