TABLE LXVIII.

Stress. First Half. Second Half Initial, 1.000 0.794 Median, 1.000 0.668 Final, 1.000 0.770

These 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 coordination 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 coordination between the periods of the whole group takes place in pa.s.sing 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 0.846 Median, 1.000 1.064 Final, 1.000 0.742

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 const.i.tuent 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 a.n.a.logous 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 coordination 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 coordination the aesthetic value of the rhythm depends.

In general, though not so unequivocally, the four-beat rhythms show a progressive increase of stability in pa.s.sing 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 coordination. Training affects more readily the single element than the composite measure, and in the most highly coordinated 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 pa.s.s 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: