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Introduction Preface The last section of Chapter 8, "Soprano-Bass Counterpoint," provides a preliminary discussion of counterpoint, and you may wish at this point to go back and review the terms and concepts that are defined in that discussion. While the treatment of counterpoint in Chapter 8 was primarily from the perspective of analysis, the approach in the present discussion is compositional. The history of counterpoint instruction is one that is many centuries old. Certainly the most famous and influential counterpoint manual of all time is Gradus ad Parnassum by Johann Joseph Fux (1660-1741), an Austrian composer and theorist, whose text was used by Haydn, Mozart, and Beethoven, among many others. Fux's approach was to teach counterpoint in the context of five "species," which were defined as follows:
In addition, an important aspect of Fux's method was that it did not make use of the major/minor harmonic language of his time but instead used the traditional church modes* and a style that was based, not upon chords, but upon intervals between the voices. This is probably both the greatest strength and the greatest weakness of his approach. Our brief introduction to the art of writing counterpoint makes some use of Species 1, 2, and 4, but it does so in a harmonic context. That is, we will try to keep in mind the principles of good counterpoint while at the same time writing lines that conform to good tonal progressions. * The church modes, which enjoyed a revival in the 20th century, are explained in Chapter 28. Part I: Composing an Unembellished Bass Line Introduction Counterpoint is the art of combining relatively independent musical lines (parts, voices) into a cohesive and musically satisfying whole. The independent parts in a contrapuntal texture are independent in that they have their own contours and rhythms. In tonal music the contrapuntal lines must also combine in such away as to make a convincing harmonic progression, which means they can never be completely independent. A fugue is a good example of counterpoint, and you have probably heard some of Bach's fugues. In a fugue, all of the lines (voices) are based upon the same material, but they move with contrasting rhythms and contours. Even in music that is not strongly contrapuntal (like a chorale, or a song with piano accompaniment), there is usually an important contrapuntal relationship between the outer parts (the highest and lowest sounding parts). This is sometimes called the outer-voice (or soprano/bass) framework. In this part of our counterpoint unit, we will practice writing unembellished bass lines -- that is, bass lines in which there is only one note for each chord. The Given Harmonic Progression For most of these beginning exercises you will be given a harmonic progression to use instead of creating your own. 1. Length: Some of them will be a phrase in length (about four measures), and others will be a period in length (two phrases). 2. Harmonic Rhythm: The chords (and the bass line) will generally move in half notes in 4/4 time, and in a half-quarter pattern in 3/4 time. 3. Beginning and Ending: Each phrase will begin and end on tonic or dominant harmonies. Composing the Bass Line 1. Notate in Root Position: The first step is to notate the bass line in root position using the given progression. 2. Range: Stay within the approximate range of E2 to C4, and use leaps larger than a 5th only occasionally. Example I-1 illustrates a root position bass line. Example I-1. Root Position Bass Line
Chords that Remain in Root Position There are certain chords that should always be left in root position for the purposes of these exercises. 1. First and Last Chords: The first and last chords of each phrase should be in root position. 2. V in a V-I Cadence: In addition, if the cadence (the last two chords of the phrase) is V-I, the V should also be in root position. 3. vi in a V-vi Progression: If a progression contains the deceptive progression V-vi (or V-VI in minor), the vi should be in root position. The bass line from Example I-1 is shown again below, with circles around the notes that should remain in root position. Example I-2. Mandatory Root Position Chords
Chords to be Used in First Inversion Next, there are a few triads that should be used in first inversion rather than in root position. 1. Diminished triads: These include the iio in minor keys and the viio in major and minor. 2. V or I in an Internal V-I Progression: If the progression contains a V-I within the phrase (not at the very beginning or at the cadence), it is usually best to keep it from sounding too final by using V6-I or V-I6 (but not V6-I6). Example I-3 shows our bass line with the viio now as a viio6 and the iio as a iio6. Example I-3. Mandatory First Inversion Chords.
