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STUDIES IN MELODY



A Dissertation submitted to the Faculty of the Graduate School of Arts

and Literature in Candidacy for the Degree of Doctor of

Philosophy



DEPARTMENT OF PSYCHOLOGY



By

W. Van Dyke Bingham

Instructor in Educational Psychology, Teachers College,
Columbia University



(Published as Monograph Supplement No. 50 of the Psychological Review)

THE REVIEW PUBLISHING COMPANY

BALTIMORE, MD.

1910






WAVERLY PRESS

WILLIAMS 4 WILKINS COMPANY

BALTIMORE



PREFACE.

In the first portion of this monograph are presented the
results of investigations made in the psychological labora-
tory of the University of Chicago during the years 1905-07.
The experiments which form the basis of the remainder of the
work were carried on during the year 1907-08 in the Harvard
psychological laboratory.

To the directors of these two laboratories, Professor James
Rowland Angell and Professor Hugo Miinsterberg, the writer
desires to express his gratitude for patient counsel and stimu-
lating criticism. He wishes also to acknowledge his obliga-
tion to the fellow-students of experimental psychology, who,
in the capacity of observers, made possible the prosecution of
these studies.

To the investigations of Professor R. H. Stetson in the
field of rhythm the writer owes the method of attack employed
in studying the relationships of muscular movement to the
melody experience ; and the outline of a motor theory of melody
with which the present study is brought to a close is obviously
the outgrowth of suggestions from Professor Stetson's impor-
tant publications. Indebtedness to Professor Max Meyer is
likewise evident, and nowhere more plainly than in those pas-
sages which express disagreement with his views.

My controversy with Professor Meyer is in part made
necessary because of what seems to me to be an equivocal use of
the term 'tonal relationship' on his part ; and lest a similar ambig-
uity creep in to vitiate the discussions of the following pages,
I have taken pains in each instance to specify in which of its
two common meanings the term "relationship " is used. Musi-
cians speak of two tones as directly "related" when the ratios
of their vibration-rates are so simple that one tone is found
among the first five partials of the other, or, what amounts to
the same thing, when the two tones belong to a major triad,
the 'chord of nature.' The "feeling of relationship" is the



218505



iv PREFACE

experience of coheience, of 'belonging- togetherness,' which
characterizes the hearing of two successive tones of the sort
described. The question as to what pairs of tones arouse this
feeling of " relationship " must of course be answered not by an
arbitrary definition but by reference to the facts of experience.

Now it is perfectly evident that this particular kind of tonal
"relationship," arising out of certain acoustical properties
of the sounds, is not the sole kind of relationship which may
bind tones together in our experience. Two tones may come
to be felt as related, in a way, merely because they have often
been heard together. Moreover any two tones whatsoever, be
their ratios simple or complex, are felt to be related to each
other as higher and lower. Here the term relationship is used
in its ordinary broad, untechnical sense.

Whenever, in the following pages, the terms "relationship"
and "related" are employed in the technical sense, they are
enclosed in quotation marks; and where these marks are not
used, the reader is to understand that the broader, untech-
nical connotation is indicated.

What the musician designates as tone-color or timbre, I
have called by the usual psychological terms, clang-color, or
briefly, color.



CONTENTS
Part I. The Melody Problem page

§1. The nature of melody. Three usages of the term, corresponding to three
distinct melodic phenomena. A melody is a succession of tones which
are not only related, but which also constitute an esthetic unity, a whole . . i

§2. An illustration 3

§3. The melody problem: How can a series of discrete tonal stimuli generate

the experience of melodic unity? 4

§4. Elements of melodic structure : actual duration of the sounds, pitch, color and

intensity 5

§5. Relative duration, intensity and color 6

§6 . Pitch relations , the sine qua non : Melodic ' ' relationship ' ' direct and indirect ;
pitch distance; definite and indefinite pitch relations; the phenomenon of
the falling inflection 8

§7. The phenomenon of melodic trend: certain pairs of tones heard in succession
end better on the upper tone, others on the lower. Lipps formulates these
facts in the ' law of the powers of 2.' His theoretical assumptions 10

§8. Restatement of the melody problem and limitation of the present study to

effects of pitch 13

Part II: The Phenomena of Melodic "Relationship," and of Melodic

Trend.

