Notes on Prosody: numerical classification of rhythms

November 27th, 2013 § 0 comments § permalink

I will be posting more of these “notes” from time to time. They are mostly drawn from old drafts of writings on prosody, but some will be new. This second posting is a continuation of the first. I hope readers will not be too put off by this overgrown thicket of definitions. The aim was to find a more useful and consistent terminology for describing rhythms in the abstract. A lot is borrowed, naturally, from music, but oriented towards a more general application that would encompass verse as well. 

First of all, we will need terms to refer to a rhythm’s basic “count.” Standard terms like binary or duple for rhythms of two, ternary or triple for rhythms of three, quaternary or quadruple for rhythms of four, etc., will be used here, along with the simpler expressions rhythms in or of two, three, four, etc. To these we may add unary to denote rhythms in, or of, one.

Every rhythm, in a sense, has a unary component to it, since this merely denotes the fact of repetition as such. So the term is perhaps of limited usefulness; nevertheless, we will occasionally have need of it to refer to rhythms that achieve their effect by conspicuous repetition of a single element throughout, e.g. a chant based entirely on a refrain.

The number that defines a rhythm’s basic count is called its numerator, on the analogy of a time signature in music, where the number of beats in a measure is given as the upper of a pair of numbers, the lower one (denominator) giving the unit of measurement. We can dispense with the latter: it is a result of the convention of infinite divisibility of time in Western musical practice. In poetry, a lower limit of divisibility is already set, for metrical purposes, by the syllable, and any larger divisions (foot, line, stanza) are more clearly referred to by name.

Rhythms metrically organized on more than one level are said to be nested. The number of levels at which a rhythm is metrically organized is its degree or level of nesting. This is counted inclusively, e.g. a rhythm of four overlying a rhythm of two is nested to two levels.

Nesting may be either multiplicative or additive. In multiplicative procedures, a numerator is multiplied, either by itself or by another, to yield larger metric units.

The ability of a numerator to compose larger units in multiples of itself, as, for instance, quatrains out of couplets or eight-bar phrases out of measures in duple time, gives the degree of multiplicativity of rhythms based on that numerator. .

Unary rhythm is the most multiplicative of all, but in a fairly trivial way, for the same reason that it is trivial mathematics to say that all whole numbers are divisible by one. The most significantly multiplicative rhythms are binary ones, because of the special place two has among whole numbers, as the one that makes all the others even or odd. It has a special relation to the idea of symmetry, being indeed at some level identical with it. But perhaps at least as important, as applied to rhythm, is the fact that multiples of two can yield a maximum of nested levels of rhythm within the narrow range of tempos at which rhythm as such is perceptible to the human organism. Multiples of three, or any higher number, more quickly reach the threshold at which repetitions, being too far apart, fail to be perceived as rhythms.

Three, however, is the next most important number rhythmically, and in combination with two and multiples of two, it is perhaps even more important than it is on its own. The special qualities ascribed to three, aesthetic and spiritual as well as mathematical, need not be pointed out to anyone who has grown up in the Western tradition. It is not symmetrical in the same sense as two, but another kind of symmetry, represented by the image of a triangle, can be felt in it.

If a numerator is not multiplied, or multiplied only by itself, to yield larger levels of rhythm, then the rhythm as a whole is said to be simple. Two, and, to a much lesser degree, three, are really the only numbers usable as numerators for nested simple rhythms. It is quite possible, though, to have simple rhythms that use a higher numerator, and are not nested.

Rhythms that multiply different numerators we will refer to as compound. Examples of compound rhythms in poetry are the French trimètre, which divides the twelve syllables of the alexandrine into three groups of four, and the tétramètre, which divides them into four groups of three.

The terms simple and compound are used somewhat differently in musical metrics. There the first refers to rhythms that are not multiplied at all, and the second to rhythms that are multiplied by three, whatever their numerator. Both terms apply only within the musical bar, ignoring any larger units, as well as any that are smaller than the bar’s “denominator.” In practice, the majority of compound musical rhythms are binary rhythms multiplied by three; my use of the term can be seen as a generalization from that category.

