Species Counterpoint: Cantus Firmi

[WattsUrizen]

My guide is 'Counterpoint in Composition' by Salzer & Schachter, so refer to that text for more in depth discussion of the concepts.

We'll begin contrapuntal writing with the construction of the cantus firmus, the given melodic line. We must note the significance of the cantus firmus, and its purpose. It is melody in its purest form: Each tone is determined by its context in the linear dimension, there is no harmonic implication, rhythmic skeleton or motivic/thematic design. Basically, the cantus firmus is an abstraction from melody, designed so that we can study voice leading at its most accessible and pure. Let's look at the factors we need to take into consideration when writing a cantus firmus.

1. Rhythm: We write cantus firmus as whole tones as to emphasise their rhythmic indifferentiation. Quarter tones, half tones, etc would all suggest metre, and so disturb our major purpose.

2. Length: Cantus Firmi must be a logical whole; that is, they must have a beginning, a climax, and an end. However, due to their simplicity and austerity, they should not be so long as to be tiresome. For our purposes, most cantus firmi will be somewhere in the order of twelve tones, although it may range from eight to sixteen.

3. Intervals: Only consonances are allowed. That is, between any two notes of the cantus firmus, the interval must be consonant. Also, no leaps larger than an octave should be used. We must make an important note here regarding enharmonics. A minor third may be used freely, but an augmented second may not. The reason being that a minor third does appear in the diatonic scale, the augmented second does not. In summary, the allowed intervals are: Major and minor seconds; Major and minor thirds; Perfect fourths; Perfect fifths; Major and minor sixths; Perfect octaves.

4. Range: Cantus Firmi should be modelled on vocal music. Thus the range should not exceed a tenth.

5. Direction: Melody is the driving force behind music, and as such, successful melody requires direction. In other words, we need a clearly defined climax, from which motion to and from is clearly identified. So from the beginning, we have clear direction to a climax, and clear direction from this climax to resolve at the end. To emphasise a climax, it should not be repeated. To repeat the climax would reduce its effectiveness, and thus reduce the directional drive.

6. Continuity: There must be a logical connection between all members of the melody. Thus, there should not be many leaps. Indeed, continuity is best satisfied if stepwise motion predominates.

7. Variety: Melody requires contrast to be exciting. Thus we should use leaps to offset bland constant stepwise motion, and we should temporarily divert direction from the quickest route to the climax.

8. The Use of Leaps: In light of the previous, how should one tackle the problem of continuity versus variety (indeed, this is an age old musical problem)? In general, leaps larger than a fourth are the most difficult to deal with, since they disrupt the continuity most greatly. Thirds are more inconspicuous, and fourths slightly less so. For large leaps, one should follow the leap with stepwise motion in the opposite direction to the leap (ie, an ascending octave should be followed by a descending second). This fills in the 'gap' between the leap - try moving in the same direction after the leap, it seems like two voices rather than one. Consecutive leaps are also a problem. In general, two leaps in the same direction should not be used consecutively. Two consecutive thirds should not be used due to their strong harmonic implications - they resemble an arpeggiation (a prolongation technique, something entirely different to our purpose). Two consecutive leaps in which a change of direction is involved are more usable, although still somewhat troublesome.

9. Balance: All members must contribute to the whole, but none to the extent that it overpowers the coherence of the melody. Also, melodic motion should be balanced so that certain characteristics of it do not disturb the line. Consideration should be paid to: Excessive motion in a single direction (purely by step, or involving leaps); Unresolved melodic tension; Repetition of single tones; Repetition of groups of tones. Obviously repeating a single tone makes that tone a point of emphasis, and thus the melody will seem to be a prolongation of a single tone, thus destroying our abstract contrapuntal purpose. Also, repeating a group of tones makes that group seem part of a motivic design, again destroying our purpose. Excessive melodic direction depends upon context, if the motion continues for too long it will sound awkward; too short, and it will sound abrupt.

10. Unresolved Melodic Tension: If the melody outlines a dissonant interval, we have unresolved melodic tension. This should be avoided, as it disturbs the linear balance.

