Music

Parallel Octaves

Parallel octaves are forbidden in traditional counterpoint because – so the textbook explanation goes – they destroy the independence of voices. They create the impression that two simultaneous melodic lines – entities which should be perceived as separate at all times – have become indistinguishable, temporarily fusing into one. Of course, parallel octaves occur when instruments or voices explicitly double each other, but in that context the listener is not meant to hear separate melodies: the composer has assigned the same line to multiple players to achieve a certain sonority, not to suggest polyphony. The problem occurs when contrapuntal independence is the composer’s goal, which is to say that the parts are not supposed to be heard as doubling each other, and yet they seem to be doing just that, crossing the chasm from polyphony to monophony and leaving the number of voices – even if for just a moment – indeterminate.

The detection of parallel octaves could be called an industry within the larger field of music theory instruction. It is a rite of passage for every beginning student of harmony and counterpoint to submit an exercise and receive it back with the parallels circled in red (and points deducted accordingly), to perhaps question the sensibility or fairness of this demerit, but to eventually realize that if he or she wants to pass the class it will be necessary to get good – very good – at identifying and avoiding parallel perfect consonances. The teacher may say “First you need to learn the rules before you can break them” but the question of when and how the rules should be broken is prone to deferment. Stepping outside of an academic context, there are two broad scenarios where a composer need not think too deeply about parallel octaves but can simply adopt an appropriate blanket policy. First, the composer can say, “I aim to look back and write counterpoint that is idiomatic to some stretch of the Renaissance or the common practice period, and since the composers of those times avoided parallel octaves, I must do so too.” Second, the composer can say “I am a 21st century person, writing in a fully contemporary style, and there’s no need for me to adopt the rules of the past, particularly given that composers before me have already broken those rules to such great effect.” In each case, any detailed inquiry into whether the parallel octave restriction serves a valuable musical purpose can be cut short, and the composer may simply embrace the attitude of whatever style he or she wishes to work in.

There is cause for deeper questioning in a third scenario, when the composer aims to look forward and back at the same time, writing in a style that combines elements of the past with new ideas. Specifically which elements of the past should be preserved, and is the parallel octave restriction among them?  There’s room for questioning too if the composer says, “I want to write the best counterpoint I can, no matter what style it happens to fall in, and I’ll adopt any rule, or break any rule, to make the counterpoint as good as possible.” Of course this raises the question of what goodness means as applied to counterpoint. Certainly it is a valid goal to write counterpoint that is deliberately thick and tangled, immersing the listener in a jungle of melodic ideas where independence is less important a value than denseness or maximality of texture; however, for the purpose of this essay I want to consider only two-voice counterpoint where clarity and perceptual independence of the lines is treated as the fundamental aesthetic goal. Our metric is the ease or difficulty a listener has in understanding the two lines as separate entities, in keeping track of them as they proceed, in following their courses and comprehending those courses as distinct. (This is a subjective metric as it depends on the nature of the listener, and yet there’s enough in common between listeners that generalizations are not altogether futile; in referring “the listener” I am in fact referring to myself, and yet I believe that what’s true of me has some likelihood of applying to you as well, so for simplicity I will gloss over the distinction.)

The question is: do parallel octaves always degrade the perceptual independence of melodies in two-voice counterpoint, or is it possible to use parallel octaves in a way that preserves or even enhances this independence? Can parallel octaves be used in a way that does not confuse a listener who is trying to follow two separate lines, perhaps in a way that even pleases or excites the listener? Is such a “virtuous” use of parallel octaves possible only in a contemporary style, or can it be achieved in a traditional style where the rules and conventions of historical counterpoint are left in place except for this one major departure?

I believe that while it’s tempting to speculate and theorize about such questions, the best way to address them is through experiment, that is to say, to try writing counterpoint with parallel octaves, to give parallel octaves the benefit of the doubt and search for the most pleasing ways of employing them, and then to listen to the outcome and reflect on it. With the composer doing everything in his or her ability to make parallel octaves work, how does it actually sound? Perhaps one reason parallel octaves have such a bad reputation is because they are often discovered as oversights in a contrapuntal effort (“Oh, I didn’t notice them before; now I wonder, can I get away with them?”) rather than as features the composer deliberately included.

Much has been written on parallel octaves and many composers have assessed them before me, but my aim here is not to survey the vast literature but just to share my own experience: no matter how much has already been said and done, I think every composer should perform the basic experiments anew in his or her own “laboratory.” I have experimented with parallel octaves in just a few of my first sixty canons, but I wrote Canon 62 and Canon 63 with the goal of studying them. I will describe a few of my observations from the composition process and then share the pieces themselves so you can draw your own conclusions.

First I should say I think parallel octaves must be examined separately from parallel fifths. While octaves have a transparent quality, parallel fifths have such a distinctive signature that, even if they can be used without sacrificing contrapuntal independence, they may simply be the wrong “flavor” to introduce into a certain musical dish, so to speak. In my own experience, I have found that parallel fifths are easiest to incorporate into a texture that emphasis octaves, fifths, and fourths (the so-called perfect intervals), whereas parallel octaves are more flexible and can be blended into a thirds-based texture without triggering a sense of “that doesn’t belong here.” In this essay, I’m only considering octaves.

A first observation is that, like any element in art, parallel octaves can seem intentional, or they can seem accidental, depending on how they are employed. While there is no formula for making any artistic element convey intent, here is one specific way I’ve tried make parallel octaves recognizable as deliberate in my work: employ parallel octaves in short runs, followed by octave-free passages, in a discernible alternating pattern. In sections where parallel octaves occur, make them the only thing that occurs in that confined space.

