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I am harmonizing a Mozart soprano melody with a musical friend. Now, I could scour the internet for a week trying to figure this out, but I figured I would instead ask the music.stackexchange Gods first to greater effect.

I am having trouble wrapping my brain around counterpoint dissonance handling, specifically in the correct designation of “strong” and “weak” beats.

enter image description here

This is where I am so far with the harmonization. In second species counterpoint, you have two half notes per measure, and the second half note can hold a dissonance. Now, this piece is in 4/4, but if the chord changes are occurring twice per measure, beat 3 there could theoretically hold a dissonance? Measure 2 changes chords twice like this. (Note that there is no dissonance in this measure but I'm bringing it up to compare it with measure 4.)

In the 4th measure, you have chord changes that are occurring on the 3rd and 4th beat. Please notice that I do indeed have a dissonance on beat 3 and this is where I'm lost...

Now, if this is 3rd species, where there are 4 beats in a measure, the 3rd beat is strong(ish) and not fitting for a dissonance.

So measure 4's dissonance on beat 3 is correct in 2nd species, but wrong in 3rd?

Can individual measures be treated as quadruple meter and some in duple depending on the chord changes?

Can someone provide me some insight?

Thanks!

EDIT:

Thanks to Heather S. and some reading I've been doing, I think I've come up with my own answer to this problem.

Now, what I didn't realize before and what I realize now is that there are two aspects to this whole "strong beat/weak beat" issue.

1. Strength/weakness as related to the meter of the piece/measure.

Ex: 4/4: First and 3rd beats are strong. 2/4: First beat is strong etc.

2. Strength/weakness as related to note(s) against a note in different ratios.

Ex: 2 notes against 1: first note is strong, 4 notes against 1: first and 3rd notes are strong etc.

This has helped me to understand the issue, because I wasn't able to separate the two aspects previously.

Now, I also believe I have the answer to best applying these ideas...

In Alfred Mann's intro in his translation of Fux's Gradus Ad Parnassum, he basically spells out one of the main goals of counterpoint: balance.

So, whatever you choose to do in terms of applying dissonance in meter and note-against-note situations, your main goal is creating balance in your music.

Thanks for all who helped.!

Edit for Michael:

Michael thank you again for your responses!

Please take this image for example:

enter image description here

I have altered some things in the first few measures to better help explain my point.

For starters, I know a first inversion tonic chord is poorly placed so early, but I only did it for the sake of allowing a passing 6/4 V chord.

Now, looking at the bass voice: if we pretend there is an invisible cantus firmus present in measure 2 as tonic note C, then we can see how a 2:1 dissonance on "beat 3" works - it is a dissonance that resolves in the same direction by step. It also justifies common theory about proper placement of dissonant chords like the passing 6/4. Notice I put beat 3 in quotes a moment ago: If this was duple meter, then this would be beat 2; I feel the chord change here makes this segment act like duple meter justifying 2nd species 2:1.

Now, applying this "invisible whole note cantus" over measures justifies what many theorists say about dissonant chords over the bass (ex: passing 6/4 on weak beat.) The voices show respect the bass, and the bass shows respect to the the invisible cantus.

However, with that logic, we are already in some sort of contradiction here: Because beat 3's bass note places the melody in error with species 2 - a 4th above the bass that does not resolve by step. It leaping down to the D correctly makes a proper leap to a consonance in regard to the prevailing chord, but, if looking at the bass voice, we see a dissonance being leapt away from.

Perhaps this is a better example:

enter image description here

Here the 4th above the bass never resolves down - it is instead the movement of the bass that provides the resolution - calling into question where/what the true cantus is.

It seems as though two schools of thought are meeting in this thread.

And...

Do you see how all of this is making my brain leak out my ears?? :)

  • What piece/movement is the Mozart melody from? – Michael Curtis Feb 14 at 21:45
  • I honestly don't know, my friend forwarded it from a music workbook. – William Egert Feb 14 at 21:58
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Species 2 counterpoint is 2:1. The note values will change, but the ratio is always 2:1. Two quarters to a half note, 2 eighth notes to a quarter note, two half notes to a whole note, etc.

What counts as a weak or strong beat (or portion of beat) depends on what note values you are using. If you are in a measure of 4/4 and one voice has half notes, the other voice will use quarter notes. The strong beats will then be beats 1 and 3, and the weak beats will be 2 and 4. In an eighth note to quarter note situation, the first half of the beat is strong, and the second half of the beat is weak. In two half notes to a whole note situation, the first half note is strong, the second half note is weak.

Species 2 counterpoint can use a mix of these note values within the same piece, but the idea is that one voices is moving at a proportion of two against the other voice's one. The upper voice might move faster in one place, but the lower voice might move faster in another place. The idea is to use the same principles of handling the dissonance in each setting.

