Chapter XVIII: Section II: showed that the shorter filled distances are (14)

An analysis of the material in successive pairs of two-beat groups revealed a pronounced rhythm in the values of the mean variations of the first and second members of the pair respectively, the fixity of the second group being much greater than that of the first, the mean variation having a ratio for all subjects of 0.801:1.000. The interpretation of this rhythmical variation, as in the preceding reaction series, must be speculative in the absence of quantitative measurement of intensive changes, but is still not left in doubt. The rhythmic material is combined in larger syntheses than the groups of two beats, alternately accented and unaccented, which were avowedly in mind. This secondary grouping appears in at least a measure of four beats, into which the unit group enters as the elementary interval entered into the composition of that unit. In this larger group the initial period, or element of stress, is characterized by a greater mean variation than the unaccented period which follows it. There are present in this first interval two factors of instability: the factor of accent, that element which receives the stress, being in general characterized by a greater mean variation than the unaccented; and the factor of position, the initial member of a rhythmical group, independent of accentuation, being marked by a like excess of mean variation over those which follow it. The interpretation of the latter fact lies in the direction of a development of uniformity in the motor habit, which is partially interrupted and reëstablished with the ending and beginning of each successive group, large or small, in the series of reactions.

Further, when the material is arranged with four unit groups in each series, the same relation is found to hold between the first period composed of two unit groups and the second like period, as obtained within these pairs themselves. The mean variation of the first period of four beats is greater than that of the second in the case of all subjects but one, with an average ratio for all subjects of 1.000:0.745. The analysis was not carried further; there is, however, nothing which points to a limitation of the process of synthesis to groups of this magnitude; rather, to judge from the close approximation in definition of the two orders manifested here, there is suggested the probability that it is carried into still higher groupings.

In the next rhythmical type analyzed--the iambic form--that relation of the first to the second interval holds which was found to obtain in the preceding forms. The excess of mean variation in the former over the latter presents the ratio 1.274: 1.000. In amount it is less than in either of the previous types (2.290:1.000 and 1.722:1.000). For here, though both elements have constant relations as accented or unaccented members of the group, the factor of stress has been transferred from the initial to the final beat. Instead, therefore, of combining in a single member, the factors of inconstancy due to stress and to position are distributed between the two elements, and tend to neutralize each other. That the preponderance of irregularity is still with the initial interval leads to the inference that position is a greater factor of inconstancy than accentuation.

Also, the group presents here, as in the preceding forms, a greater fixity than does the individual interval. This relation holds for all subjects but one, the average mean variations of the simple interval and of the unit group having the ratio 1.000:0.824.

In larger groupings irregularities in the relations of higher and lower again occur, and again the greater constancy obtains between the first and second orders of higher grouping (in which for only one subject has the lower group a greater fixity than the higher, and the averages for all subjects in the two cases are in the ratio 1.149:0.951), and the lesser constancy between the unit group and the first higher (in which two subjects manifested like relations with those just given, while three present inverted relations). The whole series of relations, on the basis of unity for the mean variation of the simple interval, is given in Table LXIV.

TABLE LXIV.

Proportional. Single Beat. 2-Beat Group. 4-Beat Group. 8-Beat Group
M.V. 1.000 0.824 1.149 0.951

There is also presented here, as in the preceding forms, a synthesis of the material into groups of four and eight beats, with similar differences in the fixity of the first and last periods in each. A single subject, in the case of each order of grouping, diverges from the type. The ratio of difference in the mean variations of the first and second members of the groups is, for series of four beats, 1.000:0.657, and for series of eight beats, 1.000:0.770. This indicates a diminishing definition of rhythmical quantities as the synthesis proceeds, but a diminution which follows too gradual a curve to indicate the disappearance of synthesis at the proximate step in the process.

Three-beat rhythms were next taken up and the same method of analysis carried out in connection with each of the three accentual forms, initial, median, and final stress. In these types of rhythm the intra-group intervals are more than one in number; for the purpose of comparison with the final, or inter-group interval, the average of the first and second intervals has been taken in each case.

The results agree with those of the preceding types. The mean variation of the interval separating the groups is less throughout than that of the average group-interval. The ratios for the various rhythm types are as follows:

TABLE LXV.

