Chapter XIV: Section II: showed that the shorter filled distances are (10)

Returned 0 times, 44
" 1 " 26
" 2 " 18
" 3 " 25
" 4 " 16
" 5 " 16
" 6 to 10 " 28
" more than 10 times, 24
Total, 197

Seventy-three and three fifths per cent. of all the experiments have five or fewer returns of the suppressed images.

The subjects suppressed the image as soon as possible after each return, the average time taken to accomplish these later suppressions being 6.46 sec., while the average time of absence of the suppressed image was 32.14 sec.

Including the first efforts and the first absences of the suppressed image, the average time required to suppress the image was 7.60 sec., and the average time of absence of the suppressed image was 41.86 sec.

Arranging the subjects according to the average time they required to accomplish a suppression, we have the following order. J. and F. had more recurrences of the suppressed image than any of the other subjects.

J. 1.64 sec.
F. 2.40 "
C. 4.80 "
B. 4.98 "
I. 6.06 "
G. 11.15 "
H. 11.84 "
A. 16.05 "
K. 16.70 "
D. 25.80 "

Arranging them by the average absence of the suppressed image we have this order:

B. 251.08 sec
D. 193.89 "
H. 81.02 "
C. 62.07 "
I. 59.72 "
K. 31.83 "
J. 31.75 "
G. 19.47 "
A. 10.44 "
F. 10.09 "

It is to be remarked, however, that the ability to keep the suppressed image out of the field increased with practice and that A. and F. had less than half the number of experiments that the rest had. D., who had but two thirds as many as most of the other subjects and therefore had less practice in suppressing the image, stands yet second in respect to this ability.

If we compare the subjects with regard to _first_ efforts and _first_ absences only, we obtain the following orders:

According to Ave. Time req. According to Ave. Absence
for first Suppression. of Image after first Suppression.
J. 3.59 sec. B. 270.44 sec.
B. 5.79 " D. 190.07 "
C. 7.88 " F. 86.07 "
I. 9.77 " H. 73.27 "
F. 12.67 " K. 71.90 "
H. 15.27 " I. 53.83 "
K. 21.63 " C. 43.08 "
G. 21.88 " J. 32.18 "
D. 23.28 " G. 20.39 "
A. 28.32 " A. 11.29 "

Arranging the groups of images suppressed according to the average times of all suppressions and absences we have these orders:

Suppression. Absences.
Central Images, 5.41 Marginal Images, 125.12
Upper " 6.95 Sundry " 68.78
Left " 8.60 Left " 51.26
Right " 8.94 Lower " 50.04
Lower " 9.11 Right " 43.93
Marginal " 11.35 Upper " 32.35
Sundry " 12.09 Central " 26.54

SUBJECTIVE.

Most of the subjects imaginatively placed the image to be suppressed behind the screen, in a drawer, in their closed hands, pushed it forward into the remote distance, sliced up, burned up, or pulverized and so destroyed it. B. and D. 'thought it away' directly, without mechanism or device, or got rid of it 'by a pure act of will.' Superposition was tried, frequently with success, but at times the under image shone through. When the objects were colored discs one superposed on the other, the subject spread over the whole surface the color of the image to be retained, but at times this resulted in there being two shades of the upper color, and a yellow above a red changed to an orange. When red was above yellow, the red appeared more highly illuminated. Associations with objects of the color of the retained image were found helpful but tended to modify the original color. Such associations also, at times, by secondary associations brought back the suppressed image. For example, when thinking of buttercups to enforce a yellow image, the picture of grass surrounding the flowers brought back the suppressed green image. Concentration of the attention on the image to be retained and an ignoring of the other was, on the whole, the method usually and successfully followed. This concentration was helped by imagining the image marked off into minute squares which were carefully counted. Numerous other devices of a similar character were used. Objects having many details and those lending themselves readily to suggestions of action (as a china animal) were the most helpful in enabling the subject to concentrate his attention on their image to the exclusion of another. Some subjects conceived themselves as tracing with a pencil the outline and details of the retained image. Frequently, when the two images were originally near each other and one alone was being held by close scrutiny of its parts, when this scrutiny reached the part of the image which was nearest the position of the suppressed image, the suppressed image returned. The original association between the two images was often broken up by change of the position or shape of the one to be suppressed. But devices soon became 'worn out' and new ones had to be resorted to.

Motor impulses played a large part in the process of suppression, such as head and eye movement away from the image to be suppressed, contraction of the muscles of the forehead and scalp, occasional 'setting' of the teeth, pressure together of the hands when they were supposed to be holding the image and of the knees under like circumstances. The eye traced outline and details and the more actively it could be so employed the more successful was the suppression. The sensations of accommodation and of focusing previously referred to were repeated in this series. Enunciation also was very common.

Frequent comparison of the image with the percept was made at the close of experiments and showed the utmost diversity in size, vividness and distinctness. During an experiment when the suppressed image came back, it was rarely more than a mere blur of color; in two or three instances the form came without color. Green was found to be a difficult color to hold. C. had an orange after-image from a retained yellow image, a red image having been suppressed. Between the images of a gray disc and an orange disc, three inches apart, he had a blue disc. J., while suppressing an orange disc and retaining a green disc, noticed that 'when off the fovea the whole green disc became bright orange.' There was always a sense of readiness on the part of the suppressed image to slip back. As C. expressed this, "The thing suppressed exists in the fringe of consciousness." The recurring image usually came back at its original position even when the retained image was being held in a different part of the field. In such cases the retained image at once resumed its original place.