Rhythms may also be nested by being mixed. Mixing is an additive procedure. Different numerators are applied not simultaneously, but in succession. Now, if numerators are mixed randomly, in no particular sequence, they cease by that token to be significant numerators; therefore rhythms that are mixed in a strictly metrical way have different numerators that occur in a regular, predictable sequence. Examples from poetry would include “regular” classical hexameters, consisting of five dactyls plus a spondee, and many stanzaic forms, such as the ottava rima, whose abababcc rhyme scheme gives a line grouping that could be expressed in terms of numerators as (3 X 2) + 2. We will count any mixed sequence as being nested to at least two levels, one for the sequence as a whole, another for its components. These, in turn, may individually contain further levels, as in the compound part (3 X 2) of the last example.

Four has a special importance as a numerator because of its “dual” nature, in several senses. Though it is always more or less felt as the multiplication of a duple rhythm, it can often be perceived as a simple numerator in its own right. As the first power of two, it is unique in this regard. Six is the only other even number that can even be perceived, generally speaking, as a simple numerator, and clearly much less so than four, especially in English-language poetry. Eight will almost always be perceived as two groups of four, or some other nested sequence, whether multiplicative (4 X 2) or additive ( 3 + 2 + 3).

Of course these generalizations are relative, not absolute, and how well they hold will depend on many factors. We can’t deny, for instance, that in languages that base their versification on syllable count rather than feet or accents, higher numerators may often be perceived as such. Since the basic unit is smaller, multiplications of it will stay within a more perceptible range, and even twelve- or fourteen-syllable sequences may sometimes be perceived without being broken down into multiplicative or additive components. Mostly, of course, verse written in such languages does so break them down, and often in a consistent pattern from line to line.

Five and seven are the last numbers we need mention here. Being odd, they obviously can only be broken down additively, and this gives them an asymmetry that none of the lower numbers has. Of course three can be broken down this way as well, but it is most often perceived as simple and, in a certain sense, symmetric. Five is important in English, naturally, because of the prevalence of the pentameter. Seven occurs mostly as a regular additive sequence of 4 + 3.

Instead of or in addition to being nested, rhythms may overlap. In this case there is no overall numerical coordination between them, though there may be moments at which they coincide. An example would be a poem with one rhythm given by its metrical lines, and another by its syntax and phrasing. These two rhythms, unless they happen to coincide perfectly, would overlap.

The properties of numbers can tell us a good deal about the properties of the rhythms they describe. But there is a sense in which, the more completely we can define a rhythm numerically, the less complex it really is. Complexities may in fact be too subtle for analysis, though a person speaking or reading a poem, hearing music, or watching a dance, can readily feel them. From this point of view, we could say that the possibilities of even the simplest unary rhythm are far from having been exhausted.

Griboyedov: a second look

November 26th, 2013 § 0 comments § permalink

In the course of preparing a second edition of my 1992 translation of Griboyedov’s The Woes of Wit, I recently went on Youtube to see what new material might be available there. I wasn’t disappointed. There’s a lot new since last time I looked, most notably the complete 1977 Soviet film version of the Maly Theater’s production of the play. Watching it repeatedly and seeing how different parts are played has been quite a revelation. It’s easily the best of the three versions I’ve now seen (none of them live, though Oleg Menshikov’s video version was basically a recording of his stage production).

The actors playing Chatsky (Vitaly Solomin) and Sofya (Nelly Kornienko) in the Maly’s production were both superb. The latter role is probably the harder to do convincingly. Sofya, Chatsky’s childhood friend, fancies herself in love with Molchalin, her father’s obsequious live-in secretary. The witty, irreverent, and outspoken Chatsky, who loves her himself, is at first unbelieving, and finally, dismayed. It is this that drives the action of the play.

But Sofya is no shallow dupe. D.S. Mirsky in his History of Russian Literature says of her:

She is a rare phenomenon in classical comedy: a heroine that is neither idealized nor caricatured. There is a strange, drily romantic flavor in her, with her fixity of purpose, her ready wit, and her deep, but reticent, passionateness.

There’s the rub: Sofya is mistaken about Molchalin, but her mistake is an honorable one. One must feel, when she defends him in the face of Chatsky’s ridicule, that, but for that mistake, she is entirely justified in doing so. Beyond that, one must be able to see things from her point of view. Chatsky is admirable, intelligent, passionate, but seeing how uncomfortable he makes people, and what eventually happens to him, who can blame her for not wanting to tie her fate to someone like that? That is the way Kornienko, with complete conviction, plays her.

It is wonderful that Mosfilm has chosen to make so many great movies available online. Given that, I can’t complain too much about them blocking the excerpts from two of their unsubtitled films that I put up on Youtube with my own subtitles added. I know they’re just following a general policy. I have, however, received some disappointed queries from people who have tried to view them since then. In the three years that the 5-part Mozart and Salieri sequence from Shveitser’s malenkie tragedii was viewable, the first part had 6,555 viewers.