Rhythm Form. Initial Stress. Median Stress. Final Stress.
Ratios, 1.000 : 0.758 1.000 : 0.527 1.000 : 0.658

This relation, true of the average intra-group interval, is also true of each interval separately. Among these ratios the greatest departure from unity appears in the second form which all subjects found most difficult to reproduce, and in which the tendency to revert to the first form constantly reasserts itself. The difference in value of the mean variations is least in the first form, that with initial accent, and of intermediate magnitude in the third form when the accent is final. The contrary might be expected, since in the first form--as in the second also--the factors of stress and initial position are both represented in the average of the first two intervals, while in the third form the factor of stress affects the final interval and should, on the assumption already made concerning its significance as a disturbing element, tend to increase the mean variation of that interval, and, therefore, to reduce to its lowest degree the index of difference between the two phases. That it does so tend is evident from a comparison of the proportional mean variations of this interval in the three forms, which are in order: initial stress, 4.65 per cent.; median stress, 4.70 per cent., and final stress, 7.15 per cent. That the consequent reduction also follows is shown by the individual records, of which, out of four, three give an average value for this relation, in forms having final stress, of 1.000:0.968, the least of the group of three; while the fourth subject departs from this type in having the mean variation of the initial interval very great, while that of the final interval is reduced to zero.

If, as has been assumed, the magnitude of the average mean variation may be taken as an index of the fixity or definition of the rhythm form, the first of these three types, the ordinary dactylic is the most clearly defined; the second, or amphibrachic, stands next, and the third, the anapæstic, has least fixity; for in regard to the final interval, to the average of the first and second and also to each of these earlier intervals separately, the amount of mean variation increases in the order of the accents as follows:

TABLE LXVI.

Interval. Initial Stress. Median Stress. Final Stress.
First, 5.82 per cent. 9.95 per cent. 11.95 per cent.
Second, 6.45 " 7.87 " 9.77 "
Third, 4.65 " 4.70 " 7.15 "

In these triple rhythms, as in the two-beat forms, the simple interval is more variable than the unit group, and the lower group likewise more unstable than the higher. The series of proportional values for the three forms is given in the table annexed:

TABLE LXVII.

Rhythm Form. Single Interval. 3-Beat Group. 6-Beat Group.
Initial Stress, 1.000 1.214 1.037
Median " 1.000 0.422 0.319
Final " 1.000 0.686 0.524

A comparison of the second and third columns of the table shows an excess of mean variation of the smaller group over that of the larger in each of the three forms. It is true also of the individual subjects except in two instances, in each of which the two indices are equal. This proportion is broken in the relation of the primary interval to the unit group in the dactylic rhythm form. A similar diversity of the individual records occurred in the two-beat rhythms.

The same indication of higher groupings appears here as in the case of previous rhythms. Rhythmical variations are presented in the amount of the mean variations for alternate groups of three beats. Chronologically in the records, as well as in dependence on theoretical interpretation, the first member of each higher group is characterized by the greater instability. The amounts of this difference in coördination between the first and last halves in series of six beats is set down for the three rhythm forms in the following table:

TABLE LXVIII.

Stress. First Half. Second Half
Initial, 1.000 0.794¹
Median, 1.000 0.668
Final, 1.000 0.770

¹These figures are made up from the records of three out of
four subjects. In the exceptional results of the fourth
subject no mean variation appears in the first half and 6.3
per cent, in the second, making the average for the whole
group 1.000:1.023.

There is still other evidence of higher rhythmical grouping than these oscillations in the amount of the mean variation of alternate groups. Exactness of coördination between the individual intervals of successive groups might undergo development without affecting the relative uniformity of such total groups themselves. But, throughout these results, an increase in coördination between the periods of the whole group takes place in passing from the first to the second member of a composite group. The relation here is not, however, so uniform as in the preceding case. The series of proportional values is given on page 403.

TABLE LXIX.

Stress. First Half. Second Half.
Initial, 1.000 0.846¹
Median, 1.000 1.064
Final, 1.000 0.742

¹ Here also the records of three subjects only are involved,
the results of the same reactor as in the preceding cases
being discarded. Including this, the ratio becomes
1.000:1.016.

