2-part invention in counterpoint

Hi everyone. So far, I have studied with Percy Goetschius books and am practicing small 2-part inventions (about 1 minute long) as taught in his Elementary Counterpoint and Applied Counterpoint books. I wonder if there are other beginners working on this and willing to share our works. My goal is to use counterpoint with freedom, yet in a sensible way. I use Myriad Melody Assistant piano. Here is one example, with a motive from Handel (F maj). I apologize for the poor sound quality (I'll try to find a good alternative for my .myr files). Thanks!  

Welcome to the forums.

Can you provide a score to your music? I'd be able to provide better feedback with a score.

12 hours ago, muchen_ said:

Welcome to the forums.

Can you provide a score to your music? I'd be able to provide better feedback with a score.

 

I have made changes to measure 13, last note: C3 instead of C. Leave the C in Bass, for modulation.

Sounds good.
The 13th bar is strange, but I see you've made a correction.
I think there's some pretty good imitative treatment, characteristic of the Inventions.
So many colours confuse me a bit. I suppose they highlight imitations or motifs, but as I'm colour blind, I can't tell.
Best regards.
 

5 hours ago, Luis Hernández said:

Sounds good.
The 13th bar is strange, but I see you've made a correction.
I think there's some pretty good imitative treatment, characteristic of the Inventions.
So many colours confuse me a bit. I suppose they highlight imitations or motifs, but as I'm colour blind, I can't tell.
Best regards.
 

 

Thanks. Yes the colours in the pdf help working and recognizing the motives. I've put it in b&W (below) 😉. After over 1600 small exercises in melody, harmony and counterpoint (all with 6 Goetschius books) + 25 invention, I don't know what 'level' I am at. I've never had feedback until now!

I don't think this theme was meant to be treated as the usual antecedent/consequent imitation at the octave, like in Bach’s two-part Inventions. The subject comes from a harpsichord suite by Sheeles (not by Händel); the ascending F–G–A–B is actually a codetta leading to the real answer a fifth above. As for your solution, it keeps hitting the octave far too often — you should avoid that, as it’s too harsh for two‑part counterpoint (and there are a few voice‑leading mistakes as well). The modulations to related keys could be prepared more effectively, for example by using simple sequences built from fragments of the theme. Introducing the inversion was a good idea; it adds a bit of variety.

43 minutes ago, Fermata said:

I don't think this theme was meant to be treated as the usual antecedent/consequent imitation at the octave, like in Bach’s two-part Inventions. The subject comes from a harpsichord suite by Sheeles (not by Händel); the ascending F–G–A–B is actually a codetta leading to the real answer a fifth above. As for your solution, it keeps hitting the octave far too often — you should avoid that, as it’s too harsh for two‑part counterpoint (and there are a few voice‑leading mistakes as well). The modulations to related keys could be prepared more effectively, for example by using simple sequences built from fragments of the theme. Introducing the inversion was a good idea; it adds a bit of variety.

 

This was just an exercise from Applied Counterpoint book by Prof. Percy Goetschius. I made the inventory of octaves and there are 30! lol.  Here are the details.

too many 8ves  

1st beat, Primary accent 
5 in V or V7 = me6,9,12,15,18,24,27,30.These are good according to Goetschius.
4 in IV =me13, 16,25(?)

3rd beat, secondary accent
8 in I = me19, 25, 31
3 in I = me5, 8, 26 NOT GOOD

2nd beat, ternary accent 
8 in I = me17
6 in IV = me7, 28 BAD

4th beat, ternary accent
8 in I = me11, 14
2 in I = me12, 15, 18 BAD because foreign to the chord.
2 in vii = me30

other unaccented fraction locations:
me10: G is either doubled leading tone or doubled chord 7th. 
me22: F is doubled chord 7th
According to Goetschius, these can be tolerated in fast tempo and at unaccented fractions. Is this fast enough?

Any other mistakes I could learn from? Thanks.  

There are some problematic parallels, such as the G–A octaves in m. 6 (this corresponds to m. 7 in your score — the notation software misnumbered the measures because the initial upbeat should not be counted as a full measure), or the E–F♯ parallels in m. 9 [m. 10 in the score], and so on.

Also, you can’t reuse the countermelody that you introduce just after the lower voice’s entry simply by transposing it, because it is not written in invertible counterpoint. For example, the fifth on the fourth beat of m. 4 [m. 5] becomes a fourth when the two voices are inverted. You can see the result of this in m. 7 [m. 8], where an A–D fourth appears. The interval of a fourth is always treated as a dissonance in traditional two‑part counterpoint. A passing fourth may sometimes be tolerated in the instrumental style, though.

