2-part invention in counterpoint

1 hour ago, Fermata said:

Well, it is a fugue subject that begins on the 4th degree of the scale.
And in fact, fugue subjects can begin on any scale degree, not only the tonic or dominant (see examples below).

I suppose a subject beginning on the 4th is as about as allowed as an interrupted cadence in a chorale. You can find them every now and then but they are so exceedingly rare in the oeuvre. This fugue would also be the second part of an overture, following a perfect cadence in F. So the issue of your subject establishing the key centre is no longer significant. If one were to compose a standalone piece, the 4th would most certainly be raised to a 5th, then un-raised in later entries as tonal answers.

1 hour ago, Fermata said:

I'm sorry, but this is neither invertible nor correct counterpoint.

How embarassing. Fixed below!

19 hours ago, muchen_ said:

• No invention themes/fugal subjects begin on the 4th degree of the scale. The theme does recur throughout but it also must be stated at the beginning of your piece, and here, the presence of the 4th degree is detrimental to establishing the home key of your piece. If you wanted to write an invention you would raise this note to the 5th degree instead.
• The themes of inventions are based on simple and common harmonic gambits (I-V-I,  I-IV-V-I,  I-VI-II-V and so on). This theme strongly suggests I-IV-I-IV in the first bar which I have never seen before in a theme/subject. 

It's nonetheless possible to write an invention here, but it'd require a few tricks. A possible solution for the countertheme is:

• The anacrusis has been raised by a tone, as discussed before.
• Note the presence of an inner pedal F in the first bar. This serves three purposes: it strongly establishes the tonic key, it introduces the semiquaver rhythm to be used throughout the rest of the piece, and it reimagines the otherwise problematic I-IV-I-IV progression as a simple decoration of the tonic chord I.
• The second bar uses scalic passages, and is essentially a decorated dominant chord V. Together with the first bar, what would be an otherwise very unwieldly theme (if harmonised at quaver or crotchet speeds) is now a simple I-V gambit.
• There is a nice phrase ending at the beginning of bar 3 with the bottom F reached by the bass.
• The counterpoint here is fully invertible.
• There's much material here that you can take for your episodes: the scalic passages, the lower mordent-like figure found in bar 2 of the main theme, and the bariolage introduced by the inner pedal in bar 1. Bariolage especially is an absolute motivic goldmine that you can and should exploit in the episodes.

It's C and B-flat. Also this kind of dissonance, treated this way, is completely allowed. Take a look at BWV 773 (Invention No. 2) for some beautiful examples.

There's nothing wrong with the fast passing vii6.

No. Note that the imitation enters 2 crotchets earlier compared to the other solution. You can in theory not do this, and write a 2 crotchet-long continuation, but this is unnecessary for imitation at the fifth here, and therefore slightly inelegant.

 

(1) Yes the 4^th surprised me, but I blindly trusted 'my' Pr. Goetschius. It is strange that he proposed this piece with all those defects and limitations.

(2) Thanks for the example. I’ll look at it. Actually, I will modify further the motive for my own sake, adapted to the ideas I have tried to develop so far with the original. I’ll create a new posting with that.

(3) My appreciation of your version was just a matter of subjective taste. I never stated it was incorrect or wrong. You like what you did. I don’t. Some member found what I did sounded good, another found it irritable. Every brain has it’s own sensitivity. Even the physical body has specific resonance frequencies. It shows up when you sing. I’m particularly a B flat, lol.

(4) About the imitation at the 5^th, I just wanted to figure out what you did. Is it a ii6? If not then what did you do?

17 hours ago, Fermata said:

Well, it is a fugue subject that begins on the 4th degree of the scale.
And in fact, fugue subjects can begin on any scale degree, not only the tonic or dominant (see examples below).

I'm also pasting the original fugue exposition here to show how it was actually realized by its author.

I'm sorry, but this is neither invertible nor correct counterpoint.

1) The C against the B-flat would work as an implied root-position dominant seventh harmony (or as a third inversion when the subject is transposed below the countermelody). The repeated F's could be interpreted as figuration over a tonic inner pedal point, but they undermine the effect of the implied dominant harmony. That marked F should really be E instead, even if it disrupts the figuration.

2) You leap down to D, resulting in an unprepared dissonance. That D could work only if the C above were treated as a suspension.
That C in the subject implies either a dominant or a tonic harmony.

3) These intervals produce perfect parallel fifths.

 

Thanks for the original score of the fugue. I will transcribe it and listen to it.

And I’ll keep the page of themes for the future. Who knows if one day I'll be capable of composing good fugues, lol.

If I may ultimately ask again: Do you have books or authors to recommend to me? Thanks.

19 minutes ago, Frederic Gill said:

If I may ultimately ask again: Do you have books or authors to recommend to me? Thanks.

The fugue subjects are from Marchant's collection 500 Fugue Subjects and Answers, which you can also find online.

It was a very long time ago when I studied counterpoint; my teacher recommended Jeppesen’s Counterpoint, which I used. It deals with 16th‑century vocal polyphony, but the fundamental principles remain valid in later centuries as well.

From a didactic point of view, I would definitely start with the vocal counterpoint idiom—either Renaissance practice or the tonal counterpoint foundations laid out by Fux. I would only move on to Baroque / Classical instrumental practice (such as the approach in Goetschius’s book) after you’ve mastered the basics of pure voice leading.