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  • Thank you for your thoughtful answer. I do understand what you're saying about the two-to-one ratio in second species. However, I'm still a bit lost. For example, how does species Counterpoint relate to chord changes? How do I know which species of CounterPoint to use at all in given situations? I know that Bach and Mozart study from fux gradus, but it's still difficult for me to get the whole picture at how species Counterpoint is used in composition. – William Egert Feb 15 at 2:42
  • Also, if I may, as you seem knowledgeable of this topic, can you reference also the above measures? Can Counterpoint be applied to this example? – William Egert Feb 15 at 2:51
  • @WilliamEgert, counterpoint is essentially about the independence of the voices and the thoughtful use of dissonance. Principles of counterpoint can always be used (and if writing something atonal, even a "negative" counterpoint can be used as if changing the rules of consonance and dissonance to their opposites, like a negative of a photograph.) A fully formed piece of music (as opposed to an exercise) will use a variety of counterpoint species, depending on what is going on in the music. Some measures/sections of measures will be 1:1, some 2:1, some 3:1 and so on. – Heather S. Feb 15 at 2:59
  • Chords are often secondary thought when dealing with counterpoint. The consonances brought about by the various intervals used will form their own chords. If you are considering specific chords, that will limit the options of notes that can be used to find the appropriate intervals according to the species counterpoint you are using. Now, of course, rules are broken all the time. But the masters know when and why they break the "rules" and use dissonances or "improper" parallel movement judiciously for a specific sound or effect. I recommend looking at some two-part Bach minuets. – Heather S. Feb 15 at 3:04
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    Thank you heather. You have helped me arrive at what I feel is my answer. I actually added some text to my original question detailing the answer I've come up with. Again thank you for your time and detailed explanations. – William Egert Feb 16 at 17:08
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I think part of what Heather explained is you don't need to think about the meter, but instead the subdivisions of the two voices. In your example you are essentially dealing with 2:1 and 4:1 rhythms between the parts which are 2nd and 3rd species in Fux.

But there are two things I think you want to consider.

At m. 4, beat 3...

enter image description here

...you have a dissonant fourth above the bass. In terms of species beat 3 is 2:1 - 2nd species - and that first note of the two should be either a consonance or a ligature (a suspension.)

But the other thing I think you should consider is the problem of using a Mozart melody for species counterpoint exercises.

It may sound obvious, but species counterpoint is polyphonic whereas most Mozart's melodies (at least the one in the example) are homophonic. The treatment of dissonance is not exactly the same for both. On the whole I would say the homophonic style gets a lot of its sensibilities regarding dissonance handling from counterpoint, but adds a lot of things not found in species counterpoint.

I don't know the source of this melody. I tired to find it in the piano sonatas, but didn't find it there. The following is based on what I think the original is like.

The Mozart melody uses a short 2 bar phrase which is repeated then varied at the end...

enter image description here

...the varied end is in the green box.

If the original works like I suspect, the G5 of the varied ending (boxed in orange) is an appoggiatura above the F5 of the first iteration of the phrase. That means two things: in the homophonic style that G5 should be a non-chord tone to be heard as an appoggiatura, and the dissonance is unprepared.

I imagine the original is harmonized mm. 2-5 like | I viio6 | I6 | I IV6 | V6... |

It seems m.4, beat 3 shouldn't be a V chord, or else the G5 becomes a chord tone and won't sound like an appoggiatura.

I really hope my suspicion about the original is correct. I'm going out on a limb guessing what it actually is.

Back to the species counterpoint. We can no see two problems that come up using a homophonic melody like this for species counterpoint.

  1. The melody repeats a phrase which is not ideal for a cantus firmus.

  2. (If my suspicion about the original is correct) the appoggiatura is an unprepared dissonance which isn't supposed to happen in species counterpoint.

Of course you can do whatever you like with combining different styles. But if you want to work through traditional species counterpoint, I think you want to choose from existing cantus firmi. It will probably be easier to follow Fux's lessons when you work with the kind of material Fux had in mind.

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  • Hi Michael! Thank you for your response. I'm still trying to figure out if there is any sense to be made out of all this or I am doing mental gymnastics trying to make it work. The only cantus firmus that is really used in practice is the fugue, and typically the fugue subject is much more than whole notes or half notes. In regard to m.4 beat 3 of the Mozart example. You say this is 2:1. This confuses me because....It could also be considered 4:1 because of the soprano's rhythm. Also, what do you make of it when there are more voices involved in movement? – William Egert Feb 19 at 10:16
  • If you look at music theory sites and how they advise you on dissonant chords like the passing 6/4, they advise that you put them on a weak beat, which looks at the meter itself to determine the true "weak beat." But as you, Heather S. and possibly Fux are saying is that you are only looking at the note against note relationships. I can definitely dig it as there is much sense to be made in it, his goal was just keeping balance in the music, and balance and symmetry makes for good art! (In my mind.) – William Egert Feb 19 at 10:19
  • Again pointing at measure 4, beat 3 in the Mozart example. The soprano may be 2:1 against the quarter notes in that beat, but the bottom voices (bass and tenor) are 2:1 with the half note in the alto! It all gets confusing really fast... – William Egert Feb 19 at 10:25
  • Is it that we are only look at the notes above the bass when making these determinations? I suppose that would make things simpler.... – William Egert Feb 19 at 10:42
  • Perhaps, and I know I'm making of ton of comments here, that you combine meter and note-against-note aspects when making determinations as to where dissonances should fit? – William Egert Feb 19 at 12:06

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