The temporal conditions of such equilibrium are a strict function of the degree of accentuation which the rhythm group presents. The location of the indifference point must, therefore be independently determined for each intensive value through which the accented element may pass. Its changes are given for five such increments in the following table, in which the values of the various intervals are represented as proportions of the absolute magnitudes which appear in the first, or undifferentiated series.
TABLE LII.
| Intensive Form. | 1st Interval. | 2d Interval. | 3d Interval. | ||
|---|---|---|---|---|---|
| 1/8 | 1/8 | 1/8 | 1.000 | 1.000 | 1.000 |
| 3/8 | 1/8 | 1/8 | 1.042 | 1.010 | 0.948 |
| 7/8 | 1/8 | 1/8 | 1.142 | 1.021 | 0.862 |
| 15/8 | 1/8 | 1/8 | 1.146 | 1.042 | 0.808 |
| 24/8 | 1/8 | 1/8 | 1.291 | 1.000 | 0.708 |
IV. THE COMBINATION OF RHYTHMICAL GROUPS IN HIGHER SYNTHESES AND THEIR EQUIVALENCES.
In the elaboration of higher rhythmical forms the combination of formally identical groups is rather the rule than the exception, since in poetical structures the definition of the metrical form and the maintenance of its proper relations depend on a clear preponderance of its own particular unit-type over local variants. In the experimental investigation of composite rhythm forms the temporal relations of structures presenting such likeness in their constituent groups were first taken up. In the conduct of the research those differences of intensity which are actually expressed and apprehended in the utterance of a rhythmic sequence were uniformly employed. While there is no doubt that a succession of perfectly identical forms would, under the requisite temporal conditions, be apprehended as presenting major and minor phases of accentuation, yet in the expression of rhythmic relations the subordination of accents is consistently observed, and all our ordinary apprehension of rhythm, therefore, is supported by an objective configuration which fulfils already the form of our own subjective interpretation.
The temporal relations of these major and minor phases cannot be considered apart from the index of their respective accentuations. As the distribution of elements within the simple group fluctuates with the changes in intensive accentuation, so does the form of temporal succession in larger structures depend on the relations of intensity in their primary and secondary accentuations. The quantitative values hereafter given apply, therefore, only to those specific intensities involved in the experiment. Two types were chosen, the trochee and the dactyl. The series of sounds was given by successive hammer-falls of 7/8 and 1/8 inch for the major, and 3/8 and 1/8 inch for the minor phase. The distribution of time-values within each group was made on the basis of previous experimentation to determine those relations which support psychological uniformity. These internal relations were maintained unchanged throughout the series of ratios which the durations of the two groups presented. Four subjects took part in the experiment. The quantitative results in the composition of trochaic forms are given in the following tables (LIII., LIV.), the figures of which present, in the form of percentages of total judgments, the apprehension of sensible equality or disparity in the two groups.
In the earlier set of experiments the series of ratios diverged in both directions from unity; in the later it departed in one only, since every divergence in the opposite direction had, in the previous experiments, been remarked at once by the observer. In this second set the series of differences is more finely graded than in the former; otherwise the two sets of figures may be considered identical. Using the equilibrium of errors as an index of sensible equality, the two trochaic groups are perceptually uniform when the temporal ratio of major and minor lies between 1.000:0.757 and 1.000:0.779.
TABLE LIII.
| Ratio of Duration of 1st Group to 2d. | 2d Group Judged to be | |||||
|---|---|---|---|---|---|---|
| + | = | - | ||||
| 1.000 : 1.250 | 100 | per cent. | ||||
| 1.000 : 1.116 | 100 | " | ||||
| 1.000 : 1.057 | 100 | " | ||||
| 1.000 : 1.000 | 100 | " | ||||
| 1.000 : 0.895 | 68 | " | 22 | per cent. | ||
| 1.000 : 0.800 | 25 | " | 75 | " | ||
| 1.000 : 0.714 | 100 per cent. | |||||
| Ratio of Duration of 1st Group to 2d. | 2d Group Judged to be | |||||
|---|---|---|---|---|---|---|
| + | = | - | ||||
| 1.000 : 1.000 | 100.0 | per cent. | ||||
| 1.000 : 0.973 | 87.5 | " | 12.5 | per cent. | ||
| 1.000 : 0.870 | 66.6 | " | 33.3 | " | ||
| 1.000 : 0.823 | 33.3 | " | 22.2 | " | 44.4 | per cent. |
| 1.000 : 0.777 | 50.0 | " | 50.0 | " | ||
| 1.000 : 0.735 | 33.3 | " | 33.3 | " | 33.3 | " |
| 1.000 : 0.694 | 33.3 | " | 66.6 | " | ||