11. Ending the melody: The final note must be tonic, to emphasise completeness. Also, the final note must be approached by step, and preferably in descending motion. The reason being that a descending second is the strongest resolution. Upward motion and leaps implies further motion (moreso than downward motion and steps). The final note can be approached in ascending motion, if the melody requires, and thus the preceding note should be the seventh. In the minor scale, the seventh is raised. If the sixth precedes the seventh, the sixth should be raised also to prevent an augmented second. Note that throughout the exercise, in a minor scale, at all other times the seventh and sixth are natural.

I have posted examples of 'bad' cantus firmi, and 'good' cantus firmi. These can be found on the second page of this thread, approximately posts 20 and 24.

Two part counterpoint in first species will be coming up soon.

(Edit: Some spelling and grammatical errors, and some slight clarification).

[ninjaaron]

Interesting, but why no seventh intervale? you can have a minor second but no seven of any kind?? that is a load of poop!:D

seriously thanks for the lesson this is just the kind of thing I am trying to learn about right now!

[r0g3r]

Originally posted by ninjaaron
Interesting, but why no seventh intervale? you can have a minor second but no seven of any kind?? that is a load of poop!:D

seriously thanks for the lesson this is just the kind of thing I am trying to learn about right now!


You should be aware that you should follow these rules ONLY if you're writing a species counterpoint. The rules of species counter point are a bit archaic and limiting by today's standards, but learning and practicing species counterpoint can really improve your sense of melody and harmony.

So use the 7th interval at will! (unless you're composing species counterpoint)

[WattsUrizen]

Originally posted by ninjaaron
Interesting, but why no seventh intervale? you can have a minor second but no seven of any kind?? that is a load of poop!:D

seriously thanks for the lesson this is just the kind of thing I am trying to learn about right now!

You are thinking harmonically rather than melodically. Yes, the inversion of a second is a seventh. Yes, harmonically, the second and the seventh have similar stability.

But melodically, the second is a step, and thus the 'smoothest' melodic interval. The major seventh tends to resolve to the tonic, and thus should be avoided. The minor seventh is less troublesome since it doesn't tend to resolve to the tonic as strongly. However, it is still a dissonant leap, and all dissonant leaps should be avoided. Remember that species counterpoint is modelled on vocal music.

[r0g3r]

An important bit that was missed here, is the fact that the Cantus Firmi (and indeed the subsequent counterpoint harmonies) should be written in a mode of the diatonic scale. The options are:

Ionioan
Dorian
Phrygian
Lydian
Mixolydian
Aeolian

The locrian mode is not to be used.

Also another minor related note: If you use the Phrygian mode you don't need to augment the 7th for resolution as you would in the Dorian or Aeolian modes. The Phrygian's b2 acts as an "upper leading tone" and serves this function instead.

[WattsUrizen]

Originally posted by r0g3r
You should be aware that you should follow these rules ONLY if you're writing a species counterpoint. The rules of species counter point are a bit archaic and limiting by today's standards, but learning and practicing species counterpoint can really improve your sense of melody and harmony.

So use the 7th interval at will! (unless you're composing species counterpoint)

As we will see, the so called 'rules' - which are really just guidelines to helping you write successfully - find themselves in Beethoven, Chopin, Brahms, etc. Species counterpoint abstracts the characteristics of contrapuntal texture, and it is within this texture that composers prolong the underlying progression using extended figurations.

Yes, the 7th interval is a totally valid interval to use melodically and harmonically. However, it is advisable not to use it where species counterpoint is concerned. It isn't an arbitrary rule, it will help you write better melody.

[r0g3r]

Originally posted by Anomandaris


As we will see, the so called 'rules' - which are really just guidelines to helping you write successfully - find themselves in Beethoven, Chopin, Brahms, etc. Species counterpoint abstracts the characteristics of contrapuntal texture, and it is within this texture that composers prolong the underlying progression using extended figurations.

Yes, the 7th interval is a totally valid interval to use melodically and harmonically. However, it is advisable not to use it where species counterpoint is concerned. It isn't an arbitrary rule, it will help you write better melody.

