TABLE XVIII.

Subject.           Ratio. 
J.           1.000:1.042
K.           1.000:1.025
N.           1.000:1.010

It is perhaps significant that the extent of this differentiation—­and inferably the definition of rhythmical synthesis—­corresponds to the reported musical aptitudes of the subjects; J. is musically trained, K. is fond of music but little trained, N. is without musical inclination.

The relations of these larger rhythmical series repeat those of their constituent groups—­the first is shorter, the second longer.  The two sets of ratios are brought together for comparison in the annexed table: 

TABLE XIX.

Subject.    Unit-Groups.   Five Groups. 
J.      1.000:1.354   1.000:1.042
K.      1.000:1.388   1.000:1.025
N.      1.000:1.326   1.000:1.010

It is to be noted here, as in the case of beating out specific rhythms, that the index of differentiation is greater in simple than in complex groups, the ratios for all subjects being, in simple groups, 1.000:1.356, and in series of five, 1.000:1.026.

There is thus present in the process of mechanically accompanying a series of regularly recurring auditory stimuli a complex rhythmization in the forms, first, of a differentiation of alternate intervals, and secondly, of a synthesis of these in larger structures, a process here traced to the third degree, but which may very well extend to the composition of still more comprehensive groups.  The process of reaction is permeated through and through by rhythmical differentiation of phases, in which the feeling for unity and equivalence must hold fast through really vast periods as the long slow phases swing back and forth, upon which takes place a swift and yet swifter oscillation of rhythmical values as the unit groups become more limited, until the opposition of single elements is reached.

III.  THE CHARACTERISTICS OF THE RHYTHMICAL UNIT.

A. The Number of Elements in the Group and its Limits.

The number of elements which the rhythmical group contains is related, in the first place, to the rate of succession among the elements of the sequence.  This connection has already been discussed in so far as it bears on the forms of grouping which appear in an undifferentiated series of sounds in consequence of variations in the absolute magnitude of the intervals which separate the successive stimuli.  In such a case the number of elements which enter into the unit depends solely on the rate of succession.  The unit presents a continuous series of changes from the lowest to the highest number of constituents which the simple group can possibly contain, and the synthesis of elements itself changes from a succession of simple forms to structures involving complex subordination of the third and even fourth degree, without other change in the objective series than variations in tempo.