The index of mean variation for the individual elements of the group also shows a progressive decrease from first to last as follows:

TABLE LXX.

Stress. Interval I. Interval II. Interval III.
Initial, 5.82 per cent. 6.45 per cent. 4.65 per cent.
Median, 9.95 " 7.87 " 4.70 "
Final, 11.95 " 9.77 " 7.15 "

The relation holds in all cases except that of I. to II. in the rhythm with initial stress. From this table may be gathered the predominance of primacy of position as a factor of disturbance over that of stress. Indeed, in this group of reactions the index of variation for the accented element, all forms combined, falls below that of the unaccented in the ratio 6.95 per cent. : 7.91 per cent.

In rhythms of four beats, as in those of three, the estimation of values is made on the basis of an average of the mean variations for the three intra-group intervals, which is then compared with the final or inter-group interval. As in those previous forms, sensitiveness to variations in duration is greater throughout in the case of the latter than in that of the former. The proportional values of their several mean variations are given in the annexed table:

TABLE LXXI.

Interval. Initial Stress. Secondary Stress. Tertiary Stress. Final Stress.
Intra-group, 1.000 1.000 1.000 1.000
Inter-group, 0.941 0.775 0.725 0.713

This relation, true of the average of all intra-group intervals, is not, as in the preceding forms, true of each of the three constituent intervals in every case. In the second and fourth forms, those marked by secondary and final stress, it holds for each member of the group of intervals; in the first form it fails for the second and third intervals, while in the third form it fails for the last of the three.

The proportional amount of this difference in mean variation continuously increases from beginning to end of the series of rhythmical forms. This cannot be interpreted as directly indicative of a corresponding change in the definition which the four forms possess. The absolute values of the several mean variations must simultaneously be taken into account. First, then, in regard to the final pause there is presented the following series of values:

TABLE LXXII.

Stress. Initial. Secondary. Tertiary. Final.
M.V. 6.57 per cent. 9.50 per cent. 4.90 per cent. 15.70 per cent.

A very striking rhythmical alternation in the magnitude of the mean variation thus occurs according as the accents fall on the first member of the subgroups when its amount is smaller or on the second member when it is larger. Further, the cases noted above, the second and fourth forms, in which each of the intra-group intervals is severally of greater mean variation than the final pause, are just those in which the index of mean variation in the final pause itself is at a maximum.

The average mean variations of the earlier intervals thus present changes which are analogous to and synchronous with those of the final pause. Their values in proportion to the whole duration of the intervals are as follows[13]:

[13] In the second line of figures has been added the series of
values of the average mean variation for all four intervals of
the group.

TABLE LXXIII.

Stress. Initial. Secondary. Tertiary. Final.
M.V. 6.98 per cent. 12.25 per cent. 6.57 per cent. 22.0 per cent.
M.V. 6.87 " 11.56 " 6.15 " 20.45 "

Those rhythmical forms having their accentual stress initial, or on the initial elements of the subgroups, are marked by a sensitiveness almost twice as great as those in which the stress is final, or on the final elements of the subgroups.

Finally, if we take the whole series of intervals severally, we shall find that this rhythmical variation holds true of each element individually as it does of their average. The whole series of values is given in the table annexed.

TABLE LXXIV.

Stress.
Interval. Initial. Secondary. Tertiary. Final.

First, 9.57 per cent. 13.23 per cent. 9.00 per cent. 11.45 per cent.
Second, 5.53 " 10.60 " 8.70 " 9.00 "
Third, 5.83 " 12.93 " 2.00 " 12.90 "
Fourth, 6.57 " 9.50 " 4.90 " 7.85 "

It is an obvious inference from these facts that the position of the accent in a rhythmical group is of very great significance in relation to the character of the rhythmical movement. The initial accent gives incomparably greater coördination and perfection to the forms of uttered (produced) rhythm than does the final. It is in this sense the natural position of the accent, because on the success and fluency of this coördination the æsthetic value of the rhythm depends.