G. and J. were successful in proportion as they freed themselves from the nervous strain of anxiety as to the result.

V. MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURING THE EXPOSURE.

In an additional series of experiments with five of the same subjects (B., G., H., I. and K.), the object was moved during the five seconds of exposure either right, left, up or down, a distance of about six to eight inches, and back again. In this way the subject was supplied with further material of a pure memory type and it was believed that some addition to our knowledge of the nature of the control of the image might thus be made by securing data contrasting the construction and the more purely reminiscent work of the imagination.

The question proposed is as follows: Does the fact that a certain movement of an object was presented to the optical perception give an advantage in time, or ease, to the mental recall of that object as so moving, over its recall as moving in other directions? The subjective experiences during such recalls may be expected to throw light upon the matter.

The subject, with closed eyes, was requested to move the mental image of the object in the four directions indicated above, returning it after each movement to its original position, and the time of each movement was recorded and, as well, the report of the subject with regard to his subjective experiences. There were sixteen hundred movements in all, eight hundred away from the original position of the image (two hundred in each of the four directions mentioned above) and eight hundred in returning to the original position.

Besides these experiments, other movements of the object during exposure were made, such as inversion, rotation, change from the vertical to the horizontal position and vice versa, rolling, oblique movements and the subjective phenomena were recorded when the subject had repeated with the image the designated movements. In all the experiments the objects were moved by the hand of the conductor of the experiment.

Table VII. gives the time record in seconds of these experiments for each subject under each of the four variations: Movement of the object to right, left, up, down.

TABLE VII.

MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURING THE
TIME OF OPTICAL STIMULATION. AVERAGE TIME IN SECONDS. TEN MOVEMENTS IN
EACH DIRECTION FOR EACH SUBJECT.

_a_. Object moved to right.

Subject R. Return L. Return Up Return Down Return Aver.
B. 0.57 0.75 0.62 0.60 0.64
0.35 0.42 0.37 0.62 0.44
G. 0.55 0.60 0.55 0.57 0.57
0.27 0.25 0.27 0.25 0.26
H. 6.95 6.90 6.47 6.40 6.65
5.40 5.55 4.50 5.00 5.11
I. 2.05 2.10 2.05 2.22 2.10
1.15 1.35 1.32 1.57 1.35
K. 2.35 2.97 2.42 2.62 2.59
1.17 1.20 1.17 1.55 1.28
Ave. 2.49 2.66 2.02 2.48 2.52
1.67 1.75 1.53 1.80 1.69

Ave. to right, 2.49
Ave. of other movements, 2.52
Grand average, 2.10

_b_. Object moved to left.
B. 0.72 0.60 0.62 0.60 0.64
0.52 0.40 0.52 0.42 0.47
G. 0.67 0.45 0.55 0.67 0.59
0.42 0.35 0.35 0.37 0.37
H. 8.22 5.95 6.52 6.42 6.78
5.82 4.10 4.37 5.55 4.96
I. 2.40 1.30 2.25 2.72 2.17
1.97 1.22 0.95 1.47 1.40
K. 2.45 2.57 2.25 2.00 2.30
1.70 1.60 1.32 1.35 1.49
Ave. 2.89 2.17 2.44 2.48 2.50
2.09 1.53 1.50 1.83 1.74

Ave. to left, 2.17
Ave. of other movements, 2.60
Grand average, 2.12

_c_. Object moved up.
B. 0.75 0.62 0.42 0.57 0.59
0.32 0.50 0.42 0.37 0.40
G. 0.65 0.57 0.45 0.47 0.54
0.35 0.27 0.25 0.27 0.29
H. 6.77 6.25 6.85 6.15 6.57
5.27 5.55 5.30 5.30 5.35
I. 2.47 2.27 1.85 2.65 2.31
1.25 1.00 0.87 1.10 1.05
K. 3.40 2.72 1.42 2.20 2.44
1.50 1.37 1.27 1.17 1.33
Ave. 2.81 2.49 2.20 2.41 2.48
1.74 1.74 1.62 1.70 1.69

Ave. up, 2.20
Ave. of other movements, 2.57
Grand average, 2.08

_d_. Object moved down.
B. 0.80 0.72 0.70 0.57 0.70
0.42 0.42 0.50 0.42 0.44
G. 0.60 0.60 0.55 0.47 0.55
0.25 0.25 0.27 0.27 0.26
H. 6.77 6.80 6.80 8.77 7.29
5.90 6.35 4.55 5.55 5.59
I. 2.30 2.20 2.22 1.80 2.13
1.30 1.20 1.15 1.42 1.27
K. 3.15 2.75 2.95 2.30 2.79
1.62 1.57 1.12 1.25 1.39
Ave. 2.72 2.61 2.64 2.78 2.69
1.90 1.92 1.52 1.78 1.79

Ave. down, 2.78
Ave. of other movements, 2.66
Grand average, 2.24

NUMERICAL.

As each movement may be compared with three other movements, and as there were five subjects and four variations in the conditions, there are sixty opportunities of comparing the time required to move the image in the direction in which the object was moved with the time taken to move it in the other directions. In 45 instances the time was less, in 3 the same, and in 12 greater.

