TIGHT BINDING BOOK
Drenched Book
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PSYCHOLOGY OF MUSIC
BY
CARL E. SEASHORE,
PH.D., LL.D., BC.D., D.LITT.
McGRAW-HILL BOOK COMPANY, INC.
NEW YORK AND LONDON
COPYRIGHT, 1938, BY THB McGRAW-HiLL BOOK COMPANY, INC.
PRINTED IN THE UNITED STATES OF AMERICA
All rights reserved. This book, or
parts thereof* may not be reproduced
in any form without permission of
the publishers.
To my comrades in research
for the last forty years
this volume is affectionately
dedicated.
npms volume is dedicated to my comrades in research, professors J. and students, for the last forty years. I am writing as a spokes- man for them all, attempting to present in high lights the new approaches developed during this period. This involves the right to draw freely from more than one hundred publications emanating from the group. Wherever possible I have named the person pri- marily responsible for the contribution; but the text embodies facts which in large part are common stock in the laboratory.
In doing the overhead work for all these years, it has been difficult to separate my own ideas from the ideas of collaborators because our policy has been to share ideas with the utmost gener- osity. In the interest of condensation and clarity, I have interpreted and classified as much as is consistent with the purpose and, there- fore, have not used quotation marks extensively.
It is difficult to give proper acknowledgment to all the persons and sources represented. All authors of publications from which substantial units are drawn are mentioned in the text with a super- script number which refers to the corresponding number in the bibliography. The sources of illustrations are indicated in the text. Acknowledgment to authors and publishers for permission to use material is herewith gratefully extended.*
Owing to the nature of the situation, I have counted upon many of my collaborators to read and criticize the manuscript in whole or in part both from the point of view of science and from the point of view of music.
*The following note from the Music Educator* Journal, September, 1937, IB self- explanatory :
"In a series of reports from the laboratory-studio for the Psychology of Music, Carl E. Seashore has presented to Journal readers specimens of scientific findings dealing with various phases of the psychology of music. Appearing in the October issue of the Journal will be the tenth in a series, which will deal with the problem of the tempered scale a*
x PREFACE
The Psychology of Musical Talent,1*7 published by Silver Burdett & Company, in 1919, is a monograph which marks a ne\v vantage ground in the psychology of music. It covers a restricted field in which it has permanent value and should, therefore, not be revised, but supplemented. In the present volume, I have aimed to avoid duplication of that work to which this is a logical sequel.
Concentration in this field of work has been favored by a gen- erous attitude on the part of the University of Iowa toward this project and through a series of generous fellowships provided by Mr. George Eastman, the National Research Council, the Guggen- heim Foundation, and the Carnegie Foundation. Through a special interest in this subject and such generous financial support, it has been possible to maintain a continuous project through trained investigators, working on a unified program for a generation.
The purpose of this book is to stimulate and guide the student of music in scientific observation and reasoning about his art. It is, therefore, not a summary of all the known facts on any subject, but rather a series of flashes illustrating the scientific approach from as many angles as space and material permit in an elementary textbook. Since the book is written for beginners, no technical description of apparatus or method is given except in most elementary general principles. Material for the student to work upon is, however, furnished abundantly. My attitude throughout may be expressed in the invitation, "Come with me into the laboratory-studio for the psychology of music and see how the study of science of the art of music works." As in my other text- books the motto has been
Not psychology but to psychologize.
This book has been many years in the making. Certain chapters have been revised periodically as knowledge in the field has advanced. The present edition may, therefore^ be regarded as a report of progress subject to revision in the near future; yet an effort has been made to deal only with firmly established facts,
opposed to the natural scale and others. Beginning in March, 1936, successive issues of the Journal have Carried articles on the following subjects: (1) Pitch Intonation in Singing, (2)' Approaches to the Experimental Psychology of Music; (3) Quality of Tone: Timbre, (4) Quality of Tone: Sonance; (5) Measurement of Musical Talent: The Eastman Experi- ment; (6) The Vibrato: What Is It?; (7) The Vibrato: What Makes It Good or Bad?; (8) The Vibrato: How Can We Approach an Ideal Vibrato?; (9) A Performance Score with Phrasing Score for the Violin."
PREFACE xi
even though fragmentary. Diversity in the style of figures is justified on the policy of retaining the form given each figure by its original author.
Upon invitation from my Alma Mater to give the so-called academic address at an anniversary celebration last year, I chose as my subject The Power of Music. This had been the subject of my class oration when graduating from the academy fifty-one years before. Half a century ago the adolescent lover of music began his oration as follows:
Music is the medium through which we express our feelings of joy and sorrow, love and patriotism, penitence and praise. It is the charm of the soul, the instrument that lifts mind to higher regions, the gateway into the realms of imagination. It makes the eye to sparkle, the pulse to beat more quickly. It causes emotions to pass over our being like waves over the far- reaching sea.
That was what the music I lived in meant to me half a century ago. It was the expression of the genuine thrill of young enthusiasm. Considering what music meant to me then and what it means to me now after a life career in the science of music, there comes to me an analogy from astronomy. Then I was a stargazer; now I am an astronomer. Then the youth felt the power of music and gave expression to this feeling in the way he loved and wondered at the stars before he had studied astronomy. Now the old man feels the same "power of music," but thinks of it in the manner that the astronomer thinks of the starry heavens. Astronomy has revealed a macrocosm, the order of the universe in the large; the science of music has revealed a microcosm, the operation of law and order in the structure and operation of the musical mind. It is a wonder- ful thing that science makes it possible to discover, measure, and explain the operations of the musical mind in the same attitude that the astronomer explains the operation of the stars.
It is not easy to pass from stargazing to technical astronomy. It is not easy to pass from mere love and practice of mu. ic to an intelligent conception of it. To help the lover of music bridge this gap is the purpose of this volume.
CARL E. SEASHORE.
PAQH
PREFACE ix
LIST OF ILLUSTRATIONS xvii
CHAPTER
1. THE MUSICAL MIND 1
The sensory capacities — Musical imagery, imagination, and memory — Musical intelligence — Musical feeling — Musical performance — The meaning of this analysis
2. THE MUSICAL MEDIUM IS
Musician, music, listener — Characteristics of the sound wave — Fre- quency: pitch — Musical aspects of pitch intonation — Intensity: loud- ness — Musical aspects of loudness — Duration: time — Musical aspects of time — Wave form: timbre — Musical aspects of tonal timbre — The musical performance score
3. THE SCIENCE OP Music £3
Scope of the subject — The performer, the music, the listener — General principles of science — Basic principles in the psychology of music
4. A MUSICAL ORNAMENT, THE VIBRATO 33
Nature of the vibrato — An example of the vocal vibrato — An example of instrumental vibrato — Frequency of occurrence, extent and rate of vibratos — Normal illusions which make for beauty of vibrato — The nature of beauty in the vibrato — Ear training for the vibrato — Use and abuse of the vibrato — The vibrato, good, bad, indifferent, and ideal
5. PITCH: FREQUENCY 53
The nature of pitch — Limits of audible pitch — Pitch discrimination — ^Absolute pitch-^The significance of individual differences — Normal illusions of pitch — Subjective tones — The first difference tone — Other difference tones — Summation tones — Subjective harmonics — The dif- ference tone a substitute for a low fundamental — Pitch performance
6. LOUDNESS: INTENSITY 76
The role of intensity — Sensitivity or hearing ability — Deterioration with age : presbycousis — Children's hearing — Discrimination : the sense of intensity — Number of audible differences in loudness — Motor
xiii
xiv CONTENTS
CHAPTER PAGE
capacities — Intensity characteristics of musical tones — Amplification of sound
7. DURATION: TIME 90
Nature of the perception of time — Discrimination : the sense of time — Normal illusions of time — Motility
8. TIMBRE: WAVE FORM 95
The nature of timbre — Harmonic analysis — Synthetic tones — Timbre discrimination: the sense of timbre
9. TONE QUALITY: SONANCE 1015
Analogy in moving pictures — Types of sonance — Sonance in attack, release, and portamento — The inside of ji vocal tone — What is m a name? — Sonance in speech — Nature of the vowel in music and speech- •*/ The problem of formant regions — Dependence of harmonic structure upon fundamental pitch and total intensity in the vowel — Conversa- tional vs. audience voice ^
10. CONSONANCE . . . 125
The nature of consonance — The psychological approach — Six psycho- logical problems — Order of merit in each of four criteria — Order of rank on three criteria combined — The sense of consonance
11. VOLUME 134
Spatial factors — Quantitative factors — Qualitative factors — Temporal factors — Subjective factors — Carrying power
12. RHYTHM , . . . 138
v/ The nature of rhythm — What rhythm does — Individual differences in
musical rhythm — Psychology of rhythm ^
/13. LEARNING IN Music . 14P
Twelve rules for efficient learning in music (to the pupil) — Some specific applications (to the instructor)
14. IMAGINING IN Music 161
The analogy in sculpture and painting — Comparison of musicians and scientists — R. Schumann — Mozart — Berl »"'>z — Wagner — Supplemen- tary imagery — Living in a tonal world — The development of imagery — Individual differences in mental imagery
/15. THINKING IN Music 173
The issue — The nature of musical intelligence — How musicians rate
46. NATURE OF MUSICAL FEELING . 178
Determined by capacities — Intensified by pursuit — Characterized by intelligence and motor skills — Transfer to other situations
CONTENTS xv
CHAPTER PAO«
17. TIMBRE OF BAND AND ORCHESTRAL INSTRUMENTS 182
The bassoon — The clarinet — The French horn — The baritone horn — The cornet — The slide trombone — The flute — The oboe — The tuba
18. VIOLIN 199
The violin performance score — The violin phrasing score — Comparison of the performance of two players — The pitch factor — The intensity factor — The temporal aspect — The timbre aspect — Intervals: the problem of scales
19. PIANO 225
Piano touch — The piano camera — The piano performance score — Section of Chopin Nocturne No. 6 — Similarity in statement and restatement — Consistency of interpretation — Asynchronization of chords
20. VOICE 254
Singing — The tonal aspect: pitch — The dynamic aspect: intensity — The temporal aspect: time — Time and stress: rhythm — The qualita- tive aspect; timbre and sonance
21. PRINCIPLES OF GUIDANCE IN Music 286
The problem — Paving the way — Reminiscent incidents — Principles of measurement and guidance — Sources of error in guidance procedures
22. MEASURES OF MUSICAL TALENT 302
What can we measure ? — Principles involved in the elementary battery of measures of musical talent — Criticisms of this approach — Purpose of the phonograph records and supplementary procedures — Reliability — The basis for rank order — The uses of these measures
23. ANALYSIS OF TALENT IN A Music SCHOOL 312
Origin of the Eastman School experiment — Plan and purpose of the experiment — Classification — Representative profiles — Stability of the classification — Retests of adults and children — Bearing on success in the college music course
24. ANALYSIS OF TALENT IN THE PUBLIC SCHOOL .321
The Lincoln experiment — The Rochester service — Procedure in the guidance program — The training of teachers and supervisors — The organization of a guidance program for the public school
%5. THE INHERITANCE OF MUSICAL TALENT 330
The nature of the inheritance of musical talent — Basic approaches now available — Possible ways of organizing investigation — The naturalist's point of view
xvi CONTENTS
CEU.FTBB PAQB
£6. PRIMITIVE Music 346
Musical anthropology through phonophotography — Negro songs
27. THE DEVELOPMENT OF MUSICAL SKILLS 360
Control of pitch intonation — Control of intensity — Control of time and rhythm — The rhythm meter — Training for precision in rhythmic action — Control of timbre — General significance of specific training for skills
28. MUSICAL ESTHETICS 373
Approaches to musical esthetics — Esthetics as a normative science — The musical message
APPENDIX 383
BIBLIOGRAPHY . 387
INDEX TO AUTHORS MENTIONED OR QUOTED IN THE TEXT 399
INDEX TO MUSICIANS 401
INDEX TO COMPOSITIONS 403
SUBJECT INDEX 405
LIST OF ILLUSTRATIONS
PAOB
Oscillogram of a pure and steady tone 16
The Bach-Gounod Ave Maria as sung by Herald Stark 35
Bach's A ir for the G String, as played by Arnold Small 39
Drink to me only with thine eyes, as sung by Lawrence Tibbett 48
Variation with frequency level and sensation level 60
A scale of just perceptibly different pitch steps 61
Number of times filter condition was correctly preserved as function of cut-off
frequency for the piano 69
Audible frequency range for music, speech, and noise 71
Compass of musical instruments 73
Audiograms showing types of hearing loss 79
Limits of audible sound 82