In general, though not so unequivocally, the four-beat rhythms show a progressive increase of stability in passing from the simple interval to the group, and from the smaller group to the larger. The series of values for the four accentual positions follows.

TABLE LXXV.

Stress. Single Interval. 4-Beat Group. 2-Beat Group.
Initial, 7.27 per cent. 8.20 per cent. 8.17 per cent.
Secondary, 11.60 " 9.60 " 6.25 "
Tertiary, 3.20 " 3.40 " 2.25 "
Final, 10.22 " 6.30 " 6.00 "
Average, 8.07 " 6.87 " 5.67 "

Here, as in the preceding rhythmical forms, the most constant relation is that of smaller and larger groups, in which no exception occurs to the excess of mean variation in the former over the latter. The cases in which this relation is reversed are found, as before, in comparing the simple interval with the duration of the unit group; and the exceptional instances are just those, namely the first and third forms, in which the mean variation of this uncompounded interval is itself at a minimum. This means that the simple interval presents a more mobile character than that of the group; and while in general it is less stable than the latter, it is also the first to show the influence of increased coördination. Training affects more readily the single element than the composite measure, and in the most highly coördinated forms of rhythm the simple interval is itself the most perfectly integrated unit in the system of reactions.

Here, as in the preceding rhythmical forms, evidence of higher grouping appears in the alternate increase and decrease of mean variation as we pass from the first to the second subgroup when the material is arranged in series of eight beats. The proportional values of the indices are given in the following table:

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 coördinated 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 coördination which are encountered as one passes from the first to the last of the four rhythm forms, extends, when the reactions are analyzed 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 coördination, 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 constituent 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 coördinated 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 modicum 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 LXXX.

TABLE LXXX.

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 quantitative 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 LXXXI.
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 analysis 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 constitute the rhythmical sequence.

These several metrical forms should be explored and the characters of each measure in the series quantitatively 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 constituent 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 anapæsts among iambics, and the like--and the occurrence of points of origin, emphasis, interruption, and finality in special accentuations, syncopated measures, cæsural 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 repetition 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 Brücke.[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' (Sämmt. Werk,
herausgeg. von Hartenstein), Leipzig, 1850-2, Bd. VII., S. 291
ff.

[2] Lotze, R.H.: 'Geschichte der Æsthetik,' München, 1863, S.
487 ff.

[3] Vierordt, K.: 'Untersuchungen über d. Zeitsinn,' Tübingen,
1868.

[4] von Brücke, E.W.: 'Die physiol. Grundlagen d.
neuhochdeutschen Verskunst,' Wien, 1871.

[5] Mach, Ernst: 'Unters. ü. d. Zeitsinn d. Ohres,' _Wiener
Sitz. Ber., mathem. naturw. Classe_, 1865, Bd. 51, II., S. 133.
_Beiträge zur Physiol. d. Sinnesorgane_, S. 104 ff.

Many of the recent theories of rhythm are based on Wundt's analysis. The work of Wundt and Dietze,[6] was concerned with rhythmic series; but it may be noted that the 'span of consciousness' and the 'synthetic activity of consciousness' were the subjects actually under investigation. Rhythm was considered as a special temporal form of this 'psychic synthesis.' There are three different elements in a sound series, declared these writers, which contribute to this synthesis: qualitative changes, intensive changes and melodic changes. Of these the intensive changes are the most important. Every increase in intensity, that is, every beat ('Hebung') is followed by a decrease, and the next increase which follows is recognized as a repetition of the preceding beat and as the forerunner of the beat which is to follow. From this comes the synthetic power of the rhythm. Just as the simple unit groups are built up by this synthesizing power, so they in turn are combined into larger phrases and periods. The motor factor has little place in Wundt's own discussion,[7] the 'mental activity' is the all-important thing. Bolton[8] also made a very important contribution to the experimental knowledge of rhythm. His work was based entirely on Wundt's theory. His method of experimentation was accurate and his observations copious. The arrangement of his apparatus, however, led him to emphasize objective uniformity as a condition of rhythmic grouping; so that Meumann's criticism of his application of this principle to poetry is quite just. Nevertheless Bolton established the essential facts of subjective accentuation and apparent temporal displacement. It is noteworthy that he laid great emphasis on the motor aspect of rhythm, and made many careful observations on the 'motor accompaniment.' While inclining strongly to a motor interpretation he did not attempt to cut loose from the Wundtian 'apperceptive process' as the primary factor.

