Third,Fourth, and Fifth Species Counterpoint

Glen Halls ©All Rights Reserved

Third Species Counterpoint basically refers to a four-to-one ratio of moving notes with respect to the cantus firmus or original,single tone. ( Three-to-one for triplet-type meters ) Third species gives the potential for generating rhythmic interest, filling in relatively large melodic leaps as a stepwise line, and at the same time to express the harmony more fully if appropriate. ( I.e. it allows you to move to and through the third tone of a triad by line and not leap )

In the strict style third species does seem to carry the most restrictions. It is curious in some respects: on the one hand, the rhythmic relationship between original and counterpoint is the most extreme permitted in the style. Considering a phrase as a whole, a measure of third species rhythmic subdivison is already an 'accent', if entered suddendly. If approached gradually, however, third species relations seem to give an entire phrase a point of natural climax.( note: An excerise in 3rd species implies only 3 or 4 to one relations, but in actual music one typically encounters a variety of rhythms and mixtures of species. We refer to this as 5th species, or free counterpoint. Acutally that's another strange term. Free Species counterpoint is still not as free as Bach-style counterpoint, which is instrumental in nature and permits all manor of leaps and expressive melodic accents. ) Given the 'heightened interest' inherent in 3rd species, this might account for the large number of rules incurred which , really, limit accent in the parameters of dissonance treatment and countour.

So, here is an example of third species as it might appear in a strict counterpoint excercise.

Given the following Cantus Firmus:

A Third Species Counterpoint above might be:

A few things to notice and mention.

I think this is a pretty good solution, but there might be a better one in there.

Note it is basically linear, but not completely linear.

There is only one ascending leap and it occurs between the 2nd and 3rd beats. This is the ONLY Place an ascending leap is permitted in the strict style.

Descending leaps ussually occur from the first or third beat ( though in one instance, if the first and second beats are consonant, one may also leap down from the second beat. ) Leaps are always FROM AND TO CONSONANCES.

There are no leaps across barlines ( and into the first beat, which is already a kind of accent- don't leap into it to exaggerate the accented effect.)

There are all kinds of dissonances on the 2nd and 4th beats, and in most cases these are passing tones. The one exception, in the first measure, is the neighbor tone, which is now permitted in 3rd species.

Accidentals are permitted to avoid dissonances and make the cadence.

SO, now that we have the basic gist of it, here are some formal 'rules' of third species counterpoint.

As in second species, all diissonances must be preceded and followed by consonances.

One may begin the counterpoint on the 1st, 2nd, or 3rd beats. - Upper counterpoint may begin on the 3rd or 5 or tonic.

- A whole note is allowed in the penultimate measure, or two quarters followed by a half note.

-The dissonant neighbor tone is now permitted ( but only in 1/4 notes, only on beats 2 or 4, and only when preceded and followed by consonances.

-There is one NEW figure ( which actually breaks its own rules ) called the CAMBIATA. Cambiata remains as a generic term which may describe any leap from a dissonance. In the strict Palestrina style, however, the cambiata has a much more limited meaning. Specifically, it is a 5 note figure which is often employed to facilitate a decending second ( beat one of one bar to beat one of the next bar= a descending second) in third species. It looks like this:

c (-2) b (-3) g (+2) a (+2) | b

Note that stepwise contrary motion is now created across the barline.

The fourth note of the cambiata may be a dissonant passing tone, as above. ( In other words beats 3, 4, and then one will be

like a small unit of 2nd species counterpoint and adhere to those rules. )

Beats one and three must be consonant, beat four may be a dissonant passing tone, as above, but beat two is open to interpretation. In the strictest possible style beat two must also be consonant. As more personal expression works its way into counterpoint this rule is relaxed. For some beat two may be dissonant. The thing is this: Do you want an accent or not?

Another interesting variation on the cambiata- This five note pattern may begin on beat three, not beat one. Again, in the strictest style it is best if beat four is also consonant. The change here is that we now permit a descending leap across the barline. This certainly creates an accent, a mild syncopated effect.

Note: The cambiata from the 3rd beat idea is something we will typically find in free or fifth species writing, i.e. where the figure is preceded or followed by half notes, or perhaps involved in second species part of the time. The example given above is weak in that the first measure contains a strong beat octave and no other consonance. This could be addressed in free counterpoint.

There is another exception to the rules and another kind of dissonance allowed, with caution: the accented passing tone. In Bach style counterpoint of course the accented passing tone occurs virtually all the time. Here, however, it is only permitted as the third note in a descending four note diatonic pattern, and only when surrounded by consonances ( ie. on beat two and four ) . This pretty well limits one's use of the figure to the following example:

We've been trying really hard to avoid speaking of harmony here, but it might help to remember this context as basically an elaboration of a firts inversion triad, in which the faster line moves from the root down to the fifth.