§9. Previous experimental studies. Meyer finds melodies played with an intona-
tion which admits the 7 ratio are preferred to the same melodies played in
the diatonic scale 15

§io. Meyer's theory of melody. Melodic " relationship " observable in intervals

involving the 7 ratio. The 'complete scale' 17

§11. Dangers arising from the use of arithmetical ratios to express" relationship."
Any given feeling of "relationship" is the property not of a single interval
alone, but of a whole zone of intervals 21

5i2. First series of experiments on the phenomenon of melodic trend, or finality

in two-tone sequences. Method. Observers 23

§13. Discussion of results, (a) The trend of the different intervals compared 27

§14. (Jb) The second tone of a two-tone group is judged to be a final tone less often

than it is judged to be lacking in finality 28

§15.^ (c) A small preponderance exists in favor of descending intervals as more
" ;i definitely final. Meyer's experiments on this point. Need of separating
effects of the falling inflection phenomenon from effects due to more
definite pitch relations 28

§16. {d) When 2 is the end-tone, effects of rising and falling inflection come
clearly to view. When 2 is the first tone, the number of affirmative judg-
ments of finaUty is nearly the same for ascending and for descending
intervals, being less than one-fourth of the total in each case 30



vi CONTENTS

§17. Final summary lends some support to the Lipps-Meyer law, but numerous page
exceptions demand explanation 32

518. Further experiments point toward the 'law of the return,' and toward the

fact that tonality, resting on a harmonic basis, determines melodic
trends even in tv/o-tone sequences 33

519. Third series of experiments: When a definite tonality is in mind, the

trend of a two-tone sequence is uniformly toward one of the tones of

the tonic chord 35

§20. The nature of 'tonality.' A tonality is an 'attitude,' probably motor at

basis 36

i2i. The effects of habituation 39

« 22. Summary, and new formulation of problem 41

Part III. Effects of Melodic Stimuli upon Muscular Movement.

§23. Apparatus for recording rate, amplitude and form of tapping movement of

finger 43

§24. Method of procedure 46

§25. Observers: tests of their musical ability; individual differences in natural

rate and form of tapping 48

§26. Results. Records of tapping without stimulus or distraction 53

§27. Effect of auditory stimuli upon rate of tapping 54

§28. Experiments with melodic stimuli : the perfect fourth. Characteristic vari-
ations of rate of tapping appear, which are different for the ascending and

the descending fourth 57

§29. Hypothesis regarding the significance of accelerations and retardations of

rate of tapping 59

§30. The hypothesis applied in detail to the results of experiments with ascending

and descending fourth 61

§3 1 . And tested in the light of experiments with the perfect fifth, diminished fifth,

major third and minor sixth 63

§32. A group of experiments with three-tone sequences. The 'return;' the

octave 69

§33. Effects of a longer series of tones upon the rate of tapping 77

$34. Summary jg

Part IV. Suggestions Toward a Motor Theory of Melody.

§35. Sketch of a motor theory of melodic unity. Motor phenomena of mel-
ody and of rhythm compared. Final summary 81



PART I.

THE MELODY PROBLEM.

§1. Neither musicians nor psychologists are agreed as to
the meaning of the term melody. Divergent usage, leading to
misunderstanding and dispute, has arisen because within the
range of melody experience there exist several distinguishable
mental phenomena, each of which has in turn been construed
as the essential mark of a melody. Weinmann,^ following Lipps,^
says that a melody is a unity, a whole, no mere succession of
tones. It is, further, an esthetic unity in which the con-
stituent tonal elements are subordinated to a single dominating
element, the tonic. This definition operates to limit the scope
of his study to such melody phenomena as those exhibited in
modern European diatonic music, since it a priori excludes the
possibility of melodies which lack tonality.

The doctrine of Lipps and his followers that esthetic unity
always involves the subordination of the separate elements of a
manifold to a single chief element is opposed by Meyer^. In
his view, the statement that a melody is a unity means
merely that we experience relationship between the tones.
Indeed Meyer defines melody in terms of relationship.* To say
that two tones are related and to say that they form a melody is
the same thing. Such a definition avoids a narrow conception
of melody. The scope of the term becomes much contracted,
however, by the technical meaning which Meyer attaches to the
term relationship. The essence of melody consists, for Meyer,
not in the experience of any kind of relationship whatever
between the successive tones, but in the experience of a very

^Tritz Weinmann: "Zur Struktur der Melodic" Zeits.f. Psychol. 1904, 35, 340.