Loudness-level contours 83
The number of just noticeable steps in loudness (j.n.d.) between the thresh- old of audibility and the threshold of pain 85
Dominant partials in a violin tone 98
Tone spectrum in terms of percentage of energy 98
Tone spectrum in terms of decibel values 98
Types of vocal attack 106
The harmonic structure of a beautiful tone 107
Record of the speech from The Judgment Day by Josephine Victor 112
Timbre and sonance in a vowel; same vowel spoken twice by the same person 114
Timbre and sonance in a vowel; the same vowel spoken by two persons . . 115
Formant regions 116
The effect of variations in pitch, intensity constant, and variations in inten- sity, pitch constant, on the harmonic composition of the vowel "Ah " . 119
The variation of harmonic constitution with pitch 120
Acoustic spectra and total intensity level under the three conditions. . . . 122
Order of merit of interval in the consonance-dissonance series 1S2
xvii
xviii LIST OF ILLUSTRATIONS
PAGE
Distribution of ratings in tonal auditory imagery 163
The bassoon 189
The clarinet 191
The French horn 191
The baritone horn 193
The cornet 193
The slide trombone 195
The flute 195
The oboe 197
The tuba 197
Ave Maria as played by Slatkin 200, 202
Ave Maria as played by Small 201, 203
Phrasing score for first half of Fig. 1 204
Phrasing score for Fig. 2 204
Pitch, intensity, and temporal deviations for the Air for the G String (Bach-
Wilhelmj) as played by Small 208
Pitch, intensity, and temporal deviations for the Tzigane (Ravel) as played
by Menuhin 208
Intensity and temporal deviations for the Air for the G String (Bach- Wil- helmj) as played by Elman 209
Intensity and temporal deviations for the Air for the G String (Bach- Wil- helmj) as played by Small (second performance) 209
G string 216
D string 216
A string 217
E string 217
Score of the Kreutzer Etude showing passage, between the two arrows, which
was played 218
Phrasing score for pitch rendition of the passage in Fig. 13 by four players 219
Group performance for five intervals 221
Comparison of performances in three selections 222
Comparison of the tempered and the natural scales with the Pythagorean
scale 223
Drawing from actual photogram taken with the Iowa piano camera .... 234
Schematic drawing of the mechanism of the piano camera 235
The photogram of Fig. 1 transcribed into the musical pattern score .... 238
The chorale section of Chopin's sixth nocturne 239
The musical pattern score of the chorale section of Chopin's sixth nocturne,
as played by pianist A 240
The musical pattern score of the chorale section of Chopin's sixth nocturne,
as played by pianist B 241
LIST OF ILLUSTRATIONS xix
PAOI Relative duration of melody notes and the corresponding relative intensity
values 245
Duration of measures in two renditions of the first 24 measures of Chopin's
Polonaise, op. 40, no. 1, by Bauer 246
Duration of phrases in same performance as for Fig. 8 246
Duration of the first 4 phrases in three renditions of the first 4 phrases in
Beethoven's Sonata, op. 57, by Clapp 247
Comparison of artistic time and attempted metronomic time in the rendition
of the first 25 measures of Chopin's Nocturne, op. 27, no. 2, by Clapp 247
Asynchronization of chords 250
Drink to me only with thine eyes as sung by Arthur Kraft 256
All through the night as sung by Arthur Kraft 258
The aria Come unto Him (Messiah) as sung by Lucy Marsh 260
The aria Come unto Him (Messiah) as sung by Mrs. Carl Seashore, Jr.. . . 263
Samples of mean-pitch lines from Stark 269
Samples of mean-pitch lines from Kraft 270
Type forms of gliding, rising attack 271
Type forms of portamento 272
Spread of tonal powers within a song 275
Durational progress of the songs from measure to measure 276
Durational progress of the songs from phrase to phrase 277
Kraft 1 and Tibbett. The role of several factors in rhythm 280
Samples of types of profiles 816
Distribution of Test 1 and Test 2 raw scores in five measures with a 3-year
interim between measurements 317
Distribution of Test 1 and Test 2 raw scores for three groups in five measures,
with a 3-year interim of musical training between measurements . . . 318 The percentage of students graduating within 4 years in each of the five
groups 319
Family pedigree chart of musical talent of the Rho group 343
On ma journey 350
Att my days 353
You ketch dis train 355
Negro laugh 356
Transfer of training in pitch intonation 364
The effect of training for precision in rhythmic action 370
PSYCHOLOGY OF MUSIC
THE MUSICAL MIND
npHE late Horatio Parker once said in the way of a witticism, JL "There are no musicians in this country," and to my intimation that there must be some near-musicians he said, after some delibera- tion, "Well, there is one." On inquiry as to what his particular merits were, it came out that he was a composer. "But," I asked, "how about our great singers and instrumental performers?" "Ah, they are technicians." Ranging from such a conception of the musical mind to that of the mind of Blind Tom or, in a more extreme case, the musicial prodigies which we frequently find in the institutions for the feeble-minded, it is possible to recognize countless varieties of musical minds.
Avoiding as much as possible the account of technical methods of approach, analysis, and measurement, I shall aim to set up in this introductory chapter a skeletal structure in terms of which musical minds may be described and interpreted.
The point of view here presented as a result of laboratory experience is based upon the analysis of the musical medium — the physical sound. This rests upon the assumption that a^musical mind must be capable of sensing sounds, of imaging these sounds in reproductive and creative imagination, of being aroused by them emotionally, of being capable of sustained thinking in terms of these experiences, and ordinarily, though not necessarily, of giving some form of expression of them in musical performance or in creative music.)
( In this objective approach, we must keep in the foreground the fundamental fact that the musical mind does not consist of its
* Reprinted by permission from the Atlantic Monthly. IM
1
2 PSYCHOLOGY OF Music
dissected parts, but in an integrated personality. In its evaluation we must always have regard for the total personality as functioning in a total situation.
Musical talent is not one, but a hierarchy of talents, branching out along certain trunk lines into the rich arborization, foliage, and fruitage of the tree, which we call the "musical mind." The normal musical mind is first of all a normal mind. What makes it musical is the possession, in a serviceable degree, of those capacities which are essential for the hearing, the feeling, the understanding, and, ordinarily, for some form of expression of music, with a resulting drive or urge toward music.
THE SENSORY CAPACITIES
The psychological attributes of sound, namely, pitch, loudness, time, and timbre, depend upon the physical characteristics of the sound wave: frequency, amplitude, duration, and form. In terms of these we can account for every conceivable sound in nature and art — vocal or instrumental, musical or nonmusical. We therefore recognize that the musical mind must be capable of apprehending these four attributes of sound.
But in this apprehending we find an inner screen which is more significant musically, being composed of the four fundamental sensory capacities in complex forms, namely, the sense of tone quality, the sense of consonance, the sense of volume, and the sense of rhythm. These four complex forms of capacity must be evaluated by themselves and not in terms of their elemental components. For example, rhythm depends upon the sense of time and the sense of intensity, as hydrogen and oxygen combine int^o water; yet water and rhythm are practical entities in themselves. )/
This classification of sensory capacities is probably complete, because it is based upon the known attributes of the sound wave. It must be borne in mind that the sound wave is the only medium through which music as such is conveyed from the performer to the listener; everything that is rendered as music or heard as music may be expressed in terms of the concepts of the sound wave. As in good reading we are not aware of letters or phonetic elements as such, but read for meaning, so in music we are, as a rule, not con- scious of specific tonal elements or sound waves as such, but rather of musical design or impression as a whole. The lover of flowers may derive deep pleasure from flowers through his senses without knowl-
THE MUSICAL MIND 3
edge or thought of the physics or chemistry of their structure(So it is possible to enjoy and perform music without insight or knowledge of its true nature; but the musician who knows his medium and thinks intelligently ab^uLit Jiai^^IvasiTy greater satisfaction than the one
On the basis of our experiments in measuring these sensory capacities, we find that the basic capacities, the sense of pitch, the sense of time, the sense of loudness, and the sense of timbre are elemental, by which we mean that they are largely inborn and
After a comparatively early age
^
they do not vary with intelligence, with training, or with increasing age, except as the exhibition of these capacities is limited by the child's ability to understand or apply himself to the task. This fact is of the utmost importance in that it makes diagnosis of talent possible before training is begun and points to certain very definite principles of musical education. We can measure these capacities reliably by the age of ten in the normal child; and this measure is likely to stand, except for the numerous vicissitudes of life which may cause deterioration. To take an example, the sense of pitch depends upon the structure of the ear, just as acuity of vision depends upon the structure of the eye. As no amount of training or maturing tends to increase the acuity of the eye, so no amount of training or maturing can improve the pitch acuity of the ear. How- ever, training and maturing in both cases can greatly increase the functional scope of these capacities. The ear, like the eye, is an instrument, and mental development in music consists in the acquisition of skills and the enrichment of experience through this channel. This is analogous to the fact that touch and acuity of hear- ing are really on the whole as keen in seeing persons as in the blind who show apparently marvelous power of orientation through these senses.
The apparently complex forms of sensory capacities also tend to be elemental to a considerable degree; that is, the young child has the sense of tone quality, of volume, of rhythm, and the sense of consonance long before he begins to sing or know anything about music. It is the meaning, and not the capacity, of these forms of impression which we train and which matures with age in propor- tion to the degree of intelligence and emotional drive.
There seem to be four large trunks in the family tree of musical- ity, each of which may develop and ramify to a large extent hide-
4 PSYCHOLOGY OF Music
pendently of, or out of proportion to, the others. These four are the tonal, the dynamic, the temporal, and the qualitative. Each is the main trunk of a musical type. Those of the tonal type are peculiarly sensitive to pitch and timbre and dwell upon music in all its tonal forms — melody, harmony, and all forms of pitch variants and compounds; the dynamic have a fine acuity of hearing and sense of loudness and dwell by preference upon stress, or the dynamic aspect of music, in all forms and modifications of loudness; the temporal are peculiarly sensitive to time, tempo, and rhythm, and by preference dwell upon the rhythmic patterns and other media for the temporal aspect of music; the qualitative are pecul- iarly sensitive to timbre and are capable of its control, dwelling preferentially upon the harmonic constitution of the tone.
Of course, a great musician, or a balanced musician of any degree of greatness, tends to have these four trunks of capacity branching out in balanced and symmetrical form, but such cases are comparatively rare. Many distinguished musicians are domi- nantly of one of these types; their performance and appreciation and their musical creations all give evidence favoring dominance of one of the trunk lines, although within these trunk lines large and distinctive subbranchings may be recognized. Furthermore, great capacity in each of these types is not essential to marked distinc- tion in musical achievement; very extreme sensitivity in one or more of them may even be a drawback to balanced musical development.
Let me give a very striking illustration on this last point. In measuring certain phases of musical talent in all of the available living members of six of the foremost musical families in the United States, Dr. Stanton found that the brother of one of the protagons of these musical families said that he had no musical talent what- ever, and this seemed to be the opinion of the family. But the experimenter found that in the five basic capacities measured, this man was extraordinarily keen, indeed, conspicuously keener than his brother, the famous musician. The interesting confession came out that the reason he was not musical was that practically all the music that he heard seemed to him so bad that it jarred upon him and was intolerable. That was the reason that he was not musical in the conventional sense of the word; he was so keen that the ordinary humdrum of music, even in a musical family, continually jarred him. Is he in reality musical or is he not? The psychologist would say, "In terms of all the evidence at hand, he has extraordinary
THE MUSICAL, MIND 5
musical capacities." Yet in his family he was the one who had not "amounted to anything" in music.
Generalizing on the basis of all types of record available we may say that, so far as the sensory capacities are concerned, a balanced and distinctly gifted musical mind will in these capacities measure in the highest 10 per cent of the normal community. But great musical achievement may be attained by persons who may have as low as average sensory capacity in one of these four main lines.
