In the present instance two reactions are made, a pause follows, then the reactions take place again, and so on. The intervals separating successive groups of reactions thus result from the coalescence of two periods, the interval which would regularly follow the reaction and the additional pause at its close. The value of the latter I interpret as functionally equivalent to a group of two beats and not to a single interval; that is, the rhythm beaten out is essentially quadruple, the second member of each composite group being suppressed, as follows:
.
To estimate the proper value of such a rest the average relative duration of first and second intervals was taken in a continuous series of two-beat measures, in which the first member was accented sufficiently to define the rhythmical groups. The ratio was 1.000:0.760. In the present instance the values of the simple initial interval and the composite interval which follows it are, in terms of the linear measurement, 1.55 mm. and 3.96 mm. Assuming the above ratio to hold, the duration of a period which included the second beat-interval and a group-rest should be 1.16 + 1.55 + 1.16 = 3.87 mm. This is slightly less than the actual value of the period, whereas it should be greater. It must be remembered, however, that the disparity between the two intervals increases with initial accentuation, and in consequence the proportional amounts here added for the second interval (1.16 to 1.55) should be greater. This interval is not rhythmically 'dead' or insensitive. The index of mean variation in all reactors is greater for the first than for the second interval (or interval + pause) in the ratio 1.000:0.436, that is, the value of the latter is more clearly defined than that of the former, and the reactor doubly sensitive to variations occurring within it.
An analysis of the variations of these intervals separately in series of four groups reveals a secondary reciprocal rhythm, in which the changes in value of the mean variation at any moment are in opposite directions in the two intervals. These values in percentages of the total duration of the periods are given in the following table.
TABLE LXI.
| Interval. | 1st Group. | 2d. Group. | 3d Group. | 4th Group. | ||||
|---|---|---|---|---|---|---|---|---|
| First, | 15.4 | per cent. | 26.4 | per cent. | 13.8 | per cent. | 30.3 | per cent. |
| Second, | 12.4 | " | 7.0 | " | 9.6 | " | 7.5 | " |
Without measurement of their intensive values, interpretation of these variations is speculative. They indicate that the pairs of beats are combined in higher groups of four; that the differences of mean variation in the first interval are functions of an alternating major and minor accentuation, the former occurring in the second and fourth, the latter in the first and third; and that the inversely varying values of the mean variation in the second interval are functions of the division into minor and major groups, the reduced values of the second and fourth of these intervals being characteristic of the greater sensitiveness to variations occurring in the group pause than to changes occurring within the group.
The fixity of the group is markedly greater than that of the simple interval. In the one case in which the mean variation of the group is greater than that of the elementary period the material involved was meager (five instead of ten repetitions) and the discrepancy therefore insignificant.
The difference in the mean variation of the first and second intervals respectively rises to an individual maximum of 3.000:1.000, and averages for all subjects 2.290:1.000; the fixity, that is to say, of the inter-group interval in this form of tapping is more than twice as great as that of the intra-group interval. The fixity of the larger rhythmical quantities is greater than that of the smaller, whether the relation be between the elementary interval and the unit group, or between the synthetic unit and its higher composite. The average mean variation of the beat intervals exceeds that of the whole group in the relation of 1.953:1.000. The differentiation of larger and smaller groups is less clear. When the material is taken in groups of eight successive beats the mean variation is less in the case of every subject than when taken in fours, in the ratio 1.000:1.521. The comparative values for groups of two and four beats is reversed in two thirds of the cases, yet so that an average for all subjects gives the ratio 1.000:1.066 between groups of four and two beats. The whole series of values arranged on the basis of unity for the mean variation of the beat interval is given in Table LXII.