| Ratio of A to Other Intervals. | B | A | Errors | Total judgts. | Per cent. of errors | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| + | = | - | + | = | - | B | A | T | |||
| 1.000 : 0.625 | 2 | 2 | 2 | 4 | 2 | 0 | 4 | 2 | 6 | 12 | 50 |
| 1.000 : 0.666 | 4 | 2 | 0 | 1 | 3 | 2 | 4 | 5 | 9 | 12 | 75 |
| 1.009 : 0.714 | 5 | 3 | 0 | 2 | 2 | 4 | 5 | 6 | 11 | 16 | 69 |
| 1.000 : 0.770 | 5 | 4 | 0 | 1 | 1 | 7 | 5 | 8 | 13 | 18 | 72 |
| 1.000 : 0.833 | 1 | 5 | 0 | 0 | 0 | 6 | 1 | 6 | 7 | 12 | 50 |
| Totals, | 17 | 16 | 2 | 8 | 8 | 19 | 19 | 27 | 46 | 70 | |
The value of the interval following the louder sound is correctly reported eight times out of thirty; that preceding it is correctly reported sixteen times out of thirty. The influence which such a change in intensive value introduced at a single point in a series of sounds exerts on the apparent relation of its adjacent intervals to those of the remainder of the series is not equally distributed between that which precedes and that which follows it, but affects the latter more frequently than the former in a ratio (allowing latitude for future correction) of 2:1. In the case of interval A the error is one of underestimation in twenty-seven cases; in none is it an error of overestimation. In the case of interval B the error is one of overestimation in seventeen instances, of underestimation in two. The influence of the introduction of such a louder sound, therefore, is to cause a decrease in the apparent duration of the interval which follows it, and an increase in that of the interval which precedes it. The illusion is more pronounced and invariable in the case of the interval following the louder sound than of that preceding it, the proportion of such characteristic misinterpretations to the whole number of judgments in the two cases being, for A, 77 per cent.; for B, 54 per cent. The effect on interval A is very strong. In the second group, where the ratio of this interval to the others of the series is 3:2, it is still judged to be equal to these others in 50 per cent. of the cases, and less in 35 per cent. Further, these figures do not give exhaustive expression to the whole number of errors which may be represented in the judgments recorded, since no account is taken of greater and less but only of change of sign; and an interval might be underestimated and still be reported greater than the remaining intervals of the series in a group of experiments in which the relation of the interval in question to these remaining intervals ranged from the neighborhood of equivalent values to that in which one was double the other. If in a rough way a quantitative valuation of errors be introduced by making a transference from any one sign to that adjacent to it (e. g., - to =, or = to +) equal to one, and that from one extreme sign to the other equal to two, the difference in the influence exerted on the two intervals will become still more evident, since the errors will then have the total (quantitative) values of A 46, and B 19, or ratio of 1.000:0.413.
Next, the position of the louder sound in the series of six was changed, all other conditions being maintained uniform throughout the set of experiments. The series of intervals bore the following relative values: A, 0.900; B, 1.100; all other intervals, 1.000. The louder sound was produced by a fall of 0.875 inch; all others by a fall of 0.250 inch. The louder sound occurred successively in the first, second, third, fourth and fifth positions of the series. In the first of these forms it must of course be remembered that no interval B exists. The results of the experiment are shown in the following table:
TABLE XXIX.
| Position in series | Apparent Values. | Errors. | % of Errors in tot. judg. | Ditto quant. | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B | A | B | A | T | |||||||||
| + | = | - | + | = | - | B | A | B | A | ||||
| 1 | 2 | 6 | 6 | 0 | 12 | 12 | 85.7 | 85.7 | |||||
| 2 | 2 | 8 | 2 | 1 | 7 | 4 | 10 | 11 | 21 | 83.3 | 91.6 | 73.3 | 91.6 |
| 3 | 1 | 9 | 3 | 1 | 8 | 3 | 10 | 11 | 21 | 76.9 | 91.6 | 71.9 | 91.6 |
| 4 | 1 | 8 | 4 | 2 | 6 | 5 | 9 | 11 | 20 | 69.2 | 84.6 | 52.8 | 84.6 |
| 5 | 0 | 12 | 0 | 0 | 4 | 8 | 12 | 12 | 24 | 100.0 | 100.0 | 60.0 | 100.0 |
| Totals, | 4 | 37 | 9 | 6 | 31 | 26 | 41 | 57 | 98 | 82.3 | 90.7 | 64.5 | 90.7 |
Total judgments, 113; Errors (B = 31), A = 57.
The relatively meager results set forth in the preceding section are corroborated in the present set of experiments. That such a variation of intensity introduced into an otherwise undifferentiated auditory series, while it affects the time-values of both preceding and following intervals, has a much greater influence on the latter than on the former, is as apparent here as in the previous test. The number of errors, irrespective of extent, for the two intervals are: B, 82.3 per cent, of total judgments; A, 90.7 per cent. When the mean and extreme sign displacements are estimated on the quantitative basis given above these percentages become B, 64.5; A, 90.7, respectively—a ratio of 0.711:1.000.
The direction of error, likewise, is the same as in the preceding section. Since the actual values of the two intervals here are throughout of extreme sign—one always greater, the other always less—only errors which lie in a single direction are discriminable. Illusions lying in this direction will be clearly exhibited, since the differences of interval introduced are in every case above the threshold of discrimination when the disturbing element of variations in intensity has been removed and the series of sounds made intensively uniform. In case of a tendency to underestimate B or overestimate A, errors would not be shown. This problem, however, is not to be met here, as the results show; for there is recorded a proportion of 82.3 per cent. of errors in judgment of interval B, and of 90.7 per cent. in judgment of interval A, all the former being errors of overestimation, all of the latter of underestimation.
The influence of position in the series on the effect exerted by such a change of intensity in a single member can be stated only tentatively. The number of experiments with the louder sound in position five was smaller than in the other cases, and the relation which there appears cannot be absolutely maintained. It may be also that the number of intervals following that concerning which judgment is to be given, and with which that interval may be compared, has an influence on the accuracy of the judgment made. If we abstract from this last set of results, the tendency which appears is toward an increase in accuracy of perception of comparative durations from the beginning to the end of the series, a tendency which appears more markedly in the relations of the interval preceding the louder sound than in those of the interval which follows it. This conclusion is based on the succession of values which the proportion of errors to total judgments presents, as in the annexed table.