These twelve instances occurred with two subjects, three (to left) occurring with K. and nine (three each right, up, down) occurring with H. The cause was the same in all twelve instances, both H. and K. reporting that (in these cases) they had great difficulty in obtaining a reasonably vivid and distinct image when directed to move the image in the direction in which the object had been moved. The attempt to move the image resulted in a vague image spread continuously over the entire area that had been covered by the moving object, and the effort to obtain the image at the desired position only was serious and took an appreciably longer time than usual. It is to be noted, also, that the time usually taken by H. is uniformly very much greater than the time taken by the other subjects. Yet, even with these instances included, the average time of all movements of the image in the direction in which the object had been moved is less than the average time of the other movements, the former being 2.41 seconds, the latter, 2.59 seconds.

TABLE VIII.

MOVEMENTS OF A SINGLE IMAGE.

I., OBJECT PREVIOUSLY MOVED; II., OBJECT NOT MOVED.

Average Time Given in Seconds.

Subjects: B. G. H.
I II I II I II
To right, 0.57 1.30 0.55 1.46 6.95 7.15
Return, 0.35 0.58 0.27 0.92 5.40 4.51
To left, 0.60 1.06 0.45 1.15 5.95 6.42
Return, 0.40 0.73 0.35 0.89 4.10 4.41
Up, 0.42 1.05 0.45 0.99 6.85 5.96
Return, 0.42 0.46 0.25 0.76 5.30 4.36
Down, 0.57 1.10 0.47 0.82 8.77 5.85
Return, 0.42 0.45 0.27 0.06 5.55 4.40
General 0.54 1.13 0.48 1.10 7.13 6.34
Averages, 0.40 0.55 0.28 0.66 5.09 4.42

Subjects: I. K.
I II I II
To right, 2.05 1.28 2.35 4.80
Return, 1.15 0.67 1.17 2.40
To left, 1.30 1.34 2.57 4.63
Retur, 1.22 0.62 1.60 2.73
Up, 1.85 1.62 1.42 3.29
Return, 0.87 0.86 1.27 1.90
Down, 1.80 1.36 2.30 3.27
Return, 1.42 0.72 1.25 1.56
General 1.75 1.40 2.16 4.00
Averages, 1.16 0.72 1.32 2.15

If the record of H. is omitted from Table VII., _a, c, _and _d_, and that of K. from VII., _b_ (as these are the records of the twelve exceptions), the former average becomes 1.44 seconds, the latter 1.86 seconds.

The following table affords the means of comparing the time taken in moving the image in the direction in which the object had been moved with the time taken in moving the image in the same direction when there had been no movement of the object. The averages are obtained from the records of Tables VII. and I.

We have here twenty comparisons each of movements away from the original positions and movements back to the original positions:

In the first case, 15 took less time under I., 5 took more
time under I.

The 5 cases of more time occurred with two subjects (H., 3 and
I., 2).

In the second case, 12 took less time under I., 8 took more
time under I.

The 8 cases of more time occurred with three subjects (G., 1;
H., 3; I., 4).

If we omit H.'s record and take the general averages for each subject, we find the following advantages in time in form of movements where the object had been moved;

B., 0.59 seconds.
G., 0.52 "
K., 1.84 "

But I., 0.35 seconds in favor of movements when the object had not been moved.

Combining these results, we have 0.74 sec. as the average gain in time for these four subjects.

SUBJECTIVE.

With one exception (G.), the subjects found Movements I., movements in the direction in which the object had been moved, easier than Movements II. In Movements II. the eye seemed to construct and compel the motion, which was not the case with Movements I., in which the eye followed the motion. The distance to which the image went in Movements I. seemed predetermined, and these movements seemed exact copies of the original movement of the object, being purely reminiscent and reproducing its irregularities when there were any. Also, the image was usually seen _in transitu_ both out and back, which was never the case with Movements II. Eye movement and enunciation were much less frequent and the image was more vivid and distinct in Movements I.

* * * * *

STUDIES IN ÆSTHETIC PROCESSES.

* * * * *

Transcriber's Note:

Rhythmic measures in the first 2 articles of this section are
transcribed as follows:

| delineates measure
q quarter note
q. dotted quarter note
e eighth note
% quarter rest

Major accent of the measure is indicated by a >, either above
or in front of the beat. Minor accent of the measure is
indicated by ., used in the same way.

> .
| q q q q | or | >q q .q q | represent the same rhythmic pattern.

* * * * *

THE STRUCTURE OF SIMPLE RHYTHM FORMS.

BY ROBERT MACDOUGALL.

I. PROBLEMS AND METHODS OF EXPERIMENTATION.

The investigation of the problems presented by the psychological phenomena of rhythm has of late years occupied much attention and been pushed in a variety of different directions. Some researches have been concerned with an analysis of rhythm as an immediate subjective experience, involving factors of perception, reaction, memory, feeling, and the like; others have had to do with the specific objective conditions under which this experience arises, and the effect of changes in the relations of these factors; still others have sought to coördinate the rhythm experience with more general laws of activity in the organism, as the condition of most effective action, and to affiliate its complex phenomena upon simpler laws of physiological activity and repose; while a fourth group has undertaken a description of that historical process which has resulted in the establishment of artistic rhythm-types, and has sought to formulate the laws of their construction.[1]

[1] Description: (1) Of the psychological factors of the rhythm
experience: Angell and Pierce, Ettlinger, Hauptmann, Mentz,
Meumann, Stumpf, Wundt, et al. (2) Of its objective conditions
and products: Binet et Courtier, Bolton, Ebhardt, Hurst and
McKay, Meumann, Schumann, Sievers, et al. (3) Of its
physiological accompaniments: Bolton, Brücke, Dogiel,
Hausegger, Mach, Mentz, Ribot, Sherrington, Scripture, Smith,
et al. (4) Of its historical evolution: Bücher, Moritz,
Scherer, et al.

