Harvard Psychological Studies Part 41

q q q; q q % 1.000 1.025 q q %; q q q 1.000 1.267 > . . > q q q; q q % 1.000 0.984 q q %; q q q 1.000 1.112 > . . > q q q; q q % 1.000 0.766 q q %; q q q 1.000 1.119

As the disparity in numerical const.i.tution increases, so will also the divergence in time-value of the two groups concerned. When differentiation into major and minor phases is present, the duration of the former will be greater than that of the latter. Hence, in consequence of the combination of these two factors--_e.g._, in a syncopated measure of unusual emphasis--the characteristic time-values may be inverted, and the briefer duration attach to that unit which comprises the greater number of elements. Intensive values cannot take the place of temporal values in rhythm; the time form is fundamental.

Through all variations its equivalences must be adhered to. Stress makes rhythm only when its recurrence is at regular intervals. The number of subordinate factors which combine with the accented element to make the group is quite indifferent. But whether few or many, or whether that element on which stress falls stands alone (as it may), the total time values of the successive groups must be sensibly equivalent. When a secondary element is absent its place must be supplied by a rest of equivalent time-value. If these proper temporal conditions be not observed no device of intensive accentuation will avail to produce the impression of metrical equivalence among the successive groups.

B. _The Distribution of Elements Within the Group._

(_a_) The Distribution of Intensities.

In the a.n.a.lysis of the internal const.i.tution of the rhythmic unit, as in other parts of this work, the investigation follows two distinct lines, involving the relations of rhythm as apprehended, on the one hand, and the relations of rhythm as expressed, on the other; the results in the two cases will be presented separately. A word as to the method of presentation is necessary. The fact that in connection with each experiment a group of questions was answered gives rise to some difficulty in planning the statement of results. It is a simple matter to describe a particular set of experiments and to tell all the facts which were learned from them; but it is not logical, since one observation may have concerned the number of elements in the rhythmic unit, another their internal distribution, and a third their coalescence in a higher unity. On the other hand, the statement of each of these in its own proper connection would necessitate the repet.i.tion of some description, however meager, of the conditions of experimentation in connection with each item. For economy's sake, therefore, a compromise has been made between reporting results according to distribution of material and according to distribution of topics. The evidence of higher grouping, for example, which is afforded by variations in duration and phases of intensity in alternate measures, will be found appended to the sections on these respective cla.s.ses of material.

In all the following sections the hammer-clang apparatus formed the mechanism of experimentation in sensory rhythms, while in reactive rhythms simple finger-tapping was employed.

In comparing the variations in stress which the rhythmical material presents, the average intensities of reaction for the whole group has been computed, as well as the intensities of the single reactions which compose it. This has been done chiefly in view of the unstable intensive configuration of the group and the small amount of material on which the figures are based. The term is relative; in ascertaining the relations of intensity among the several members of the group, at least ten successive repet.i.tions, and in a large part of the work fifty, have been averaged. This is sufficient to give a clear preponderance in the results to those characteristics which are really permanent tendencies in the rhythmical expression. This is especially true in virtue of the fact that throughout these experiments the subject underwent preliminary training until the series of reactions could be easily carried out, before any record of the process was taken. But when such material is a.n.a.lyzed in larger and smaller series of successive groups the number of reactions on which each average is based becomes reduced by one half, three quarters, and so on. In such a case the prevailing intensive relations are liable to be interfered with and transformed by the following factor of variation. When a wrong intensity has accidentally been given to a particular reaction there is observable a tendency to compensate the error by increasing the intensity of the following reaction or reactions. This indicates, perhaps, the presence of a sense of the intensive value of the whole group as a unity, and an attempt to maintain its proper relations unchanged, in spite of the failure to make exact coordination among the components. But such a process of compensation, the disappearance of which is to be looked for in any long series, may transpose the relative values of the accented elements in two adjacent groups when only a small number of reactions is taken into account, and make that seem to receive the major stress which should theoretically receive the minor, and which, moreover, does actually receive such a minor stress when the value of the whole group is regarded, and not solely that member which receives the formal accentuation.

The quant.i.tative a.n.a.lysis of intensive relations begins with triple rhythms, since its original object was to compare the relative stresses of the unaccented elements of the rhythmic group. These values for the three forms separately are given in Table XXII., in which the value of the accented element in each case is represented by unity.