*Th. Lipps: "Zur Theorie der Melodie," Zeits. f. Psychol. 1902, 27, 237. See also
his Psychologische Studien, 2te Aufl. 1905, 193 ff.

*M. Meyer. "Unscientific Methods in Musical Esthetics." Jour, of Phil.
Psy., and S. M. 1904, i, 711.

* Elements of a Psychological Theory of Melody. Psych. Rev, 1900, 7, 246.



W. VAN DYKE BINGHAM.



speckildrid-HiTiited kind of relationship, namely that to which
the technical musical term "relationship" has come to be
applied. This narrowing of the meaning of the term operates
to exclude from the realm of melody those songs of primitive
peoples in which vague and indefinite pitch intervals appear,
as well as the so-called melodies of speech.

Can we assent to Meyer's contention against Weinmann
that melodic unity means nothing more than relationship
between the parts? The esthetic unity which characterizes
a melody does indeed involve experience of relationship among
the several tones; but this is not all. For example, it involves
also the experience of completeness. If the feeling of complete-
ness is destroyed, the 'unity' is shattered. Not merely tonal
relationship, but 'form' is necessary to constitute the esthetic
unity of a melody. Meyer's deed here is better than his word :
for throughout his investigations he searches for something
more than mere "relationship" in his melodies, namely, for an
organization of relationships, a combination of related tones
ordered in one way rather than another, — arranged, indeed, so
that they generate not a mere consciousness that the elements
are related, but a perception that they are so related as to form
a complete structure, a whole.

There are then, three clearly distinguishable phenomena,
each one of which has been put forward as the peculiar differ-
entia of melody: (a) "relationship" between the constituent
tones; (b) esthetic unity or wholeness, such as distinguishes a
definite melodic phrase when contrasted with a mere fragment
of melody, or which characterizes even more clearly a com-
plete melody that is brought into comparison with any portion
of itself; (c) tonality, or the dominance of the entire sequence
by a single tone, the tonic. Weinmann's definition stresses
the third of these phenomena: if there exists a song of some
alien people in which the preponderance of one tone over the
others fails to appear, such a song must be called by some
other name than melody. Meyer at the opposite extreme,
emphasizes only the phenomenon of "relationship." Wher-
ever "relationship" between successive tones is felt, a melody
exists, even though the succession be fragmentary and the
hearer be left in suspense, unsatisfied.



STUDIES IN MELODY. 3

For the purpose of the present exposition, it has seemed best
in defining what shall be meant by a melody, to place emphasis
upon the second of these three phenomena, — upon the esthetic
unity, the wholeness, which characterizes the completed expe-
rience. This usage of the term is adopted with full realization
that it is not wholly unobjectionable. After such a definition,
how shall one speak of Wagner 's ' endless melodies ? ' By what
name shall one describe the effect when in a Brahms chorus,
one of the middle voices for a few brief measures stands
prominently forth only to be lost to the ear again in a maze
of counterpoint? Is not this tonal group without distinguish-
able beginning or end a most delightful melody? It would
certainly be called a melody if, with Meyer, we had chosen to
make "relationship" the sole essential; but in the terminology
we have chosen, it must be called a melodic fragment, and not,
strictly, a melody.

The matter of prime importance is, of course, to realize
that by whatever names they may be called, we are confronted
with three different phenomena — "relationship," phrase- or
period-unity, tonality — which, no matter how intimately they
may prove to be bound up together, are nevertheless in intro-
spection clearly distinguishable, and must not be confused.

§2. At the risk of incurring the charge of prolixity from
readers who are most at home in this field, I shall venture to
develop somewhat more fully what I mean by a melody, before
attempting to formulate explicitly the melody problem.