This differentiation has already made such progress as to constitute the general topic a field within which specialization is called for, instead of an attempt to treat the phenomenon as a whole. It is the purpose of this paper to describe a set of experiments having to do with the second of these problems, the constitution of objective rhythm forms. In the determination of such forms it is, of course, impossible to avoid the employment of terms descriptive of the immediate experience of rhythm as a psychological process, or to overlook the constant connection which exists between the two groups of facts. The rhythm form is not objectively definable as a stable type of stimulation existing in and for itself; the discrimination of true and false relations among its elements depends on the immediate report of the consciousness in which it appears. The artistic form is such only in virtue of its arousing in the observer that peculiar quality of feeling expressed in calling the series of sensory stimuli rhythmically pleasing, or equivalent, or perfect. In no other way than as thus dependent on the appeal which their impression makes to the æsthetic consciousness can we conceive of the development and establishment of fixed forms of combination and sequence among those types of sensory stimulation which arouse in us the pleasurable experience of rhythm. The artistic rhythm form cannot be defined as constituted of periods which are 'chronometrically proportionate,' or mathematically simple. It is not such in virtue of any physical relations which may obtain among its constituents, though it may be dependent on such conditions in consequence of the subordination to physical laws of the organic activities of the human individual. The view must be subjectively objective throughout.

The need for simplicity and exactness has led to the very general employment of material as barely sensorial as could be devised for the carrying on of experiments upon rhythm. Rich tones and complex combinations of them are to be avoided, for these qualities are themselves immediate sources of pleasure, and the introduction of them into the material of experimentation inevitably confuses the analysis which the observer is called upon to make of his experience and of the sources of his pleasure in it. Still more objectionable than the presence of such complex musical tones in an investigation of rhythm is the introduction of the symbols of rational speech in concrete poetical forms. This element can be only a hindrance to the perception of pure rhythmical relations, in virtue of the immediate interest which the images called up by the verbal signs possess, and further, in view of the fact that the connections of significant thought impose upon the purely rhythmical formulation of the series of stimulations an unrelated and antagonistic principle of grouping, namely, the logical relations which the various members of the series bear to one another.

The demand for a simplification of the material which supports the rhythm experience, for the purpose of obtaining a more exact control over the conditions of experimentation, has been met by the invention of a variety of devices whereby the sequences of music, song and poetical speech have been replaced by elementary conventional symbols as the vehicle of the rhythmical impression or expression. On the one side there has commonly been substituted for musical tones and rhythmical speech the most simple, sharply limited and controllable sounds possible, namely, those due to the action of a telephone receiver, to the vibrations of a tuning-fork placed before the aperture of a resonator, or to the strokes of metallic hammers falling on their anvils. On the other side, the form of the reproduced rhythm has been clarified by the substitution of the finger for the voice in a series of simple motor reactions beaten out on a more or less resonant medium; by the use--when the voice is employed--of conventional verbal symbols instead of the elements of significant speech; and--where actual verse has been spoken--by a treatment of the words in formal staccato scansion, or by the beating of time throughout the utterance. The last of these methods is a halting between two courses which casts doubt on the results as characteristic of either type of activity. There is no question that the rhythmic forms of recitative poetry differ vastly from those of instrumental music and chanted speech. The measures of spoken verse are elastic and full of changefulness, while those of music and the chant maintain a very decided constancy of relations. The latter present determinable types of grouping and succession, while it is questionable whether the forms of relationship in spoken verse can ever be considered apart from the emotion of the moment. In so far as the rhythmic form which these differing modes of expression embody are to be made the subject of experimental investigation their characteristic structures should be kept intact as objects of analysis in independent experiments, instead of being combined (and modified) in a single process.

The apparatus employed in the course of the present investigation consisted of four different pieces of mechanism, one affording the vehicle of expression throughout the series of reproduced rhythms, the others providing the auditory material of the various rhythms apperceived but not designedly reproduced. The first of these consisted of a shallow Marey tambour, placed horizontally upon a table with its rubber film upwards, and connected by means of rubber-tubing with a pneumographic pen in contact with the revolving drum of a kymograph. A Deprez electric marker, aligned with the pneumographic stylus, afforded a time record in quarter seconds. Upon this tambour, placed within comfortable reach of the reactor's hand, the various rhythm types were beaten out. The impact of the finger-tip on the tense surface of the drum gave forth a faint and pleasing but at the same time clearly discernible and distinctly limited sound, which responded with audible variations of intensity to the differing stresses involved in the process of tapping, and which I have considered preferable to the short, sharp stroke of the Kraepelin mouth-key employed by Ebhardt. The rate of revolution in the drum was so adjusted to the normal range of excursion in the pneumographic pen as to give sharp definition to every change of direction in the curve, which hence allowed of exact measurements of temporal and intensive phases in the successive rhythm groups. These measurements were made to limits of 1.0 mm. in the latter direction and of 0.5 mm. in the former.[2]

[2] Professor Binet's doubt (_L'Année Psychologique_ 1895, p.
204) that the propulsion of air from the elastic chamber and
the rebound of the pen might interfere with the significance of
the graphic record is more serious in connection with the
application of this method to piano playing than here; since
its imperfection, as that writer says, was due to the force and
extreme rapidity of the reactions in the former case. The
present series involved only light tapping and was carried on
at a much slower average rate.