Improving the Bass Contour Here are a few additional suggestions concerning the overall flow and contour of the bass line. 1. Repeated Bass Notes: First, it is a good idea to avoid repeating bass notes across the barline because such repetitions tend to confuse the harmonic rhythm. There was a repetition across the barline in Example I-3 (the two C3's), which Example I-4 corrects by inverting the iv chord. Example I-4. Repeated Note Avoided.
2. Focal Point: Also, it is best if the bass line contains a focal point, a single highest point or a single lowest point in the line. In Example I-4, above, the Eb3 provides the focal point. 3. Convert Large Leaps: Inversions of chords are often used to convert large leaps into smaller leaps or into stepwise motion. Use first inversions only. The sixth between G2 and Eb3 in Example I-4 becomes a fourth in Example I-5 by inverting the i chord. 4. Tonal Variety: Notice that inverting the i chord also helps the bass line in another way. Where we once had three G's (out of seven notes), we now have only two, and we have added a new pitch class, Bb, to the line. This is called "tonal variety," and it is preferred over "tonal redundancy," the overuse of a single pitch class. Example I-5. Leap Converted and Tonal Variety Achieved
5. Change of Direction: If a large leap (a 4th or a 5th or larger) occurs in the line, change the direction of the line after the leap. 6. Dissonant Intervals: Avoid the use of augmented intervals, sevenths, and any interval larger than an octave. The only diminished intervals used are the o4 (scale degrees 3-7-1 in minor) and the o5 (4-7-1 in major or minor or 6-2-3 in minor). In either case, the line changes direction after the leap. Example I-6. Allowed o4 and o5.
7. Melodic Minor: In minor keys, use melodic minor. This may occasionally change the quality of a triad. For example, in the progression iv-V-I, if you invert the first two chords, you will create a major IV6, as in Example 1-7. Example I-7. Use of melodic minor.
Six-Four Chords You may have noticed that all of the inverted triads we have used have been first inversion triads. Second inversion triads, or six-four chords, are discussed in Chapter 9 of the text and are not to be used at this point. Exercises Review the paragraphs above, and compose bass lines to the following progressions. Follow the suggested procedures, and explain your decisions. Example:
1.
2.
3.
4.
Part II: Composing a Counterpoint to the Bass Line Introduction Once you have composed a simple bass line to a given progression, the next step is to compose a simple contrapuntal line above it. The two lines will not be independent rhythmically, but they will have their own contours. While the counterpoint is still rather elementary, we are learning principles that will serve as the foundation for more advanced compositional or analytical procedures. The "rules" in this unit--and there are quite a few of them--are not as arbitrary as they may seem. Some of them pertain only to tonal counterpoint, but others would hold true for counterpoint in any period or style of music. Notating the Harmonic Fabric Assuming you have composed a bass line like that seen in the bottom staff of Example II-1, the next step is to notate the harmonic fabric -- the chord tones from which the notes of the contrapuntal top voice will be selected. 1. Distance Between the Voices: Keep the top voice within a 10th or so of the bass line. Also, avoid allowing the voices to cross, and avoid unisons anywhere except for the first and last notes of the phrase. You will often find it easier to notate the top voice in the transposing treble clef, which sounds an octave lower than written, as in the examples below. 2. Notate the Chords: First, notate on the upper staff the pitches that form unisons with the first and last bass notes of each phrase. Then notate on the upper staff above each bass note the next four chord tones higher than the bass note. This will give you all the chord tones available within a 10th of the bass. Example II-1 illustrates. Example II-1. Harmonic Fabric Notated
Eliminating Certain Notes Before proceeding to compose the top voice from the harmonic fabric, certain notes may be eliminated from consideration. 1. Octaves Above Scale Degrees 3, 6, and 7: In our exercises we will use a P8 above the bass only when the bass has degrees 1, 2, 4 or 5. Therefore, any octaves above degrees 3, 6, and 7 may be eliminated, or X-ed out. 2. Scale Degree 5 Over the Final I Chord: If the last chord in a phrase is a I chord (or a i chord in minor), the 5th scale degree above it may be X-ed out to avoid the unsatisfactory ending that would result from its use. 3. Overlaps: Also to be avoided is overlapping, which is similar to voice crossing. It occurs when the upper voice dips below where the bass was in the previous chord, or when the bass rises up above where the upper voice was on the previous chord (Example II-2). Example II-2. Overlapping.