But here it must be pointed out, of course, that success depends upon following the lead of natural capacity. For example, a person who has only an average sense of pitch can never become a good violinist or a great singer; but, with the other three skills well developed, he may become a pianist or a composer of great distinc- tion. A person relatively lacking in dynamic capacities cannot become a great pianist, but might well find success with voice or wind instruments. It is not that the musician always engages in fine distinctions; it is rather that his possession of a fine sensitivity makes him live dominantly in that musical atmosphere to which he is most sensitive and responsive, even when he employs the most dissonant, rough, or unrhythmic characteristics of sound.
MUSICAL IMAGERY, IMAGINATION, AND MEMORY
Granting the presence of sensory capacities in adequate degree, success or failure in music depends upon the capacity for living in a tonal world through productive and reproductive imagination. The musician lives in a world of images, realistic sometimes even to the point of a normal illusion. This does not mean that he is aware of the image as such any more than he needs to be aware of sensation in seeing an object. But he is able to " hear over " a musical program which he has heard in the past as if it were rendered in the present. He creates music by "hearing it out," not by picking it out on the piano or by mere seeing of the score or by abstract theories, but by hearing it out in his creative imagination through his "mind's ear." That is, his memory and imagination are rich and strong in power of concrete, faithful, and vivid tonal imagery; this imagery is so fully at his command that he can build the most complex musical structures and hear and feel all the effects of every detailed element before he has written down a note or sounded it out by voice or instrument. This capacity, I should say, is the outstanding mark of a musical mind at the representation level — the capacity of
6 PSYCHOLOGY OF Music
living in a representative tonal world. This capacity brings the tonal material into the present; it colors and greatly enriches the actual hearing of musical sounds; it largely determines the char- acter and realism of the emotional experience; it is familiarity with these images which makes the cognitive memory for music realistic. Thus, tonal imagery is a condition for learning, for retention, for recall, for recognition, and for the anticipation of musical facts. Take out the image from the musical mind and you take out its very essence.
No one maintains at the present time that a person can be of a single imaginal type; but, in natural musicians with a rich feeling for music, the auditory type dominates, and perhaps largely because realistic imagery is always intimately associated with organic responsiveness. The motor imaginal type is ordinarily also well developed. It is not necessary for us to quarrel about the relation of kinesthetic imagery to kinesthetic sensation, but we can agree upon this: that the motor tendency to image the tone or execute it in inceptive movements is highly developed in the musical mind. The auditory and the motor images are normal stimuli for organic reaction in musical emotion.
The necessity of living in a world of representation tends to bring out vivid visual imagery as well as imagery in the other senses, because there is a general tendency to reinstate, in the repre- sentation of a sensory experience, the whole of the original setting. Thus a musician not only hears the music but often lives it out so realistically in his imagination and memory that he sees and feels a response to the persons, instruments, or total situation in the rendi- tion represented. Without this warmth of experience, music would lose its essential esthetic nature. It is a well-known fact that many persons who ply the art or business of music report having no devel- oped imaginal life or concrete imagination. And it has been very interesting to observe in many such cases that, although they are engaged in the practice of music, their musical life is quite devoid of the genuine musical experience. They are often mere pedagogues or musical managers.
The power of mental imagery may be developed to a marked degree with training. There is also good evidence to show that the power of vivid imagery deteriorates with nonuse. A comparison of musicians and psychologists shows that the musicians stand very high in auditory imagery and the psychologists as a class compara-
THE MUSICAL MIND 7
lively low. This marked difference is probably due partly to selec- tion and partly to training. There seems to be no doubt but that there are very great differences in the original nature of children in this respect.
Mere strength and fidelity of imagery is, however, of little value except insofar as it is the medium for imagination. Music is an art, and he who plies it successfullyjias the power of creative imagina- tion.. This may be of the sensuous type which Is characterized by luxuriant and realistic imagery without much reflection; it may be of the intellectual type in which creation takes the form of purpose, theories, or postulates as to the material of musical content; it may be of the sentimental type in which the flow of imagery is under the sway of the higher sentiments which are often nursed into esthetic attitudes, sometimes called "musical temperament"; it may be of the impulsive type in which the drive or urge of emotion flares up but is not long sustained; it may be of the motor type, sometimes called "architech tonic," which takes the form of a realistic experience of action or of mere performance. According as a person is dominantly of any one or of a combination of these types, his personality as a whole may in large part be designated by such a pattern. Thus, among others, we may recognize as types the sensorimotor, sentimental, impulsive, reflective, motile, and the balanced musician.
While retentive and serviceable memory is a very great asset to a musical person, it is not at all an essential condition for musical- mindedness. A person may have naturally very poor memory of all kinds and get along well in music, just as an absent-minded philoso- pher may get along very well in his field. Furthermore, the possibility for the development of memory is so very great that with careful training a person with very poor memory may improve this many- fold to the point of serviceability. The musical mind that can repro- duce many repertoires with precision is, however, a different mind from one which has neither large scope nor fidelity in retention or reproduction. But both may be musical. The personal traits in memory and imagination color and condition the musical life and often set limits to achievement in music.
MUSICAL INTELLIGENCE
Insofar as the power of reflective thinking is concerned, musical intelligence is like philosophical, mathematical, or scientific
8 PSYCHOLOGY OF Music
intelligence. Intelligence is musical when its background is a store- house of musical knowledge, a dynamo of musical interests, an outlet in musical tasks, and a warmth of musical experiences and responses. Here, as in the case of imagination, the type and the degree of intelligence may characterize or set limits for the musical achievement. The great composer, the great conductor, the great interpreter live in large intellectual movements. They have the power of sustained thought, a great store of organized information, and the ability to elaborate and control their creative work at a high intellectual level. At the other extreme are the various kinds of small musicianship in which reflective thinking does not function; the experience and the performance are on a sensorimotor level. Such music is to real music as fantasy is to creative imagination. Between these extremes we may sort musicianships into markedly different qualities and levels in terms of some sort of intelligence quotient — a hypothetical musical intelligence quotient — which we might designate as M.I.Q. Thought is, however, not limited to the difficult and ponderous in music, for, as in all other realms of reflection, the highest and most beautiful achievements of thought often have the charm of simplicity.
We should not infer from this that a great mathematician or philosopher, who plays the violin or sings beautifully, does so as a great thinker. The violin and the voice are often a relief to him from the strain of sustained cogitation. He may not create music at all; he may not even interpret at the level at which he philosophizes; yet his sensuous and his imaginative experiences are chastened, mellowed, and balanced by the fact that he is a contemplative man.
Again the great intellect in music may dwell so exclusively upon the musical forms and upon conceptions of new musical structures as to become calloused to the more spontaneous appreciation and expression of music. He becomes hypercritical and may even lose the ability to enjoy music. The penetrating critic often derives more pain than pleasure out of music as it is.
My main point, however, is : as is the intelligence of a man, so is his music. If he is in a school for feeble-minded, his music may be spontaneous and appealing to a high degree; but it will, neverthe- less, be feeble-minded. If it is the expression of the philosophical and highly trained composer or conductor, it will be a thought creation whether or not it has the more elemental musical appeals which reach the masses.
THE MUSICAL MIND 9
MUSICAL FEELING
' Music is essentially a play upon feeling with feeling. It is ap- preciated only insofar as it arouses feeling and can be expressed only by active feeling. On the basis of the degree and the kind of feeling, we may again classify persons into characteristic types in terms of affective responsiveness. )
As a fundamental proposition we may say that the artistic expression of feeling in music consists in esthetic deviation from the regular — from pure tone, true pitch, even dynamics, metro- nomic time, rigid rhythms, etc. All of these deviations can be measured so that we can now compare singers quantitatively in terms of their use of a particular one of the countless devices for deviating from the regular or rigid, including also adherence to the regular as a means of expressing emotion in music. The emotional medium at one moment may be primarily fine modulation in tonal timbre, at another in rhythm, at another in stress, and each of these in countless forms of sublimation or hierarchies. In the ensemble of such deviation from the regular lies the beauty, the charm, the grandeur of music. When Tetrazzini catalogues among the chief faults of singing "faulty intonation, faulty phrasing, imperfect attack, scooping up to notes, digging or arriving at a note from a semitone beneath" she, of course, is right but may fail to realize that in just such variables lie the resources for beauty and power of music.
In other words, our concept of feeling as expressed in music may become concretely scientific, so that, if the music critic praises or blames a singer for a certain emotional quality, it need no longer remain a question of dispute or opinion; but, just as we could snap the profile of the singer with the camera, we can get the profile of the sound wave and settle the dispute about the musical quality. The music critics, of course, have not yet adopted this technique, but the next generation will make a beginning. The ex- pression of feeling in music, that mysterious and enchanting retreat for all things musical, is being explored; trails are being blazed, and the music critic will soon talk about musical expression of feeling in terms of precise and scientific concepts.
When Grace Moore sings in New York and the critics opine about the technique of quavers in her voice, we may have at the footlights a recording instrument which photographs every sound
10 PSYCHOLOGY OF Music
wave and enables us to preserve for all time the form of her expres- sion of emotion. We are, of course, not thinking here about that mystic inner something which is spoken of as feeling, as such, but of the expression of feeling. In modern psychology, to feel is always to do, to express something — action of the organism. The expression does not take ethereal, magical, or even mystic form but comes to us through the media to which our senses are open.
(There are two other aspects of feeling in music. One is the nature of esthetic experience, and the other is what we may call the "creative feeling" as it operates in the composer. It is evident that both of these will stand out in an entirely new light the moment the conception of the concreteness, describability, and tangibleness of the expression of emotion in music is recognized.
MUSICAL PERFORMANCE
Musical performance, like all other acts of skill involving un- usually high capacity, is limited by certain inherent and inherited motor capacities. For example, a child may be slow and sure or quick and erratic in certain specific activities, or he may be found in any other combinations of the two series from the extremely slow to the extremely quick, and extremely precise to the extremely erratic. And, as a child is found, so will be the youth and the man. Such a "personal equation" is a personal trait, like stature or color of hair. Singing involves the possession of a favorable structure of the vocal organs and motor control. Playing various kinds of instru- ments calls for a high order of natural capacity, for speed and accu - racy in control. Such motor capacities can be measured before musical training is begun. Musical action is, of course, also limited by limitations in each and all of the talents heretofore discussed; for example, a person who is low in sense of rhythm will of necessity be low in rhythmic performance. In the next generation, the music student and the music teacher and theorist will rate progress and quality in musical performance in relation to capacity, just as at the present time we are beginning to consider it reasonable not to expect as much from a moron as we do from a philosopher.
It is quite possible to recognize fundamental types of motor resourcefulness in musical performance, but for the present purpose the main thing to be stressed is that there is nothing indescribable about it and that individual motor fortes or faults of a basic char- acter often determine the character of the musician.
THE MUSICAL, MIND 11
' The musician, in passing judgment upon a prospective musician, rightly says, "Give me the child with the musical instinct." By that he does not mean any one of the specific capacities we have discussed, but rather a fundamental urge, drive, or emotional dominance, craving expression in music from early childhood. This general trait is often feigned, fragmentary, or imaginary, but when genuine it constitutes the most certain indication of the presence of the musical mind that we have. When submitted to analysis, it is found to represent an effective grouping, dominance, or balance of fundamental sensory and motor capacities and therefore yields to measurement and scientific description and evaluation. *
THE MEANING OF THIS ANALYSIS
This, in brief, is the skeletal structure I promised. In many respects it is but dangling and rattling dry bones. "Atomistic!" some of my confreres will say. Now, atoms are not roses, resplendent in bloom, fragrance, and configuration — living roses! The esthete, whiffing and raving about the beauty of the rose, can ignore the atom, but the botanist cannot. It is to the botanist that we look for a true revelation of the origin, the growth, the nature, and the role of roses in the economy of nature. It is the botanist who can make verifiable and permanent distinctions among roses.
Fifty years ago, Wundt was asked, "What have you learned from the reaction experiment?" to which his whole laboratory force had devoted its first three years. His reply was, "It has given me a new conception of the human mind." Speaking for those who take the scientific point of view in the psychology of music, I may say that experiment has given us a new conception of the musical personality as a whole — its infinite capacities and the intimate relationships among them, the marvelous range for possible train- ing, growth, and substitution, the sublimation of musical interests in daily life, the necessity of viewing the personality as a dynamic whole.