The second piece of apparatus consisted of an ordinary metronome adjusted to beat at rates of 60, 90, and 120 strokes per minute. This instrument was used in a set of preliminary experiments designed to test the capacity of the various subjects for keeping time by finger reaction with a regular series of auditory stimulations.

The third piece of apparatus consisted of an arrangement for producing a series of sounds and silences, variable at will in absolute rate, in duration, and, within restricted limits, in intensity, by the interruptions of an electrical current, into the circuit of which had been introduced a telephone receiver and a rheostat. Portions of the periphery of a thin metallic disc were cut away so as to leave at accurately spaced intervals, larger or smaller extents of the original boundary. This toothed wheel was then mounted on the driving-shaft of an Elbs gravity motor and set in motion. Electrical connections and interruptions were made by contact with the edge of a platinum slip placed at an inclination to the disc's tangent, and so as to bear lightly on the passing teeth or surfaces. The changes in form of a mercury globule, consequent on the adhesion of the liquid to the passing teeth, made it impossible to use the latter medium. The absolute rate of succession in the series of sounds was controlled by varying the magnitudes of the driving weights and the resistance of the governing fans of the motor. As the relation of sounds and intervals for any disc was unalterable, a number of such wheels were prepared corresponding to the various numerical groups and temporal sequences examined--one, for example, having the relations expressed in the musical symbol 3/4 | >q e |*; another having that represented in the symbol 4/4 | >q e e |;* and so on. Variations in intensity were obtained by mounting a second series of contacts on the same shaft and in alignment with those already described. The number of these secondary contacts was less than that of the primary connections, their teeth corresponding to every second or third of those. The connections made by these contacts were with a second loop, which also contained within its circuit the telephone receiver by which the sounds were produced. The rheostatic resistances introduced into this second circuit were made to depart more or less from that of the first, according as it was desired to introduce a greater or slighter periodic accent into the series. This mechanism was designed for the purpose of determining the characteristic sequences of long and short elements in the rhythm group.

*Transcriber's Note:

The original article showed "3/4 | q q q |" and "4/4 | q q q q |".
Applying the erratum after the article (below) resulted in
fewer beats per measure than indicated by the time signature.
Other possibilities are "3/4 | >q e q. |" and "4/4 | >q e e q q |".

"ERRATUM:

On page 313, line 23, the musical symbols should be a quarter
note, accented, followed by an eighth note; in the following
line the symbols should be a quarter note, accented, followed
by two eighth notes."

The fourth piece of apparatus consisted essentially of a horizontal steel shaft having rigidly attached to it a series of metallic anvils, fifteen in number, on which, as the shaft revolved, the members of a group of steel hammers could be made to fall in succession from the same or different heights. The various parts of the mechanism and their connections may be readily understood by reference to the illustration in Plate VIII. On the right, supported upon two metal standards and resting in doubly pivoted bearings, appears the anvil-bearing shaft. On a series of shallow grooves cut into this shaft are mounted loose brass collars, two of which are visible on the hither end of the shaft. The anvils, the parts and attachments of which are shown in the smaller objects lying on the table at the base of the apparatus, consist of a cylinder of steel partly immersed in a shallow brass cup and made fast to it by means of a thumb-screw. This cup carries a threaded bolt, by which it may be attached to the main shaft at any position on its circumference by screwing through a hole drilled in the collar. The adjustment of the anvils about the shaft may be changed in a moment by the simple movement of loosening and tightening the thumb-screw constituted by the anvil and its bolt. The device by which the extent of the hammer-fall is controlled consists of cam-shaped sheets of thin wood mounted within parallel grooves on opposite sides of the loose collars and clamped to the anvils by the resistance of two wedge-shaped flanges of metal carried on the anvil bolt and acting against the sides of slots cut into the sheets of wood at opposite sides. The periphery of these sheets of wood--as exhibited by that one lying beside the loose anvils on the table--is in the form of a spiral which unfolds in every case from a point on the uniform level of the anvils, and which, by variations in the grade of ascent, rises in the course of a revolution about its center to the different altitudes required for the fall of the hammers. These heights were scaled in inches and fractions, and the series employed in these experiments was as follows: 1/8, 2/8, 3/8, 5/8, 7/8, 15/8, 24/8 inch. Upon a corresponding pair of standards, seen at the left of the illustration, is mounted a slender steel shaft bearing a series of sections of brass tubing, on which, in rigid sockets, are carried the shafts of a set of hammers corresponding in number and position to the anvils of the main axis. By means of a second shaft borne upon two connected arms and pivoted at the summit of the standards the whole group of hammers may at any moment be raised from contact with the cams of the main shaft and the series of sounds be brought to a close without interrupting the action of the motor or of the remainder of the apparatus. By this means phases of acceleration and retardation in the series, due to initial increase in velocity and its final decrease as the movement ceases, are avoided. The pairs of vertical guides which appear on this gearing-shaft and enclose the handles of the several hammers are designed to prevent injury to the insertions of the hammer shafts in their sockets in case of accidental dislocations of the heads in arranging the apparatus. This mechanism was driven by an electrical motor with an interposed reducing gear.