You may also want to revise some of the crotchets in the countermelody to avoid frequent dissonant clashes with the passing quavers of the theme (see the example below).

2 hours ago, Fermata said:

There are some problematic parallels, such as the G–A octaves in m. 6 (this corresponds to m. 7 in your score — the notation software misnumbered the measures because the initial upbeat should not be counted as a full measure), or the E–F♯ parallels in m. 9 [m. 10 in the score], and so on.

Also, you can’t reuse the countermelody that you introduce just after the lower voice’s entry simply by transposing it, because it is not written in invertible counterpoint. For example, the fifth on the fourth beat of m. 4 [m. 5] becomes a fourth when the two voices are inverted. You can see the result of this in m. 7 [m. 8], where an A–D fourth appears. The interval of a fourth is always treated as a dissonance in traditional two‑part counterpoint. A passing fourth may sometimes be tolerated in the instrumental style, though.

You may also want to revise some of the crotchets in the countermelody to avoid frequent dissonant clashes with the passing quavers of the theme (see the example below).

 

Oh boy! parallel octaves! I didn't check these on fractions of a beat. BAD.

{A,D} inverted to {D,A} on 3rd beat is bad indeed. 

'Passing quavers': They are not essential by definition. Especially useless when they make an interval of a P4th! I guess I found it gave stamina and authority to the sequence in the motive. (NB, your picture above is not of mine). So I looked at the "frequent dissonant clashes with the passing quavers" in my exercise. I found one p4th (me24, to be corrected!), one p5th (me6, bad?), and 2 8ves (me9, 21, dissonant?). Is there more?

Conclusion:
I was so carried away and happy with my experience and creative process for that piece (developing the 'horizontal mirror' of the motive, what you call 'inversion' and that PC calls 'contrary motion'), that I didn't pay attention (deficit!) to all those defects and even neglected to check! That happens when I spend too much time on something, I just lose perspective. I'm definitely not a MATURE COMPOSER yet, lol. Also I knew the modulatory episodes were almost absent. I have to develop good episodes even when the tempo is fast and am afraid to lose momentum. Thanks for your feedback.
 

By the issue of 'passing quavers,' I meant the following. Take a look at the attached example. As you can see, the G quaver connects two consonant intervals, while it forms a seventh with the upper voice, which is a dissonant interval. Technically this is not incorrect, but musically it's very disadvantageous — since we're dealing with two‑voice counterpoint, the musical texture is very 'thin,' and this dissonant friction becomes quite audible. The same problem occurs with the other G as well.

Regarding the A marked with the exclamation mark: the harmony is too 'empty' this way. If you put the subject into the bass and try to harmonize it on piano, it's obvious that an F-major (first-inversion) chord should be implied there. 

I think most of these issues (including the ones I mentioned earlier) can be corrected fairly easily.
 

7 hours ago, Fermata said:

By the issue of 'passing quavers,' I meant the following. Take a look at the attached example. As you can see, the G quaver connects two consonant intervals, while it forms a seventh with the upper voice, which is a dissonant interval. Technically this is not incorrect, but musically it's very disadvantageous — since we're dealing with two‑voice counterpoint, the musical texture is very 'thin,' and this dissonant friction becomes quite audible. The same problem occurs with the other G as well.

Regarding the A marked with the exclamation mark: the harmony is too 'empty' this way. If you put the subject into the bass and try to harmonize it on piano, it's obvious that an F-major (first-inversion) chord should be implied there. 

I think most of these issues (including the ones I mentioned earlier) can be corrected fairly easily.
 

 

I'll show you a relevant sample (attached) of what I have learned with P. Goetschius. I assume that you'll dissagree with him. Unless I didn't catch something. Do you have a book(s)/author(s) on Music Theory that summarize your knowledge/approach? 

This doesn’t contradict what I wrote above at all (I already mentioned it’s not a technical mistake). The technical side of this is covered in pretty much any standard counterpoint textbook; Goetschius’s book should work fine for that as well.

However, musically it feels weak because it’s only in two voices, so it really sticks out. In a fuller texture (with three or four, or even more voices) it wouldn’t be much of an issue.

I listened to your invention and digged around for the Goetschius book. I suppose my question would be: have you looked at the prerequisite book to this, namely The Material Used In Musical Composition?

1 hour ago, muchen_ said:

I listened to your invention and digged around for the Goetschius book. I suppose my question would be: have you looked at the prerequisite book to this, namely The Material Used In Musical Composition?

 

Yes. (MUMC in short) 1909 & 1941, up to figuration. And also Theory & Practice of Tone Relations (1918) which less thorough than MUMC. I have noticed that PG has allowed over the decades more licences to his rules.

