Various - Harvard Psychological Studies, Volume 1

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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.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VIII.
Opposite p. 314.]

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 deg., 240 deg., and 120 deg.; if the temporal
relations desired be in the ratios 2:1:1, the arrangement will be
360 deg., 180 deg., 90 deg.; if in the ratios 5:4:3, it will be 360 deg., 210 deg., 90 deg.;
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 deg., 270 deg., 180 deg.; 360 deg., 240 deg., 180 deg., and 360 deg., 260 deg., 180 deg..
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 cooerdination 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 aesthetic 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 cooerdinated 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 aesthetic 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 aesthetic 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.