The intervals between the successive hammer-strokes are controlled in the following way: on the inner face of the group of pulleys mounted on the main shaft of the mechanism (this gang of pulleys appears at the extreme right in the illustration) is made fast a protractor scaled in half degrees. Upon the frame of the standard supporting these pulleys is rigidly screwed an index of metal which passes continuously over the face of the scale as the shaft revolves. The points of attachment (about the shaft) of the cams are determined by bringing the point of fall of each cam in succession into alignment with this fixed index, after the shaft has been turned through the desired arc of its revolution and made fast by means of the thumb-screw seen in the illustration at the near end of the shaft. Thus, if three strokes of uniform intensity are to be given at equal intervals apart and in continuous succession, the points of fall of the hammers will be adjusted at equal angular distances from one another, for example, at 360°, 240°, and 120°; if the temporal relations desired be in the ratios 2:1:1, the arrangement will be 360°, 180°, 90°; if in the ratios 5:4:3, it will be 360°, 210°, 90°; and so on. If double this number of hammers be used in a continuous series the angular distances between the points of fall of the successive hammers will of course be one half of those given above, and if nine, twelve, or fifteen hammers be used they will be proportionately less.

An interruption of any desired relative length may be introduced between repetitions of the series by restricting the distribution of angular distances among the cams to the requisite fraction of the whole revolution. Thus, if an interruption equal to the duration included between the first and last hammer-falls of the series be desired, the indices of position in the three cases described above will become: 360°, 270°, 180°; 360°, 240°, 180°, and 360°, 260°, 180°. In the case of series in which the heights of fall of the various hammers are not uniform, a special adjustment must be superimposed upon the method of distribution just described. The fall of the hammer occupies an appreciable time, the duration of which varies with the distance through which the hammer passes. The result, therefore, of an adjustment of the cams on the basis adopted when the height of fall is uniform for all would appear in a reduction of the interval following the sound produced by a hammer falling from a greater height than the rest, and the amount of this shortening would increase with every addition to the distance through which the hammer must pass in its fall. In these experiments such lags were corrected by determining empirically the angular magnitude of the variation from its calculated position necessary, in the case of each higher member of the series of distances, to make the stroke of the hammer on its anvil simultaneous with that of the shortest fall. These fixed amounts were then added to the indices of position of the several cams in each arrangement of intervals employed in the experiments.

This apparatus answers a variety of needs in practical manipulation very satisfactorily. Changes in adjustment are easily and quickly made, in regard to intensity, interval and absolute rate. If desired, the gradation of intensities here employed may be refined to the threshold of perceptibility, or beyond it.

The possible variations of absolute rate and of relative intervals within the series were vastly more numerous than the practical conditions of experimentation called for. In two directions the adaptability of the mechanism was found to be restricted. The durations of the sounds could not be varied as were the intervals between them, and all questions concerning the results of such changes were therefore put aside; and, secondly, the hammers and anvils, though fashioned from the same stuff and turned to identical shapes and weights, could not be made to ring qualitatively alike; and these differences, though slight, were sufficiently great to become the basis of discrimination between successive sounds and of the recognition upon their recurrence of particular hammer-strokes, thereby constituting new points of unification for the series of sounds. When the objective differences of intensity were marked, these minor qualitative variations were unregarded; but when the stresses introduced were weak, as in a series composed of 3/8-, 2/8-, 2/8-inch hammer-falls, they became sufficiently great to confuse or transform the apparent grouping of the rhythmical series; for a qualitative difference between two sounds, though imperceptible when comparison is made after a single occurrence of each, may readily become the subconscious basis for a unification of the pair into a rhythmical group when several repetitions of them take place.

In such an investigation as this the qualification of the subject-observer should be an important consideration. The susceptibility to pleasurable and painful affection by rhythmical and arrhythmical relations among successive sensory stimuli varies within wide limits from individual to individual. It is of equal importance to know how far consonance exists between the experiences of a variety of individuals. If the objective conditions of the rhythm experience differ significantly from person to person it is useless to seek for rhythm forms, or to speak of the laws of rhythmical sequence. Consensus of opinion among a variety of participators is the only foundation upon which one can base the determination of objective forms of any practical value. It is as necessary to have many subjects as to have good ones. In the investigation here reported on, work extended over the two academic years of 1898-1900. Fourteen persons in all took part, whose ages ranged from twenty-three to thirty-nine years. Of these, five were musically trained, four of whom were also possessed of good rhythmic perception; of the remaining nine, seven were good or fair subjects, two rather poor. All of these had had previous training in experimental science and nine were experienced subjects in psychological work.

II. THE ELEMENTARY CONDITIONS OF THE APPEARANCE OF THE RHYTHM IMPRESSION.

The objective conditions necessary to the arousal of an impression of rhythm are three in number: (_a_) Recurrence; (_b_) Accentuation; (_c_) Rate.

(_a_) _Recurrence._--The element of repetition is essential; the impression of rhythm never arises from the presentation of a single rhythmical unit, however proportioned or perfect. It does appear adequately and at once with the first recurrence of that unit. If the rhythm be a complex one, involving the coördination of primary groups in larger unities, the full apprehension of its form will, of course, arise only when the largest synthetic group which it contains has been completed; but an impression of rhythm, though not of the form finally involved, will have appeared with the first repetition of the simplest rhythmical unit which enters into the composition. It is conceivable that the presentation of a single, unrepeated rhythmical unit, especially if well-defined and familiar, should originate a rhythmical impression; but in such a case the sensory material which supports the impression of rhythm is not contained in the objective series but only suggested by it. The familiar group of sounds initiates a rhythmic process which depends for its existence on the continued repetition, in the form of some subjective accentuation, of the unit originally presented.