Keeping these principles in mind, we can X out six of the pitches from Example II-1. Before looking at the next example, see if you can determine which six pitches will be X-ed out. Example II-3. Some Tones Eliminated.
The Shape of the Top Voice Before going on to compose the counterpoint, there are several suggestions concerning the shape of the top voice that should be kept in mind. Each suggestion in the list below is followed by an example drawn from the remaining notes in Example II-3, showing what is to be avoided by following the suggestion. 1. Motion should be more conjunct (stepwise) than disjunct (leapwise).
2. Tonal variety is preferred over tonal redundancy.
3. Use no more than two consecutive occurrences of the same pitch.
4. Avoid augmented or diminished intervals, sevenths, or leaps larger than an octave. (Exception: See the discussion of the o4 and the o5 in Part I, page 5.).
5. Two consecutive leaps in the same direction should together span a fifth, a sixth, or an octave. Use no more than two consecutive leaps in the same direction.
6. Don't let the melody pull too much in one direction.
7. Have one high focal point, but not simultaneous with the focal point in the bass.
8. Resolve scale degree 7 up to 1, except in the stepwise descent: 1–7–6.
9. The range of the added voice should be no less than a fifth and no more than a tenth.
Contrapuntal Considerations There are also some concepts concerning the intervals between the two voices that need to be understood before actual compositions of the top line can begin. Some of these are familiar to you already. 1. Parallel Fifths and Octaves: A cardinal sin in tonal counterpoint is the use of parallel fifths or octaves. These result when the two parts are separated by a P5 or a P8 and move to new pitch classes which are also separated by the same interval. They are objectionable even if the voices move in contrary motion.
2. Other Parallels: Parallel thirds, sixths, and tenths are fine, but try not to use more than three in a row of any interval between the voices. 3. Direct Fifths and Octaves: A sound similar to parallel fifths and octaves, direct fifths and octaves result when the two parts move in the same direction into a P5 or P8 with a leap in the upper voice. In other words, the upper voice must move by step in such situations. A special case is that in which both voices move upward into a P8: here the top voice must move by half step to be acceptable.
4. Miscellaneous: Two additional suggestions: First, keep in mind that "imperfect consonances" (thirds and sixths) have a more pleasing sound in the tonal style and should predominate over "perfect consonances" (P5 and P8), especially in the middle of a phrase. Second, try to avoid having both parts leap simultaneously in the same direction in order to avoid displacing the texture suddenly into another register. Composing the Top Voice The next step is to "thread" the melody through the available chord tones, keeping in mind the rules having to do with the shape of the top voice and contrapuntal considerations. As you work, shade in each notehead as you select it, and write between the staves an arabic numeral representing the interval between that note and the bass. This will help you to avoid objectionable parallels. Keep these pages handy as you work, and don't be afraid to revise. Use a pencil with a good eraser, not a pen! After you get a satisfactory solution, copy it and the bass line onto two clean staves. Two possible solutions to our bass line from Example II-3 are shown below. Example II-4. Solutions.
Exercises Construct "harmonic fabrics" above these bass lines using the suggested procedures. Then eliminate appropriate notes, as described on pp. 7-8. The result should look something like Example II-3. 1.
2.
Compose good counterpoints to the bass lines above. Turn in both your "working copy" (like Example II-4) and your final copy. 3. Use the bass from #1 above. 4. Use the bass from #2 above. Compose a good bass line using one of the progressions below. Then follow the instructions for #3. 5.
6.
