significance of the measure might be seen, heard and felt [here Mattheson inserts the following foot- note: “Tactus means nothing other than a feeling in which all meaning subsists”] is that with a great striking-clock, whose plumb-line carries a steady, even stroke and through which the minutes, sec- onds, and the canonical hours are kept exactly ac- cording to the time-measures. In this comparison it should be noted that the measures of the clock- work lie only in equal relationship to the funda- mental stroke, whereas the musical measure not only itself can be unequal but can also have quite diverse members and articulations. (Mattheson 1735/1980, pp. 92 – 93)
The rhythmic comprises not only the measur- ing of time, but also, and with equal importance, the “movement” this measuring achieves in melody:
Rhythmic is accordingly a measuring and or- derly disposition of time and movement in the melodic science, how slow or fast such is to be. . . . In other words it is, in the common parlance, the tempo and beat which derive from the sense of feeling (a tactu [from or according to the tactus or measure]).
For no melody has the power to arouse a true affection or a real feeling in us, if the rhythmic does not regulate all movement of the tone-feet to such an extent that they achieve a certain pleasing rela- tionship with and against one another. (Mattheson 1739/1981, p. 364)
Movement (Bewegung) concerns tempo, but our notion of tempo as “rate of speed” does not, I think, capture Mattheson’s meaning. Movement concerns the character or expression that emerges from proper tempo, indicated, as Mattheson sug- gests, by markings such as “affettuoso, con dis-
crezione, con spirito, and the like.” However, move-
ment is not reducible to a type. These markings are only crude indications for an expression that is itself the mark of individuality and particularity. Although mensuration and movement are presented as the two aspects of the rhythmic, Mattheson in a remarkable dialetical turn refers to these aspects as the two classifications of Zeitmaße or “time measure.” Thus, the rhythmic is not op- posed to time measure but functions as a concept that brings to light the dual nature of time mea- sures in an actual composition. Of these two
components of time measures—mensuration and movement — the first “concerns the usual mathe- matical classifications; though through the other one the hearing prescribes certain extraordinary rules, according to the requirements of the affec- tions, which do not always correspond with mathematical propriety but look more towards good taste” (Mattheson 1739/1981, p. 365):
The above-mentioned arithmetic or mathe- matical part of the rhythmic, namely mensuration, could be illustrated and learned quite well. . . .
However, the second and more spiritual thing, since the former is more physical, I mean Move-
ment, can hardly be contained in precepts and pro-
hibitions: because such depends principally upon the feeling and emotion of each composer, and sec- ondarily upon good execution, or the sensitive ex- pression of the singer and player.
Those who would want to remedy such a diffi- culty with many expletives miss the mark. Every- thing allegro, grave, lento, adagio, vivace, and however the list reads further, indeed indicates things which pertain to time-measures; however, they produce no change in the thing.
Here each one must probe and feel in his own soul, his heart: since according to the state of these our composing, singing, and playing to a certain degree will obtain an extraordinary movement which otherwise neither the actual mensuration, in and of itself, nor even the perceptible slowing or accelerating of it, much less the notes’ own value, can impart; but which stems from an imperceptible impetus. One indeed observes the effect, but does not know how it happens. (Mattheson 1739/1981, pp. 366 – 367)
To conclude his discussion of the rhythmic in
Zeitmaß, Mattheson refers to Jean Rousseau’s at-
tempt to define the relationship of mensuration and movement:
What is the difference between mensuration and movement? Answer: mensuration is a means; its
aim however is movement. Now just as one must distinguish between the means itself and the end whence the means leads: thus there is also a dif- ference between mensuration and movement. And as the voice or song must be led by mensu- ration, thus mensuration itself is led and animated by movement.
Hence, with one sort of mensuration the movement often turns out quite differently: for it Two Eighteenth-Century Views 23
is sometimes more lively, sometimes more languid, according to the various passions which one is to express.