The rhythmical form, in all such cases, is adequately and perfectly apprehended through a single expression of the sequence.[3] It lacks nothing for its completion; repetition can add no more to it, and is, indeed, in strict terms, inconceivable; for by its very recurrence it is differentiated from the initial presentation, and combines organically with the latter to produce a more highly synthetic form. And however often this process be repeated, each repetition of the original sequence will have become an element functionally unique and locally unalterable in the last and highest synthesis which the whole series presents.

[3] When the formal key-note is distinctly given, the
rhythmical movement arises at once; when it is obscure, the
emergence of the movement is gradual. This is a salient
difference, as Bolton, Ettlinger and others have pointed out,
between subjective rhythms and those objectively supported.

Rhythmical forms are not in themselves rhythms; they must initiate the factor of movement in order that the impression of rhythm shall arise. Rhythmical forms are constantly occurring in our perceptional experience. Wherever a group of homogeneous elements, so related as to exhibit intensive subordination, is presented under certain temporal conditions, potential rhythm forms appear. It is a mere accident whether they are or are not apprehended as actual rhythm forms. If the sequence be repeated--though but once--during the continuance of a single attention attitude, its rhythmical quality will ordinarily be perceived, the rhythmic movement will be started. If the sequence be not thus repeated, the presentation is unlikely to arouse the process and initiate the experience of rhythm, but it is quite capable of so doing. The form of the rhythm is thus wholly independent of the movement, on which the actual impression of rhythm in every case depends; and it may be presented apart from any experience of rhythm.

There is properly no repetition of identical sequences in rhythm. Practically no rhythm to which the æsthetic subject gives expression, or which he apprehends in a series of stimulations, is constituted of the unvaried repetition of a single elementary form, the measures, | >q. q |, or | >q. q q |, for example. Variation, subordination, synthesis, are present in every rhythmical sequence. The regular succession is interrupted by variant groups; points of initiation in the form of redundant syllables, points of finality in the form of syncopated measures, are introduced periodically, making the rhythm form a complex one, the full set of relations involved being represented only by the complete succession of elements contained between any one such point of initiation and its return.

(_b_) _Accentuation._--The second condition for the appearance of the rhythm impression is the periodic accentuation of certain elements in the series of sensory impressions or motor reactions of which that rhythm is composed. The mechanism of such accentuation is indifferent; any type of variation in the accented elements from the rest of the series which induces the characteristic process of rhythmic accentuation--by subjective emphasis, recurrent waves of attention, or what not--suffices to produce an impression of rhythm. It is commonly said that only intensive variations are necessary; but such types of differentiation are not invariably depended on for the production of the rhythmic impression. Indeed, though most frequently the basis of such effects, for sufficient reasons, this type of variation is neither more nor less constant and essential than other forms of departure from the line of indifference, which forms are ordinarily said to be variable and inessential. For the existence of rhythm depends, not on any particular type of periodical variation in the sensory series, but on the recurrent accentuation, under special temporal conditions, of periodic elements within such a series; and any recurrent change in quality--using this term to describe the total group of attributes which constitutes the sensorial character of the elements involved--which suffices to make the element in which it occurs the recipient of such accentuation, will serve as a basis for the production of a rhythmical impression. It is the fact of periodical differentiation, not its particular direction, which is important. Further, as we know, when such types of variation are wholly absent from the series, certain elements may receive periodical accentuation in dependence on phases of the attention process itself, and a subjective but perfectly real and adequate rhythm arise.

In this sense those who interpret rhythm as fundamentally dependent on the maintenance of certain temporal relations are correct. The accentuation must be rhythmically renewed, but the sensory incentives to such renewals are absolutely indifferent, and any given one of the several varieties of change ordinarily incorporated into rhythm may be absent from the series without affecting its perfection as a rhythmical sequence. In piano playing the accentual points of a passage may be given by notes struck in the bass register while unaccented elements are supplied from the upper octaves; in orchestral compositions a like opposition of heavy to light brasses, of cello to violin, of cymbals to triangle, is employed to produce rhythmical effects, the change being one in _timbre_, combined or uncombined with pitch variations; and in all percussive instruments, such as the drum and cymbals, the rhythmic impression depends solely on intensive variations. The peculiar rhythmic function does not lie in these elements, but in a process to which any one of them indifferently may give rise. When that process is aroused, or that effect produced, the rhythmic impression has been made, no matter what the mechanism may have been.

The single objective condition, then, which is necessary to the appearance of an impression of rhythm is the maintenance of specific temporal relations among the elements of the series of sensations which supports it. It is true that the subjective experience of rhythm involves always two factors, periodicity and accentuation; the latter, however, is very readily, and under certain conditions inevitably, supplied by the apperceptive subject if the former be given, while if the temporal conditions be not fulfilled (and the subject cannot create them) no impression of rhythm is possible. The contributed accent is always a temporally rhythmical one, and if the recurrence of the elements of the objective series opposes the phases of subjective accentuation the rhythm absolutely falls to the ground. Of the two points of view, then, that is the more faithful to the facts which asserts that rhythm is dependent upon the maintenance of fixed temporal intervals. These two elements cannot be discriminated as forming the objective and subjective conditions of rhythm respectively. Both are involved in the subjective experience and both find their realization in objective expressions, definable and measurable.

