Harvard Psychological Studies Part 49

TABLE LXXVI.

Subgroups Init. Stress Sec. Stress Tert. Stress Fin. Stress 1st Four, 1.000 1.000 1.000 1.000 2d Four, 0.950 0.762 0.984 0.790

The first member of the larger group, in the case of every rhythm form here in question, is less exactly coordinated than the second, the interpretation of which fact need not here be repeated. Several additional points, however, are to be noted. The differences in stability of coordination which are encountered as one pa.s.ses from the first to the last of the four rhythm forms, extends, when the reactions are a.n.a.lyzed in series of eight beats, to both members of the compound group, but not in equal ratios. The mean variation of the second and fourth forms is greater, both in the first and second subgroups, than that of the corresponding subgroups of the first and third forms; but this increase is greatest in the first member of the composite group. That is, as the group grows more unstable it does so mainly through an increase in variation of its initial member; or, in other words, the difference in variability of the beat intervals of the first and last subgroups reaches its maximum in those rhythmic types in which the indices of mean variation for these intervals are themselves at their maxima.

This process of coordination, with its indication of a higher rhythmical synthesis, appears also in the transformations in the value of the mean variations in duration of the total groups, when the material is treated in series of eight beats, as in table LXXVII.

TABLE LXXVII.

Subgroups. Init. Stress. Sec. Stress. Tert. Stress. Final Stress.

1st Four, 1.000 1.000 1.000 1.000 2d Four, 0.773 0.768 0.943 0.579

The total initial group, therefore, as well as each of its const.i.tuent intervals, is less stable than the second.

Within the unit group itself the values of the mean variation show here, as in the preceding forms, a progressive increase in sensitiveness to temporal variations from first to last of the component intervals. The proportional values for the four intervals in order are, 1.000, 0.786, 0.771, 0.666. The distribution of these relative values, however, is not uniform for all four rhythmical forms, but falls into two separate types in dependence on the position of the accents as initial or final, following the discrimination already made. The figures for the four forms separately are as follows:

TABLE LXXVIII.

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

Initial, 9.57 per cent. 5.53 per cent. 5.83 per cent. 6.57 per cent.

Secondary, 13.23 " 10.60 " 12.93 " 9.50 "

Tertiary, 9.00 " 8.70 " 2.00 " 4.90 "

Final, 11.45 " 9.00 " 12.60 " 7.85 "

In the first type (Rhythms I. and III.) appear a descending curve followed by an ascending; in the second type (Rhythms II. and IV.) a second descending curve follows the first. The changes in the first type are not coordinated with a similar curve of variation in the intensive magnitude of the beats. It is to be noted here that the smallest mean variation presented in this whole set of results is found in that element of the first form which receives the stress, an exception to the general rule. The variations in the contrasted type have their maxima at those points on which the group initiation-- primary or secondary--falls, namely, the first and third.

As in preceding rhythmical forms, while the separation of accentual stress from primacy in the series tends to increase the mean variation of that element on which this stress falls and to raise the index of mean variation for the whole group, yet the mean variation of the initial element is also raised, and to a still greater degree, reinforcing the evidence that primacy of position is a more important factor of instability than the introduction of accentual stress.

In the investigation of mean variations for units (if we may call them such) of more than four beats only a modic.u.m of material has been worked up, since the types of relation already discovered are of too definite a character to leave any doubt as to their significance in the expression of rhythm. The results of these further experiments confirm the conclusions of the earlier experiments at every point.

These higher series were treated in two ways. In the first the reactor beat out a rhythm consisting in the simple succession of groups of reactions, each of which contained one and only one accent. These units in each case were marked by initial stress, and were composed of five, six, seven, eight and ten beats respectively. The results are given in the following table, which contains the series of mean variations in duration both for single intervals and for total groups.

TABLE LXXIX.

No. Med. Unac'td of Beats. Acc'td Beat. Beats. Final Beat. Average. Group.

Five, 12.2% 6.8% 7.1% 7.9% 6.3% Six, 9.2 10.6 6.9 9.7 8.3 Seven, 7.1 5.2 7.9 5.8 3.6 Eight, 12.4 9.5 8.8 9.7 8.0 Ten, 7.5 6.6 7.3 6.8

The averages for the combined, median, unaccented intervals are given separately from those of the final interval, for the reason that the mean variation of the latter is greater in three cases out of five than that of the former, a relation which apparently contradicts what has already been said concerning the sensitiveness to variations which marks the intervals separating rhythmical groups. The reason for this final increase in variation appears when the relative intensities of the series of reactions are considered. They are given in Table Lx.x.x.

TABLE Lx.x.x.

No. of Beats. Acc. Beat. Av. Unacc. Final. Pre-final.

Five, 1.000 0.543 0.518 0.500 Six, 1.000 0.623 0.608 0.592 Seven, 1.000 0.515 0.544 0.437 Eight, 1.000 0.929 0.949 0.863 Ten, 1.000 0.621 0.640 0.545

In every case the final element is marked by an increase over that which precedes it (see last two columns of table) of the average value for all rhythms of 1.000:0.900; an increase which raises it above the average value of the whole series of preceding unaccented beats in three cases out of five. To this final accentuation the increase in variation is to be attributed. Yet despite the additional element of disturbance due to this increased final stress the average value of the mean variation for this final interval is lower than that of the median unaccented intervals in the ratio (all rhythms combined) of 0.992:1.000.

Turning, then, to Table LXXIX., there is presented, firstly, an excess of variation in the accented element over that of the average unaccented elements in every case but one (the six-beat rhythm in which the values are nearly identical), which for the whole series of rhythms has a value of 1.000:0.794. Secondly, in every completed case (part of the figures in the last rhythm are inadvertently lacking), the average mean variation of the single interval preponderates over that of the total group.