TABLE XXII.

Rhythm. 1st Beat. 2d Beat. 3d Beat.

Dactylic, 1.000 0.436 0.349 Amphibrachic, 0.488 1.000 0.549 Anapaestic, 0.479 0.484 1.000

The dactylic form is characterized by a progressive decline in intensity throughout the series of elements which const.i.tute the group. The rate of decrease, however, is not continuous. There is a marked separation into two grades of intensity, the element receiving accentual stress standing alone, those which possess no accent falling together in a single natural group, as shown in the following ratios: first interval to third, 1.000:0.349; second interval to third, 1.000:0.879. One cannot say, therefore, that in such a rhythmic form there are two quant.i.ties present, an accented element and two undifferentiated elements which are unaccented. For the average is not based on a confused series of individual records, but is consistently represented by three out of four subjects, the fourth reversing the relations of the second and third elements, but approximating more closely to equivalence than any other reactor (the proportional values for this subject are 1.000; 0.443; 0.461). Moreover, this reactor was the only musically trained subject of the group, and one in whom the capacity for adhering to the logical instructions of the experiment appears decidedly highest.

In the amphibrachic form the average again shows three degrees of intensity, three out of four subjects conforming to the same type, while the fourth reverses the relative values of the first and third intervals. The initial element is the weakest of the group, and the final of median intensity, the relation for all subjects being in the ratio, 1.000:1.124. The amphibrachic measure begins weakly and ends strongly, and thus approximates, we may say, to the iambic type.

In the anapaestic form the three degrees of intensity are still maintained, three out of four subjects giving consistent results; and the order of relative values is the simple converse of the dactylic.

There is presented in each case a single curve; the dactyl moves continuously away from an initial accent in an unbroken decrescendo, the anapaest moves continuously toward a final accent in an unbroken crescendo. But in the anapaestic form as well as in the dactylic there is a clear duality in the arrangement of elements within the group, since the two unaccented beats fall, as before, into one natural group, while the accented element is set apart by its widely differentiated magnitude. The ratios follow: first interval to second, 1.000:1.009; first interval to third, 1.000:2.084.

The values of the three elements when considered irrespective of accentual stress are as follows: First, 1.000; second, 1.001; third, 0.995. No characteristic preponderance due to primacy of position appears as in the case of relative duration. The maximum value is reached in the second element. This is due to the cooperation of two factors, namely, the proximity of the accentual stress, which in no case is separated from this median position by an unaccented element, and the relative difficulty in giving expression to amphibrachic rhythms. The absolute values of the reactions in the three forms is of significance in this connection. Their comparison is rendered possible by the fact that no change in the apparatus was made in the course of the experiments. They have the following values: Dactylic, 10.25; amphibrachic, 12.84; anapaestic, 12.45. The constant tendency, when any difficulty in coordination is met with, is to increase the force of the reactions, in the endeavor to control the formal relations of the successive beats. If such a method of discriminating types be applied to the present material, then the most easily coordinated--the most natural--form is the dactyl; the anapaest stands next; the amphibrach is the most unnatural and difficult to coordinate.

The same method of a.n.a.lysis was next applied to four-beat rhythms. The proportional intensive values of the successive reactions for the series of possible accentual positions are given in the following table:

TABLE XXIII.

Stress. 1st Beat. 2d Beat. 3d Beat. 4th Beat.

Initial, 1.000 0.575 0.407 0.432 Secondary, 0.530 1.000 0.546 0.439 Tertiary, 0.470 0.407 1.000 0.453 Final, 0.492 0.445 0.467 1.000

The first and fourth forms follow similar courses, each marked by initial and final stress; but while this is true throughout in the fourth form, it results in the first form from the preponderance of the final interval in a single individual's record, and therefore cannot be considered typical. The second and third forms are preserved throughout the individual averages. The second form shows a maximum from which the curve descends continuously in either direction; in the third a division of the whole group into pairs is presented, a minor initial accent occurring symmetrically with the primary accent on the third element. This division of the third form into subgroups appears also in its duration aspect. Several inferences may be drawn from this group of relations. The first and second forms only are composed of singly accented groups; in the third and fourth forms there is presented a double accent and hence a composite grouping. This indicates that the position in which the accent falls is an important element in the coordination of the rhythmical unit. When the accent is initial, or occurs early in the group, a larger number of elements can be held together in a simple rhythmic structure than can be coordinated if the accent be final or come late in the series. In this sense the initial position of the accent is the natural one. The first two of these four-beat forms are dactylic in structure, the former with a postscript note added, the latter with a grace note prefixed.