7. (Two phrases)
Invent a harmonic progression following the instructions below. Then follow the instructions for #5. 8. F Major, 4/4, one four-measure phrase with an anacrusis. 9. E Minor, 3/4, one five-measure phrase. 10. A Major, in 4/4, one two-phrase period. 11. G Minor, 4/4, one two-phrase period. Part III: Adding Weak-Beat Motion: Introduction 1. The Basic Framework: Most tonal music can be analyzed as an elaboration of the kind of simple two-voice texture that we have been studying so far. In the next two units we will explore just a few of the many ways in which these simple textures can be elaborated into more interesting compositions. 2. Elaboration on Weak Beats: The unit you are reading now will deal with the addition of motion on weak beats of the measure: beats 2 and 4 in 4/4 meter and beat 2 of 3/4 meter. Passing Tones 1. Definition: A passing tone is a tone that is approached and departed from in stepwise motion in a single direction. In other words, it "passes" from or connects one tone to the next. There are many different kinds of passing tones. For example, in a I-viio6-I6 progression, the bass note of the viio6 is a passing tone that connects two positions of the tonic triad. For our purposes, however, we will be using a more restricted definition: in this unit, a passing tone will be a non-chord tone (a tone not belonging to the harmony at that point) connecting two tones a third apart. 2. Adding Passing Tones: In order to add passing tones to a note-against-note (or 1:1) texture, such as those we have been using, you have only to find a leap of a third in one of the voice parts. The only thirds that cannot be used are those in 3/4 time that occur between beat 3 and beat 1, because we will not be using eighth notes yet. Otherwise, any leap of a third in a 1:1 framework may be filled in with a passing tone if you feel it is musically desirable unless it causes objectionable parallels (discussed below). For example, the bass line in Example III-1 is shown in two versions, one embellished and one containing passing tones wherever possible. Notice that the passing tones are in parentheses; this is the method we will use throughout the text to indicate non-chord tones. Example III-1. Bass Line with Passing Tones Added
Arpeggiations 1. Definition: An arpeggiation is movement from one tone to another, with both tones belonging to the same chord. Because we are working only with triads, an arpeggiation will involve a leap of a 3rd, 4th, 5th, 6th, or 8ve. 2. Adding Arpeggiations: With the exception of beat 3 in 3/4 time, arpeggiations may be used anywhere that passing motion is not used. Smaller leaps are generally better than larger ones, but the leap of an 8ve is an effective cliché when used in the bass over a V chord, as in Example III-2. Example III-2. Cadential Cliché.
Below is the bass line from Example III-1, with arpeggiations embellishing the two bass notes that had been left unembellished by passing tones. However, this is not a good example of a bass line in the style we are working with, because (1) the monotony of constant half notes has been replaced by the monotony of constant quarters, and (2) the V-I cadence has been weakened by the first inversion V chord. Example III-3. Overembellished Bass Line.
Two similar but better versions of the same bass line appear in Example III-4. Notice that the second one calls for a D2 from the basses (sorry, basses!) and lowers the last note an octave. Example III-4. Two Better Versions.
Contrapuntal Considerations 1. Dissonances: In most tonal music, the consonant intervals between the bass and an upper voice are P1, m3, M3, P5, m6, M6 and octave duplications of these. Any other intervals are considered to be dissonant. Passing tones and, less often, arpeggiations, are apt to cause dissonances, and that is fine--this is one reason for using them. 2. Objectionable Parallels: Even if you start with a good 1:1 version, you will have to be careful so that added passing tones and arpeggiations do not create parallel fifths or octaves. Example III-5 illustrates how this can happen. Remember that these are to be avoided. Example III-5. Embellishments Creating Undesirable Parallels.
3. Simultaneous embellishments: Occasions may arise in which you want to embellish both of the lines at the same time with passing tones, arpeggiations, or a combination of the two. This is fine, as long as the harmonic interval formed by the two embellishing notes is a consonance (P1, m3, M3, P5, m6, M6). Example III-6. Simultaneous Embellishments.
