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

the results of the same reactor as in the preceding cases

being discarded. Including this, the ratio becomes

1.000:1.016.

The index of mean variation for the individual elements of the group

also shows a progressive decrease from first to last as follows:

TABLE LXX.

Stress. Interval I. Interval II. Interval III.

Initial, 5.82 per cent. 6.45 per cent. 4.65 per cent.

Median, 9.95 ” 7.87 ” 4.70 “

Final, 11.95 ” 9.77 ” 7.15 “

The relation holds in all cases except that of I. to II. in the rhythm

with initial stress. From this table may be gathered the predominance

of primacy of position as a factor of disturbance over that of stress.

Indeed, in this group of reactions the index of variation for the

accented element, all forms combined, falls below that of the

unaccented in the ratio 6.95 per cent. : 7.91 per cent.

In rhythms of four beats, as in those of three, the estimation of

values is made on the basis of an average of the mean variations for

the three intra-group intervals, which is then compared with the final

or inter-group interval. As in those previous forms, sensitiveness to

variations in duration is greater throughout in the case of the latter

than in that of the former. The proportional values of their several

mean variations are given in the annexed table:

TABLE LXXI.

Interval. Initial Stress. Secondary Stress. Tertiary Stress. Final Stress.

Intra-group, 1.000 1.000 1.000 1.000

Inter-group, 0.941 0.775 0.725 0.713

This relation, true of the average of all intra-group intervals, is

not, as in the preceding forms, true of each of the three constituent

intervals in every case. In the second and fourth forms, those marked

by secondary and final stress, it holds for each member of the group

of intervals; in the first form it fails for the second and third

intervals, while in the third form it fails for the last of the three.

The proportional amount of this difference in mean variation

continuously increases from beginning to end of the series of

rhythmical forms. This cannot be interpreted as directly indicative of

a corresponding change in the definition which the four forms possess.

The absolute values of the several mean variations must simultaneously

be taken into account. First, then, in regard to the final pause there

is presented the following series of values:

TABLE LXXII.

Stress. Initial. Secondary. Tertiary. Final.

M.V. 6.57 per cent. 9.50 per cent. 4.90 per cent. 15.70 per cent.

A very striking rhythmical alternation in the magnitude of the mean

variation thus occurs according as the accents fall on the first

member of the subgroups when its amount is smaller or on the second

member when it is larger. Further, the cases noted above, the second

and fourth forms, in which each of the intra-group intervals is

severally of greater mean variation than the final pause, are just

those in which the index of mean variation in the final pause itself

is at a maximum.

The average mean variations of the earlier intervals thus present

changes which are analogous to and synchronous with those of the final

pause. Their values in proportion to the whole duration of the

intervals are as follows[13]:

[13] In the second line of figures has been added the series of

values of the average mean variation for all four intervals of

the group.

TABLE LXXIII.

Stress. Initial. Secondary. Tertiary. Final.

M.V. 6.98 per cent. 12.25 per cent. 6.57 per cent. 22.0 per cent.

M.V. 6.87 ” 11.56 ” 6.15 ” 20.45 “

Those rhythmical forms having their accentual stress initial, or on

the initial elements of the subgroups, are marked by a sensitiveness

almost twice as great as those in which the stress is final, or on the

final elements of the subgroups.

Finally, if we take the whole series of intervals severally, we shall

find that this rhythmical variation holds true of each element

individually as it does of their average. The whole series of values

is given in the table annexed.

TABLE LXXIV.

Stress.

Interval. Initial. Secondary. Tertiary. Final.

First, 9.57 per cent. 13.23 per cent. 9.00 per cent. 11.45 per cent.

Second, 5.53 ” 10.60 ” 8.70 ” 9.00 “

Third, 5.83 ” 12.93 ” 2.00 ” 12.90 “

Fourth, 6.57 ” 9.50 ” 4.90 ” 7.85 “

It is an obvious inference from these facts that the position of the

accent in a rhythmical group is of very great significance in relation

to the character of the rhythmical movement. The initial accent gives

incomparably greater coördination and perfection to the forms of

uttered (produced) rhythm than does the final. It is in this sense the

natural position of the accent, because on the success and fluency of

this coördination the æsthetic value of the rhythm depends.

In general, though not so unequivocally, the four-beat rhythms show a

progressive increase of stability in passing from the simple interval

to the group, and from the smaller group to the larger. The series of

values for the four accentual positions follows.

TABLE LXXV.

Stress. Single Interval. 4-Beat Group. 2-Beat Group.

Initial, 7.27 per cent. 8.20 per cent. 8.17 per cent.

Secondary, 11.60 ” 9.60 ” 6.25 “

Tertiary, 3.20 ” 3.40 ” 2.25 “

Final, 10.22 ” 6.30 ” 6.00 “

Average, 8.07 ” 6.87 ” 5.67 “

Here, as in the preceding rhythmical forms, the most constant relation

is that of smaller and larger groups, in which no exception occurs to

the excess of mean variation in the former over the latter. The cases

in which this relation is reversed are found, as before, in comparing

the simple interval with the duration of the unit group; and the

exceptional instances are just those, namely the first and third

forms, in which the mean variation of this uncompounded interval is

itself at a minimum. This means that the simple interval presents a

more mobile character than that of the group; and while in general it

is less stable than the latter, it is also the first to show the

influence of increased coördination. Training affects more readily the

single element than the composite measure, and in the most highly

coördinated forms of rhythm the simple interval is itself the most

perfectly integrated unit in the system of reactions.