Let the reader ask himself in what way his experience of a
melody differs from his experience of a mere succession of
musical sounds of varying pitch. Possibly he will reply that
the group of sounds that he calls a melody is more pleasing.
But this agreeableness he will admit is not the essential char-
acter. One may, for example, upon hearing a flageolet of ob-
noxious tone quality find the whole experience disagreeable
and. yet recognize that what he is hearing is a melody ; or on
the other hand one may take delight in a perfectly random
series of sounds drawn from a beautifully voiced instrument.
Something other than the pleasurable affective aspect of the



4 W. VAN DYKE BINGHAM.

total experience must be present to differentiate the melody
from the non-melodic succession of pitches.

Upon further comparison of the two kinds of experience the
observer will notice that the sounds of the melody seem to be-
long together, to cohere, and to stand in such a relationship
each to the others that the entire series is felt to be a unity.
The tones of the non-melody, by contrast, are felt to be unre-
lated : they do not ' hang together' as it were. Or, even if one
discovers that some of the tones of the non-melodic group
exhibit a close connection with some of the others, the group
as a whole is not a unity : it is felt to lack consistency or internal
coherence, or continuity, or completeness.

An example will make more obvious this contrast between the
melody and the non-melody. I played to a group of moderately
musical observers the following simple succession of musical
sounds : c' e' g' e' f d' c' . The tempo was slow, the duration of
the tones uniform. I then played a second series beginning on the
same tone and ending on the same tone, and employing the same
five degrees of pitch as the first but in a different order: c' f d! g'
e' f c' . The hearers reported that in the first group the sounds
seemed to follow each other naturally, coherently, and in a way,
inevitably, and with the last sound the series seemed to come to a
definite close. Each element articulated with the others and the
group as a whole was felt to be a unity. In other words, it was
judged to be a melody. But with the second series of tones the
hearers failed to discover this naturalness or inevitableness
about the order of the sounds. The pitch, they said, wandered
rather incoherently and disconnectedly here and there. More-
over when the last sound was heard it failed to bring the feeling
of completeness, of finality, which characterized the close of the
former series. This second succession of tones was judged by
these observers to be no melody.

§3. Our definition of a melody places stress upon the experi-
ence of unity; but it does not prejudge the question as to
whether this necessitates the subordination of all the elements
to one dominating 'monarch element.' Neither does it imply
that the experience of definite "melodic relationships" (in the
technical sense of the term) is the sine qua non. A melody we



STUDIES IN MELODY. 5

shall define as a succession of musical sounds which is felt to con-
stitute an esthetic unity, a unity toward the establishment of
which the pitch relations of the successive tones contribute.^

The melody problem, then, is the problem of explaining how a
series of discrete tonal stimuli can arouse this feeling of unity.

As a matter of fact any actual melody such as a gamin whistles
on the street or a Pawnee Indian sings to the dawn, gains its
unity, its coherence, its wholeness, through the combined oper-
ation of many factors. The factors of intensity and duration,
for example, are coordinate with pitch in the determination of
the total psychosis: tempo, rhythm, dynamic structure share
in determining what the melody shall be. A brief analysis of
these factors will bring into prominence the particular phases
of the melody problem with which these studies are concerned.

§4 It is to be remembered that musical sounds can vary
one from another in only four ways: in duration, intensity,
clang-color (i. e., tone-quality or timbre) and pitch. But each of
these four aspects or attributes of the constituent tones affects
in a two-fold manner the nature of the melody. The total effect
is what it is, partly because of the relative duration, intensity,
pitch and color of the separate sounds employed, and partly
because of the actual pitch, intensity, duration and color. The
'actual duration' factor, for instance, is the tempo. The rela-
tive duration of all the sounds remaining constant, the nature
of the melody may be entirely altered merely by changing the
speed, i. e., the actual duration of the sounds. A familiar melody
played in an unusual tempo may be hardly recognizable, and
if the change of time is carried beyond certain limits in either
direction the melody is utterly destroyed, — it becomes a con-
fusion of noises or a broken succession of sounds without signifi-
cance or interest.

Similarly, the actual or ' absolute ' pitch of a melody enters in
to make it what it is. The low rumbling melody with which
Grieg begins the "Dance of the Trolls" in the first Peer Gynt
suite is almost a totally different thing when played in the twice-
accented octave, instead of three octaves lower.

1 Here and throughout the paper, whenever the technical connotation of the term
"relationship" is indicated, the word is enclosed in double quotation marks.