I agree with you, and that's basically what I was getting at. However, some of the rules of species counterpoint are even more arbitrary, such as the exclusion of the tritone, and the locrian mode, which were more for religious purposes than anything else. If you follow these rules strictly you'd never achieve melodies or harmonies that have the "evil' or "eerie" vibe that those elements can create.

Excellent thread though. I certainly haven't seen anything like this on the forum before. And the whole thing is dead on accurate as far as I can tell.

[WattsUrizen]

Originally posted by r0g3r
An important bit that was missed here, is the fact that the Cantus Firmi (and indeed the subsequent counterpoint harmonies) should be written in a mode of the diatonic scale. The options are:

Ionioan
Dorian
Phrygian
Lydian
Mixolydian
Aeolian

The locrian mode is not to be used.

Also another minor related note: If you use the Phrygian mode you don't need to augment the 7th for resolution as you would in the Dorian or Aeolian modes. The Phrygian's b2 acts as an "upper leading tone" and serves this function instead.

I won't discuss modal counterpoint since in the future what I will be discussing mostly applies in tonal systems, rather than modal - especially the treatment of dissonance.

A good book on modal counterpoint is Jeppesen's 'Counterpoint: The Vocal Style of Palestrina'.

[r0g3r]

I think the thread would benefit from a definition of Species Counterpoint for those who are unfamiliar with the term:

(From the Schenker Guide to Species Counterpoint) Species counterpoint is a method used for centuries to teach students how to compose the sort of counterpoint found in the works of Palestrina. The student is introduced to counterpoint in five stages. For each stage the student is asked to write a different species (or type) of contrapuntral line to go with a given melody in semibreves called the cantus firmus.

[r0g3r]

Originally posted by Anomandaris


I won't discuss modal counterpoint since in the future what I will be discussing mostly applies in tonal systems, rather than modal - especially the treatment of dissonance.

A good book on modal counterpoint is Jeppesen's 'Counterpoint: The Vocal Style of Palestrina'.

Sorry, in my limited exposure to the subject, I was of the impression that all of the modes save locrian were always options when writing a species counterpoint.

[WattsUrizen]

Originally posted by r0g3r
I agree with you, and that's basically what I was getting at. However, some of the rules of species counterpoint are even more arbitrary, such as the exclusion of the tritone, and the locrian mode, which were more for religious purposes than anything else. If you follow these rules strictly you'd never achieve melodies or harmonies that have the "evil' or "eerie" vibe that those elements can create.

Excellent thread though. I certainly haven't seen anything like this on the forum before. And the whole thing is dead on accurate as far as I can tell.

The problem with the tritone is that it is quite difficult to sing. Also, because it is a relatively large leap, motion afterwards should follow in the opposite direction, and thus we see that we have outlined a dissonant interval.

The tritone can be freely used as a prolongation technique. Species counterpoint is predominantly found in composition as a structural framework, within which other entities move. In tonal music, it is rather troublesome to have the tritone as a major structural entity.

Of course, many concepts of species counterpoint do not apply as greatly once we start exploring 20th century music, as is to be expected. But I am not aiming at this anyway.

[WattsUrizen]

Originally posted by r0g3r
Sorry, in my limited exposure to the subject, I was of the impression that all of the modes save locrian were always options when writing a species counterpoint.

No, I am sorry, since you are correct. :)

Modes are indeed options, and I would encourage people to explore this avenue. However, I will only explore tonal counterpoint, since this is the dominant system in Western music, and also since the principles of modal counterpoint can be deduced from the principles of tonal counterpoint.

[r0g3r]

Originally posted by Anomandaris


The problem with the tritone is that it is quite difficult to sing. Also, because it is a relatively large leap, motion afterwards should follow in the opposite direction, and thus we see that we have outlined a dissonant interval.

The tritone can be freely used as a prolongation technique. Species counterpoint is predominantly found in composition as a structural framework, within which other entities move. In tonal music, it is rather troublesome to have the tritone as a major structural entity.

