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

which represents an attempt to produce a definite and constant

rhythmical accent, than in a series in which such an accent is

spasmodically given and repressed.

For a like reason, the difference in value between the mean variations

of the elementary interval and the unit group should be less in the

case of the positive rhythm form than in that of a series which

combines a definite temporal segregation with an attempt to maintain

intensive uniformity. The mean variation of the interval is still of

greater value than that of the unit group, but stands to it in the

reduced ratio 1.000:0.969.

The relations of higher groups present certain departures from the

preceding type. In three cases out of five the unit has a greater

> .

fixity than its immediate compound ( | q. q; q q |), with an average

_______/

ratio of 0.969:1.072. The original relation, however, is reëstablished

in the case of the next higher multiple, the eight-beat group, the

whole series of values, arranged on the basis of unity for the simple

interval, being as follows:

TABLE LXIII.

Proportional Single Beat 2-Beat Group 4-Beat Group 8-Beat Group

M.V. 1.000 0.969 1.072 0.859

An analysis of the material in successive pairs of two-beat groups

revealed a pronounced rhythm in the values of the mean variations of

the first and second members of the pair respectively, the fixity of

the second group being much greater than that of the first, the mean

variation having a ratio for all subjects of 0.801:1.000. The

interpretation of this rhythmical variation, as in the preceding

reaction series, must be speculative in the absence of quantitative

measurement of intensive changes, but is still not left in doubt. The

rhythmic material is combined in larger syntheses than the groups of

two beats, alternately accented and unaccented, which were avowedly in

mind. This secondary grouping appears in at least a measure of four

beats, into which the unit group enters as the elementary interval

entered into the composition of that unit. In this larger group the

initial period, or element of stress, is characterized by a greater

mean variation than the unaccented period which follows it. There are

present in this first interval two factors of instability: the factor

of accent, that element which receives the stress, being in general

characterized by a greater mean variation than the unaccented; and the

factor of position, the initial member of a rhythmical group,

independent of accentuation, being marked by a like excess of mean

variation over those which follow it. The interpretation of the latter

fact lies in the direction of a development of uniformity in the motor

habit, which is partially interrupted and reëstablished with the

ending and beginning of each successive group, large or small, in the

series of reactions.

Further, when the material is arranged with four unit groups in each

series, the same relation is found to hold between the first period

composed of two unit groups and the second like period, as obtained

within these pairs themselves. The mean variation of the first period

of four beats is greater than that of the second in the case of all

subjects but one, with an average ratio for all subjects of

1.000:0.745. The analysis was not carried further; there is, however,

nothing which points to a limitation of the process of synthesis to

groups of this magnitude; rather, to judge from the close

approximation in definition of the two orders manifested here, there

is suggested the probability that it is carried into still higher

groupings.

In the next rhythmical type analyzed—the iambic form—that relation

of the first to the second interval holds which was found to obtain in

the preceding forms. The excess of mean variation in the former over

the latter presents the ratio 1.274: 1.000. In amount it is less than

in either of the previous types (2.290:1.000 and 1.722:1.000). For

here, though both elements have constant relations as accented or

unaccented members of the group, the factor of stress has been

transferred from the initial to the final beat. Instead, therefore, of

combining in a single member, the factors of inconstancy due to stress

and to position are distributed between the two elements, and tend to

neutralize each other. That the preponderance of irregularity is still

with the initial interval leads to the inference that position is a

greater factor of inconstancy than accentuation.

Also, the group presents here, as in the preceding forms, a greater

fixity than does the individual interval. This relation holds for all

subjects but one, the average mean variations of the simple interval

and of the unit group having the ratio 1.000:0.824.

In larger groupings irregularities in the relations of higher and

lower again occur, and again the greater constancy obtains between the

first and second orders of higher grouping (in which for only one

subject has the lower group a greater fixity than the higher, and the

averages for all subjects in the two cases are in the ratio

1.149:0.951), and the lesser constancy between the unit group and the

first higher (in which two subjects manifested like relations with

those just given, while three present inverted relations). The whole

series of relations, on the basis of unity for the mean variation of

the simple interval, is given in Table LXIV.

TABLE LXIV.

Proportional. Single Beat. 2-Beat Group. 4-Beat Group. 8-Beat Group

M.V. 1.000 0.824 1.149 0.951

There is also presented here, as in the preceding forms, a synthesis

of the material into groups of four and eight beats, with similar

differences in the fixity of the first and last periods in each. A

single subject, in the case of each order of grouping, diverges from

the type. The ratio of difference in the mean variations of the first

and second members of the groups is, for series of four beats,

1.000:0.657, and for series of eight beats, 1.000:0.770. This

indicates a diminishing definition of rhythmical quantities as the

synthesis proceeds, but a diminution which follows too gradual a curve

to indicate the disappearance of synthesis at the proximate step in

the process.