[6] Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893, Bd.
II., S. 83.

[7] Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893,
II., S. 89 ff.

[8] Bolton, T.L.: _Amer. Jour. of Psych._, 1894, VI., p. 145 et
seq.

The most elaborate consideration of rhythm yet published is that of Meumann.[9] He avowedly worked out and defended the theory of Wundt. The only important difference is the larger place which he gave to the 'motor accompaniment,' although he was always careful to emphasize its secondary and derived character. He insisted that the 'mental activity' is always primary, and that without it there can be no rhythmization; and he opposed vigorously the motor inclinations of Mach and Bolton. It is certainly unfortunate that rhythm has always fallen into the hands of the investigators of the 'attention,' or the 'span of consciousness,' or the 'perception of time.' It is but an incident that judgments of time are often based on rhythms; and everything that Meumann has said of a 'mental prius,' or a 'synthesizing activity' in the case of rhythms, may just as well be said in the case of any coördinated act.

[9] Meumann, E.: _Phil. Stud._, 1894, X., S. 249 ff.

Meumann discussed in detail the characteristics of the rhythm of a simple series of sounds, of music, and of verse. He assumed that in the simple sound series we have rhythm in its barest form, and only the rhythmic synthetic activity is at work; while in music there is a content which to some extent prescribes unities, and the objective regularity of the rhythm is broken. In verse we have much more content, and the rhythmization is no longer regular in its temporal relations; it is entirely dominated at times by the 'logical unities' of the 'thought.'

One great difficulty with such a differentiation of the three types of rhythms presents itself when one inquires into the objective regularity of the types; the fact is that music is by far the most regular in its time values, though it has more content than the sound series; and that just as great irregularities are possible in the bare sound series as in the rhythm of verse with its rich and definite content.

Later statements of the facts and theories relating to rhythm have inclined more and more to an emphasis of the motor aspect, even on the part of Wundtians. Since Meumann there has been some detailed laboratory work published, but the amount of accurately measured rhythmic material is astonishingly small. Meumann established experimentally the well-known relation between the length of a rhythmic element and its accent, and corroborated the earlier work on subjective accentuation. The reports contain the measurements of but about eighty individual unit groups (iambs, trochees, etc.). Ebhardt[10] gave the measurements of from 150 to 300 taps from each of three subjects. But his work is vitiated, as far as any application to rhythm is concerned, because he based everything on the judgment of _equality_, which has nothing to do with rhythm.

[10] Ebhardt, K.: _Zeilschr. f. Psych, u. Physiol. d.
Sinnesorgane,_1898, Bd. 18, S. 99.

Hurst, McKay and Pringle[11] published measurements of about 600 individual unit groups from three different subjects; in several cases, the material consists rather too much of records of the experimenters themselves, but in general their results agree very well with those of other authors. Scripture[12] published the measurements of a single stanza of poetry. It is but a single stanza and quite too little material on which to base any conclusions, but it is notable as a measurement of freely spoken rhythm. No experiments have been published which bear on the nature of the rhythmic phrase, of the period, or of the stanza.

[11] Hurst, A.S., McKay, J., and Pringle, G.C.F.: _Univ. of
Toronto Studies,_ 1899, No. 3, p. 157.

[12] Scripture, E.W.: _Studies from the Yale Psych. Lab.,_
1899, VII., p. 1.

Our problem is: What part do the recurrent qualitative factors, like rhyme, play in the grouping of rhythms? They function evidently, in the main, as factors determining the periods or larger phrases of the rhythm structure--the verses and stanzas of poetry and nonsense verse. As no work has been done on the nature of such larger rhythmic unities, a large share of the investigation was concerned with the nature of the verse unity.

Two methods of investigation were used: Subjects listened to rhythmic series, into which various modifications were introduced; and secondly, rhythms of a prescribed type, produced by the subject, were recorded and measured.