3 hours ago, Fermata said:

This doesn’t contradict what I wrote above at all (I already mentioned it’s not a technical mistake). The technical side of this is covered in pretty much any standard counterpoint textbook; Goetschius’s book should work fine for that as well.

However, musically it feels weak because it’s only in two voices, so it really sticks out. In a fuller texture (with three or four, or even more voices) it wouldn’t be much of an issue.

 

My point was that he said these intervals were 'good', not 'poor', or, as you said, 'clashy' (BAD in my limited SL English). Now I understand that you meant 'musically weak'. Also, all (diatonic) passing notes in 2-notes to a beat, like here, are unavoidably dissonances. So I didn't understand you. Besides, I have seen similar passing movements in some of his many 'BACH' examples, but in 3- or 4-notes to a beat. Then each dissonance is less prominent. So it is a matter of taste. I agree with you that it sticks out, also being the same tone G. I'm glad I finally understood that. Perhaps I simply can't combine the motive with this counterpoint of me4.  

12 hours ago, Frederic Gill said:

Yes. (MUMC in short) 1909 & 1941, up to figuration. And also Theory & Practice of Tone Relations (1918) which less thorough than MUMC. I have noticed that PG has allowed over the decades more licences to his rules.

Since this book is a fairly comprehensive text in harmony, you should keep what you've learnt from this book in mind - not only for these counterpoint pastiches you're writing, but for everything you write from now. The reason why I'm mentioning this is: 18th-century counterpoint (which is what the Goetschius book deals with) and all of the counterpoint-employing music that comes after, is completely interwoven with harmony. All of the harmonic devices/features you have learnt so far, you should find readily in these inventions. And so with this in mind, you can hopefully see the two major problems:

• There are no strong cadences (V-I in root position etc.) anywhere in the piece. This is the musical equivalent of writing a paragraph of text with no punctuation whatsoever.
• Some of what you write is either harmonically ambiguous, or does not follow common harmony rules. Examples:
  - In bar 6, what are the first two crotchets supposed to be? Is this V-IV? This is a forbidden progression. Is this I-IV? Then why is the root of I missing? Contrast this with the last two crochets of bar 7, which clearly spells out a C major chord and is well-written.
  - What are the last two crochets of bar 12 trying to spell out? Is this V? vii°? i?
  - What is bar 16? You start off with a G chord (fine), introduces the C# in the upper voice which strongly suggests a chord that is the dominant seventh in third inversion of D minor (also fine), but then this dominant seventh resolves to a B natural chord (?)

Point 1 can be easily fixed. Regarding point 2: if you look at Bach's 15 Inventions, you will find that 14 of them have semiquaver prevailing rhythms, and the remainder uses broken chords extensively. This is completely deliberate in 2-part writing. Writing in semiquavers gives you more notes to work with, and one advantage of that is it allows you to trace out chords easily thereby making your harmony unambiguous. I would recommend a similar approach here.

The other problem here is form. The main material in a 2-part invention is a section of invertible counterpoint, which is then repeated but often inverted (in the sense of two voices exchanging the material they play) and/or transposed, often called the theme. You have indeed written this. But you also need material between these sections, called episodes. These have multiple functions: they serve as modulatory material, they provide a break from the theme, they introduce devices not often found in the theme such as sequences, they allow motifs found in the theme to be presented in a new context (e.g. harmonised differently), they facilitate strong cadences mentioned above, and so on. You need to write these episodes in for your invention to adhere to the form.

1 hour ago, muchen_ said:

Since this book is a fairly comprehensive text in harmony, you should keep what you've learnt from this book in mind - not only for these counterpoint pastiches you're writing, but for everything you write from now. The reason why I'm mentioning this is: 18th-century counterpoint (which is what the Goetschius book deals with) and all of the counterpoint-employing music that comes after, is completely interwoven with harmony. All of the harmonic devices/features you have learnt so far, you should find readily in these inventions. And so with this in mind, you can hopefully see the two major problems:

• There are no strong cadences (V-I in root position etc.) anywhere in the piece. This is the musical equivalent of writing a paragraph of text with no punctuation whatsoever.
• Some of what you write is either harmonically ambiguous, or does not follow common harmony rules. Examples:
  - In bar 6, what are the first two crotchets supposed to be? Is this V-IV? This is a forbidden progression. Is this I-IV? Then why is the root of I missing? Contrast this with the last two crochets of bar 7, which clearly spells out a C major chord and is well-written.
  - What are the last two crochets of bar 12 trying to spell out? Is this V? vii°? i?
  - What is bar 16? You start off with a G chord (fine), introduces the C# in the upper voice which strongly suggests a chord that is the dominant seventh in third inversion of D minor (also fine), but then this dominant seventh resolves to a B natural chord (?)

