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 participating. The ratios in their several cases are annexed: 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._