5 W. VAN DYKE BINGHAM.

The difference which the actual clang-color makes is of course
at the basis of artistic orchestration of melodies ^and of organ-
registration. When a theme given out by the oboe is repeated
by the violins we say it is the same melody, and yet it is not
wholly the same.

Fourthly, the dynamic factor, the actual loudness or softness
of the melody as a whole, remains to be mentioned as one of the
contributors to the nature of the melody.

§5. These four factors taken in their actual or 'abso lute'
aspects are, however, of very secondary significance as com-
pared with these same factors operating within the melody
itself to contrast and to bind together the separate tonal ele-
ments. With reference to the relative duration, pitch, etc., of
the individual tones, it will be convenient to treat of {i) the re-
lation of each tone to its immediate associates, and {ii) the
relation of the tone to the whole melody. {Cf. accompanying
outline).

ELEMENTS OF MELODIC STRUCTURE CLASSIFIED ACCORDING TO THE

FACTORS OF



I.


Duration


\




a) Actual


b) Relative




{,Tempo)


i. Measure pattern

Rhythmical figuration
ii. Accel., Rit., etc.


II.


Intensity






a) Actual


b) Relative

i. Accent, stress, etc.
ii. Cresc. , decresc. , etc.


III.


Color






a) Actual


b) Relative




(Orchestraiion; Registration)


i.
ii.


IV.


Pitch






a) Actual


b) Relative




(Absolute pitch)


i. Interval relationships
ii. Tonality relationships



Relations of duration of the first sort are at the basis of the
measure-form and rhythmical figures, while accelerando and



STUDIES IN MELODY.



ritardando illustrate the relations to a more inclusive group.
Rhythm is usually a result of the combination of intensity and
duration relations, although this is not always the case. Thus a
melody played on the organ or on a mechanical piano player
lacks variations of intensity of the separate tones.

In the case of the loudness factor, the former type of relation
determines the effects of accent, of stress; while the latter gives
dynamic form to the whole group, the crescendo-decrescendo
effects, etc.

The relative color of thf separate tones has, in the enumer-
ation of the factors of melodic structure, usually been neglected.
But a priori, one would expect this attribute of tone-sensation,
as well as the others, to be of significance ; and a posteriori, color
is found to be of vastly greater importance to melody than one
might suppose who had never given the matter careful thought.
The reason why this factor has been overlooked is that it usually
remains constant throughout the melody. Its presence as a
unifying factor first comes into evidence when an unwonted
change of color enters and makes itself felt as a disturbing ele-
ment: as when a singer is not skillful in passing from one
register of the voice to another, or a clarinetist meets a similar
difficulty in making the transition from the lower to the middle
register of his instrument. The changes in color which are thus
unwittingly or unavoidably introduced have their disintegrating
effect, be it never so slight, upon the melody. Among violinists
this is a well known fact, a commonplace. Even so slight a
change of color as is involved in the passage from one string to an-
other is recognized as of importance in artistic phrasing, and the
resources of technical proficiency are sometimes taxed in the ef-
fort to meet the requirements which this principle imposes. Such
a principle raises a prohibition against careless shifts of color,
and at the same time offers a positive aid to artistic phrasing, —
it ^rjables the violinist to give to a group of tones a peculiar unity
of its own not otherwise obtainable. Surely such a factor in the
determination of melodic form as clang-color, — a factor which has
a recognized place in musical practice, — does not deserve to be
entirely neglected. A careful experimental study of the effects
and of the possible extent of alterations of color within the mel-
ody is a psychological desideratum.



8 W. VAN DYKE BINGHAM.

§6. All of the factors which have been discussed, the rela-
tive clang-color, loudness and duration of the sounds, have been
shown to contribute to the structural unity of a melody. But
not all of these taken together are sufficient to make a melody.
The essential factor is still lacking, namely the pitch relations.
A sequence of tones of the proper relative loudness and duration
to constitute a vigorous rhythm would not be called a melody if
the pitch of the tones were either uniform or random.

The pitch, too, of each tone bears certain relations to the
group of tones as a whole. This makes possible such phenom-
ena as tonality, of which it will be necessary to treat in due
time. At present let us focus attention upon the relations which
may exist between individual tones.


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