Does this point of view oversimplify the musical mind? The argument I have made is that it can and should vastly enrich and deepen the concept; if you ask one question of nature in the labora- tory, nature asks you ten, and each of these when pursued in turn multiplies into tens of tens of tens. For laboratory procedure is but the setting of conditions for more and more precise observations of specific, concrete, verifiable facts or features. What I have stated
12 PSYCHOLOGY OF Music
is, after all, merely a point of view. The details remain to be worked out, filled in, modified as science progresses. The whole appeal is to and for verifiable facts.
What shall it profit ? Perhaps I may bring together in a construc- tive way some of the features which seem to me to be involved in the acceptance of scientific procedure in the interpretation, evaluation, and education of the musical mind.
It gives us a psychology of music in that it furnishes describable and verifiable facts as a basis for classification. The particular data I have presented are just plain psychology; not any particular brand, but rather an attempt to select and consolidate what is usable in the various modern points of view.
It furnishes us a technique for the development of musical esthetics. The armchair deductions about the nature of beauty in music give way to experiment, and conclusions must be limited to factors under control. Musical esthetics will soon loom up as one of the applied and normative sciences.
It forms a basis for the analysis and evaluation of musical talent and will furnish helpful data for vocational and avocational guid- ance in music.
It develops an intimate relationship between music and speech. Speech, especially dramatic art, is gaining recognition in esthetics because of its close relationship to music.
It lays the foundations for musical criticism, musical biography and autobiography, and musical theory in general, even for intelli- gent parlor conversation about musical thrills.
It furnishes the foundation for the essential facts for the con- struction of the curriculum, for the selection and motivation of the musically educable, for the evaluation of progress in training, and for countless improvements in the technique and economy of teach- ing. If a committee of scientifically trained musicians should make a survey of the economies or wastes involved in current methods of teaching music and should be free to set forth the pedagogical consequence of facing the new scientifically known facts about the musical mind, very radical changes would follow.
It helps to give music its true place and influence by enhancing the musical life for the musically gifted and thereby furnishing a natural drive for the effective functioning of music in the life of the people.
THE MUSICAL MEDIUM
THE medium with which the musician works is the sound wave; his works of art take the form of artistically built sound struc- tures. The painter creates his work of art through the medium of physical paints; the sculptor models his creation in clay, or chisels, hews, and molds in metals or stone. The musician has but one medium, the physical sound.
MUSICIAN, MUSIC, LISTENER
^The psychology of music may be divided into three large fields dealing with the musician, the music, and the listener, respectively. It is concerned with the description and explanation of the opera- tions of the musical mind, the music as a thing in itself, and the musical activities of the listener. Naturally, it deals primarily with the music as a work of art in sound and from that works back to the producer of music and forward to the listener who hears it musically . Psychology proceeds systematically by analyzing situations and reducing them progressively to their simplest terms. The first great step in approaching the psychology of music is to recognize that everything that the singer or player conveys to the listener is con- veyed through sound waves or in terms of these. This conception simplifies our approach immensely in that it frees us from confusion with unnecessary accessories, furnishes us with a basis for classifica- tion and terminology, and paves a way for preservation of findings, measurement, and scientific explanation.
v^But, the reader may say, music is more than sound. It must have atmosphere; it ordinarily involves some degree of dramatic action; it is modified by the character of the audience, the personal appear-
13
14 PSYCHOLOGY OF Music
ance, manners and mannerisms of the performed the total situation of which the performance is a part. In other words, music is essen- tially tied up with a larger setting in which it plays a leading role. This must be taken for granted, and we may recognize that there is a very interesting psychology of each of these accessories, such as the picture hat, the smile, the anticipated applause, the sentiment connected with the national anthem, or the mood of the listener. These contribute to the atmosphere and should be cultivated with care, but they are not the music. They present very interesting psychological problems; but it is to the advantage of the psychology of music to separate clearly the music in itself from its accessories.
(It also is admitted that the music is in the first and last instances, in the mind of the composer and in the mind of the listener, not actual sounds but images, ideas, ideals, thoughts, and emotions. We shall find, however, that these are always in terms of the physical sound to which they refer. In this respect, the creations of the musician are analogous to the creations of the painter and the sculptor; they are purely objective, j
The musical instrument or voice or any other sound-producing body sends out puffs or waves of air which radiate in all directions from the source. When segments of these waves strike the ear, they set up vibrations in the tympanic membrane. These in turn are transmitted through the middle ear as vibrations of three bones. They are taken up by the oval membrane, which in turn transmits them to the liquid of the inner ear. The vibrations in this liquid are transferred to the receiving mechanism of the nerve cells, the end organs of hearing in the inner ear. For each vibration, the mechanical shaking of the end organs of the auditory nerve sets up a nerve impulse. These nerve impulses are transmitted to the brain and give rise to the tone that is heard.
Thus, in terms of waves, we may trace the physical medium of sound from the vibration of the sounding body, such as a reed or the vocal cords, through the air as air waves and through the tym- panic membrane, the bony system, the oval membrane, the liquid of the inner ear, and the receiving mechanism of the nerve cells, as physical vibrations of material bodies. Then follow the physio- logical stages consisting of the arousing of the nerve impulse in the end organ, its transmission over the auditory nerve, and the action set up in the various brain centers reached. It is this nerve impulse that primarily determines the tone which we hear.
THE MUSICAL, MEDIUM 15
In this way nature has provided a means of transforming the musical medium from one form of energy to another; and in this process the waves are adapted progressively to each medium, finally resulting in brain activity associated with the musical experience. The experience is not that of a wave, but of a tone having pitch, duration, loudness, and timbre. The following state- ment in The Psychology of Musical Talent1*7 is apposite:
Thinking of musical experience in terms of this physical medium, we are confronted with one of the greatest marvels of nature, the wondrous "transformation from matter to mind": out of mere vibration is built a world of musical tones which do not in themselves suggest vibration at all. So it is in all the senses. The vibrations of light reflected from the landscape give us the mental experience of color and form, and our minds are so endowed that we can experience beauty and see meaning in this display. It is the physical flower that we love and admire and seek to understand. No one doubts the existence of this physical flower; no one doubts the experience of its beauty. The love and understanding of things seen in nature and art take for granted this physical-physiological-mental series as an integrated unit. The artist and the common man who experience it need not think in terms of light vibrations, but the scientist who is to explain the experience must think in terms of physical, physiological, and mental processes as units — in terms of light waves, nerve impulses, and mental process.
So it is with music. Musical art and the everyday experience of sound may proceed without any knowledge of physics, physiology, or psychology; but when the scientist attempts to explain these experiences he must deal with the series as a whole, the sound wave, the nerve impulse, and the experience of sound. The object of our study is music from the psychological point of view. Music is the center and core of our interest, the goal toward which we are working.
It is possible to intercept the sound wave by measuring instru- ments at any of these stages : in the condensation and rarification of the air, in the physical vibration of the various parts of the ear, or in the physiological pulsations of the nerve impulse in the end organ, the nerve, or the brain center.
16 PSYCHOLOGY OF Music
The most serviceable approach is that of phonophotography, by which the air waves are intercepted and recorded faithfully with cameras suitable for the purpose. Our descriptions of the musical medium will, therefore, be given largely in terms of these phonophotograms which reveal all the characteristics of the sound wave in measurable form.
CHARACTERISTICS OF THE SOUND WAVE
As we have seen, sound waves have four, and only four, char- acteristics; namely, frequency, amplitude, duration, and form. Sounds of every conceivable sort, from pure tone to the roughest noise, can be recorded and described in terms of these four. The same four characteristics may be traced in the nerve impulse which results from the physical vibration; corresponding to these four
FIG 1. — Oscillogram of a pure and steady tone.
characteristics of physical wave and nerve impulse, we have the four characteristics of musical tones. The full and serious recogni- tion of this parallelism vastly simplifies our problem and furnishes us a key to the understanding, the recording, the production, the description of musical phenomena; it enables us to know that we are taking all factors into account, since these four are all-inclusive; it furnishes us a terminology which is simple, consistent, and verifiable; it facilitates the adoption of units of measurement; it does away with the notion that tones may vary in an " infinite and unknowable variety of ways"; it furnishes a cornerstone for the psychology of music and musical esthetics.
Figure 1 is a phonophotogram of a pure tone, lasting 0.1 sec. In this picture there are 5 waves in this tenth of a second. There- fore, the number of waves in 1 second is 50, the frequency of the tone. The pressure or energy of the sound wave, which determines the intensity of the physical tone and loudness of the tone as heard, is expressed in terms of the amplitude or height of the wave from crest to trough. The duration* is, of course, expressed in terms
* In physics, duration is not spoken of as a characteristic of the wave except insofar as it refers to wave length, which is the reciprocal of frequency. For psychological reasons,
THE MUSICAL MEDIUM 17
of time length of the tone, that is, the continuation of the sound waves as recorded over the time line. The form of the wave deter- mines its harmonic constitution, which gives us the experience of timbre. In this case, the smooth sine curve is an indication of the pure tone.*
Before proceeding to describe the sounds which we hear in terms of these four characteristics, it should be made clear that in reality the hearing of tones is rarely an exact copy of these phys- ical characteristics of the sound, because hearing is seldom complete and many principles of distortion operate. We are subject to a great variety of faults and errors in hearing. These are due primarily to five sources: the physical limit of the sense organ, the physiolog- ical limitations, inaccurate or inadequate perception, principles of economy in hearing, and principles of artistic hearing. These devia- tions from direct correspondence to the actual physical sound we call " normal illusions." It is significant that they are not mere errors but may serve in the interests of economy, efficiency, and the feeling of beauty in mental life. And it is particularly significant for us at this stage that all these illusions may themselves be measured in terms of these same four attributes of the sound wave.
This principle is true in all our perception. When we see the color and form of the Japanese cherry tree in blossom, we rarely see the exact color or the exact detail or shape of the parts of the tree, yet we assert that we see the tree and recognize that it is the actual thing which really exists and which we ought to see. But we know numerous laws of illusion of color and form and the limits of sensation, all of which tend to modify the thing that we see. So, in musical hearing, we are fully justified in speaking in quantitative terms of the physical sound wave as the true description of the physical tone. But a large and very interesting part of the psy- chology of musical hearing consists of principles of deviation from the actual physical tone.
FREQUENCY: PITCH
The terms "frequency," "double vibrations" (d.v.), "number of vibrations per second," "cycles," and "waves" are synonymous
duration of the recurrence of waves is here spoken of as a wave characteristic; that is, something that can be measured in terms of waves.
* For latest definitions of terms in hearing see Report of Committee on Acoustical Standardization . a
18 PSYCHOLOGY OF Music
and may be used interchangeably to designate frequency and pitch. It is now customary to use the sign ~ to designate these. Histor- ically, the term " pitch" has been used appropriately in two mean- ings : first, in the narrow sense, to denote an attribute of the sound as heard, that is, the mental experience; second, in a broader sense, to denote the total process, physical, physiological, and psycholog- ical. Current practice attempts to use " pitch" to designate the psychological experience and "frequency " to designate the physical vibration. However, in the science of music and speech we con- stantly have occasion to mean the whole situation — mental, physiological, physical; and then we employ the term "pitch" in the broader sense. The context generally indicates which of these connotations is intended.
In determining frequency, we count the number of waves per second or we measure the length of successive waves, counting from characteristic points such as from crest of one wave to the corresponding point in the next.
In musical hearing and performance, we demand answers to questions like these: What is the actual pitch of the tone? How faithful is it? How does it vary artistically? In what respects is it faulty? What license has the performer taken? How is pitch ren- dered in the attack, the release, or the portamento? What unusual characteristics of intonation, if any, are there? We may picture problems of this kind in terms of the following skeletal outline:
Musical aspects of pitch intonation
Actual pitch in terms of frequency Faults of intonation
Ex. Level flatting or sharping; progressive flatting or sharping; erratic fluctuations
Musical ornaments
Ex. Trills and grace notes indicated in the score; vibrato and other periodic inflections not indicated in the score
Other varied inflections involving art principles Unconventional artistic license
Ex. Pitch swoops in primitive music or semispeech intonation for dramatic effect
Glides in attack, release, or portamento Intervals: melody, harmony
THE MUSICAL MEDIUM 19
INTENSITY: LOUDNESS
For psychological purposes, the intensity of tone is expressed in terms of decibels (db). The decibel is a new term devised by elec- trical engineers for the measurement of sound in radio, talking pictures, sound abatement, and architecture; but it is destined to take its place among the common units of measurements, such as a degree of temperature. Like pitch and loudness, the decibel is a psychological unit representing the degree of loudness. Its physical counterpart, intensity, is expressed in terms of units of electrical energy. On the physical side, we speak of dynamic value in terms of intensity and on the mental side in terms of loudness.