Point 1 can be easily fixed. Regarding point 2: if you look at Bach's 15 Inventions, you will find that 14 of them have semiquaver prevailing rhythms, and the remainder uses broken chords extensively. This is completely deliberate in 2-part writing. Writing in semiquavers gives you more notes to work with, and one advantage of that is it allows you to trace out chords easily thereby making your harmony unambiguous. I would recommend a similar approach here.

The other problem here is form. The main material in a 2-part invention is a section of invertible counterpoint, which is then repeated but often inverted (in the sense of two voices exchanging the material they play) and/or transposed, often called the theme. You have indeed written this. But you also need material between these sections, called episodes. These have multiple functions: they serve as modulatory material, they provide a break from the theme, they introduce devices not often found in the theme such as sequences, they allow motifs found in the theme to be presented in a new context (e.g. harmonised differently), they facilitate strong cadences mentioned above, and so on. You need to write these episodes in for your invention to adhere to the form.

 

I'm not sure you have read all the previous comments, because you are over-lecturing me. But I'll put the blame on the bad quality of my 'pastiche'. I have admitted earlier that my episodes were short or absent. And that I have neglected the general check up. Because of that, I will delete this post once we've closed the discussion. 

As for the motive itself, it has a degree 4# in bar 3, which I interpret as a short modulation into the dominant. Otherwise it would just be an altered chord (IV#). So I have assumed for the last bar of the motive a Tonic: I / dom: IV-I. Please, let me know what you think of my choice.

Back to your comment: At bar 6(7) we have {Sop,Bass} = {A,F}-{G,G}-{A,A} = F:I / C:IV. But what do you mean by V-IV? Or did you follow the (wrong) numbering in the score? At bar 5(6),{Bb,G}-{-.E}. This is F:vii6, followed at next bar by F:I / C:IV.
The last two crochets of bar 7(8) are {D,A}-{Bb,G} = d minor: (ambiguously) i or iv. And the next bar is d:V. The key of C is at 6(7), {C,E}-{G,E}, the tonic chord of the dom key in the end of the motive, as I've just explained. I'll not explain for the other bars (12, 16).

About Bach's 2-part inventions, I mentioned (in a previous comment) that Bach's faster rhythm (3 or 4 notes to a beat) is a good asset for handling unessential tones (compared to my 2-notes to a beat). But this motive has a constant, fast rhythm and has only quavers (or semi-). It doesn't leave much room for maneuver of the counter motive and trying to avoid dissonances or ambiguous chords with the motive. And I didn't want to accelerate in the counter-motive. On the contrary, I used 'augmentation' (slower rhythm applied to segments of the motive) in the counter motive. Thank you for your time.

38 minutes ago, Frederic Gill said:

About Bach's 2-part inventions,

Just wanna disturb the great discussion between you and @muchen_, but just one observation looking the opening bar in your piece: in Bach's inventions either with long subject both voices begin at the beginning, or with short subject usually the other voice join after a bar or so. The opening sounds more like a fugue to me.

38 minutes ago, Frederic Gill said:

As for the motive itself, it has a degree 4# in bar 3, which I interpret as a short modulation into the dominant. Otherwise it would just be an altered chord (IV#). So I have assumed for the last bar of the motive a Tonic: I / dom: IV-I. Please, let me know what you think of my choice.

I think the 4# would work well if you modulate to C major for the answer, but you return to F major in the answer so it sounds a bit weird to me.

38 minutes ago, Frederic Gill said:

Back to your comment: At bar 6(7) we have {Sop,Bass} = {A,F}-{G,G}-{A,A} = F:I / C:IV. But what do you mean by V-IV? Or did you follow the (wrong) numbering in the score? At bar 5(6),{Bb,G}-{-.E}. This is F:vii6, followed at next bar by F:I / C:IV.

I think he's talking about the {C, C} in b.6 and then the {Bb, D} follows, which causes some ambigous harmonic progression to me as well since a bare C can indeed imply a V, altho I think you are going for an implied I 6/4 here.

38 minutes ago, Frederic Gill said:

The last two crochets of bar 7(8) are {D,A}-{Bb,G} = d minor: (ambiguously) i or iv. And the next bar is d:V. The key of C is at 6(7), {C,E}-{G,E}, the tonic chord of the dom key in the end of the motive, as I've just explained. I'll not explain for the other bars (12, 16).

for the D minor entrancr in b.8, you will prepare it better with C# before it.

Henry