TABLE VIII.

(_b_) First and Second Halves of the Preceding Combined in Series of Five.

Subject. I II III IV V J. 1.058 1.031 1.041 1.054 1.048 K. 1.043 1.050 1.076 1.102 1.082 N. 0.990 1.025 1.051 1.028 1.024

Aver. 1.030 1.035 1.056 1.061 1.051

TABLE IX.

AVERAGES OF ALL RATES AND SUBJECTS ACCORDING TO PHASES OF METRONOME.

(_a_) In Series of Ten Successive Reactions in Accompaniment of Each Phase.

Phase. I II III IV V VI VII VIII IX X First, 1.000 1.055 1.102 1.097 1.082 1.066 1.053 1.123 1.120 1.074 Second, 1.000 0.988 0.992 1.007 1.016 1.055 1.015 1.009 1.024 1.001

TABLE X.

(_b_) First and Second Halves of the Preceding Combined in Series of Five.

Phase. I II III IV V First, 1.033 1.054 1.112 1.108 1.078 Second, 1.027 1.001 1.000 1.015 1.008

TABLE XI.

AVERAGES OF ALL SUBJECTS ACCORDING TO RATES AND PHASES OF METRONOME.

(_a_) First Phase, Series of Ten Successive Reactions.

Rate. _I II III IV V VI VII VIII IX X_ 60 1.000 1.168 1.239 1.269 1.237 1.209 1.265 1.243 1.237 1.229 90 1.000 1.048 1.063 1.095 1.086 1.069 1.102 1.127 1.168 1.095 120 1.000 1.004 0.942 1.043 1.057 0.978 0.949 1.065 1.065 0.967

TABLE XII.

(_b_) Second Phase, Series of Ten Successive Reactions.

Rate. I II III IV V VI VII VIII IX X 60 1.000 0.963 0.942 0.947 1.009 0.695 0.993 0.995 1.023 0.996 90 1.000 0.893 0.987 1.018 1.036 1.005 0.995 1.000 0.977 1.000 120 1.000 1.000 0.990 1.048 1.040 1.007 0.986 1.030 1.037 0.962

TABLE XIII.

AVERAGES OF ALL SUBJECTS AND BOTH PHASES OF METRONOME ACCORDING TO RATES.

(_a_) In Series of Ten.

Rate. I II III IV V VI VII VIII IX X 60 1.000 1.065 1.140 1.108 1.123 0.952 1.129 1.119 1.130 1.112 90 1.000 0.970 1.025 1.056 1.061 1.037 1.048 1.063 1.072 1.047 120 1.000 1.000 0.990 1.048 1.040 1.007 0.986 1.030 1.037 0.962

TABLE XIV.

(_b_) Above Combined in Series of Five.

Rate. I II III IV V 60 0.976 1.097 1.129 1.119 1.117 90 1.018 1.009 1.044 1.059 1.054 120 1.003 0.993 1.010 1.042 1.001

In the following table (XV.) is presented the average proportional duration of the intervals separating the successive reactions of these subjects to the stimulations given by the alternate swing and return of the pendulum.

TABLE XV.

Subject. Rate: 60. Rate: 90. Rate: 120.

B. 0.744 : 1.000 0.870 : 1.000 0.773 : 1.000 J. 0.730 : 1.000 0.737 : 1.000 0.748 : 1.000 K. 0.696 : 1.000 0.728 : 1.000 0.737 : 1.000 N. 0.526 : 1.000 0.844 : 1.000 0.893 : 1.000

The corresponding intensive values, as measured by the excursion of the recording pen, are as follows:

TABLE XVI.

Subject. Rate: 60. Rate: 90. Rate: 120.

B. (1.066 : 1.000) 0.918 : 1.000 (1.010 : 1.000) J. 0.938 : 1.000 0.943 : 1.000 0.946 : 1.000 K. 0.970 : 1.000 0.949 : 1.000 (1.034 : 1.000) N. 0.883 : 1.000 0.900 : 1.000 0.950 : 1.000

These figures present a double process of rhythmic differentiation, intensively into stronger and weaker beats, and temporally into longer and shorter intervals. The accentuation of alternate elements has an objective provocative in the qualitative unlikeness of the ticks given by the swing and return of the pendulum. This phase is, however, neither so clearly marked nor so constant as the temporal grouping of the reactions. In three cases the accent swings over to the shorter interval, which, according to the report of the subjects, formed the initial member of the group when such grouping came to subjective notice. This latter tendency appears most p.r.o.nounced at the fastest rate of reaction, and perhaps indicates a tendency at rapid tempos to prefer trochaic forms of rhythm. In temporal grouping the coordination of results with the succession of rates presents an exception only in the case of one subject (XV. B, Rate 120), and the various observers form a series in which the rhythmizing tendency becomes more and more p.r.o.nounced.

Combining the reactions of the various subjects, the average for all shows an accentuation of the longer interval, as follows:

TABLE XVII.

Rate. Temp. Diff. Intens. Diff.

60 0.674 : 1.000 0.714 : 1.000 90 0.795 : 1.000 0.927 : 1.000 120 0.788 : 1.000 0.985 : 1.000

The rhythmical differentiation of phases is greatest at the slowest tempo included in the series, namely, one beat per second, and it declines as the rate of succession increases. It is impossible from this curve to say, however, that the subjective rhythmization of uniform material becomes more p.r.o.nounced in proportion as the intervals between the successive stimulations increase. Below a certain rapidity the series of sounds fails wholly to provoke the rhythmizing tendency; and it is conceivable that a change in the direction of the curve may occur at a point beyond the limits included within these data.

The introduction from time to time of a single extra tap, with the effect of transposing the relations of the motor accompaniment to the phases of the metronome, has been here interpreted as arising from a periodically recurring adjustment of the reaction process to the auditory series which it accompanies, and from which it has gradually diverged. The departure is in the form of a slow r.e.t.a.r.dation, the return is a swift acceleration. The r.e.t.a.r.dation does not always continue until a point is reached at which a beat is dropped from, or an extra one introduced into, the series. In the course of a set of reactions which presents no interpolation of extra-serial beats periodic r.e.t.a.r.dation and acceleration of the tapping take place. This tertiary rhythm, superimposed on the differentiation of simple phases, has, as regards the forms involved in the present experiments, a period of ten single beats or five measures.

From the fact that this rhythm recurs again and again without the introduction of an extra-serial beat it is possible to infer the relation of its alternate phases to the actual rate of the metronome.

Since the most rapid succession included was two beats per second, it is hardly conceivable that the reactor lost count of the beats in the course of his tapping. If, therefore, the motor series in general parallels the auditory, the r.e.t.a.r.dations below the actual metronome rate must be compensated by periods of acceleration above it. Regarded in this light it becomes questionable if what has been called the process of readjustment really represents an effort to restore an equilibrium between motor and auditory processes after an involuntary divergence. I believe the contrasting phases are fundamental, and that the changes represent a free, rhythmical accompaniment of the objective periods, which themselves involve no such recurrent differentiation.

Of the existence of higher rhythmic forms evidence will be afforded by a comparison of the total durations of the first and second five-groups included in the decimal series. Difference of some kind is of course to be looked for; equivalence between the groups would only be accidental, and inequality, apart from amount and constancy, is insignificant. In the results here presented the differentiation is, in the first place, of considerable value, the average duration of the first of these groups bearing to the second the relation of 1.000:1.028.

Secondly, this differentiation in the time-values of the respective groups is constant for all the subjects partic.i.p.ating. The ratios in their several cases are annexed:

TABLE XVIII.