Harvard Psychological Studies Part 44

In the amphibrachic form the changes manifested by the const.i.tuents of the unit group are more obscure. No progressive r.e.t.a.r.dation of the accented element is apparent. In the initial and final intervals the difference in duration between the first and last members of the series is small and appears early in the process. If we a.s.sume the general application of the laws of change presented in the preceding section, there should be here two influences concerned in the determination of the relations presented, the factors, namely, of position and accent. The falling of the accentual stress on the median interval eliminates one of the two factors of progressive reduction in that element and replaces it by a factor of increase, thereby doing away with the curve of change; while at the same time it decreases the changes which occur in the bounding intervals of the group by removing the accent from the first and by the proximate position of its own accent tending to reduce the last interval.

Under this same a.s.sumption there should be expected in the anapaestic form of rhythm an exaggeration of the progressive increase in the final interval, together with a further reduction in the duration of the initial; since from the falling of the accent on the final interval two factors of increase combine, while in the initial, which immediately follows the accented interval in the series, a positive factor of reduction appears. This is actually the type of change presented by the quant.i.tative relations, which are given as proportional values in the following table.

TABLE XLI.

Interval. I II III IV V VI VII VIII IX X First, 1.000 0.950 1.000 0.950 1.000 0.950 1.000 1.000 1.000 1.050 Second, 1.000 1.100 1.000 1.050 1.100 1.000 1.000 1.050 1.100 1.000 Third, 1.000 1.073 1.073 1.024 1.024 1.122 1.098 1.098 1.098 1.146

Between its first and last terms the first interval shows a departure slightly less than that of the previous rhythm from the rate of change which characterizes the dactylic type; but if the average values of the whole series of intervals be taken in each of the three cases, the progressive reduction will be seen clearly to continue in pa.s.sing from the second to the third form. The figures annexed give these averages as proportions of the first interval in the series.

TABLE XLII.

1st Av. of Rhythm. Interv. all others.

Dactylic, 1.000 : 1.188 Amphibrachic, 1.000 : 1.019 Anapaestic, 1.000 : 1.000

The relations of the various intervals in the three forms are put together here for comparison:

TABLE XLIII.

Rhythm. 1st Interval. 2d Interval. 3d Interval.

Dactylic, 1.000 : 1.231 1.000 : 1.000 1.000 : 1.066 Amphibrachic, 1.000 : 1.045 1.000 : 1.000 1.000 : 1.054 Anapaestic, 1.000 : 1.050 1.000 : 1.000 1.000 : 1.146

An a.n.a.lysis of the factors of accentual stress and of position in the rhythmical group in isolation from each other, confirms the a.s.sumptions already made as to their influence in defining the form of the rhythmic unit. Table XLIV. exhibits the series of temporal changes taking place in accented and unaccented intervals, respectively, for the three forms combined, and therefore independent of position in the group.

TABLE XLIV.

Interval. I II III IV V VI VII VIII IX X Accented. 1.000 1.064 1.064 1.064 1.064 1.094 1.094 1.064 1.094 1.129 Unaccented, 1.000 1.000 1.000 1.080 1.040 1.040 1.040 1.040 1.040 1.040

Similarly, in Table XLV. are given the proportional values of the series of intervals in order of their position in the group and independent of accentual stress:

TABLE XLV.

Interval. I II III IV V VI VII VIII IX X First, 1.000 1.043 1.087 1.043 1.087 1.043 1.043 1.121 1.043 1.121 Second, 1.000 1.000 1.000 1.043 1.000 0.956 1.000 0.956 1.000 0.956 Third, 1.000 1.028 1.028 1.055 1.028 1.083 1.083 1.083 1.083 1.083

The former table makes clear the predominance of the increase in the accented element over the average of all unaccented elements of the series; the latter shows the independence of increase in the initial and final, and of decrease in the median interval, of any relation to the position of the accentual stress. Both the intensive accentuation and the demarcation of successive groups thus appear to be factors of definition in the rhythmic unit. Those types which are either marked by a more forcible accent or separated by longer pauses are more distinctly apprehended and more easily held together than those in which the accent is weaker or the pause relatively less. It would follow that the general set of changes which these series of reactions present are factors of a process of definition in the rhythmical treatment of the tapping, and are not due to any progressive change in the elementary time relations of the series.

The figures for measures of four beats are incomplete. They show an increase in the average duration of the group from first to last of the series in three out of the four forms, namely, those having initial, secondary and final stress.