The classic third species cadence is rather strict-the quarter note motion in an upper voice continues right to the first beat of the final bar, where we again 7- 8, 2-1 type of cadence.

When the counterpoint is below, however, we have a problem. Ascending quarternote motion in the penultimate measure leads to a p4th dissonance on the 3rd beat. It is therefore conventional to stop the 4:1 counterpoint in the third to last measure.

There are a couple of different 'openings' in 3rd species. Voices may of course begin on the unison or 8ve on beat one, as before. However, the counterpoint starting on the 8ve or unison may also be delayed two beats.

Some texts also allow the following opening for upper voice counterpoints: (0) 3 5 4 | 3 in terms of scale degrees, starting on beat two.

Some thoughts on parallel, accented, and hidden fifths and 8ves.

It is generally considered that 8ves and fifths occuring on beat one of consecutive measure,is poor. This is sometimes called parallel accented fifths. This is where things get very grey. It is arguable that in 3rd species where there are four quarter notes of separation parallel accented 8ves are fine. If you must use them try to approach the second one in contrary motion. From my own point of view I would call them poor, as there is in almost all cases a better alternative. ( I.e. in two voices. As we get into 3,4,5 and more voice textures rules about parallelism must be relaxed. Accented 5ths and 8ves are evident in Paletrina, but he usually tries to have at least one of the two parallel voices as an inner voice.

. It is not wrong to have 8ves and 5ths on the first beats of measures, but it isn't the best. It sounds 'hollow'. 8ves and 5ths are not as 'sweet' as thirds and sixths, and we've kind of been expecting a kind of 'harmonic rhythm' where we get a sweet 3rd or 6th on the first beat. If we don't got one it suddenly sounds like the piece is over, or there is a problem of some kind. If you have to use a beat one 8ve or fifth try to move to a third or 6th for beat three.( In the Bach style we would insist you fill out the triad with the other consonance on beat three. ) Alternately, one could aim for placing, kind of 'hiding' 8ves and fifths on beat three. This is very good third species counterpoint. The only thing to watch out for now are consecutive 'hidden 8ves' or fifths. In other words-beat 3 8ves or fifths in consecutive measures. Actually this is fine in third species- just don't do it more than three times in a row. Also, going from a hidden 8ve on beat 3 to an accented 8ve on beat 1 in the next measure is poor.

Note, even the above example which is OK could be improved by approaching the second of the two 8ves in a direction contrary to the approach to the first. ( I.e. by ascent, rather than decent- this hides it even more. )

Some fine lines of steps and leaps.

So we're not supposed to have an ascending leap from beat one or three, and yet in actually Palestrina masses they abound. As mentioned, in multivoice setting some of the rules are relaxed a bit anyway, but it would appear that though ascending step motion is ideal , a 'skip' of a third, followed by stepwise motion is OK. ( note, some texts call a leap of a third a 'skip' and a leap of a 4th more a 'leap'. )

It also seems that a skip of a third, no more, from beat three to four is tolerable. Remember, with the exception of the cambiata ( and even then only in freer contexts) in the strict style we cannot leap into or from a dissonance, so both the third and fourth beat must be consonant. Further, we would only want to do this ( skip a third from beat three to four) if we wanted a stepwise arrival and direction change into beat one of the next bar. This would be considered a kind of 'justification' for bending the rule.

The only time you would want to use a skip at the top of an ascending line ( it's preceded by stepwise ascent ) is in the situation above, where the upper note of the skip initiates a direction change. It is kind of a rare event, marks a climax perhaps, and should be used rarely and with care. In most other instances the use of the ascending skip from beat three to four is better as below.

( Generally we have a kind of scale in strict counterpoint: Good- OK - weak - tolerable- poor- wrong ) We try to keep the counterpoint Good or OK, as when we get into poor and tolerable we really have a perceivalbe loss of ease and grace, again- an undesireable accent. )

For Practice, try and identify the errors in the third species counterpoint below:

Poor.

A possible solution.

Poor.

A possible solution

As a point of reference, the following are third species figures common in upper counterpoints.

In fact, though it is not usually done, one could work with a kind of template of 'interval-solutions'. Basically, third species is easy for unisons, 3rd, and 5ths, but requires a little finesse for 2nds, 4ths, and 6ths.

Fourth Species Counterpoint.

Glen Halls © All rights reserved.

