Teacher

It may seem odd to move from a discussion of line directly to one of harmony, while postponing discussion of the ways in which lines interact; however, harmony is best understood as the integration of simultaneous musical lines into a coherent ensemble. No matter how independent the lines in question, we always hear a whole — although with some perception of foreground and background — and not simply independent sounds. Put another way, music, no matter how dense, is understood by one brain at a time. This point merits further discussion. We do not contend that the musical ear is unable to distinguish independent lines, but that one cannot simultaneously pay equal attention to them at the same time. Nor can one hear them out of their harmonic context, at least as long as they are being played together. If the listener is to have the impression of related events occuring at the same time, the strands must coalesce into a coherent whole. This largely results from harmonic and rhythmic coordination. If the harmonic language is coherent, it will create expectations about the music’s direction. If the various lines regularly meet at metrical points of reference, it is hard to impute to them complete independence. Human hearing, it seems, does not require much encouragement to seek out such connections.

We will only look at aspects of harmonic design that specifically relate to contrapuntal textures. For a more general discussion of harmonic questions, the reader is referred to our work on harmony.

RICHNESS

Random vertical encounters do not constitute harmony, in any serious sense: a harmonic language implies coherence. And there are many artistic advantages to be gained from fine control of harmonic tension and direction.

If the counterpoint is not to sound haphazard or rough, the harmony needs to be as rich as possible. “Rich”, in a classical, triadic context, generally means full — containing the third of the chord, and often using sevenths — as well as participating in a lively progression, not limited to a few primary chords in root position. (This is an area where the standard species approach fails pitifully.) In non—classical contexts, richness would imply prominent and frequent presentation of whatever characteristic chordal sonorities are being implied, and variety in the control of tension/relaxation.

The weaknesses listed below — very common in student work — all attract the listener’s attention, due to momentary emptiness or harshness of harmonic effect. The result  distracts the listener from the flow of the music.

• Salient parallel 5ths and 8ves. The key word here is “salient”.
  

  The parallel octaves in the first example here are extremely prominent: Each of the first two bars begins and ends with the same note; the ear notices both the accented notes, and the progression from the last note of the bar to the first note of the next. The situation in the second example is only slightly better: now the last notes no longer return to the octaves.But the accented first beat octaves are still very salient.
  

  However, certain parallel 5ths and 8ves, although prohibited in conventional species counterpoint, are quite innocuous, even unnoticeable. In most species approaches, the octaves created between the C in the first bar of the above example and the D in the second measure would be prohibited as being rhythmically too close. However, they are not really very disturbing to the ear, because the notes in question are not accented, not on corresponding beats, and the motives in the two bars do not correspond. The ear is thus not encouraged in any way to associate these octaves.In effect, the “rule” in the species approach is poorly formulated. Pedagogically, it is more useful to discuss why certain cases are less disturbing than some others. Such discussions help the student refine his hearing and better predict how specific musical situations will be perceived; whereas blanket prohibitions do not encourage aural sensitivity.

• Direct 5ths and 8ves (where the parts move in similar motion into an octave or a fifth, especially if by leap in the upper part) between outer parts, unless softened by a suspension or other prominent harmonic richness elsewhere.
  

Compare the direct octave (into the 1st beat, 2nd bar) in the first example, which is rather prominent, since all the parts move in the same direction, with that in the second, where the suspension in the middle part creates a counterbalancing richness, and distracts the ear from the outer parts.

• Approaching dissonances in similar motion, especially in outer parts. This is especially flagrant when they leap.



In the first example, the similar motion between soprano and bass creates a strong accent on the tritone in bar 2. In the second example, this accent is somewhat weakened by the contrary motion of the bass.

Parallel dissonances; overuse of bare intervals

The parallel 7ths between alto and soprano, from the 1st to the 2nd beat, sound particularly harsh, especially since the 7th on the 2nd beat is major and it resolves onto a bare octave (and further, its resolution makes a bare fourth with the bass). Then, the last beat of the bar has no 3rd. The 7ths sound rough, and what follows sounds empty.