Of the relative amounts contributed by the several elements to the total progressive variation of the measures in the first form, the least marks those intervals which follow unaccented beats, the greatest those which follow accented beats; among the latter, that shows the greater increase which receives the primary accent, that on which falls the secondary, subconscious accent shows the less; and of the two subgroups which contain these accents that in which the major accent occurs contributes much more largely to the progressive change than does that which contains the minor.

When the phases of accented and unaccented elements are compared, irrespective of their position in the rhythmic group, the same functional differences are found to exist as in the case of triple rhythms. Their quant.i.tative relations are given in the following table.

TABLE XLVI.

Phase. I II III IV V VI VII VIII IX X Accented. 1.000 1.103 1.069 1.172 1.241 1.139 1.206 1.310 1.241 1.310 Unacc., 1.000 1.083 1.128 1.169 1.159 1.208 1.169 1.250 1.169 1.169

The cause of the apparent r.e.t.a.r.dation lies, as before, in a change occurring primarily in the accented elements of the rhythm, and this progressive differentiation, it is inferable from the results cited above, affects adjacent unaccented elements as well, the whole const.i.tuting a process more naturally interpretable as a functional accompaniment of progressive definition in the rhythmical treatment of the material than as a mark of primary temporal r.e.t.a.r.dation.

The contribution of the several intervals according to position in the series and irrespective of accentual stress is given in the table following.

TABLE XLVII.

Interval. I II III IV V VI VII VIII IX X First, 1.000 1.136 1.136 1.182 1.227 1.227 1.227 1.273 1.318 1.318 Second, 1.000 1.042 1.042 1.125 1.166 1.042 1.042 1.083 1.083 1.166 Third, 1.000 1.150 1.250 1.250 1.250 1.250 1.400 1.400 1.450 1.450 Fourth, 1.000 1.059 1.059 1.147 1.179 1.147 1.179 1.294 1.206 1.179

A rhythmical alternation is here presented, the contributions of the first and third elements being far in advance of those of the second and fourth. The values of the minor pair are almost equal; of the major the third exceeds the first. Under the a.s.sumption already made this would indicate the existence at these points of nodes of natural accentuation, of which the second marks the maximum reached in the present series.

The determination of relative time-values for accented and unaccented intervals was next sought by indirect experimentation, in which the affective aspect of the experience was eliminated from consideration, and account was taken only of the perception of quant.i.tative variations in the duration of the successive intervals. Proceeding from the well-known observation that if every alternate element of a temporally uniform auditory series receive increased stress, the whole series will coalesce into successive groups of two elements in which the louder sound precedes and the weaker follows, while the interval which succeeds the unaccented sound, and which therefore separates adjacent groups, will appear of greater duration than that which follows the accented element, the investigation sought by employing the method of right and wrong cases with a series of changing time-values for the two intervals to determine the quant.i.tative proportion of the two durations necessary to produce the impression of temporal uniformity in the series.

Two rhythm forms only were tested, the trochaic and dactylic, since without an actual prolongation of considerable value in the interval following the louder sound, at the outset, no apprehension of the series as iambic or anapaestic could be brought about. The stimuli were given by mechanism number 4, the distance of fall being 2/8 and 7/8 inch respectively for unaccented and accented sounds. The series of changes included extreme proportional values of 0.714 and 1.769 in duration of the two intervals. Six persons took part in the investigation. In the following table is given the percentage of cases in which the interval following the unaccented element was judged respectively greater than, equal to, or less than that which followed the accented element, for each of the series of ratios presented by the time-values of the intervals in trochaic rhythm.

TABLE XLIX.

Ration of Unaccented to Unaccented Interval Judged to be Accented Interval. + = - 1.000 : 1.769 0.0 per cent. 100.0 per cent 0.0 per cent.

1.000 : 1.571 12.5 " 50.0 " 37.5 "

1.000 : 1.400 22.0 " 56.0 " 22.0 "

1.000 : 1.222 16.0 " 84.0 "

1.000 : 1.118 26.0 " 74.0 "

1.000 : 1.000 61.6 " 38.4 "

1.000 : 0.895 100.0 "

1.000 : 0.800 88.8 " 11.2 "

1.000 : 0.714 100.0 "

The anomalous percentage which appears in the first horizontal row needs explanation. The limit of possible differentiation in the time-values of accented and unaccented intervals in a rhythmical group is characteristically manifested, not by the rise of a perception of the greater duration of the interval following the accented element, but through an inversion of the rhythmical figure, the original trochee disappearing and giving place to an iambic form of grouping, the dactyl being replaced by an anapaest. In the case in question the inversion had taken place for all subjects but one, in whom the original trochaic form, together with its typical distribution of intervals, remained unchanged even with such a great actual disparity as is here involved.