II. THE PERCEPTION OF A RHYTHMIC SERIES.

Apparatus: A disc (Fig. 1, Plate IX.) about 50 c. in diameter, rotating on a vertical pivot, was driven by a pulley-cone underneath mounted on the same spindle (not shown in the figure). On the face of the disc were four concentric rings of regularly spaced holes, which received pegs of uniform height and provided with a shoulder. Corresponding holes of each circle lay on the same radius. On a plate supported by a bracket were mounted four levers whose heads stood in line radially to the movable disc. When the disc rotated to the right under the levers, the pegs forced up the lever heads and made an electric contact. The dip of the levers was controlled by a screw adjustment. The apparatus was driven by a motor and reducing gear, which were isolated in a sound-proof box. The rate of speed was controllable.

The apparatus was built for use with sounders connected with the binding-posts, but in this investigation sounders were dispensed with, and the clicks from the apparatus itself were used, since but one qualitative difference was introduced. As a rule, the objective accent of the foot was not given; the subjective accentuation was nearly always sufficient. Subjects were quite unable to say whether the accent was objective or not. If necessary, an accentuation was produced by raising the pegs representing the accentuated part of the foot. The group elements were represented by single, simple clicks made by a brass screw on the lever arm striking an iron plate (the noise of the brass peg striking the lever head was eliminated by damping with cloth). The rhyme was represented by a compound noise consisting of a click higher in pitch than the verse element click, made by the peg striking the lever head, and an almost simultaneous click lower in pitch than the verse element click, made by the screw of the lever arm striking another iron plate. The rhyme noise was not louder than the verse element click, and as a whole gave the impression of being a lower tone because the first click was very brief. Subjects did not analyze the rhyme noise, and had no difficulty in making it represent rhyming syllables. The pauses throughout had no filling.

The subject was always given a normal series until the type was clearly established, and when the variations to be judged were introduced his attention was directed as far as possible to the factor to be introduced. This seemed the only way to obtain trustworthy judgments. If the subject waits blindly for some perceptual change in the whole complicated mass of sensations which the simplest rhythmic series constitutes, he is apt to fit his attention on some irrelevant detail, and the change may not be noted until greatly exaggerated, and he may not judge that particular factor at all.

The subject was always asked to choose a rate of delivery which would correspond to his natural rate of reading nonsense verse, and the clicks were always associated with syllables, though not with words. An effort was made to keep the series as colorless and devoid of content as possible, to eliminate uncertain association. Beyond suppressed articulation, the subject was not encouraged to mark the rhythm with any part of the body, but a number of involuntary movements of neck, body, hand, or foot were nearly always observed. Occasionally, when a subject's expression was doubtful, he was asked to say a nonsense series with the clicks.

The nomenclature to be used in this paper is that of meter, but it is always subject to the reservation that the material is only analogous to series of nonsense syllables.

Records were kept in terms of the intervals on the revolving disc; the time of revolution was also taken, so that the figures may be translated in time intervals if desired. Thus, 34, 34, 34, 34, 34 represents a series of iambs in which the unaccented click has the length of three, and the accented click the length of four spaces between pegs. A uniform verse represented by a digit giving the number of feet, followed by digits in parenthesis giving the character of the foot, _e.g._, 4 (34), is an iambic tetrameter.

For convenience, the verse pause is written independently of the last foot of the verse, _e.g._, 4 (34) p. 7 represents a tetrameter line having the intervals 34, 34, 34, 37. The interval of the last accented syllable is counted twice.

Occasionally this is disregarded and vs. p. equals o is written to indicate that the vs. p. is equal to the foot pause.

The results of the experiments may be grouped under three heads:

1. Why does a synthesizing factor such as rhyme occur at the end of the verse?

2. What is the relation between the verse pause and the rhyme?

3. What is the relation of rhyme to the cyclic movement of the unit group and of the verse?

_1. Why the Synthesizing Factor Occurs at the Close of the Verse_.

To determine a possible difference in the sense of rhythm at the beginning and the close of a verse, pauses ('lags') were introduced into the earlier and later parts of the verse. These pauses were made barely perceptible, _i.e._, barely perceptible in any part of the verse. Usually in iambic verse the barely perceptible lag shows the following proportions to the other pauses:

34 _35_ 34 etc., or
47 _48.5_ 47.