[UPDATE, 2016: These videos have again been viewable for some time now: Mosfilm has allowed them to appear with ads that you can click out of after 3 seconds.]

Notes on Prosody: rhythm and number

November 25th, 2013 § 0 comments § permalink

The following is drawn from some notes on prosody I began writing some years ago. Prosody, and rhythm generally, has been a central preoccupation of mine, as might be guessed from my domain name, the former name of this website, and many of the articles and posts in it. In this draft I was attempting to clarify some very broad terms that might be applied to a general study of rhythm. To speak of rhythm from the standpoint of psychology or physiology, or musicology or poetics, generally assumes that we already understand what rhythm is. I make no such assumption, and the approach here might be thought of as belonging more to philosophy than to anything more specialized.

Rhythm and number

Meter is the countable aspect of rhythm. If a rhythm has nothing in it that we can meaningfully count, then we generally consider it unmetered.

In order to count, we must regard different things or events as the same. All rhythm involves recurring events. We can thus see how any rhythm involves a sort of incipient counting.

Sameness is of course a matter of degree, and there is often some doubt about which events in a rhythm “count” and which do not. Indeed, a rhythm that is absolutely countable will be monotonous. However, a rhythm that is monotonous on one level may be quite unpredictable on another.

It is hard to say where real counting begins. If there is only one level of repetition, for instance in a steady drumbeat with no accents, then there is obviously no need to count at all. Still, the drummer’s effort to make all the time intervals between beats, as well as the beats themselves, the same, suggests that a subliminal sort of measurement is occuring.

If we add an accent to every other beat, then we clearly have a rhythm counted “in two.” This is usually considered, in music, to be the simplest meter. However, for consistency, it would perhaps be better to consider the first example, the steady beats without accents, to be the simplest. Its “measure” would be an isochronous beat, counted “in one.” To vary the monotony, we could add occasional accents, in no consistently countable pattern. Such a rudimentary “meter” can have a suprisingly lively effect.

The higher the number, the greater the need for deliberate counting. If we enter a room with three people in it, we hardly need to count to know how many are there. If on the other hand there are nine people there, we will have to count to know it.

Other factors may affect the need to count. If we see a row of three windows, at each of which three people are standing, we can appreciate that whole fact in an instant, even if we don’t know that three times three is nine. If the windows, moving left to right, have four, two and three people in them respectively, that situation will probably take a bit longer to register, and be a lot harder to remember.

When we are dealing with events that appear in succession, as we are with rhythm, there is also the factor of speed or “tempo.” In the “midrange” of tempo, where we find – probably not coincidentally – important bodily rhythms like the heartbeat and breathing, the perception of number is most immediate. At much slower tempos we will need to count just to keep track of where we are, and at much faster ones, we will need to slow things down to count at all, as separate events start to merge into a continuum, e.g. a musical tone or a moving picture. It is, roughly speaking, only in this midrange that we directly perceive rhythm at all. Of course what we barely sense, or see only on reflection, can sometimes be as important as what we perceive directly.

It is usual in poetics to distinguish more or less sharply between meter and rhythm. A favorite analogy is of a container (meter) and what it contains (rhythm). It might be better, though, to think of meter as a sort of skeleton of rhythm. A container, after all, is separate from what it contains; a skeleton is part of the whole animal.

If a rhythm can be known without counting, then there is no need to count it. We rarely need to count an animal’s vertebrae or its digits to know what species it belongs to. We may still find it helpful to do so, however, whether to understand its relationship to other species or to explain some aspect of its behavior.

In Western music, with its highly articulated rhythm, it is customary to regard all rhythms as more or less countable. This is partly due to the necessity of keeping different performers in time with each other. The convention is therefore not as strictly observed in solo performances, and in certain kinds of cantillation, for instance, it may be dispensed with altogether.

Western poetry, to the extent that it has divorced itself from music or any kind of coordinated performance, makes no assumption that its rhythms are always countable. If they are, roughly speaking, the poetry is said to be in meter, if not, it is said to be unmetered or “free” verse.

In principle, though, there seems to be no reason why we could not, if we wanted to, consider all poetic rhythms to be more or less countable, if only for purposes of analysis. We might then find it convenient to make use of some conventions borrowed from musical practice.

Where am I?

You are currently viewing the archives for November, 2013 at Spoken and Sung.