For this group of observers and for the series of intensities taken account of in the present experiment, the distribution of time-values necessary to support psychological uniformity lies near to the ratio 1.400:1.000 for accented and unaccented intervals respectively, since here the distribution of errors in judgment is arranged symmetrically about the indifference point. Overestimation of the interval following the louder sound appears by no means invariable. Under conditions of objective uniformity the judgment of equality was given in 38.4 per cent, of all cases. This cannot be baldly interpreted as a persistence of the capacity for correct estimation of the time values of the two intervals in the presence of an appreciation of the series as a rhythmical group. The rhythmic integration of the stimuli is weakest when the intervals separating them are uniform, and since the question asked of the observer was invariably as to the apparent relative duration of the two intervals, it may well be conceived that the hearers lapsed from a rhythmical apprehension of the stimuli in these cases, and regarded the successive intervals in isolation from one another. The illusions of judgment which appear in these experiences are essentially dependent on an apprehension of the series of sounds in the form of rhythmical groups. So long as that att.i.tude obtains it is absolutely impossible to make impartial comparison of the duration of successive intervals. The group is a unit which cannot be a.n.a.lyzed while it continues to be apprehended as part of a rhythmical sequence.

We should expect to find, were observation possible, a solution of continuity in the rhythmical apprehension in every case in which these distortions of the normal rhythm form are forced on the attention.

This solution appears tardily. If the observer be required to estimate critically the values of the successive intervals, the attention from the outset is turned away from the rhythmical grouping and directed on each interval as it appears. When this att.i.tude prevails very small differences in duration are recognized (_e.g._, those of 1.000:1.118, and 1.000:0.895). But when this is not the case, the changes of relative duration, if not too great for the limits of adaptation, are absorbed by the rhythmical formula and pa.s.s un.o.bserved, while variations which overstep these limits appear in consciousness only as the emergence of a new rhythmic figure. Such inversions are not wholly restricted by the necessity of maintaining the coincidence of accentuation with objective stress. With the relatively great differences involved in the present set of experiments, the rhythmical forms which appeared ignored often the objective accentuation of single groups and of longer series. Thus, if the second interval of a dactyl were lengthened the unaccented element which preceded it received accentuation, while the actual stress on the first sound of the group pa.s.sed un.o.bserved; and in a complex series of twelve hammer-strokes the whole system of accentuation might be transposed in the hearer's consciousness by variations in the duration of certain intervals, or even by simple increase or decrease in the rate of succession.[6]

[6] Bolton found one subject apperceiving in four-beat groups a series of sounds in which increased stress fell only on every sixth.

In the experiments on dactylic rhythm the changes introduced affected the initial and final intervals only, the one being diminished in proportion as the other was increased, so that the total duration of the group remained constant. The figures, arranged as in the preceding table, are given in Table L.

The percentage given in the case of the highest ratio is based on the reports of two subjects only, one of them the exceptional observer commented on in connection with two-beat rhythms; for all other partic.i.p.ants the anapaestic form had already replaced the dactylic. The distribution of values which supports psychological uniformity in this rhythmic figure lies between the ratios 1.166, 1.000, 0.800, and 1.250, 1.000, 0.755, since in this region the proportion of errors in judgment on either side becomes inverted. The two rhythmic forms, therefore, present no important differences[7] in the relations which support psychological uniformity. A comparison in detail of the distribution of judgments in the two cases reveals a higher percentage of plus and minus, and a lower percentage of equality judgments throughout the changes of relation in the dactylic form than in the trochaic. This appears to indicate a greater rhythmical integration in the former case than in the latter. On the one hand, the illusion of isolation from adjacent groups is greater at every point at which the intervening interval is actually reduced below the value of either of the internal intervals in the dactylic than in the trochaic rhythm; and on the other, the sensitiveness to differences in the whole series is less in the case of the trochee than in that of the dactyl, if we may take the higher percentage of cases in which no discrimination has been made in the former rhythm as a negative index of such sensibility.