Conversely, richness can be enhanced by:

• paying particular care to semitone conflicts: They are almost always improved by addition of a third or sixth to one or both of the involved notes, in another part.
• doubling dissonances at the third or the sixth. As will be seen later, this is the main use for invertible counterpoint at the tenth: By rigorously avoiding parallel motion, such counterpoint guarantees that adding such doublings will not create parallel 8ves and 5ths.
  

  These two versions of the same example display how a dissonant note can be either be softened or be heightened. In the first, the arrival on the major seventh in bar 3 (second beat) is very harsh since the upper parts move in similar motion. Further, the resolution (by exchange) does not diminish the level of interval tension. In the proposed variant, the dissonant F# and its resolution are doubled at the 6th in the middle part, creating a much richer effect, more in tune with the style of the opening bars.

• aiming at the fullest chord possible at metrical stresses.
• frequent use of suspensions (softening squareness of harmony and rhythm).

One other point: Rather than limiting the student to simple consonant harmony throughout study of the species, it is better to gradually enlarge the harmonic vocabulary to include seventh chords, modulation and chromaticism. My own goal is to arrive at the same harmonic resources as in a course of chromatic harmony, by the end of four part contrapuntal study. This also helps bring together the two disciplines. In fact, the further one explores harmonic richness, the more it becomes a matter of refined voice leading, and the further one advances in counterpoint, the more sophisticated the harmonic resources required to solve problems.

HARMONIC DEFINITION

One frequent problem for students in dense contrapuntal textures is harmonic definition: Particularly with accented dissonances, the underlying harmony can easily be obscured.

The listener must “deduce” the underlying harmony from the information presented. This information includes:

• the relative number of chord and non-chord tones sounding simultaneously.
  

  The beginning of measure 2 in this example illustrates a common problem in student work. Here the top parts arrive at a consonance suggesting a D minor chord, and the bottom parts, in their turn, suggest a first inversion C major chord. The fact that the tied F in the alto progresses by leap suggests that it is a chord tone; the fact that the lower parts do not move to a clear consonance make it difficult to consider them as just passing tones. In short, the information presented is unclear, and leaves the listener trying to puzzle out the harmony from conflicting cues. The overall effect is distracting, creating an inappropriate accent.

• the relative rhythmic importance accorded chord and non-chord tones.
• the placement of leaps: Leaps are normally made to and from chord tones; when there are several in a row, they are heard as outlining chords. The only major exception to this rule is the appogiatura (approached by leap); however in this case the leap to the dissonance is used as a motive. Otherwise, apart from very occasional special cases, like word painting, the dissonant note will sound like a mistake.
• (to a lesser extent) the harmonic direction of previous chords.

What seems to happen here is that the listener “weighs the evidence”, and tries to parse the harmony in a meaningful way.

MODULATION

Although a full discussion of modulation is really the province of a book on harmony, contrapuntal texture does create some special problems in defining tonal direction within a modulation. Schoenberg’s counterpoint book is the only text, to my knowledge, which includes exercises specifically requiring the student to modulate within contrapuntal textures. Such exercises are challenging, and should be part of every program of contrapuntal study.

Most explanations of modulation focus on pivot chords; however the way newly altered tones are approached melodically is at least as important in making a modulation convincing to the ear. Alterations create novelty. There is always one line introducing each alteration. (Otherwise the altered note would be doubled, creating harshness as well as a weak resolution.) If the modulation is not to seem confused, this line must be in the foreground. This means avoiding distracting motivic or harmonic events elsewhere, and giving the new accidental at least some rhythmic weight.The composer must draw the listener’s ear to the active notes in the modulation. One excellent way to do this is to make the new alteration the resolution of a suspension.

Here the accidentals announcing D minor (C# and Bb) are both treated as suspension resolutions. The suspension attracts the listener’s ear, and the fact that the newly altered note acts as a resolution makes its arrival particularly smooth.

Of course, the degree of accent accorded these notes will depend on the modulation’s importance in the form: Is it merely local color or does it articulate the arrival of a major new section?