To Embellish or to Compose? 1. Composers and Counterpoint: It may have occurred to you that what we're suggesting in this unit is a very strange way to compose, and that surely no tonal masterpieces were composed in this way-- and you're right! On the other hand, what student composers tended to study in Mozart's time, for example, was figured bass (roughly equivalent to our study of harmony) and counterpoint, and that study of counterpoint was a rigorous, systematic approach based upon the species system popularized by Fux. It is reasonable to assume that as the composer matured, his or her craft was still based upon the contrapuntal principles that had been studied. As you become more proficient at tonal composition, you may want to leave out the first step--the composition of a good 1:1 framework--as tonal composers doubtless did. For now, however, you should begin each time with the framework, which you then embellish. 2. Where to Add Motion: The object is not to add motion over every chord in both voices. As you know, the term "counterpoint" implies a certain amount of rhythmic independence between the voices, so it would be best if they did not both move in steady quarter notes. On the other hand, if one part has all or almost all of the quarter-note motion, it tends to be heard as the "melody," while the other becomes the "accompaniment," even if the embellished part is the bass line. For now, try to keep the motion distributed fairly evenly between the two parts. Below are two examples of 1:1 frameworks with their embellished versions. Example III-7. Embellished Frameworks.
Exercises Embellish the 1:1 frameworks below. Remember to put parentheses around non-chord tones (but not around arpeggiations). 1.
2.
Compose good 1:1 frameworks based upon the progressions below. Then add arpeggiations and passing tones. Turn in both versions. 3.
4.
Make up progressions conforming to the instructions below. Then compose 1:1 and embellished versions. Turn in both versions. 5. A period in G Major. End the first phrase with a half cadence and the second with an imperfect authentic cadence. 6. A period in C Minor. End the first phrase with an imperfect authentic cadence and the second with a perfect authentic cadence. Part IV: Dissonance on the Strong Beat: Strong Beat Dissonances In the preceding unit we introduced embellishments on certain weak beats: beats 2 and 4 in 4/4 time and beat 2 in 3/4. Now we will discuss the suspension, which is one of the primary sources of dissonance on the strong beat. The strong beats are beats 1 and 3 in 4/4 and beat 1 in 3/4. 1. Definition: For now, we will define a suspension as a non-chord tone that delays a descending stepwise motion from one chord tone to the next by suspending (holding over) the note from the first chord into the time span of the second chord. For example, we might begin a two-voice counterpoint as in Example IV-1a. The stepwise descent in the top voice could be delayed as in Example IV-1b, forming a suspension (in parentheses). The suspension may be tied to the previous note or not tied; it is a suspension in either case. Example IV-1. Adding a Suspension.
2. Metric Restrictions: For the purposes of this unit, suspensions may occur only on strong beats. This means that we will use suspensions in 4/4 on beats 1 and 3 and in 3/4 on beat 1 only. Suspensions in the Bass Voice 1. The 2-3 Suspension: The only bass suspension we will use is the 2-3 suspension. The "2-3" means that the suspension causes a dissonance of a 2nd (or octave equivalent) between the two voices, which then becomes a 3rd when the bass descends to its resolution, as in Example IV-2. Example IV-2. Adding a 2-3 Suspension.
Suspensions in the Top Voice 1. The 7-6 Suspension: The most successful top-voice suspension in a two-voice texture is one in which a suspended 7th resolves down to a 6th, as in Example IV-3. Example IV-3. Adding a 7-6 Suspension.
2. The 4-3 Suspension: Also good is the 4-3 suspension, as in Example IV-4, although this works somewhat better in fuller textures. Example IV-4. Adding a 4-3 Suspension.
3. The 9-8 Suspension: The 9-8 suspension tends to fall flat in two-voice textures (see Example IV-5). It works much better when the bass arpeggiates at the same time as the top voice resolves the suspension (to be discussed below). Subtracting an octave from the 9-8 yields a 2-1 suspension, which should be avoided for now. Example IV-5. Adding a 9-8 Suspension.