(_c_) _Rate._--The appearance of the impression of rhythm is intimately dependent on special conditions of duration in the intervals separating the successive elements of the series. There appears in this connection a definite superior limit to the absolute rate at which the elements may succeed one another, beyond which the rapidity cannot be increased without either (_a_) destroying altogether the perception of rhythm in the series or (_b_) transforming the structure of the rhythmical sequence by the substitution of composite groups for the single elements of the original series as units of rhythmic construction; and a less clearly marked inferior limit, below which the series of stimulations fails wholly to arouse the impression of rhythm. But the limits imposed by these conditions, again, are coördinated with certain other variables. The values of the thresholds are dependent, in the first place, on the presence or absence of objective accentuation. If such accents be present in the series, the position of the limits is still a function of the intensive preponderance of the accented over the unaccented elements of the group. Further, it is related to the active or passive attitude of the æsthetic subject on whom the rhythmical impression is made, and there appear also important individual variations in the values of the limits.

When the succession falls below a certain rate no impression of rhythm arises. The successive elements appear isolated; each is apprehended as a single impression, and the perception of intensive and temporal relations is gotten by the ordinary process of discrimination involved when any past experience is compared with a present one. In the apprehension of rhythm the case is altogether different. There is no such comparison of a present with a past experience; the whole group of elements constituting the rhythmic unit is present to consciousness as a single experience; the first of its elements has never fallen out of consciousness before the final member appears, and the awareness of intensive differences and temporal segregation is as immediate a fact of sensory apprehension as is the perception of the musical qualities of the sounds themselves.

The absolute value of this lower limit varies from individual to individual. In the experience of some persons the successive members of the series may be separated by intervals as great as one and one half (possibly two) seconds, while yet the impression is distinctly one of rhythm; in that of others the rhythm dies out before half of that interval has been reached. With these subjects the apprehension at this stage is a secondary one, the elements of the successive groups being held together by means of some conventional symbolism, as the imagery of beating bells or swinging pendulums. A certain voluminousness is indispensable to the support of such slow measures. The limit is reached sooner when the series of sounds is given by the fall of hammers on their anvils than when a resonant body like a bell is struck, or a continuous sound is produced upon a pipe or a reed.

In these cases, also, the limit is not sharply defined. The rhythmical impression gradually dies out, and the point at which it disappears may be shifted up or down the line, according as the æsthetic subject is more or less attentive, more or less in the mood to enjoy or create rhythm, more passive or more active in his attitude toward the series of stimulations which supports the rhythmical impression. The attention of the subject counts for much, and this distinction--of involuntary from voluntary rhythmization--which has been made chiefly in connection with the phenomenon of subjective rhythm, runs also through all appreciation of rhythms which depend on actual objective factors. A series of sounds given with such slowness that at one time, when passively heard, it fails to produce any impression of rhythm, may very well support the experience on another occasion, if the subject try to hold a specific rhythm form in mind and to find it in the series of sounds. In such cases attention creates the rhythm which without it would fail to appear. But we must not confuse the nature of this fact and imagine that the perception that the relations of a certain succession fulfil the the form of a rhythmical sequence has created the rhythmical impression for the apperceiving mind. It has done nothing of the kind. In the case referred to the rhythm appears because the rhythmical impression is produced, not because the fact of rhythmical form in the succession is perceived. The capacity of the will is strictly limited in this regard and the observer is as really subject to time conditions in his effortful construction as in his effortless apprehension. The rhythmically constructive attitude does not destroy the existence of limits to the rate at which the series must take place, but only displaces their positions.

A similar displacement occurs if the periodic accentuations within the series be increased or decreased in intensity. The impression of rhythm from a strongly accented series persists longer, as retardation of its rate proceeds, than does that of a weakly accented series; the rhythm of a weakly accented series, longer than that of a uniform succession. The sensation, in the case of a greater intensive accent, is not only stronger but also more persistent than in that of a weaker, so that the members of a series of loud sounds succeeding one another at any given rate appear to follow in more rapid succession than when the sounds are faint. But the threshold at which the intervals between successive sounds become too great to arouse any impression of rhythm does not depend solely on the absolute loudness of the sounds involved; it is a function also of the degree of accentuation which the successive measures possess. The greater the accentuation the more extended is the temporal series which will hold together as a single rhythmic group.

This relation appears also in the changes presented in beaten rhythms, the unit-groups of which undergo a progressive increase in the number of their components. The temporal values of these groups do not remain constant, but manifest a slight increase in total duration as the number of component beats is increased, though this increase is but a fraction of the proportional time-value of the added beats. Parallel with this increase in the time-value of the unit-group goes an increase in the preponderance of the accented element over the intensity of the other members of the group. Just as, therefore, in rhythms that are heard, the greatest temporal values of the simple group are mediated by accents of the highest intensity, so in expressed rhythms those groups having the greatest time-values are marked by the strongest accentuation.

Above the superior limit a rhythm impression may persist, but neither by an increase in the number of elements which the unit group contains, nor by an increase in the rate at which these units follow one another in consciousness. The nature of the unit itself is transformed, and a totally new adjustment is made to the material of apprehension. When the number of impressions exceeds eight or ten a second--subject to individual variations--the rhythmical consciousness is unable longer to follow the individual beats, a period of confusion ensues, until, as the rate continues to increase, the situation is suddenly clarified by the appearance of a new rhythm superimposed on the old, having as its elements the structural units of the preceding rhythm. The rate at which the elements of this new rhythm succeed one another, instead of being more rapid than the old, has become relatively slow, and simple groups replace the previous large and complex ones. Thus, at twelve beats per second the rhythms heard by the subjects in these experiments were of either two, three or four beats, the elements entering into each of these constituent beats being severally three and four in number, as follows:

TABLE I.