However, intensity is frequently used to designate either the mental or the physical, or both, for the reason that it is the recog- nized term expressing an attribute of sensation in psychology, and, in a great variety of situations, the object is not to distinguish between the physical and the mental but to represent the total situation. Likewise, the decibel is used to designate both the phys- ical and the mental. Types of questions which may be answered in terms of decibels are indicated in the following skeletal outline:
Musical aspects of loudness
Degree of loudness, or absolute intensity Dynamic modulation
Ex. Periodic variations in intensity as in the vibrato; progressive variations in intensity as in crescendo, diminuendo, swell, circumflex; dynamic license, as in acute swells and dips characteristic of primitive music and certain rare artistic modulations for the dramatic effect; and attack, release, and portamento
Dynamic rhythm (see Chap. 12) Volume (see Chap. 11)
Ex. Dynamic changes in relation to pitch, time, intensity, and timbre Erratic changes in intensity
DURATION: TIME
Pitch and intensity are always recorded against time, expressing the duration of notes, pauses, or any specific feature of these. We may, therefore, take our time values from either the pitch record or the intensity record. Some of the musically significant time values are shown in the following skeletal outline:
20 PSYCHOLOGY OF Music
Musical aspects of time
Actual duration of tones, pauses, or any specific aspect of these Time and tempo Temporal rhythm
Ex. Measure rhythm, phrase rhythm, or sentence rhythm
Time of attack and release
Ex. Asynchronization of chords or overlapping of notes through pedal action and syncopation
Artistic variations
Ex. Accelerando, retardando, holds, legato, staccato, vibrato Erratic and faulty variations in time
WAVE FORM: TIMBRE
Timbre is described in terms of the form of the sound wave. It ranges from the pure tone through an infinite number of changes in complexity up to the pitchless sound we call "noise." As we shall see later, timbre is determined primarily by the number, the order, and the relative intensity of the fundamental and its overtones as expressed in the wave form. It also is modified by the absolute pitch and total intensity of the tone as a whole. The physical structure of the complex sound is called its "harmonic composition." Psycholog- ically it may be spoken of as the overtone structure. This is fully illustrated in Chaps. 8, 9, and 17.
In actual music, it is possible to have as many as 30 or 40 partials in combination, constituting a rich tone. As we shall see in the chapter on timbre, the wave form may be analyzed so as to show how many partials are present, the form of their distribution, and the relative amount of energy that each contributes. In terms of such facts, we can represent the harmonic constitution and, therefore, the timbre of the tone by a graph called a "tone spectrum."
An unscientific person listening to all the sounds in art and nature is tempted to pronounce the variety of differences indescrib- able; but, from the physicist's point of view, every physical tone is describable in terms of its partials which, from the point of view of hearing, we call "overtones," as expressed in timbre. In other words, the sound wave is capable of as many types of form as nature and
THE MUSICAL MEDIUM 21
art may be capable of sounding as variations in tone quality. We should here recognize that timbre as a fourth attribute of tone is by far the most important aspect of tone and introduces the largest number of problems and variables. Some of these may be indicated in the following skeletal outline:
Musical aspects of tonal timbre
The actual description of the quality of any tone
Ex. The exact and objective description of any voice, any instrument, any
vowel
\
Variation in tone quality
Ex. Variation of timbre with register, loudness, duration, location of tone, nasality, placement, breathing
Norms
Ex. The determination of norms of beauty in tones, either actual or ideal: the relation of timbre to art forms
Ex. The expression of love, grief, fear, rage: musical mood
Any musician could extend this list in terms of questions about tone quality which he would like to have measured. Many of these questions arise alike in both music and speech, and the findings in one transfer to the other.
In this very brief outline, we have become aware of the ele- ments which function in the musical medium, which are measurable in terms of the sound wave and which have distinct psychological and musical meaning. For full illustrations and discussion, we must pursue in turn Chaps. 5, 6, 7, and 8.
THE MUSICAL PERFORMANCE SCORE
If we bear in mind that all of these aspects of music which have been mentioned are measurable and capable of description and statement in exact scientific form, the question of scientific musical notation becomes urgent. Without such notation, the psychology of music would be in a position of mathematics without mathe- matical symbols. As has been outlined, every aspect of the musical medium can be measured, analyzed in great detail, recorded, de- scribed, and explained. We should soon be swamped with the mass of that type of information unless we had some standardized, very simple, scientifically accurate, and musically significant graphical
22 PSYCHOLOGY OF Music
language or symbols in which the facts could be preserved and made readily available in music.
Such language has been devised in the form of what has been called the musical performance score. Instead of taking space to illustrate and explain such scores at this stage, we may ask the reader to turn to Figs. 1 and 2 in Chap. 4, Fig. 1 in Chap. 18, Fig. 3 in Chap. 19, and Fig. 3 in Chap. 20, where we have full illustrations of its nature and use. It will be observed that these performance scores record three factors: namely, pitch, time, and intensity. Timbre is of such a complex nature that it must be re- ported in individual tone spectra as seen and explained in Chaps. 8, 9, 17, 18, and 20.
THE SCIENCE OF MUSIC
THE preceding chapter was an attempt to introduce the reader to the psychology of music by showing how this science describes and explains musical phenomena in terms of the musical medium. Let us now seek further insight into this new field of applied science and art, and obtain a bird's-eye view of the ground which lies before us. A full science of music cannot be written in one or in 3, small number of volumes. It therefore is necessary to select a specific point of view and recognize important limitations of the subject treated in this volume.
SCOPE OF THE SUBJECT
1. The subject is limited to a scientific approach. Description and explanation in music draw upon several sciences: primarily, physics, mathematics, physiology, anatomy, anthropology, and psychology, as well as the history and theory of musical practice. But it has come to be a function of the psychologist, as a student of human experience and behavior, to integrate these under the gen- eral concept of the "psychology of music." Although there may be much practical wisdom in popular psychology, resting on loose theory not suitable for verification by scientific method, such topics are excluded, and so is also the legitimate subject of philosophy of music ^
2. It is limited to those topics which are peculiarly amenable to treatment in the psychological laboratory, thus excluding problems specific to other sciences, such as physics, physiology, and mathe- matics, except as accessories.
3. It is further limited to the treatment of topics on which the author has firsthand experience, emanating directly or indirectly
24 PSYCHOLOGY OF Music
from the psychological laboratory. It therefore is necessarily selec- tive, skeletal, and illustrative rather than systematic. It constitutes only a series of fair samples of problems, procedures, facts, and principles, both theoretical and applied.
Psychology of music, even in a narrow sense, is unlimited, because music involves countless varieties of musical performance, countless varieties of moods, emotions, and ideas to be expressed, and countless attitudes, capacities, urges, and interests of the listener. In a way it involves all psychology; because the under- standing, description, and explanation of musical experience and behavior implies understanding, description, and explanation of fundamental experience and behavior in general. We must therefore seek to confine ourselves to the most essential situations exhibited in music and, among these, to those immediately essen- tial for the understanding, appreciation, and expression of music.
Yet the treatment is not restricted to music. It carries many implications and interpretations which have a bearing on the science of fine arts in general. Because of the common elements involved, the analysis of the situation in the psychology of music has its analogies in other fine arts and interests, such as graphic and plastic art, dramatic art, and poetry. In other words, the science of music transfers in various degrees to each of these fields, in both their pure and their applied aspects. Furthermore, any contribution to the psychology of music becomes also a contribution to general psychology. Therefore, while music is our specific objective, a study of this kind throws much light upon the interrelations of the fine arts and their common problems, particularly with reference to vocational and educational guidance and training for skills.
THE PERFORMER, THE MUSIC, THE LISTENER
The musical performer. We must consider here the performer, either vocal or instrumental, his instrument, his physical organism and physiological condition on the physical side, and on the mental side, the cognitive, affective, and motor aspects of his performance.
On the physical side, we are concerned with the instrument, which may be the human voice or any other sound-producing mechanism that may have musical significance. The self-expression of the musician is naturally related to, and characterized by, the physical instrument which serves as his tool.
THE SCIENCE OF Music 25
With reference to this aspect, we must take into account not only natural capacity for voice, as in singing, but also a number of other physical and neural mechanisms which favor or interfere with successful performance, in either voice or instrument. The character of the performance and the limits of achievement often are set by the physique of the performer, his physiological condition, such as the state of health, fatigue, adaptation, and other chronic or temporary physiological factors which affect sensitivity, mental alertness, muscular tonus, and general attitudes and impulses of the performer.
Given favorable physical and physiological conditions, we still find the largest variables in the psychological and educational aspect of the performer. Among these are the character of his knowledge and training, the development of his temperamental and emotional life, and the motor and interpretative skills which are the media of his musical expression. Each of these may be regarded from the point of view of natural ability, including his inheritance and environmental influences. On the other hand, each may be regarded from the point of view of mental development, maturation, musical tastes and leanings, and acquired skills. Thus the psy- chology of the performer involves the psychology of his instru- ment, his neuromuscular equipment, and all the factors which are determined by knowledge, feeling, action, and will power, both from the view of the natural capacity and as a result of nurture in his environment and of training.
The music. The central problem in the psychology of music is the description and explanation of the musical creation — the actual music — regarded on the one hand as the expression of musical feeling and on the other as the stimulus for arousing musical feeling. The psychology of music on the whole begins with and centers around the performance. The first step is to record it adequately, measure it, and analyze it as a work of art. As has been pointed out, the four characteristics of the sound wave may be recorded, meas- ured, and classified in a relatively complete system and to a degree which far exceeds the limits of musical hearing. They may be reported in scientific terminology which is complete and adequate for the description of every possible element or variant in the song or' instrumental performance as an art object. Therefore, the psychology of musical performance implies an adequate knowledge
26 PSYCHOLOGY OF Music
of the physical characteristics of sound, the mode of its transmis- sion, and the countless physical and physiological conditions which determine its functioning.
The psychological problem here is to convert the objective record of the physical aspects of music as performed into terms of psychological experiences and responses which have musical mean- ing. Thus, instead of being concerned with frequency, intensity, duration, and form of sound waves, we shall speak and think in terms of pitch, loudness, time, and timbre, and all their derivatives and variants, giving a scientific account of the performance in terms of musical terminology. Here we must deal with a vast array of principles, such as the psychophysics of hearing, musical evolu- tion, musical knowledge and training, the limits of the organism, individual differences, health, musical environment, musical guidance, practical norms, and esthetic principles, and shall aim in general to give an interpretative account of that which is trans- mitted from the performer to the listener as music.
Central to the interpretation of performance as musical art are a number of facts which are strictly musical; such as musical form and all its variants, musical theory involving all its aspects of composition, setting of words and themes, racial and historical aspects, and many other matters of musical esthetics.
The listener. Having considered the psychology of the per- former and the performance, there remains the very important stage of the psychology of the listener. What is characteristic of the musical message as it is received ? What are the factors, physiolog- ical, physical, psychological, and esthetic, which determine this response in hearing, interpretation, and enjoyment of music? Evi- dently the problems in the psychology of the listener are, in general, the same as the psychology of the performer, which we need not here repeat. Central among these, however, are the psychology of musical appreciation, the limits of the capacity for hearing, for interpreting and reliving the musical emotion which the artist has attempted to convey.
From these considerations it is evident that our subject is enormously involved and that therefore a single coherent treatment will of necessity be fragmentary and restricted. With this in mind, the present volume presents an outline in high lights for the purpose of stimulating and guiding the student in dealing with observation, reading, and thinking on the subject. Our aim is primarily to pre-
THE SCIENCE OF Music 27
sent the psychology of the subject in such a way as to lead the reader to psychologize about music himself.
