Sixteen Experimental Investigations from the Harvard Psychological Laboratory by Hugo Münsterberg (100 books to read .txt) 📕

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 quantitative 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 retardation 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

constituting 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 retardation.

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 assumption 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 quantitative

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 quantitative

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 anapæstic 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 anapæst. 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 attitude obtains it

is absolutely impossible to make impartial comparison of the duration

of successive intervals. The group is a unit which cannot be analyzed

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 attitude 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 pass unobserved, 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 passed unobserved; 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

participants the anapæstic 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.

[7] The ratios of initial to final intervals in the two cases

are, for trochaic measures, 1.400:1.000, and for dactylic,

1.400(to 1.666):1.000.

TABLE L.

Ration of Unaccented Unaccented Interval Judged to be

to Accented Interval. + = -

1.000 : 2.428 100.0 per cent

1.000 : 2.000 20.0 per cent. 33.3 per cent 46.7 “

1.000 : 1.666 33.2 ” 23.9