Not too much to tell on 4th Species. Bacially it refers to the suspension, a situation in which one note, though sustained, becomes 'dissonant' due to motion, ie, the striking of a new pitch, in another line. In the general sense this suspended pitch will seem to want to 'resolve' to an expected pitch , typically a more consonant tone and usually a 'chord-tone' if we are speaking in those terms. ( Actually, in strict counterpoint the resolution which follows the 'rules' is often not the one which the ear expects. Curious.)

Here is the standard strict counterpoint formula for the fourth species suspension.

Consonant Preparation- Dissonant Suspension- Consonant Resolution.

NOTE THE FOLLOWING:

a) The Prevailing pulse in the example is in half notes. In other words, there are basically two pulses per bar: a strong beat ( or downbeat) and a weakbeat ( or upbeat) , ( beats one and three respectively if we are thinking in 4/4 time and beats one and two if we are thinking in 2/2 time. ) This is actually very very important.

Because: 1) the fourth species suspension will always be at the prevailing pulse level. ( even if there appear to be lots of different rhythms going on, we can usually reduce this to a basic pusle, a prevailing controlling pulse ) ( Note, you can in complex texture and in freer counterpoint , of course, have different levels of pulse going on, and if you do, the principles of good 4th species counterpoint suggest that at whatever pulse level engaged, the figure begin on the weak beat)

2) The consonant preparation in a 4th species figure ( which sort-of has three segments) should be on the weak beat just ahead of the suspension. The Suspension will be on the strong beat of the next bar ( or cycle) and the resolution must be on the subsequent weak beat, and to the expected resolutio

n pitch. The timing is very important.

Bear in mind that when I use the term suspension to this point I am referring to a dissonant suspension. There is also a consonant suspension which is slightly freer in terms of what happens just after the actual suspended interval( segment two- the subsequent strong beat) . We will discuss this shortly.

What is happening here is that strict counterpoint is breaking one of its own rules for the sake of expression. We do have a strong beat dissonance, albeit through suspension, but it is still a strong beat dissonance, which kind of reverses the 'phase' of the bar. In 'normal' bars we have a basic rest-move kind of structure. Consonance- Dissonance- nextbar consonance. Now we have ( starting on beat one of the suspended bar) Dissonance, consonance, then next bar whatever-probably consonance.

whereas:

So, subjectively speaking, when we go to 5th species we may want to follow a suspension with some faster rhythms in order to help 'push across the barline', so to speak.

(Note: The term suspension is thorny. Sometimes it means specific things, and other times it means a generic kind of ornamentation, on whatever beat and resolved in whatever direction by whatever interval. And in the harmonic context the term suspensions can mean a great many things to a jazz musician.)

For upper voice counterpoints there are two basic suspensions in strinct counterpoint. the 4-3 and the 7-6.

Note that in each case the resolution of dissonance is DOWN by Step. In the strict style you may not resolve a dissonance by ascent.( something we later might term a ritardation )

Note also that the preparation segment ( labelled '1' here) is different in each case. Both tones may be struck or perhaps just one. The main thing is that that interval MUST BE CONSONANT. It doesn't matter which consonant interval you choose.

The following example is faulty becomes the suspension begins with a dissonance. ( i.e. there is no consonant preparation ) ( I guess it's hard to read. The lower note is an F)

Note: In any event it is always faulty to strike a dissonance in strict counterpoint. ( striking the two notes at once )

In the next example the error is that the dissonance preparation is on beat 4. All three segments of the 4th species figure ( prep-diss-resolve) must correspond to the prevailing pulse rhythm, in this case, the half note. I know this is a subjective and difficult to define concept, so just remember the rule is for this class as when doing species counterpoint in the strict

style, 4th species in half notes only.

In the next example, the error is that the dissonance, the f-e seventh via suspension, does not resolve to the D at the right time. This must happen on beat 3. ( It does resolve down by step, that part is correct. It is the timing which is wrong. )

I must point out now that some of the rules I've just discussed are relaxed for another kind of suspention common in 4th species, the consonant suspension. However, we'll talk about them shortly. First, lower voice 4th species dissonant

suspensions.

The ONLY 4th species dissonant suspension allowed for lower voice counterpoints is the 2-3, which looks like this.

Remember, the dissonance must resolve down by step on beat three. Also note that the preparation interval does not have to be a third. It could be any consonance. It is very commonly a third, and it is common to chain a string of these

suspensions together in a quasi sequence.

One last point in preparation for 5th species. In the example above the suspension is correctly resolved down to the B on beat three. In fifth species we are allowed to combine different rhythms, so this B on beat three does not necessarily have

to be a half note. A group of quarter notes could be initiated on beat three. The first note, however, has to be a B.