GENERAL PRINCIPLES OF SCIENCE
Most of our knowledge is of the common-sense variety gained in uncontrolled observation. Very little is based upon experiment; yet, where there is no experiment, there can be no science. Further- more, in a new applied science like this, there is a vast amount of so-called "experimentation" that is neither scientific nor valid. In planning an experiment or in evaluating the results of an experi- ment in the psychology of music, we should check the procedure against such criteria as the following six. Let us consider, for exam- ple, an experiment to determine the carrying power of voice or instrument.
1. The factor under consideration must be isolated in order that we may know exactly what it is that we are measuring. For exam- ple, we must take one factor, such as pitch, intensity, timbre, tempo, size of the room, or the acoustical treatment of the walls and isolate and define it adequately.
2. All other factors must be kept constant while the selected factor is varied under control. For example, if intensity is a selected factor, we must vary that factor in graded steps while all other factors in the tone and in the total environment are kept constant.
3. The observed facts must be recordable. For example, the in- tensity may be recorded in terms of the energy or power of the tone.
4. The situation must be repeatable for verification. It should be possible for any scientist with proper equipment to repeat the experiment under identical conditions.
5. The conclusion must be validated in relation to the total personality and in the total musical situation.
6. The conclusion must be limited to the factor under control. For example, we can only say that the most favorable intensity here found holds for the conditions here controlled and that it must therefore be integrated with other factors in a series of experiments in which each of these is taken in turn.
If the plan for an experiment fails on any one of these points, this may invalidate the conclusion to be drawn. If we wish to weigh the reliability of evidence from experiment, here is a fair scale. We should not maintain that every serious study in psychology should be scientific. There is nothing sacred about science. Science simply
28 PSYCHOLOGY OF Music
strives for accuracy and logical coherence of facts. In the interest of progress and practice, we must put up Tjvith a great many make- shifts, often of no scientific value but very useful in the process of trial and error at our present state of limited knowledge. The scientist makes the supreme sacrifice of being willing to devote time and energy to the study of one specific isolated factor at a time, regardless of how small a part it may be of the whole; but the re- ward for this sacrifice is adequate — the discovery of verifiable truth. The musician as a practical man must draw upon currently ac- cepted truths through tradition, common-sense observation, and general knowledge, and do the best he can in the practical situation; but as science progresses, he will be more and more open-minded and eager for the fragments of scientific facts that dribble in or that he may discover by his own experiments.
The criteria here set up represent the bedrock requirements of science. A survey of the experimental literature in psychology shows that experiments generally accepted as more or less scientific range from those which conform rigidly to these requirements to those which can scarcely be said to follow any of them. In this situation formative science can be tolerated on the ground that "doing the best we can" from time to time is often a preliminary stage to mastery. In all sciences we find such regions of exploratory effort. Therefore, while we should not flaunt the criteria for simon-pure experiment in a censorious way, we should always hold before our- selves a goal which must be approached in a stabilized science and temper and evaluate our conclusions by the limitations thus set up in relation to this goal.
BASIC PRINCIPLES IN THE PSYCHOLOGY OF MUSIC
f Laboratory experiments in the psychology of music have re- vealed progressively a number of principles which seem to facilitate experiment, introduce important elements of economy, insure exhaustive treatment, furnish criteria of validity, and form bases for the foundation of esthetic theories.
Some principles have emerged incidentally throughout the fore- going chapters. A selected number of these are here thrown into high relief in the interest of a combined review and forecast. It has been suggested that we call these a duo-decalogue for the psychology of music.]
THE SCIENCE OF Music 29
1. All that is conveyed from the musician to the listener as music is conveyed on sound waves. As was pointed out in Chap. 2, countless other factors — dramatic action, gesture, grimaces, smiles and frowns, picture hats and jewelry, personal charm, environment, and audience — all contribute to the pleasure or displeasure in the musical situation, but they are not music. Recognition of this fact simplifies our problem.*
2. The sound waves are measurable, and there are only four variables which have musical significance: frequency, intensity, duration, and form. Recognition of this is a great forward leap in that it brings order and simplicity out of chaos and despair; physically, the infinite variety of musical sounds can be reduced to these four variables and measured in terms of them.
3. The psychological equivalents or correlates of these char- acteristics of sound are pitch, loudness, time, and timbre. Rhythm, harmony, volume, and tone quality are compounds of these; thought, feeling, action, memory, and imagination are in terms of these. We thus obtain a basic classification of all musical phenomena and give each its place in the family tree with its four large branches: the tonal, the dynamic, the temporal, and the qualitative.
4. The correspondence between the physical fact and the mental fact is not entirely direct or constant; there are many illusions of hearing. While we describe, for example, the pitch of A conven- tionally and practically as having a frequency of 440 cycles per second (abbreviated 440 ~), which is an invariable factor, the experience of that pitch may vary under a large variety of condi- tions resulting in illusions of pitch, many of which are very interest- ing and of practical significance in actual music. It is a triumph of science, however, that we can identify, measure, and explain each of these illusions. Thank God for illusions! Without illusions there could be no musical art.
5. The medium of musical art lies primarily in artistic devia- tion from the fixed and regular: from rigid pitch, uniform intensity, fixed rhythm, pure tone, and perfect harmony. Therefore the
* The reader will do the author the kindness to assume that qualifying phrases could be added for this and other direct and categorical statements which lack of space compels us to make without qualifications. Such phrases as "other things being equal," "as a general principle," "subject to exceptions in minor detail," "in our present state of knowledge," etc., should be understood throughout.
30 PSYCHOLOGY OF Music
quantitative measurement of performance may be expressed in terms of adherence to the fixed and so-called "true," or deviation from it in each of the four groups of musical attributes.
6. In each of the four categories, we have a zero point for a scale of measures. Thus, for pitch we may start from a standard tone; for intensity, from silence; for duration, from zero duration; and for timbre, from the pure tone.
7. On the basis of the above considerations, we may develop a definable, consistent, and verifiable musical terminology. For example, we shall be able to say exactly what timbre is and adopt adequate terminology for its variants. In the same way we shall be asked to scrap the hundreds of loose and synonymous terms used to designate timbre and be enabled to use the selected term cor- rectly in the light of its new definition.
8. All measurements may be represented graphically in what we have called the musical pattern score or performance score, which symbolizes the language of scientific measurement in a graph that has musical meaning. This score carries the three factors, pitch, intensity, and time. Timbre must be represented in a series by itself in the form of tonal spectra.
9. Norms t)f artistic performance may be set up in terms of objec- tive measurement and analysis of superior performance for the pur- pose of evaluating achievement and indicating goals of attainment.
10. The best performance of today can be improved upon. We must therefore look forward to experimental procedures to deter- mine ideal norms which will set up new standards of attainment, vastly increased resources, power and beauty in music.
11. In the future, musical esthetics will be built upon the bases of scientific measurement and experimental analysis. With modern means of measurement, any advocated theories may be put to the acid test.
12. Where there is no experiment, direct or indirect, there is no science. Science, by virtue of its adherence to minute detail, is always fragmentary and incomplete. Its findings must always be supplemented by practical intuition, common sense, and sound philosophical theories of the art. Science deals with selected topics. The musician must deal with the situation as a whole with the means at his command.
There is an important scientific approach in the clinical field; for music may have marked therapeutic value. Clinical psychology
THE SCIENCE OF Music 31
of music will draw upon psychiatry, sociology, criminology, and education for scientific principles. But the field is yet quite un- worked. Van de Wall's Music in Institutions20* furnishes a good introduction to this subject and contains a full bibliography.
13. Musical talent may be measured and analyzed in terms of a hierarchy of talents as related to the total personality, the musical medium, the extent of proposed training, and the object to be served in the musical pursuit.
14. For musical guidance on the basis of scientific measure- ment, the application must be restricted to the factors measured; but it should be supplemented by an adequate audition, case history, and consideration of personality traits and avenues for achievement. All musical guidance should be tempered by the recognition of the extraordinary resourcefulness of the human organism and the vast variety of the possible musical outlets for self-expression.
15. Successful performance rests upon the mastery of funda- mental skills which may be isolated and acquired as specific habits; but in artistic performance, these skills should be integrated so that in the musical mood there is no consciousness of habits, skills, or techniques as such.
16. To facilitate the acquisition of musical skills, objective instrumental aids may be used to great advantage, for both economy of time and precision of achievement. Among such aids are visual projection or quantitative indication of pitch, intensity, time, and timbre at the moment the tone is produced.
17. In the coming electrical organs, pianos, and other instru- ments, and in the criticism which all instruments will be subjected to as a result of the possibility of measurement, future progress will depend upon the adoption of the scientific point of view and the utilization of measurement. We are on the frontier of a new music. With the application of science, the composer will be set new tasks and given new opportunities; the performer will constantly be facing new problems; the listener will always be expecting some- thing new.
18. If the pedagogy of music in the public schools is to keep pace with the pedagogy of all the other subjects, it must frankly face and adopt the scientific point of view. Music will have its first scientific approaches in the public schools rather than in the private studios or conservatories.
32 PSYCHOLOGY OF Music
19. The psychology of music is ultimately not a thing in itself. In employing a technique peculiar to that field, one must fall back upon a general grounding in psychology. After all, the laws of sensa- tion, perception, learning, thinking, feeling, and action in general need only be specifically adapted to the demands of the musical situation.
20. While the cold details of musical facts can be recorded and organized by a mere psychologist, validity and interpretation de- pend upon an intimate knowledge of music and feeling for it. The applied science will progress at its best when the musician can set the problem in compliance with the criteria enumerated above for scientific experiment.
4
A MUSICAL ORNAMENT, THE VIBRATO
THE vibrato is the most important of all musical ornaments, both in voice and in instrument.* It is the most important because it occurs in practically all the tones of artistic singing and in sustained tones of various instruments; because, of all orna- ments, it produces the most significant changes in tone quality; and because it is the factor on which artistic singing and playing are most frequently judged, whether the factor is consciously recog- nized as vibrato or not.
NATURE OF THE VIBRATO
Definition. A good vibrato is a pulsation of pitch, usually accompanied with synchronous pulsations of loudness and timbre, of such extent and rate as to give a pleasing flexibility, tenderness, and richness to the tone.
* The purpose of this chapter is to give a single sustained illustration of the sort of facts which can be ascertained about any musical phenomenon taken into the psychological laboratory-studio for experiment. It is based upon the author's Psychology of the Vibrato in Voice and Instrument. IM The mass of statements represents the principal con- clusions reached in that book and the volume of studies, The Vibrato,119 on which it was based. This chapter will make heavy reading because all of the detailed descriptions and illustrations in the original are omitted. The interested student will turn to the original for deeper satisfaction.
Fifteen years ago, practically none of the facts here cited was known. The vibrato was a bone of contention, grossly misunderstood and misinterpreted. The reader may judge for himself whether or not the present presentation of findings constitutes a fair sample of the science of a musical phenomenon. While every item in this chapter is based upon experiment and is verifiable, the condensation and abbreviation of findings necessarily calls for limita- tions, qualifications, and explanations which can only be given in a fuller treatment. The chapter should not be read as a story, but item for item, with time for reflection.
33
34 PSYCHOLOGY OF Music
In general, we may say that a bad vibrato is any periodic pulsa- tion of pitch, loudness, or timbre which, singly or in combination, fails to produce pleasing flexibility, tenderness, and richness of tone. Likewise, if we desire a generic definition of all vibratos, we might say that the vibrato in music is a periodic pulsation of pitch, loudness, or timbre, singly or in combination. In quantitative terms of these factors, any particular vibrato may be discussed adequately.
An experiment. To prepare for an actual and effective apprecia- tion of the magnitude, the universality, and the complication of the vibrato in good music, let the reader perform the following experi- ment at this stage: Select the most beautiful song you have avail- able on a phonograph record and play it once, listening critically for the vibrato. Then slow down the phonograph turntable to about 30 or 40 revolutions per minute and observe that: (1) these pulsations become shockingly bold; (2) they are present in every note; (3) there is a confusion of pitch, loudness, and timbre; (4) the slow rate makes the vibrato very ugly.