Three-beat rhythms were next taken up and the same method of analysis

carried out in connection with each of the three accentual forms,

initial, median, and final stress. In these types of rhythm the

intra-group intervals are more than one in number; for the purpose of

comparison with the final, or inter-group interval, the average of the

first and second intervals has been taken in each case.

The results agree with those of the preceding types. The mean

variation of the interval separating the groups is less throughout

than that of the average group-interval. The ratios for the various

rhythm types are as follows:

TABLE LXV.

Rhythm Form. Initial Stress. Median Stress. Final Stress.

Ratios, 1.000 : 0.758 1.000 : 0.527 1.000 : 0.658

This relation, true of the average intra-group interval, is also true

of each interval separately. Among these ratios the greatest departure

from unity appears in the second form which all subjects found most

difficult to reproduce, and in which the tendency to revert to the

first form constantly reasserts itself. The difference in value of the

mean variations is least in the first form, that with initial accent,

and of intermediate magnitude in the third form when the accent is

final. The contrary might be expected, since in the first form—as in

the second also—the factors of stress and initial position are both

represented in the average of the first two intervals, while in the

third form the factor of stress affects the final interval and should,

on the assumption already made concerning its significance as a

disturbing element, tend to increase the mean variation of that

interval, and, therefore, to reduce to its lowest degree the index of

difference between the two phases. That it does so tend is evident

from a comparison of the proportional mean variations of this interval

in the three forms, which are in order: initial stress, 4.65 per

cent.; median stress, 4.70 per cent., and final stress, 7.15 per cent.

That the consequent reduction also follows is shown by the individual

records, of which, out of four, three give an average value for this

relation, in forms having final stress, of 1.000:0.968, the least of

the group of three; while the fourth subject departs from this type in

having the mean variation of the initial interval very great, while

that of the final interval is reduced to zero.

If, as has been assumed, the magnitude of the average mean variation

may be taken as an index of the fixity or definition of the rhythm

form, the first of these three types, the ordinary dactylic is the

most clearly defined; the second, or amphibrachic, stands next, and

the third, the anapæstic, has least fixity; for in regard to the final

interval, to the average of the first and second and also to each of

these earlier intervals separately, the amount of mean variation

increases in the order of the accents as follows:

TABLE LXVI.

Interval. Initial Stress. Median Stress. Final Stress.

First, 5.82 per cent. 9.95 per cent. 11.95 per cent.

Second, 6.45 ” 7.87 ” 9.77 “

Third, 4.65 ” 4.70 ” 7.15 “

In these triple rhythms, as in the two-beat forms, the simple interval

is more variable than the unit group, and the lower group likewise

more unstable than the higher. The series of proportional values for

the three forms is given in the table annexed:

TABLE LXVII.

Rhythm Form. Single Interval. 3-Beat Group. 6-Beat Group.

Initial Stress, 1.000 1.214 1.037

Median ” 1.000 0.422 0.319

Final ” 1.000 0.686 0.524

A comparison of the second and third columns of the table shows an

excess of mean variation of the smaller group over that of the larger

in each of the three forms. It is true also of the individual subjects

except in two instances, in each of which the two indices are equal.

This proportion is broken in the relation of the primary interval to

the unit group in the dactylic rhythm form. A similar diversity of the

individual records occurred in the two-beat rhythms.

The same indication of higher groupings appears here as in the case of

previous rhythms. Rhythmical variations are presented in the amount of

the mean variations for alternate groups of three beats.

Chronologically in the records, as well as in dependence on

theoretical interpretation, the first member of each higher group is

characterized by the greater instability. The amounts of this

difference in coördination between the first and last halves in series

of six beats is set down for the three rhythm forms in the following

table:

TABLE LXVIII.

Stress. First Half. Second Half

Initial, 1.000 0.794¹

Median, 1.000 0.668

Final, 1.000 0.770

¹These figures are made up from the records of three out of

four subjects. In the exceptional results of the fourth

subject no mean variation appears in the first half and 6.3

per cent, in the second, making the average for the whole

group 1.000:1.023.

There is still other evidence of higher rhythmical grouping than these

oscillations in the amount of the mean variation of alternate groups.

Exactness of coördination between the individual intervals of

successive groups might undergo development without affecting the

relative uniformity of such total groups themselves. But, throughout

these results, an increase in coördination between the periods of the

whole group takes place in passing from the first to the second member

of a composite group. The relation here is not, however, so uniform as

in the preceding case. The series of proportional values is given on

page 403.

TABLE LXIX.

Stress. First Half. Second Half.

Initial, 1.000 0.846¹

Median, 1.000 1.064

Final, 1.000 0.742

¹ Here also the records of