Of course, many concepts of species counterpoint do not apply as greatly once we start exploring 20th century music, as is to be expected. But I am not aiming at this anyway.

Dude, I know that you're not trying to say that anyone should follow these rules exclusively. I was only making the point for people that are unfamiliar with the topic, that these rules are archaic, yet still useful. Many people here don't even know what species harmony is, and so may take these rules as gospel. Just trying to add a little bit to the thread. :)

Doesn't species counterpoint prohibit the tritone even in the vertical (harmonic) sense, as well as in melodic movement? I frequently use both, but I was also of the impression that the reason for these inhibitions was religious. This mode of writing harmonies was used by monks and such as well as in other forms of religious music.

[r0g3r]

Originally posted by Anomandaris


No, I am sorry, since you are correct. :)

Modes are indeed options, and I would encourage people to explore this avenue. However, I will only explore tonal counterpoint, since this is the dominant system in Western music, and also since the principles of modal counterpoint can be deduced from the principles of tonal counterpoint.

Really, because I've specifically read that Renaissance music used the different modes.

(the following web site seems to corroborate this): http://www.listeningarts.com/music/general_theory/species/modes.htm

[r0g3r]

Originally posted by Anomandaris


No, I am sorry, since you are correct. :)

Modes are indeed options, and I would encourage people to explore this avenue. However, I will only explore tonal counterpoint, since this is the dominant system in Western music, and also since the principles of modal counterpoint can be deduced from the principles of tonal counterpoint.

Really, because I've specifically read that Renaissance music used the different modes.

(the following web site seems to corroborate this): http://www.listeningarts.com/music/general_theory/species/modes.htm

Of course, I have no formal training in this, so I'll defer to your superior knowledge of the subject.

[WattsUrizen]

Originally posted by r0g3r
Dude, I know that you're not trying to say that anyone should follow these rules exclusively. I was only making the point for people that are unfamiliar with the topic, that these rules are archaic, yet still useful. Many people here don't even know what species harmony is, and so may take these rules as gospel. Just trying to add a little bit to the thread. :)

Doesn't species counterpoint prohibit the tritone even in the vertical (harmonic) sense, as well as in melodic movement? I frequently use both, but I was also of the impression that the reason for these inhibitions was religious. This mode of writing harmonies was used by monks and such as well as in other forms of religious music.

I would argue that the guidelines are not archaic, since they still find practice in tonal music. But anyway...

The tritone can appear in a vertical sense, as we will see in the later species, when we introduce dissonance. But not in first species, first species contains only consonances.

[WattsUrizen]

Originally posted by r0g3r
Really, because I've specifically read that Renaissance music used the different modes.

(the following web site seems to corroborate this): http://www.listeningarts.com/music/general_theory/species/modes.htm

Yes, Palestrina and others used the modes.

[r0g3r]

Originally posted by Anomandaris


I would argue that the guidelines are not archaic, since they still find practice in tonal music. But anyway...

The tritone can appear in a vertical sense, as we will see in the later species, when we introduce dissonance. But not in first species, first species contains only consonances.

I personally feel that they are too inhibiting. I think they are great to learn as an exercise, but when writing music, I certainly don't worry about whether my music follows these rules. In fact I probably break them more often than I follow them. That's just my opinion though.

Don't get me wrong, learning this is invaluable towards gaining proper concepts of how melodies and harmonies function. I just think you should learn this, but not think about it too much when you're actually composing music. Hopefully by working to understand these concepts and performing some excercises in writing this way, good harmonic concepts will become natural to you.

[WattsUrizen]

Originally posted by r0g3r
I personally feel that they are too inhibiting. I think they are great to learn as an exercise, but when writing music, I certainly don't worry about whether my music follows these rules. In fact I probably break them more often than I follow them. That's just my opinion though.

Don't get me wrong, learning this is invaluable towards gaining proper concepts of how melodies and harmonies function. I just think you should learn this, but not think about it too much when you're actually composing music. Hopefully by working to understand these concepts and performing some excercises in writing this way, good harmonic concepts will become natural to you.

Absolutely. It all depends on your own style.