AN EXAMPLE OF THE VOCAL VIBRATO
Figure 1, from Harold Seashore,155 is an example of the musical performance score. It is explained as follows: The pitch frequency of each note is designated by a graph. The wave in that graph on each note represents the pitch vibrato based on very precise meas- urement. Each vertical space for the pitch graph represents a half- tone step. Thus it will be seen that, while the extent of the pitch pulsation varies from note to note, the average for the whole song is about a semitone. In order to identify the graph, each note from the conventional musical staff is interpolated at the point at which the tone begins. The duration of the tone is indicated by the vertical bars which mark off seconds and by the dots and dashes which mark tenths of a second.
The loudness or intensity changes are indicated in terms of decibels. In this staff, one vertical space designates 4 db of intensity; zero is taken as the softest tone which is heard in the song. Thus, the first note comes in very softly and rises to 16 db during the first second, remains around 16 db in the second second, then goes up to 20 db in the third, and 22 db in the fourth. The main thing to bear in mind is that, as the curve rises, the intensity increases. Pauses are indicated by the drop in the intensity curve.
A MUSICAL ORNAMENT, THE VIBRATO
35
This score contains a vast amount of information about the character of the rendition of this song, but let us here consider only what it shows about the vibrato. To aid the reader, a series of
FIG. 1. — The Bach-Gounod /lt^ Maria as sung by Herald Stark. (From H Seashore.1™) Frequency (pitch) is represented by a graph for each note on a semitone staff, intensity, by the lower parallel graph in a decibel scale; and duration by dots in tenths of a second. Measures are numbered at the bottom of the btaff for ready reference.
statements are made with the suggestion that for each one he turn to the score and verify the statement.
1. The pitch vibrato is present in every tone throughout the song, whether the tone is long or short, high or low, weak or strong.
2. It is present in the portamentos of the legato rendition and in the attacks and releases of the tones.
3. The pitch extent, that is, the width of the pulsation of pitch, averages about a semitone.
4. The rate of the vibrato cycles averages about 6.5 pulsations per second.
36
PSYCHOLOGY OF Music
c
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FIG. 1. — (Continued).
A MUSICAL ORNAMENT, THE VIBRATO 87
5. The form of the pitch pulsation is fairly smooth and constant, approxi- mately that of a sine curve.
JJi
FIG. 1.— (Continued}.
6. The extent of the pulsation of pitch is fairly constant and regular.
7. The rate of pulsation in pitch is fairly constant.
8. An intensity vibrato, though very small and often insignificant, is observ- able about one-third of the time.
38
PSYCHOLOGY OF Music
9. The intensity vibrato is weak and quite irregular, seldom present at the beginning of a tone or in transitions.
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10. In view of the relative weakness and infrequent occurrence of the intensity vibrato, it must be regarded as incidental and subordinate to the pitch vibrato, which is dominant.
11. The rate of the intensity vibrato when present is about the same as for the pitch vibrato.
A MUSICAL ORNAMENT, THE VIBRATO 39
12. The crest of a pitch wave tends to coincide with the crest of the intensity wave, that is, as the pitch goes up in a vibrato cycle the intensity increases, but this relationship is neither uniform nor regular.
13. The mean pitch, that is, the mean between the crest and the trough of the vibrato cycles, coincides fairly with the true pitch.
14. The singer did not hold any note on even or true pitch.
15. If there is beauty in this pitch intonation it must lie in the artistic devi- ation from true pitch.
Here we have a very important array of scientific facts observa- ble in a single song. Many of these facts are common to all singing. Many other specific details about vibrato are to be seen in this score; such as, the variation with length of tone, register, loudness, and vowel.
The timbre vibrato is not shown in the score but may be de- duced in many respects from the pitch score. By an adequate selection of samples of songs arid a fair sampling of singers, we can build up the science of the vibrato in vocal art.
Now turn to Fig. 3, and check to see to what extent the above facts apply to the singing of Lawrence Tibbett.
AN EXAMPLE OF INSTRUMENTAL VIBRATO
A perusal of Fig. 2 will reveal the following facts about the violin vibrato as summarized by Small:166
Pitch. 1. The vibrato is present in practically all tones produced by com- pletely stopping the string, except in a trill. Ordinarily there is no pitch vibrato present when the open string is employed.
2. The vibrato is present throughout the entire duration of the tone in which it is employed.
3. As a rule, it is not present in the portamentos, although there are numer- ous exceptions.
4. The form of the pitch pulsation is fairly smooth and regular, approxi- mating a sine curve.
5. The rate of pitch pulsation is relatively constant — about six pulsations per second.
6. The extent of the pitch vibrato is about a quarter tone and is fairly con- stant and regular.
7. The mean pitch of the tones tends to coincide with the pitch indicated in the printed score.*
* Exception to this rule is found m what may be called "tendency notes," for which there are recognized reasons for augmenting or diminishing the interval. Samples of tendency notes are C# to G in the third measure, and B to F in the fourth measure The first represents both a natural tendency upward of a leading tone C# and the tendency of a diminished interval (here the diminished fifth) to contract. The second represents likewise the tendency of contraction in a diminished fifth, as well as the natural tendency of the fourth or subdominant step of a scale downward toward the mediant.
40
PSYCHOLOGY OF Music
8. The movement responsible for the pitch vibrato is initiated most fre- quently with the movement toward the bridge, and the final vibrato movement is most frequently toward the scroll.
20- 10
O
FIG. 2.— Bach's Air for the G String, as played by Arnold Small. (From Small.1**) Frequency (pitch) is represented by a graph for each note on a semitone staff, intensity, by the lower parallel graph in a decibel scale; and duration by dots in tenths of a second. Measures are numbered at the bottom of the staff for ready reference.
A MUSICAL ORNAMENT, THE VIBRATO 41
9. Change of bow does not interrupt the vibrato-producing movement. Likewise, change of finger within a single position does not interrupt the vibrato- producing movement.
10. Tones devoid of vibrato occur infrequently.
11. The extent and possibly the rate tend to diminish toward the end of a tone which just precedes the use of the open string.
12. The extent of the vibrato increases with the increase of intensity of the tone over a large range in an extended crescendo.
FIG. 2.— (Continued).
The trill. 1. The trill in measure 2 resembles the vibrato, but is faster (7.3 per second). As here employed, it begins slowly at the rate of 5 per second and increases in speed up to the third trill, from whence it is quite constant.
2. The interval between the main note and the accessory note remains quite constant from trill to trill.
Intensity. 1. The sustained intensity vibrato is present less than half as frequently as the pitch vibrato.
2. It is present on the open string as a result of the sympathetic vibrato produced intentionally by appropriate fingering.
42 PSYCHOLOGY OF Music
3. It is seldom present throughout the entire duration of a tone.
4. The rate of pulsation tends to coincide with the rate for pitch, the average rate for intensity being 6.27 as compared with 6.10 pulsations per second for pitch.
5. The average extent of pulsation is 3.3 db and is quite irregular.
6. The phase relationship between the intensity pulsation and the pitch pul- sation is not uniform or regular.
7. The intensity vibrato is of secondary importance in comparison with the pitch vibrato.
8. The extent of intensity pulsations due to sympathetic vibrations depends upon the resonance characteristics of the instrument in that they determine the prominence of the partials involved in the intensity pulsations.
9. These same pulsations may be eliminated by damping the string which is vibrating sympathetically.
The sympathetic vibrato. 1. The sympathetic vibrato is an intensity vibrato. 2. It exhibits practically the same rate as all other intensity vibratos, but is wider in extent (5.1 db).
FREQUENCY OF OCCURRENCE, EXTENT AND RATE OF VIBRATOS
The presence of the vibrato. How frequently does the vibrato oc- cur in the best music of today ? Among reasons for the existence of confusion upon this issue in musical circles are the following: the failure to know what the vibrato is; the fact that the vibrato can- not be heard by many people; the fact that it is heard as very much smaller than it really is; the assumption that the vibrato is eliminated when only the grosser and uglier forms have been omitted; habits of hearing in terms of tone quality rather than in recognition of periodic pulsations ; the fact that an even and satis- fying pitch, corresponding to the "true" pitch, is heard; musical versus analytical listening; absence of recording instruments.
All recognized professional singers sing with a pitch vibrato in about 95 per cent or more of their tones. Sustained tones, short tones, portamentos, attacks, releases, and other forms of transi- tions in pitch carry the vibrato. Successful voice students and well- trained amateurs exhibit the vibrato about as do recognized artists. Primitive peoples, such as the uneducated Negro or the Indian, exhibit the vibrato in acceptable form when singing with genuine feeling. The vibrato may appear early in childhood, as soon as the child begins to sing naturally and with genuine feeling. Great singers, teachers of voice, and voice students who are opposed to the vibrato and profess not to use it, do exhibit it in their best singing. A talented student who has no vibrato may develop it to a
A MUSICAL ORNAMENT, THE VIBRATO 43
very satisfactory degree in just a few lessons. Well-trained singers may find it difficult to produce a song or even an isolated tone without the use of the vibrato. Crooners and jazz performers in general employ the excessive vibrato ad nauseam. The vibrato fre- quently appears in emotional speech. The tendency today is for
TABLE I. THE AVERAGE EXTENT AND RATE OF PITCH VIBRATO FOR
29 SINGERS
Average rate Average extent per second of a step
All artists 66 0 48
de Gogorza . ..78 0 46
Schumann-Hemk . . 76 0 38
Galli-Curci . 73 0 44
Macbeth . . . 72 0 31
Caruso ... . 71 0 47
Rethberg . 7 0 0 49
Martinelli . 6 9 0 44
Ponselle . . 6 9 0 48
Chaliapin 68 0 54
Jeritza ... ... 6 8 0 53
Lashanska . .68 0 43
de Luca . ... 6 8 0 58
Tetrazzini . 68 0 37
Talley ... . 67 0 54
Braslau ... . . 66 0 36
Marsh 66 0 52
Tibbett . . 66 0 55
Crooks .... 65 0 47
Gigli . . 65 0 57
Rimini . 65 0 98
Stark .... 65 0 48
Onegin .... . . .... 64 0 41
Dadmun . . . 63 0 46
Seashore 63 0 44
Baker .... ... 62 0 45
Hackett ... 59 0 47
Homer 59 0 51
Kraft . . 59 0 59
Thompson . . ..59 0 53 In thia table from H. Statkore,"* data from Mttfetiel** are included with those o! ZX/fwi"1 and //. Seaihon.M
players on the violin, viola, and cello to use the vibrato on all sustained tones. The vibrato may be used in any of the band or orchestral instruments, but artists generally discourage it for wood- wind or brass instruments, except for isolated and specific effects. It is probable that the vibrato was present in the feelingful self- expression of even the most primitive speech and song. The canary
44 PSYCHOLOGY OF Music
bird which is taught to sing songs can sing with a good vibrato. It is the main appeal in the cooing of the dove. The vibrato is pres- ent in the hearty laughter of the adult and in the vigorous crying of the infant.
In general, we may say that a pulsating quality of tone in the form of periodic rise and fall in pitch is almost universal in good singing, is freely imitated by instruments, notably by the string instruments, and frequently is present in emotional speech.
The extent and rate of the vocal pitch vibrato. The average extent and rate of the pitch oscillation varies to some degree with the character of the song and the singer, but the figures in Table I represent averages for fair samples of the singers listed. The reader must refer to the original articles for names of selections, size of samples, distribution of extent and rate, and other data for each singer.
The average extent of the pitch pulsation for good singers is 0.5 of a tone. This may vary among different singers from 0.3 to 1.0, or more, with a normal distribution. For about three-fourths of the singers, the extent is between 0.45 and 0.55. Each singer tends to have a characteristic average, but may vary from this from selec- tion to selection and from tone to tone. The variation of individual vibrato cycles from this average in acceptable vibrato may be from 0.1 to 1.5 of a tone in a given singer. There are no marked and con- sistent variations with the sex of the singer, the vowel quality, the musical mode, the pitch level, or the loudness of the tone. For short tones, it is slightly wider than for long tones. The extent of the vibrato does not differentiate emotions expressed.
The intensity vibrato. The intensity vibrato, both vocal and instrumental, is seen in the performance scores, Figs. 1, 2, and 3. In general, we find for singers that the intensity vibrato is present about one-third of the time. Ordinarily it is less conspicuous than the pitch vibrato, but, like the pitch vibrato, it is underestimated in hearing.