Most of the experiments were performed with iambic tetrameter. The subject was told to note the lags in the verse: these were introduced either in both parts of the verse or at its close only. At least three verses were given, and records were kept of the false judgments. When lags of identical duration were introduced between the first and second and between the third and fourth feet, it was found that nearly always the lag would not be detected in the earlier part of the verse but would be detected in the later part. Out of eighty-two cases, there were but six in which the same lag was recognized in the first as well as in the last position. In two of these cases the subject's attention had been called to the first part of the verse; and in the four other cases the lag was still found more marked at the close than at the beginning.

There were no cases in which a lag detected in the earlier part of the verse was not also detected in the later part. False judgments, when they occurred, were made as to a lag in the earlier part of the verse. One subject falsely located a lag in the first of the verse four times. Judgments as to the earlier part of the verse were uncertain and frequently changed.

The maximum lag possible without breaking the unity of the verse was determined for the earlier and later parts of the verse. The verse unity was tested by adding enough feet to make a full verse, after the break, and asking the subject to mark the close of the verse. In every case this irregularity was introduced into the second verse, and the first verse was normal, _e.g._ (pentameter),

I. 5 (34).
II. 34 lag 34 34 34 34 34.

If the lag does not break the verse, the subject should hear the close of the verse at the end of the fifth foot in II. If the verse is broken he should ignore the first foot and make a new verse, ending with the sixth foot.

J. Iamb. tet. 1st pause of verse, max. pos. lag 9
3d 7
L. 1st 9
3d 7
R. 1st 11
3d 9
G. 1st 9
3d 7
Mi. 1st 10
3d 8
B. 1st 7
H. 1st 10
3d 6

Later, in the attempt to determine natural divisions, or nodes in the verse, the following were determined:

L. Max. pos. lags in f. p. of iamb. pent. in order 8 13 9 6
G. 10 11 9 8
Mi. 15 18 17 14
Me. 7.5 13 9.5 6
R. 9 9 11 7
B. 12 8 15 7
H. 7.5 8 10 7

B. Max pos. lags in dac. let., cat., in order 12 16 8
S. 10 11 7
Mc. 7 10 6
G. 11 11 7
L. 19 16 7
H. 7 6 4

This shows that an irregularity in the time intervals may be greater in the earlier than in the later part of the verse. This last table is further evidence of the increased exactness of the rhythmic perception at the close of the verse. As far as nodes are concerned, they show clearly two types: (1) A node after the second foot (L., G., Mi., Mc.) and (2) a node after the third foot (R., B., H.). For the tetrameter there is some indication in the cases of B., S. and Mc., but the other cases are negative and further evidence is needed.

With three of the subjects, Mi., J. and K., it was not always possible to get records of the maximum lag, since it was impossible to define the verse unity. When this was unbroken it was the unanimous testimony of the subjects, corroborated by their unconscious movements, that there was a feeling of tension during the lag. But the subjects just referred to got a type of unity, and there was no tension. The lags were indefinite and very long (35-90). This unity must be of the same kind as the unity of the stanza, which includes long expressional pauses, as well as rhythmic verse pauses.

If a subject is asked to fall in at the beginning of a rhythmic series his first attempts are decidedly incoördinated. His earliest reactions follow the clicks which they are intended to represent, but presently the series of motor impulses generated by the sounds and the voluntary movements which the subject makes fuse into a voluntary type of reaction in which the cycle has become automatic and definite, and the clicks take their proper places as coöperating and controlling factors along with the motor cues of the process itself. The accuracy of the judgments of time, if such judgments be made, or the estimation of the likeness of the groups, depends on the definiteness with which movement sensations follow each other in a regular series.

The following experiments (Table I.) concern the perception of a lag in different parts not of a verse but of a stanza. It was a question, namely, whether a lag in the first rhythmic series (first verse) which establishes the motor cycle in the subject would be detected in the later rhythmic series (later verses of the stanza) after the motor cycle in the subject has been inaugurated. This responsive motor cycle should itself, of course, contain the lag given with the first rhythmic series.