Thus it is insufficient for the performance of a piece of music for one to know well how to strike and maintain the mensuration according to the prescribed signs; but the director must as it were guess the meaning of the composer: that is, he must feel the various impulses which the piece is supposed to express. . . .
Here many a person might perhaps want to know: how is the true Movement of a musical piece to be discerned? Yet such knowledge transcends all
words which could be used: it is the highest perfec-
tion of music, and can be attained only through considerable experience and great gifts.
Now whoever listens to a piece which is per- formed by different persons, today here, tomorrow there, if the last were to achieve the true Movement but the former were to miss it, can easily say which of the two would be correct. (Mattheson 1739/ 1981, p. 368) [ Jean Rousseau, Methode claire, certaine
et facile pour apprendre a chanter la Musique, Paris,
1678, p. 86]
To close the topic, Mattheson writes: “This much is Rousseau, and so much for now on the ex- trinsic and intrinsic character of time-measures: particularly since the last can not be captured by the pen.”
I have quoted Mattheson and Rousseau at some length because we find in this writing a frank acknowledgment of an aspect of measured rhythm that resists analysis and quantification — something spontaneously produced and judged attractive or expressive in performance. What is remarkable in this account is the attempt to unite these aspects of the rhythmic within the concept of Zeitmaß. Thus, Mattheson speaks of the “intrinsic” and “extrinsic” character not of
Rhythmik, but of time measure (Zeitmaß ). This
ingenious union is, however, quite problematic. Apart from the difficulty of reconciling a fully describable means with an ineffable end, there is the difficulty of reconciling movement, anima- tion, and the particularity of musical expression with the clocklike regularity of Zeitmaß, which as the measure of time and the receptacle of mu- sical content proceeds with full autonomy and homogeneity. Wilhelm Seidel eloquently de- scribes the spacelike character of Mattheson’s concept of Zeitmaß:
Mattheson’s measure does not define the par- ticular character of musical motion which it com- prehends; it does not determine the accentual order and does not designate the mechanical mo- tions of conducting.What is it then? It is a measure
of time. To take up Walter’s metaphor, it is like a
yardstick, which is laid out against time. A deter- minate measure articulates the continuous progress of time into constant, equal time-spans. It gives to time the appearance of spatiality. Thus, it is of no importance whether this division is carried out physically or in the imagination, “only in the mind” as Walter says. The measure measures off the open space in which a composition comes to be realized. Any number of spaces may be cut out of the flow of time; however, their measure — the measure — is always the same. Only on paper does measure follow measure — in sounding, the com- position stands under the law of one measure. The law-giving compulsion of the measure is expressed in the metaphors used to describe its effect. Mat- theson speaks of the authority of measure, music as governed by measure. Janowka compares the mea- sure to the town clock “according to which every- thing is customarily regulated and directed.” Just as the tower clock establishes a manifest system for the ordering of activity (one thinks perhaps of the schedule of religious and secular events for a town in preindustrial times, of the church services, the closing of the town gates, of the night watch cry- ing the hours), similarly, the measure determines what can happen in the music during the time it is in force. And just as little as the time ordering of a clock itself describes what actually happens during its durations does the measure describe what is ac- complished musically during its time ordering. (Seidel 1975, pp. 55 – 56)
That the temporal can be assimilated to the spatial in this way I attribute to the “givenness” of Mattheson’s Takt as cyclic return (as Zeitmaß ). Certainly, measure succeeds measure, and within each measure there is the “passage of time”; but this succession and this passage are easily removed from becoming, and in the return of “the” mea- sure (Zeitmaß ) as ever-present it is possible to conceive of static being and to conceive of pas- sage, transition, and becoming as illusory. Seidel, in fact, argues for such a conception and, more- over, for such an experience of measured music:
Music thus turns away from the observation of the continual passing away of time. Music, while it
is going on, leads to a forgetting of time and, for anyone who is affected by it, seizes a consciousness of the transitory. I would like to venture the hy- pothesis that the musical event can accomplish this because it does not display itself in an open time. It does not play itself out in boundlessness, does not advance into uncertainty and obscurity, but rather divides a time span that is marked off a priori. One has the security and the satisfaction of knowing beforehand, not everything, but at least the dimen- sions of becoming. As Mattheson says, “everyone enjoys knowing in advance and judging.”