In the third and fourth forms the difficulty in coordinating the unaccented initial elements has resulted in the subst.i.tution of a dipodic division for the anapaestic structure of triple rhythms with final accent.

The presence of a tendency toward initial accentuation appears when the average intensities of the four reactions are considered irrespective of accentual position. Their proportional values are as follows: First, 1.000; second, 0.999; third, 1.005; fourth, 0.981.

Underlying all changes in accentuation there thus appears a resolution of the rhythmic structure into units of two beats, which are primitively trochaic in form.

The influence exerted by the accented element on adjacent members of the group is manifested in these forms more clearly than heretofore when the values of the several elements are arranged in order of their proximity to that accent and irrespective of their positions in the group. Their proportional values are as follows:

TABLE XXIV.

2d Remove. 1st Remove. Accent. 1st Remove. 2d Remove.

0.442 0.526 1.000 0.514 0.442

This reinforcing influence is greater--according to the figures just given--in the case of the element preceding the accent than in that of the reaction which follows it. It may be, therefore, that the position of maximal stress in the preceding table is due to the close average relation in which the third position stands to the accented element.

This proximity it of course shares with the second reaction of the group, but the underlying trochaic tendency depreciates the value of the second reaction while it exaggerates that of the third. This reception of the primitive accent the third element of the group indeed shares with the first, and one might on this basis alone have expected the maximal value to be reached in the initial position, were it not for the influence of the accentual stress on adjacent members of the group, which affects the value of the third reaction to an extent greater than the first, in the ratio 1.000:0.571.

The average intensity of the reactions in each of the four forms--all subjects and positions combined--is worthy of note.

TABLE XXV.

Stress. Initial. Secondary. Tertiary. Final.

Value, 1.000 1.211 1.119 1.151

The first and third forms, which involve initial accents--in the relation of the secondary as well as primary accent to the subgroups--are both of lower average value than the remaining types, in which the accents are final, a relation which indicates, on the a.s.sumption already made, a greater ease and naturalness in the former types. Further, the second form, which according to the subjective reports was found the most difficult of the group to execute--in so far as difficulty may be said to be inherent in forms of motor reaction which were all relatively easy to manipulate--is that which presents the highest intensive value of the whole series.

In the next group of experiments, the subject was required to execute a series of reactions in groups of alternating content, the first to contain two uniform beats, the second to consist of a single reaction.

This second beat with the interval following it const.i.tutes a measure which was to be made rhythmically equivalent to the two-beat group with which it alternated. The time-relations of the series were therefore left to the adjustment of the reactor. The intensive relations were separated into two groups; in the first the final reaction was to be kept uniform in strength with those of the preceding group, in the second it was to be accented.

The absolute and relative intensive values for the two forms are given in the following table:

TABLE XXVI.

Rhythm. 1st Beat. 2d Beat. 3d Beat. Value.

Syncopated Measures 13.00 15.12 16.50 Absolute.

Unaccented, 1.000 1.175 1.269 Relative.

Syncopated Measures 10.95 11.82 16.11 Absolute.

Accented, 1.000 1.079 1.471 Relative.

These averages hold for every individual record, and therefore represent a thoroughly established type. In both forms the reaction of the syncopated measure receives the greatest stress. In the first form, while the stress is relatively less than in the second, it is at the same time absolutely greater. The whole set of values is raised (the ratio of average intensities in the two forms being 1.147:1.000), as it has already been found to be raised in other forms difficult to execute. To this cause the preponderance is undoubtedly to be attributed, as the reports of every subject describe this form as unnatural, in consequence of the restraint it imposes on an impulse to accent the final reaction, _i.e._, the syncopated measure.

In the next set of experiments the series of reactions involved the alternation of a syncopated measure consisting of a single beat with a full measure of three beats. The same discrimination into accented and unaccented forms in the final measure was made as in the preceding group. The series of absolute and relative values are given in the following table.

TABLE XXVII.

Rhythm. 1st Beat. 2d Beat. 3rd Beat. 4th Beat. Value.