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.
| Number of Beats. | Intervals. | Groups. | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Acc. | Unacc. | Av. 1st Half. | 2d Half. | 1st Half. | 2d Half. | Average. | Total. | |||||||||
| 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.