Embellishments in the Other Voice As the strong-beat suspension resolves down to its resolution on the weak beat, the other voice is free to arpeggiate to another chord tone (passing tones, however, seldom work as well). This changes the technical name of the suspension from 2-3, for example, to something like 2-6, but we aren't really concerned with the labels. If the suspension started out as one of the allowed types (2-3, 7-6, 4-3, 9-8), the arpeggiation will probably be fine. In fact, the 9-8 suspension must be accompanied by arpeggiation to be effective in a two-voice texture. Several examples appear below. Example IV-6. Suspensions with Arpeggiation in the Other Voice.
The Logic Behind Suspensions You may wonder why only certain suspensions are used. All of the possible suspensions are listed below.
As the table shows, nearly half of the possible suspensions would "resolve" into dissonance. This is like sitting down on a thumbtack, as far as tonal music is concerned, because dissonance itself requires resolution. For this reason, the suspensions labeled "diss. res." are not used. Five of the possible suspensions would resolve into perfect consonances, which tend to have a more stark and hollow sound than do imperfect consonances. These suspensions are shown with question marks. The only one used with any frequency is the 9-8, and, as we have seen, it is usually converted into a 9-6 or a 9-3 by arpeggiation in the bass. The 5-6 suspension in the bass is "possible." It is less successful than the "good" ones largely because the 5-6 does not create a dissonance, as do the 7-6, 4-3, 9-8, and 2-3. Where to Use Suspensions To add the suspensions we have been discussing to a 1:1 framework, do the following: 1. Find a step down in the bass from a weak to a strong beat. Is the harmonic interval above the second bass note a 3rd? If so, the 2-3 suspension will work. 2. Find a step down in the top voice from a weak to a strong beat. Is the harmonic interval below the second note a 3rd, 6th, or 8ve? If so, the 4-3, 7-6, or 9-8 suspensions, respectively, will work. Remember that the 9-8 should have an arpeggiation in the bass. 3. Be sure to play the suspension to see if it gives you a good musical effect at that point. The object is not necessarily to add as many suspensions as possible. A related problem is how to compose a progression to which suspensions could be added. Here are some suggestions (by no means exhaustive): 2-3: Use in a I-V6 progression, or in any progression involving a root movement down a 4th, with only the second chord inverted. 7-6: Use in a I(6)-viio6 progression, or in any progression with root movement down a 5th and the second chord inverted. 4-3: Use in any progression with root movement a 4th down or 2nd up, the second chord in root position in either case. 9-8: Generally best in ii-V and V-I progressions. A two-voice 1:1 counterpoint is shown in Example IV-7 with possible locations for suspensions indicated by an "X". Below that is an embellished version of the 1:1 framework, containing suspensions, passing tones, and arpeggiations. Example IV-7. An Embellished Framework.
Conclusion This is the last of our four counterpoint units. When you return to the harmony text, try to apply the essentials of what you have learned here to your work in both analysis and composition. Even though the texture might involve 3, 4, or more lines, and even though the harmonic rhythm might be less steady than it has been in our exercises, the importance of the outer-voice contrapuntal framework, no matter how embellished, still applies. Exercises After reviewing this unit, especially the section titled, "Where to Use Suspensions," decide what one suspension would be best in each excerpt below. Then re-notate the excerpt with the suspension and at least one additional embellishment. Remember to put parentheses around non-chord tones (but not around arpeggiations). 1.
2.
Using the following progressions, compose 1:1 frameworks. Then add embellishments, including at least one good suspension. Turn in both versions. 3.
4.
Compose your own progressions following the outlines below. Then follow the instructions for #3-4. 5. A period in D Minor, 4/4. End the first phrase with an imperfect authentic cadence, the second with a perfect authentic cadence. 6. A period in A Major, 3/4. End the first phrase with a half cadence, the second with a perfect authentic cadence. |