A second observation is that brief periods of octave-doubling in two-voice counterpoint do not immediately trigger a shift from a polyphonic to a monophonic mode of listening. If the two voices first firmly establish their independence in the listener’s ear, and then align in a brief episode of octave-doubling, the listener can still rely on register, on the distinction between high and low, to track the lines separately until the doubling ends and the independent motion resumes. This doubling shouldn’t go on too long, or the sense of polyphony will eventually erode, but it is not as though the mere occurrence of parallel octaves is some kind of polyphony-killer that will immediately annihilate the perceived distinction between lines and cause the great edifice of Counterpoint with a big C to come crumbling down. Even if the lines have not yet established themselves as independent entities, such as in a case where one line enters alone and then the second line begins to double it, the contrast between the single and doubled texture may still put the listener on alert that two entities are now in the mix: if the second line then stops doubling and goes its own way, the listener may accept the texture as polyphonic and not expect a return to monophony, no matter that the introduction may have signaled monophony.

While parallel octaves can make it difficult to discern the relationship between lines, this confusion can be offset if the lines contain short, recognizable motifs that the listener can easily remember. If one recognizable motif overlaps another recognizable motif in a way that creates sections of parallel octaves, the listener can still perceive the lines as distinct because their structures are already known. The listener can be cued to understand that two separate things have come into temporary alignment rather than permanently fusing or giving up their individuality. Where the motifs are unfamiliar or harder to recognize, parallel octaves may create more confusion.

Contrary to undermining the objective of polyphony, parallel octaves can actually be used to energize or reinvigorate a polyphonic texture. They do this by providing contrast. Where the lines are consistently independent, the listener takes this independence as a given, but if that independence is sacrificed briefly, the eventual return to independent motion can seem all the more exciting and notable, particularly as the ear has had a momentary respite from the sometimes-taxing challenge of tracking divergent lines. Withholding a feature temporarily is one way a composer can make the listener pay more attention to the feature when it occurs, thereby increasing a sense of that feature’s abundance (the feature here being polyphony itself).

If independence of voices is really the highest objective in a contrapuntal composition, the composer should know that many factors are bigger threats to independence than parallel octaves may be. For example, I find it really hard to keep two lines separate in my ear when the lines are simply boring. That is because part of what it means to “hear two lines as distinct” is to remember the lines – to remember something different about each one – and boring lines can be hard to remember because, by definition, they don’t carry our attention or display any remarkable features; one may perceive their independence note-by-note, but after listening across a longer span of time, the entire episode of these boring-but-independent lines becomes a blur in the listener’s mind, and it didn’t matter that they were entirely free of parallel octaves. Similarly, lines that are overly complex can be hard to remember, and while the listener might maintain a sense that there are two different things going on, he or she might not actually follow them, in which case the experience of polyphony is compromised, even if the fact of it isn’t. If the composer says “I avoid parallel octaves in service to the objective of contrapuntal independence” then it behooves the composer to place higher weight on the objective than on rule-following itself, and if contrapuntal lines can be made more interesting and therefore more easily heard as independent by suspending a rule, this is the time to do it. Some composers believe that parallel octaves can always be “corrected” without sacrificing melodic interest, but while mandated revision is certainly a good way of discovering new ideas, I don’t think it always leads to something better.

I feel, after many years of exploring counterpoint, that the early, basic lesson about noticing and avoiding parallel octaves is worthwhile since it builds a composer’s awareness of interval relationships and contours, it builds a habit of careful scrutiny of the score, it builds respect for the objective of contrapuntal independence, and in many cases it does represent the best musical choice. But I have also come to feel that parallel octaves are not always antithetical to the objective of contrapuntal independence, and that in fact they can sometimes support it, not only in contemporary styles but even when writing counterpoint that is otherwise traditional.  I am excited to continue experimenting with them.

In Canon #62 – “Spinel,” you will hear full, overt runs of parallel octaves lasting four beats, constantly alternating with four-beat sections where independence is regained. When the parallel octaves occur, you might think the canonic imitation has stopped and the voices have suddenly come together without a lag, but that’s not what’s happening. In fact, this is a true canon, where one voice is always imitating the other with a four-beat lag forever maintained; the parallel octaves arise because the line has a self-similarity which allows it to perfectly coincide with its delayed version in certain places. The top voice is the leader, with the bass imitating it a third below. There are three sections: the outer two are essentially the same, with the bass in the closing section transposed an octave lower. The middle section is interesting because the bass there is transposed an octave higher, causing what were parallel octaves to become unisons, creating an even stronger sense of fusion. In each section, the music gets higher and higher, passing through many different modal centers, and through a series of rhythmic and melodic variations, as the same basic pattern is energetically and ceaselessly repeated.

Canon #63 – “Celestine” – is a second exploration of parallel octaves used deliberately in counterpoint that is otherwise traditional. This piece has a one-bar run of parallel octaves occurring every six bars. If you listen in a certain way, it sounds like certain entrances of the theme in once voice spring out of the other voice; when one voice enters, it often starts off “fused” with the other voice (i.e. moving in parallel octaves with it) and then breaks apart and does its own thing. The piece is built of a repeating motive that is never varied, though it is restated at descending scale positions, causing a gentle progression downward through the modes of C major. Unusual for my canons, it stays entirely within the notes of C major with almost no chromatic alterations, yet even with so many restatements of the same motive it stays fresh to my ear. Variety is pursued through registration: fragments are transposed up and down so we hear entrances happening in all places. Technically the top voice is the leader in this piece, with the lower voice following a fourth down, but the leader/follower relationship quickly becomes ambiguous because of the transpositions (including voice crossings), and because there are no melodic or rhythmic variations that would allow the listener to identify which line is the “source” of new material.

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