CONSONANT SUSPENSIONS

Consonant suspensions are very much allowed. The most common consonant invervals for suspension are the 6th and the 3rd, but you can also use the 8ve and the 5th ( and the 4th if the upper term of a first inverion triad in 3 part writing.) The preparation is the same as for dissonant suspensions. The initial note ( segement one) must also be consonant. You cannot begin any suspension from a dissonance. The differences are in the continuation.

That second segment of a consonant suspension. ( bar 'two' ) can now be treated like second species counterpoint. This means a) we may leap away from the suspension into another consonance and ) we may follow the suspension with a

second species passing tone.

That's about all you need to know, but there is one more thing about the consonant suspension which pertains to 5th species uses. You are allowed to initiate a third species segment from the tied and consonant beat one, ( but make sure beat

three is also consonant) This may seem to break that rule about suspensions needing to correspond to the prevailing pulse, but not really. By heading into 3rd species, in which we stress consonances on one and three, sometimes by leap, we are

still reinforcing , by the placement of these consonances, the half note pulse.

Fifth Species Counterpoint

Glen Halls © All Rights Reserved.

With Fifth species counterpoint one is permitted to mix all rhythms and devices of the previous species within the same phrase, ( though still above a cantus firmus in whole notes I suppose, - that's why it is still a 'species' and not free counterpoint or real music.) Variety is desired- it is that freshness which keeps a phrase buoyant. Symmetrical or better, complementary shapes also seem pleasing. But think like a musician here. What makes a phrase interesting, engaging, pleasing? Notwithstanding the fact that one's assessment of one phrase will depend on the phrases which precede and follow it, what we are really looking for in a good fifth species phrase is DYNAMIC, some kind of defining shape which distinguishes this phrase from all others.

Let's start with a look at a couple typical 5th species phrases:

A:

B:

I wouldn't call them perfect counterpoint, but they aren't too bad and do demonstrate some 5th species principles.

First of all, we now allow a little ornamentation of the rhythms. 1) The 'Anticipation' is 8th note ornamentation of the arrival note of a suspension. These three varieties are common:

Note, even though we may arrive at the resolution note 'early', we still need to repeat this note at the expected resolution time. One MAY NOT resolve 'early' as in an anticipation, but then continue in some kind of linear/scalar passage without

repeating that resolution note on beat three. And, yes, we did say that you weren't supposed to use repeated notes back in first species, but here they are. Remember that we advised against repeated notes because it diminished the sense of a lines independence, and also, because there was no dissonance, repeated notes really caused the momentum of a phrase or line to die. I don't think that's the case here in the resolution of a suspension.

2) The 8th notes as passing notes, kind of an ornamented 3rd species line. In fifth species one is permitted to 'fill-in' a melodic fourth interval with passing 8th notes on the WEAK BEAT. These are to be used SPARINGLY, and may ONLY be used on the weak beats, and may ONLY be used as part of an ascending or descending line, preferably descending. Ideally, this third species type line should be 6-8 beats long- perhaps starting in the middle of one measure, continuing through the next, and perhaps ending on beat three of the third bar.

In the 'normal' third species line below we note that it conveniently allows us to traverse a fifth downbeat to downbeat.

However, if a fifth is not what you need but a sixth gets you to the note you need, then this eighth note figure is perfect. This is basically the context in which to use the 8th note passing tones.

Actually I've noticed an error here, but I'm leaving the example anyway. Do you see how beat three of the first bar is dissonant? I missed this the first time.

So here is a better example of the 8th passing note figure, hopefully without a dissonance on beat 3.

Can you use that 8th figure in a 'neighbor tone' context? I.e. an ornamentation of a third species neighbor tone. Some books will say that you can. I don't recommend it, except for consonant neighbor tones. Remember that we are trying to avoid accented dissonance. Ornamenting a dissonant neighbor gives it undue weight. ( Yes, the 8th passing tone figure also gives the dissonance undue weight, but the fact that it occurs in a scalar line seems to hide it.

This is possible ( though you would have to move to a new note below to maintain a consonant third beat- so we'd be talking about free counterpoint and not 5th species above a CF)

This is poor: I.e., I wouldn't want to give the dissonant neighbor any more weight, and besides, we'd really end up with an ornamented escape tone, not a neighbor at all. ( Really a Bach-Style thing.)

There is one other new rhythm in 5th species, and that is the dotted halfnote. This figure is easily explained as a reduction of a third species neighbor tone figure. Remember that in third species the 2nd and 4th beats may be dissonant neighbors or passing tones ( as well as consonant neighbors and passing tones) and also may be a consonance approached by leap, especially descending leap. The same choices will apply to this fourth beat after the dotted half.

The neighbor and passing tone.

The neighbor and consonant skip.

Beat 4 as passing tone. ( In this case consonant, but it could've been dissonant )

Beat 4 as a consonance approached by descending leap.