A stanza of the form of A (Table I.) was clicked out by the instrument, but the subject had no clue as to the regularity or irregularity of any verse. The stanza was repeated as often as the subject wished, but not without a pause of a few moments between each repetition.

TABLE I.

THE INFLUENCE OF A LAG IN THE FIRST VERSE ON THE JUDGMENT OF IDENTICAL
LAGS IN LATER VERSES.

A. Stanza given: I. 34 34 35 34 p. 7-9
II. " " " " "
III. " " " " "

In 14 cases the following was reported:

I. Lag noted.
II. " not noted.
III. " " "

In 9 cases the following was reported:

I. Lag noted.
II. " " but shorter than first.
III. " " " " " "

In 6 cases the following was reported:

I. Lag noted.
II. " " and equal to first.
III. " " " " " "

B. Stanza given: I. 35 34 34 34 p. 7-9
II. " " " " "
III. " " " " "

Any pause large enough to be noted in I. was noted in II. and
III. (This table contains the judgments made on all trials.)

Most of the judgments of the third set are due to the fact that the subject first attended to the series on the second or third verse. The large number of cases (83 per cent.) in which the lags in the second and third verses were concealed by the equal lag in the first verse, makes it very probable that the type of a verse is somehow altered by the impression left by the preceding verse.

The method of determining the maximal lags (as previously described) gave interesting evidence on the point at which the unity of the verse is actually felt. In the form

I. 5 (34)
II. 34 lag 34 34 34 34-34

as the lag increases, a point is reached at which the unity may be made to include the first foot or to ignore it. Which of these is done depends on the subject's attitude, or _on the point at which the verse is brought to a close._ In either case the unity, the 'pentameter feeling,' is not experienced _until the end of the series unified is reached._ This is the case with all the subjects.

This development of the feeling of the particular verse form only at the end of the verse, and the fact that the subject may be uncertain which form he will hear until the series has actually ceased, shows that the verse-form movement is not of such a character that the close of it may not be considerably modified. A form which may fit the pentameter can be broken off early, and become a satisfactory tetrameter. The feeling seems to depend on some total effect of the verse at the close. This effect is probably a blending of the mass-effect of the impressions received thus far, which have a definite character and feeling significance, and which form the motor disposition for the next verse. The essential thing in the determination of verse unity seems to be the dying out of the automatism, the cessation of the coördination of the cyclic movement. The rhyme, it would seem, emphasizes the close of the automatic cycle. But it is probable that satisfactory phrasing has other characteristics, and a definite form as a movement whole.

_2. The Relation of the Rhyme to the Verse Pause._

Determinations of the minimal satisfactory verse pause were made with a view to comparing the minimum in unrhymed with that in rhymed verses.

The stanza used was of the following form:

I. 34 34 34 p.
II. " " " "
III. " " " "

The minimal satisfactory verse pauses were:

Without Rhyme. With Rhyme.
Subject. L. 6 4
" J. 5 4
" Mc. 6 4
" R. 7 4
" B. 6-7 3.5
" G. 6 3.5
" Mi. 6-7 3.25

It thus appears that the minimal pause which is satisfactory, is less when rhyme is present than when it is not present. Similar determinations were made for the maximal satisfactory verse pauses, as follows:

Without Rhyme. With Rhyme.
Subject. L. 9-10 11
" J. 8 9
" Mc. 9 9
" R. 10-11 10-11
" B. 9 9
" G. 11-12 11
" Mi. 10 10

(A few experiments were tried with verse pauses of different length in the same stanza. A difference of one fourth the value of the pause is not detected, and unless attention is called to them, the pauses may vary widely from one another.)

This shows that the rhyme reduces the _necessary_ pause in verse to the mere foot pause; while at the same time as great a pause is _possible_ with rhyme as without it. Aside from the table above, a large number of the records made for other purposes support this statement: whenever rhyme was introduced, the verse pause was made equal to the foot pause, or even slightly less than it, and was always found satisfactory.

Numerous cases of introduction of lags into the verses of rhymed stanzas go to show that irregularities in such verses do not affect the length of the pauses.