[r0g3r]

Let me again stress that I'm not trying to frustrate your efforts here. It's obvious that you have a great deal of knowledge (certainly greater than mine on this topic) and it's wonderful that you're sharing it.

I simply wished to add a different perspective to the discussion (by which I'm learning myself through your answers to my posts)

Again, excellent thread (and an excellent
idea for a series of threads) Bravo! :D

[WattsUrizen]

Here are some exercises:

Try to find what is wrong with each of these cantus firmi.

Edit: The melodies are written in the alto clef. Middle C is the middle line on the stave.

[WattsUrizen]

Originally posted by r0g3r
Let me again stress that I'm not trying to frustrate your efforts here. It's obvious that you have a great deal of knowledge (certainly greater than mine on this topic) and it's wonderful that you're sharing it.

I simply wished to add a different perspective to the discussion (by which I'm learning myself through your answers to my posts)

Again, excellent thread (and an excellent
eek!idea for a series of threads) Bravo! :D

As long as one person finds it useful, I'm happy to post it.

By all means, add your perspective. I'd be happy if there were 1000 replies with different perspectives. We'd all learn something. :)

[r0g3r]

Originally posted by Anomandaris
Here are some exercises:

Try to find what is wrong with each of these cantus firmi.

For those unfamiliar with this type of clef, the "C" clef, middle C is located where the arms of the clef meet. ;)

(You should also note that these are "movable" clefs, and that cantus firmi are usually notated using them)

[WattsUrizen]

Originally posted by r0g3r
For those unfamiliar with this type of clef, the "C" clef, middle C is located where the arms of the clef meet. ;)

(You should also note that these are "movable" clefs, and that cantus firmi are usually notated using them)

Yes, sorry, I should have mentioned this.

[WattsUrizen]

And here are some examples of 'good' cantus firmi. 4 in major, 4 in minor.

Edit: Corrections. I need to check my work more thoroughly. :o

[ninjaaron]

I like this thread just like before! But MORE

[WattsUrizen]

A few things:

Firstly, Bump.

Secondly, does anyone have any questions regarding the exercise about the 'bad' cantus firmi? They are all quite straightforward, with obvious flaws. If anyone wants something more challenging, I can whip something up quickly.

Thirdly, I finish my exams on Monday, so expect the next installment of the series, 2-Part counterpoint in First Species, on Tuesday or thereabouts.

[WattsUrizen]

Bump, for those who want to read this before the next part I have just posted.

[Dave Regio]

Originally posted by Anomandaris
Here are some exercises:

Try to find what is wrong with each of these cantus firmi.

Edit: The melodies are written in the alto clef. Middle C is the middle line on the stave.

Okay...

I wrote up my answers on a Word File but I don't know if I should post them on the thread openly. I don't mind doing so but I don't want to run the risk of putting the answers up on the screen before people get the chance to try the exercises out for themselves.

I'll email them to anyone interested in seeing what I came up with.

[WattsUrizen]

Originally posted by Dave Regio
Okay...

I wrote up my answers on a Word File but I don't know if I should post them on the thread openly. I don't mind doing so but I don't want to run the risk of putting the answers up on the screen before people get the chance to try the exercises out for themselves.

I'll email them to anyone interested in seeing what I came up with.

Can you PM them to me?

[Dave Regio]

Originally posted by Anomandaris


Can you PM them to me?

Sure. Let me give it a try.

[WattsUrizen]

Ok, here are some 'solutions' to the exercises. Here is why each melody is flawed:

1. The circling of the C tone gives no direction. It is really only a prolongation of one tone. (Extended series of neighbouring notes).

2. The climax is repeated, which diminishes the effect of the climax.

3. Too many leaps, disturbs the continuity of the melody.

4. Only stepwise motion, no variety, no interest.

5. Incorrect motion following a leap. Sounds as two distinct voices, rather than one voice.

6. The melody outlines a dissonant interval, and the leap highlights this, causing instability.

7. The first four notes are repeated sequentially in the next four notes. Sequences are beyond the scope of species counterpoint.

I'll get the next thread up tomorrow morning.