The second form of rhythmical tapping, in which the longer series were beaten out as pairs of equal subgroups, was added in order to determine the quant.i.tative relations of the mean variations for alternate subgroups when such groups were purposely intended, instead of appearing in the form of unconscious modifications of the rhythmical treatment, as heretofore. At the same time the results present an additional set of figures embodying the relations here in question. They are as follows:

TABLE Lx.x.xI.

Intervals. Groups.

Number Av. 1st 2d 1st 2d of Beats. Acc. Unacc. Half. Half. Half. Half. Average Totals Six, 27.9% 20.9% 23.4% 23.0% 14.6% 13.3% 13.9% 13.8% Eight, 16.6 14.8 13.2 17.3 6.2 3.3 4.7 2.7 Ten, 7.9 2.6 3.4 4.0 5.9 5.2 5.5 3.1

No exception here occurs to the characteristic predominance in instability of the accented element. As regards simple intervals, the relation of first and second groups is reversed, the reason for which I do not know. It may be connected with the rapid speed at which the series of reactions was made, and its consequent raising of the threshold of perceptible variation, proportional to the value of the whole interval, to which is also due the higher absolute value of the variations which appear in both tables.

These inversions disappear when we compare the relative stability of the first and second subgroups, in which the excess of variation in the former over the latter is not only constant but great, presenting the ratio for all three rhythms of 1.000:0.816. The characteristic relation of lower to higher rhythmical syntheses also is here preserved in regard to the two subgroups and the total which they compose.

The points here determined are but a few of the problems regarding the structure of larger rhythmical sequences which are pressing for examination. Of those proximate to the matter here under consideration, the material for an a.n.a.lysis of the mean variation in intensity of a series of rhythmical reactions is contained in the measurements taken in the course of the present work, and this may at a future time be presented. The temporal variations having once been established it becomes a minor point.

Such conclusions, however, are only preliminary to an investigation of the characteristic structure of the ordinary metrical forms, and to these attention should next be turned. The configuration of the common meters should be worked out both in relation to the whole formal sequence, and to the occurrence within the series of characteristic variations. There can be no question that each metrical structure, the iambic trimeter or dactylic tetrameter line, for example, composes a definite rhythmical melody within which each measure is shortened or prolonged, subdued or emphasized, according to its position and connections in the series of relations which const.i.tute the rhythmical sequence.

These several metrical forms should be explored and the characters of each measure in the series quant.i.tatively determined. Such an investigation would include an ascertainment of the proportional time-value of each successive measure, its average force, and its sensitiveness to variations, temporal and intensive. It should include an examination of the configuration of the single measure and the changes in distribution of accents and intervals which it undergoes as the rhythmical series advances. For the rhythm group must not be conceived as a simple unchanging form; both intensively and temporally it is moulded by its function in the whole sequence, the earlier iambic of a heroic measure being unlike the later, the dactyl which precedes a measure of finality different from that which introduces the series. Such a set of determinations will give the pure characteristic curves of our common poetical meters.

But these meters are no more simple forms than are their const.i.tuent measures. At every point their structure is subject to modification by factors which appear in the rhythmic utterance in virtue of its use as a medium for the free expression of thought and emotion; and the manner in which the characteristic form is altered by these factors of variation must be studied. Of these variations the more important are the effects of the introduction of variants--of spondees among dactyls, of anapaests among iambics, and the like--and the occurrence of points of origin, emphasis, interruption, and finality in special accentuations, syncopated measures, caesural pauses and elisions. These factors influence the structure both of those measures within which they appear and of those adjacent to them. The nature and extent of this wave of disturbance and its relation to the configuration of the whole sequence call for examination.

Finally, this process of investigation should be applied to the larger structures of the couplet and stanza, that the characteristic differences in the pair or series of verses involved may be determined. These characters include the whole time occupied by each verse of the stanza, the relative values of acatalectic and catalectic verses occurring within the same stanza structure, differences in rhythmical melody between the latter forms, the variations of average intensity in the accentual elements of such lines, and a determination of the values of rests of higher and lower degrees--mid-line, verse, and couplet pauses--which appear in the various stanza forms, and their relation to other structural elements.

RHYTHM AND RHYME.

BY R.H. STETSON.

I. INTRODUCTION.

The psychological theory of rhythm has its beginnings in the work of Herbart,[1] who inaugurated the treatment of rhythm as a species of time perception and suggested an explanation of its emotional effects.

While Herbart had simply pointed out the effect of a whole rhythmic series in giving rise to an emotion of expectation, delay, or haste, Lotze[2] applied the principle severally to each unit group (each foot) in the rhythm, and made the emotional effect of rhythm depend on these alternate feelings of strain, expectation, and satisfaction produced by every repet.i.tion of the unit group. Vierordt[3] did the first experimental work on rhythm, determining the period of greatest regularity in the tapping of rhythms. But the first important experiments were carried on by von Brucke.[4] By tapping out rhythms on a kymograph, he determined the well-known 'Taktgleichheit' of the feet in scanned verse, and noted a number of facts about the time relations of the different unit groups. Mach[5] added to the previous knowledge about rhythm certain observations on the subjective accentuation of an objectively uniform series, and specially he noted that the process is involuntary. With a much clearer understanding of the facts of rhythm than his predecessors had had, he really provided the foundation for the theories which follow. His most important contribution, for some time overlooked, was his emphasis of the essentially motor nature of the phenomena of rhythm, and his motor theory therefor.

[1] Herbart, J.F.: 'Psychol. Untersuchungen' (Sammt. Werk, herausgeg. von Hartenstein), Leipzig, 1850-2, Bd. VII., S. 291 ff.