Here, as in the preceding rhythmical forms, evidence of higher

grouping appears in the alternate increase and decrease of mean

variation as we pass from the first to the second subgroup when the

material is arranged in series of eight beats. The proportional values

of the indices are given in the following table:

TABLE LXXVI.

Subgroups Init. Stress Sec. Stress Tert. Stress Fin. Stress

1st Four, 1.000 1.000 1.000 1.000

2d Four, 0.950 0.762 0.984 0.790

The first member of the larger group, in the case of every rhythm form

here in question, is less exactly coördinated than the second, the

interpretation of which fact need not here be repeated. Several

additional points, however, are to be noted. The differences in

stability of coördination which are encountered as one passes from the

first to the last of the four rhythm forms, extends, when the

reactions are analyzed in series of eight beats, to both members of

the compound group, but not in equal ratios. The mean variation of the

second and fourth forms is greater, both in the first and second

subgroups, than that of the corresponding subgroups of the first and

third forms; but this increase is greatest in the first member of the

composite group. That is, as the group grows more unstable it does so

mainly through an increase in variation of its initial member; or, in

other words, the difference in variability of the beat intervals of

the first and last subgroups reaches its maximum in those rhythmic

types in which the indices of mean variation for these intervals are

themselves at their maxima.

This process of coördination, with its indication of a higher

rhythmical synthesis, appears also in the transformations in the value

of the mean variations in duration of the total groups, when the

material is treated in series of eight beats, as in table LXXVII.

TABLE LXXVII.

Subgroups. Init. Stress. Sec. Stress. Tert. Stress. Final Stress.

1st Four, 1.000 1.000 1.000 1.000

2d Four, 0.773 0.768 0.943 0.579

The total initial group, therefore, as well as each of its constituent

intervals, is less stable than the second.

Within the unit group itself the values of the mean variation show

here, as in the preceding forms, a progressive increase in

sensitiveness to temporal variations from first to last of the

component intervals. The proportional values for the four intervals in

order are, 1.000, 0.786, 0.771, 0.666. The distribution of these

relative values, however, is not uniform for all four rhythmical

forms, but falls into two separate types in dependence on the position

of the accents as initial or final, following the discrimination

already made. The figures for the four forms separately are as

follows:

TABLE LXXVIII.

Stress. 1st Interval. 2d Interval. 3d Interval. 4th Interval.

Initial, 9.57 per cent. 5.53 per cent. 5.83 per cent. 6.57 per cent.

Secondary, 13.23 ” 10.60 ” 12.93 ” 9.50 “

Tertiary, 9.00 ” 8.70 ” 2.00 ” 4.90 “

Final, 11.45 ” 9.00 ” 12.60 ” 7.85 “

In the first type (Rhythms I. and III.) appear a descending curve

followed by an ascending; in the second type (Rhythms II. and IV.) a

second descending curve follows the first. The changes in the first

type are not coördinated with a similar curve of variation in the

intensive magnitude of the beats. It is to be noted here that the

smallest mean variation presented in this whole set of results is

found in that element of the first form which receives the stress, an

exception to the general rule. The variations in the contrasted type

have their maxima at those points on which the group initiation—

primary or secondary—falls, namely, the first and third.

As in preceding rhythmical forms, while the separation of accentual

stress from primacy in the series tends to increase the mean variation

of that element on which this stress falls and to raise the index of

mean variation for the whole group, yet the mean variation of the

initial element is also raised, and to a still greater degree,

reinforcing the evidence that primacy of position is a more important

factor of instability than the introduction of accentual stress.

In the investigation of mean variations for units (if we may call them

such) of more than four beats only a modicum of material has been

worked up, since the types of relation already discovered are of too

definite a character to leave any doubt as to their significance in

the expression of rhythm. The results of these further experiments

confirm the conclusions of the earlier experiments at every point.

These higher series were treated in two ways. In the first the reactor

beat out a rhythm consisting in the simple succession of groups of

reactions, each of which contained one and only one accent. These

units in each case were marked by initial stress, and were composed of

five, six, seven, eight and ten beats respectively. The results are

given in the following table, which contains the series of mean

variations in duration both for single intervals and for total groups.

TABLE LXXIX.

No. Med. Unac’td

of Beats. Acc’td Beat. Beats. Final Beat. Average. Group.

Five, 12.2% 6.8% 7.1% 7.9% 6.3%

Six, 9.2 10.6 6.9 9.7 8.3

Seven, 7.1 5.2 7.9 5.8 3.6

Eight, 12.4 9.5 8.8 9.7 8.0

Ten, 7.5 6.6 7.3 6.8

The averages for the combined, median, unaccented intervals are given

separately