Temporal then is only the space in which the musical event completes itself, and not this space itself. For the empirical motion of music brings to consciousness only indirectly and brokenly the temporality of the space which Takt measures off. That is to say, time is not music’s object; music nei- ther grasps, alters, nor interprets time. It has time only as a space for observation. The fact that the measure, a measurement given once and for all, is in principle unalterable clearly reveals the statics of the system. One could say, rather subtly: this music has no temporal structure. It makes timelessness actual. It gives the human beings who play and hear it the illusion of an escape from time and transitoriness. Therein perhaps arises that happi- ness which music brings: it is a foretaste of eternal joy. (Seidel 1975, pp. 56 – 57)
This is a fond thought and one that doubtless inspired Mattheson in his formulation of the concept of measure as Zeitmaß. It is also a thought that places meter in opposition to the temporality of a more worldly experience of musical rhythm. If Takt is an image of eternity, how can it also be a vehicle or means for Bewe-
gung, and how can Bewegung be the “intrinsic”
and “more spiritual” part of a Zeitmaß for which mensuration is “extrinsic”?
Since Mattheson’s understanding of meter is so different from our own, we may gain some perspective on what is novel in later theories by briefly reviewing his notion of Takt. Mattheson’s conception of meter is based on traditional mensural theory, in which Takt is understood as tactus — a single “beat” conducted with two strokes of the hand, whether equal (what we call “duple” ) or unequal (what we call “triple” ). In this understanding, division takes place within the measure, but division does not constitute the measure. The measure as Zeitmaß is given for di-
vision, and its givenness precedes its division. The distinction of arsis and thesis as ebb and flow is also part of the givenness of the measure, but this distinction does not itself arise from a process of division. And as our first quotation from the Kleine General-Baß-Schule indicates, Mattheson strenuously argues against the reduc- tion of measure to an actual or imagined “beat- ing” of equal parts. In Der vollkommene Capell-
meister Mattheson writes:
Now since it was soon found that upbeat and downbeat could not always be related as equal, there arose from this observation the classifica- tions of equal and unequal measure; and these two are the only true principles of the rhythmic or time-measure. From ignorance of these basic doc- trines, as natural as they are easy and simple, more errors arise than one might suppose. Again, namely a disregard of the first principle by those who would look for four parts in an equal mea- sure and three parts in an unequal measure, whereby they give rise to nothing but confusion. (Mattheson 1739/1981, pp. 365 – 366)
The divisions that concern Mattheson are not the accented and unaccented Taktteile of later theorists, but the patterns (Rhythmi or
Klang-Füße) that can be contained in a Takt.
These patterns are types and so are repeatable. And although he lists twenty-six types corre- sponding to the categories of traditional poetic feet, Mattheson acknowledges that music can employ a virtually unlimited number of types. In the examples he gives, the integrity of the mea- sure as receptacle is retained by permitting
Klang-Füße to occur only within a bar and not
across bars. There is one exception — the first epitritus (short – long – long – long), which is il- lustrated as beginning with an eighth-note ana- crusis. The inconsistency here seems to arise from the difficulty of realizing this pattern within a single bar without creating a composite of iamb and spondee.
In his discussion of rhythmopoeia, Mattheson does not attempt to relate patterns to the organi- zation of beats in the measure except to distin- guish among the Klang-Füße those appropriate for equal or unequal measures. The closest Mattheson comes to relating pattern to pulse is
in his discussion of the dactyl. Two forms of the dactyl (long – short – short) are illustrated in our example 2.1.
