Fux: Second species in triple time

[Da Bachtopus]

I have just begun working through Fux's 'The Study of Counterpoint'.  It is fairly easy going, but I am irritated by the speed with which "Aloys" (you have to love Socratic dialogue!) dispatches the second species in triple time, i.e. writing three notes against one.  He gives the example:

cpt.:  B A G  | D ...      [First bar descending]
cf.:    G----  | G-----    [Stationary]

and says that "the middle note may be dissonant because all three of them move stepwise.  It would be different if one note or the other moved by skip, in which case all three notes would have to be consonant, as should be apparent from what I have already said."

I don't understand why the third note cannot be a dissonance if this is also part of a stepwise movement.  After all, Fux has "already said" at the start of the chapter that "n this species a dissonance may not occur, except by diminution, i.e. filling out the space between two notes that are a third distant from each other".

What is unacceptable with this:

cpt.:  B E F   | G .....    [Ascending]
cf.:    G----  | G-----    [Stationary]

?

As insignificant a point as this is, I feel like I've overlooked something important, since the only explanation given is essentially, 'Oh, come come Josephus - it's obvious!'.

Anyone who's already studied counterpoint properly, please could you help me?

(I intend to move onto other more 'scholarly' books, but feel I should at least begin with Fux).

[Da Bachtopus]

I find it rather amusing that the number of views on the accidental 'Ignore' post has increased just as rapidly as that of the real thing.

So has the number of replies...

[earl]

Da Bachtopus:

I believe the main rule being violated by two dissonances in your example would be that the first dissonace is not followed by a consonance. In strict counterpoint a dissonance is only allowed if it is followed by a resolution or other consonanace.

Probably in later species you can have two dissonances in a row, but maybe not. It's been a while since I studied counterpoint and my memory is fuzzy. I'm at work right now and don't have time to check that.

Back in the day I was a music major at a community college and Fux was the textbook for the counterpoint class, so it's quasi official. Plus, it was used by generations of students since its original publication including Mozart and Beethovan if I remember correctly.

Later on I studied conterpoint on my own using Arnold Schoenberg's "Preliminary Exercises in Counterpoint". It follows Fux's treatise in that he starts with First Species and moves to more complex ones in the same way. The advantage is the modern style of writing. He also urges the student to try every possible cobination to see what works and what doesn't and he has numerous examples (both good and bad) throughout the book with notations as to why this or that example doesn't work.

I hope this helps and I hope you enjoy counterpoint as much as I did. Lately I've been wanting to do some more studying in preparation for getting serious with composition. I feel it's a very good starting point.

Earl

[Da Bachtopus]

I believe the main rule being violated by two dissonances in your example would be that the first dissonace is not followed by a consonance. In strict counterpoint a dissonance is only allowed if it is followed by a resolution or other consonanace.

Aha!  But in my example there are no successive dissonances, which - as you say - would be incorrect.

I've drawn a proper diagram now, which hopefully should explain what's going on more effectively:

https://tinypic.com/view.html?pic=2i99fq

Back in the day I was a music major at a community college and Fux was the textbook for the counterpoint class, so it's quasi official. Plus, it was used by generations of students since its original publication including Mozart and Beethovan if I remember correctly.

Later on I studied conterpoint on my own using Arnold Schoenberg's "Preliminary Exercises in Counterpoint". It follows Fux's treatise in that he starts with First Species and moves to more complex ones in the same way. The advantage is the modern style of writing. He also urges the student to try every possible cobination to see what works and what doesn't and he has numerous examples (both good and bad) throughout the book with notations as to why this or that example doesn't work.

I know that Fux is the standard treatise, used by all the great masters (I think Haydn copied out all the examples!).  This is why I chose to start with it, since all subsequent texts adapt the 'species' idea anyway, and refer back to Fux.  Plus, the dialogue form makes it both accessible and hilarious in one ("With God's help, then, let us begin composition for two voices" - comedic genius).

To teach myself theory properly, I've decided to work through the books on the Music Faculty's reading list.  Some of these went out of print years ago, but I've managed to get a decent collection.  After Fux I intend to work through Swindale's 'Polyphonic Composition', then Felix Saltzer's 'Counterpoint in Composition', which should be enough on Renaissance style.  I'll then do some harmony, Bach Chorale, etc. (Piston and Boyd) before looking at Double Counterpoint (Piston) and Fugue (Prout and Mann).

I hope this helps and I hope you enjoy counterpoint as much as I did.

I find it very relaxing!  I read English / Literature, but find the highly abstract / logical thinking required in Music and Maths to be a pleasant relief from normal studies.  Sadly, since finishing my A-level's, I've had no need to do any calculus in the past six months, but I'm finding counterpoint to be worthy replacement!  "Pure logic in music", as Chopin said.

[earl]

Yep, you're right. (Don't know what I was thinking.)

However, if the only acceptable dissonance in this species is filling out the scale between two consonances a third apart (diminution), then your example fails on that point.

"n this species a dissonance may not occur, except by diminution, i.e. filling out the space between two notes that are a third distant from each other".

Maybe that's the reason for the "come, come it's obvious" comment. I don't have the Fux book anymore but last night I checked and there isn't a species of three against one in the Schoenberg. He goes straight to four against one. Another possibility is that you have a tritone outlined on beats one and three. Just a guess.

As you mentioned earlier this is a fairly insignificant point, but it's interesting to speculate anyway.

Good luck in your studies. Music's a neverending road, isn't it?

Earl

[Da Bachtopus]

However, if the only acceptable dissonance in this species is filling out the scale between two consonances a third apart (diminution), then your example fails on that point.

But E and G are a minor third apart!

Essentially, I wonder why - if dissonaces are only allowed in stepwise movement - this movement cannot be displaced by a beat when you are writing in three, not two.  The dissonance still falls on a weak beat.

However, I can't think of any 'real' examples of this, and my other books don't mention it!  It is utterly insignificant, but is irritating me nevertheless.

Thanks for you help!  I'll be kept busy with all this theory for quite some time yet...

[sznitzeln]

By what you wrote your example seems pretty ok to me, but sometimes you can feel absolutely positive, then you notice you made some assumption that was incorrect. Analyse exactly your definitions, and what definitions define those, etc