In the second form “the length and shortness of sounds vary as much in their proportion as 3, 2, 1: whereby the last or third in the measure, though it seems to be twice as long according to its external aspect as the middle one, is neverthe- less just as short in its intrinsic value because of the upbeat of the measure” (Mattheson 1739/ 1981, p. 355). Thus, within Klang-Füße neither shorts nor longs are required to present equal durations or equal divisions. For example, the second paeon (short – long – short – short) is rep- resented by a bar containing the succession quarter-half-eighth-eighth. Nor is the distinction “long versus short” related to accent. A short may appear on what we call the accented part of the measure, or a long may appear on an unaccented part. In all the examples, only the actual sound- ing durations of tones are considered — a long or a short is never composed of more than one note.
Mattheson’s understanding of meter was soon to be replaced by a conception of the measure in which the givenness of Zeitmaß is transferred to that of pulses which compose the measure. This idea of meter, which has with relatively little al- teration been carried into present-day metrical theory, is based on the notion of a constant train of isochronous pulses grouped by accent to form measures. The most thorough eighteenth-cen- tury exposition of this theory is found in Hein- rich Christoph Koch’s Versuch einer Anleitung zur
Composition, and it is Koch to whom I will turn
for an account of measure as the grouping of like durations. The new theory arose perhaps in part in response to the proliferation of meter signatures, whose variety is largely suppressed in Mattheson’s conservative reduction to Zeit-
maß. But its lineaments clearly reflect an assimi-
lation of classical aesthetics in the dialectic of multiplicity and unity and the more narrowly “empirical-psychological” interpretation of their play in aesthetic experience.
With the new view of meter as a unity of isochronous pulse units related to one another through the operations of multiplication and di- vision, it became possible to conceive of a prop- erly mathematical order of duration. As Ernst Cassirer writes:
The aesthetic “unity in diversity” of classical the- ory is modeled after this mathematical unity in multiplicity [i.e., to understand and deduce multi- plicity from a general law]. . . . In the realm of art the spirit of classicism is not interested in the negation of multiplicity, but in shaping it, in con- trolling and restricting it. (Cassirer 1951, p. 289)
It was Johann-Georg Sulzer who first articulated the aesthetic foundation of a pulse theory of meter that was taking shape, even as Mattheson was endeavoring to hold on to the older mensu- ral perspective. Wilhelm Seidel’s book includes an extensive and penetrating account of Sulzer’s innovation, and I return to Seidel for a glance toward Sulzer’s discussion of unity and multi- plicity and the relation of these categories to meter:
[Sulzer] writes that rhythm is at bottom nothing other “than a periodic arrangement of a series of homogeneous things whereby the uniformity of these same things is united with diversity; so that a continuous sensation, which would otherwise have been completely homogeneous (same-sounding), obtains, through rhythmic divisions, change and variety” [Sulzer 1792, vol. II, p. 96]. This is Sulzer’s version of the Greek formula — rhythm is the order of movement [i.e., the Platonic order of
Metron, as we have seen in chapter 1]. . . .
Uniformity designates “the identity of form across all the parts which belong to a single ob-
26 Rhythm and Meter Opposed
EXAMPLE2.1 Johann Mattheson, Der vollkommene Capellmeister, part 2, chapter 6, figure 5. Illustration of dactyl (long-short-short).
ject”, and is to this extent a formal category. “It is”, writes Sulzer, “the basis of unity; for many things, laid next to one another or following upon one another, whose disposition or order is deter- mined according to a single form or a single rule, can, with the support of this form, be held to- gether in a single concept, and to this extent con- stitute One thing” [Sulzer 1792, p. 21]. (Seidel 1975, pp. 92 – 93)
Koch, on the other hand, is not especially concerned with the unity of Takte and Taktteile as a “formal category,” but rather with the process through which the many become one. Rather than of Zeitmaß, Koch speaks of Zeitraum— a de- terminate duration that is inherently undifferen- tiated, lacking any distinction of arsis and thesis. A Zeitraum (represented by Koch as a whole note with no signature) becomes a measure only if it is given content and organized as a grouping of constituent pulses. But, in fact, Koch makes