In general, we may say that the intensity vibrato is less fre- quent, less regular, and less prominent perceptually than pitch vibrato. It is probably secondary to it, and is modified by room resonance. The phase relationship between the two varies widely.
The timbre vibrato. The timbre vibrato is a periodic pulsation in the harmonic structure of a complex tone (see Chap. 9). Every periodic change of pitch of a complex tone causes a parallel periodic
A MUSICAL ORNAMENT, THE VIBRATO 45
change in each of its partials. Each partial may have its own intensity vibrato depending in part upon the permanent resonance regions of the vocal cavities, and the resonance characteristics of the instrument or the room. The timbre vibrato is ordinarily of such magnitude as to make it distinctly audible to the critical ear.
Stringed instruments. All violin artists of today employ the pitch vibrato on practically all stopped notes of sufficient duration to permit its execution. An intensity vibrato frequently occurs as a result of sympathetic vibration, produced either intentionally by fingering an unbowed string or as a result of coincidence of intervals. Each artist tends to have a characteristic rate which varies but little with emotional moods but increases with proficiency. The average rate is about 7, the extremes ranging from 5 to 10. The average pitch extent is about a quarter tone and does not vary significantly with emotional moods. The mean pitch of the vibrato cycles coincides with the true pitch except in the case of tendency tones, in which deviation from true pitch would be made in the absence of the vibrato. The rate and extent are approximately the same for the violin, the viola, and the cello.
Wind instruments. The vibrato occurs in all wind instruments but is comparatively rare, intermittent, and irregular, probably owing to the difficulty of its production. In solo parts, flutists, clarinetists, and trumpeters often exhibit a beautiful and well- sustained vibrato. The intensity vibrato of the organ is used excessively and with monotonous uniformity, probably on account of the simplicity of its mechanical control by a stop.
NORMAL ILLUSIONS WHICH MAKE FOR BEAUTY
OF VIBRATO
1. The vibrato is always heard as of very much smaller extent than it is in the physical tone. For example, a pulsation of a semi- tone is ordinarily heard as less than 0.2 of a tone. It is this illusion which makes the vibrato tolerable.
The larger the pitch and intensity extent, the more it will be underestimated.
The faster the rate, within limits, the more the extent will be underestimated.
The richer the tone, the more the extent will be underestimated.
For good singing, pitch extent and intensity extent are heard as a small fraction of their true extent.
Instead of the full extent of the pulsation, we tend to hear only the extent of deviation from the main pitch or intensity.
46 PSYCHOLOGY OF Music
The end result in hearing may be higher or lower than this, depending upon the presence or absence of other motives for illusion.
These reductions in the extent of hearing of pulsations tend to make the actual vibrato tolerable.
2. Much of the most beautiful vibrato is below the threshold for vibrato hearing and is perceived merely as tone quality. Individ- ual differences in the capacity for hearing the vibrato are very large. In a normal population, one individual may be 50 or 100 times as keen as another in this hearing. Talent for hearing of the vibrato may be measured in two separate tests : (a) the capacity for hearing the presence of the vibrato and (6) the capacity for recognizing differences in vibratos. The most important factors which deter- mine capacity for hearing of the vibrato are the structure and function of the ear and the brain, knowledge of the existence of the vibrato and of its nature, the attitude of the listener, and favorable forms of the vibrato.
In view of these large and often relatively fixed individual differences each individual has his own illusion, and his individual sense of the vibrato determines what shall be good or bad for him. This introduces a most serious obstacle to the efforts toward establishing norms for a vibrato which shall be pleasant to all listeners.
3. Regardless of the extent of pitch, intensity, or timbre pulsa- tion, we always hear an even mean pitch corresponding to the true pitch, an even intensity and continuous timbre.
4. In addition to the mean pitch, a trained observer may hear an even pitch somewhat below the crest and another somewhat above the trough, so that he can hear in all four distinct pitches, namely, a pulsating pitch, a mean pitch, the upper limit pitch, and the lower limit pitch, by directing attention to them in turn.
5. The blending of pitch, intensity, and timbre vibratos.
6. Sonance (to be explained in Chap. 9), the vibrato as an aspect of tone quality.
THE NATURE OF BEAUTY IN THE VIBRATO
Beauty in the vibrato is found in artistic deviation from the precise and uniform in all the attributes of tone.
The vibrato is the most systematic, natural, and essential of musical ornaments.
A MUSICAL OKNAMENT, THE VIBRATO 47
Its beauty lies in a richness of tone, flexibility of tone, and ex- pression of emotional instability.
It represents the periodic changes of pitch, intensity, and timbre in sonance.
Richness of tone results from successive fusion of changes of tone.
Flexibility of tone results from indefiniteness of outline.
Tenderness of tone results from awareness of organic trembling.
The genuine vibrato is automatic and expresses the truth like the smile and the frown.
To cultivate the vibrato, do not cultivate a sign of feeling which is not present, but cultivate the power to feel music genuinely.
The expression of feeling. Does the vibrato differentiate the emotions? Our answer to this question is "No." We cannot dis- tinguish feelings of love from hatred, attraction from repulsion, excitement from tranquillity, by the vibrato. The expression of all kinds of feeling, even the most divergent, tends to take the same general character of the vibrato. It reveals feeling but does not differentiate in kind. This finding came to us as a great surprise in the laboratory.
We are therefore forced to the conclusion that, while the vibrato in both voice and instrument is a means for the expression of musical feeling of the first order, and is even essential to the expression of feeling, it does not differentiate among the feelings. Indeed, it is like an organ stop. So long as the stop is out, all tones have the quality represented by that stop. The vibrato merely indicates that we feel genuinely ; it does not reveal the degree of feeling or the kind of feeling.
The desirability of the vibrato. The desirability of the vibrato is attested by the universality of its use, its automatic nature, its use in instruments, its survival in conflict with precision, and its place in tone quality.
EAR TRAINING FOR THE VIBRATO
Directions are given for training the ear with the eye by listen- ing to a phonograph record and following the pattern score as in Fig. 3. This score is designed to show only the pitch vibrato. For each note, the upper number denotes the average extent of the pitch vibrato and the lower number the number of pulsations per second.
48
PSYCHOLOGY OF Music
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A MUSICAL ORNAMENT, THE VIBRATO
49
Directions for training in the recognition of the rate of the vibrato in the singing of artists. First, play the phonograph record for Fig. 3 one or more times, and coordinate what you hear with the details of what you see in the performance score (Fig. 3) as to the rate of the pulsation. Then drill extensively on the calling out of the number which designates the rate the moment each tone has been heard, and have someone check for each whether you are right or wrong. Directions for training in the recognition of the vibrato in one's own voice. First, sing a song with a playing record in the effort to
G I*
FIG 3. — (Continued).
determine whether or not your vibrato is larger or smaller in pitch extent than that of the artist. Select only sustained tones. Then proceed in the same manner with the same song in determining whether or not your rate is faster or slower than that of the artist. The same procedure may be applied to the study of the extent of the pulsation.
There are three stages in the development of good vibrato through training. The first is the acquisition of scientific informa- tion and critical artistic appreciation of the true nature of the vibrato. The second is the training of the ear to acquire skills in critical hearing and judgment of performance. The third is the de- velopment of corrective adjustment.
50 PSYCHOLOGY OF Music
USE AND ABUSE OF THE VIBRATO
As aids to the hearing, the evaluation and execution of a good vibrato, and the eradication of bad vibratos, the following contribu- tions have been made:
1. Definition, description, and explanation of the true nature of the vibrato as an aspect of tone quality.
2. The invention of instruments of precision and technique for the adequate qualitative as well as quantitative measurement of the vibrato in any and all of its possible manifestations in the nor- mal and actual musical situation.
3. The construction of a " language of the vibrato " by furnish- ing a consistent and adequate terminology and eliminating all redundant terminology which has grown up topsy-turvy in an unscientific atmosphere.
4. The development of the musical performance score, which enables us to represent graphically and with musical meaning all findings of exact observation and measurement.
5. A statistical survey of actual uses and abuses of the vibrato by accepted artists and other groups.
6. The beginnings of the factual array of the vast variety of modes of production of the vibrato, in both voice and instrument, with assignment of probable consequences.
7. The analysis of the affective values which the vibrato engenders in the beautiful and feelingful tone.
8. The discovery of the astounding difference between the actual vibrato as it exists in the physical tone and the vibrato as it is heard in the musical situation.
9. The explanation of some of the vast number of illusions which contribute toward the tolerance, beauty, or ugliness of the tone.
10. The determination of the limits of tolerance and the range of variability of rate and extent of the vibrato.
11. The isolation of the roles of pitch, intensity, and timbre as the media of pulsation, singly or in combination.
12. The exposure of the vibrato as militant against correct intonation, interval, melody, harmony, rhythm, and pure tone.
13. The explanation of the hearing of an even pitch, intensity, and timbre in the fact of the flagrant absence of these in the physical tone.
A MUSICAL ORNAMENT, THE VIBRATO 51
14. The tracing of the origin of the vibrato and its genetic development as a biological fact.
15. The provision of training devices for the effective hearing, rating, and evaluation of vibrato in one's own performance or the performance of another.
16. Suggestions for training and adjustment in its control.
17. The invention of tone integrators and other instruments by which any conceivable form of vibrato may be produced syn- thetically for experimental purposes.
18. Suggestions and procedure in the experimental musical esthetics for the purpose of determining ideals of vibrato in defina- ble situations.
19. Demonstration of the fact that the vibrato does not dif- ferentiate particular feelings such as love and rage, quiescence or excitement.
20. The establishment of the probability that we are here dealing with a physiological rhythm, present not only in man but also in the higher animals whenever paired muscles are innervated under emotional tension.
These scientifically established facts are in contrast with ex- pressed opinions of musical authorities.
THE VIBRATO, GOOD, BAD, INDIFFERENT, AND IDEAL
The most desirable average extent of pitch, intensity, and timbre, singly or in combination, is that which produces flexibility, tenderness, and richness of tone, without giving prominence to the pulsating quality as such.
Freedom from irregularity in extent is essential to a good vibrato.
An extent of the pulsation smaller than that first defined fails, in proportion to its smallness, to contribute toward the betterment of tone quality.
The most desirable average rate is that which causes the best fusion of tone quality in sonance, without producing a chattering through excessive rate.
In vocal vibrato the pulsations in pitch should be primary and dominant.
The combination of synchronous pulsations in the three media ordinarily makes a larger contribution toward tone quality than its occurrence in one or two.
52 PSYCHOLOGY OP Music
In instrumental music relatively pure intensity pulsation is permissible, as in organ stops and in the use of beats within a region of tolerance for rate.
Artistic performance demands variation in extent and rate throughout a performance.
In solo parts, both vocal and instrumental, the artist has larger latitude for giving prominence to the vibrato than he has in ensemble.
The more nearly alike the timbres of the instruments within an orchestral choir, the greater may be the demand for the vibrato in that choir.
However, an ideal vibrato which can be gradually developed through musical criticism and musical education will probably be smooth in variations of rate and extent, will have a cycle which approaches the perfect sine curve, will probably be one cycle per second faster than the present, will have a higher artistic variabil- ity, will be adapted to solo and ensemble performances, will have a pitch extent of approximately one-half of the present average for voice, and will probably be present in all tones and transitions ex- cept where the nonvibrato is used for specific effects.
If this should come true, largely as the result of scientific investigations, one might well ask, "What is it worth?" And this question we can answer only by asking other questions : How would it affect musical theory ? How would it facilitate musical training ? How would it affect musical criticism? How much sweeter would music be to the listener ?
PITCH: FREQUENCY
THE NATURE OF PITCH
PITCH is that qualitative attribute of auditory sensation which denotes highness or lowness in the musical scale and is condi- tioned primarily on the frequency of sound waves.
We note in this definition (1) that pitch is one of the four at- tributes of tonal sensation, and that it is qualitative in that it designates the kind of sensation, thus distinguishing sensations of tone from the other sensory modalities, such as color, odor, and taste; (2) that it denotes highness or lowness in the tonal continuum along which we locate the musical scale; and (3) that it is the mental and musical correlate of the frequency of the vibrations which constitute the physical tone.
While all music is objectively due to physical sound waves, we must bear in mind that we can never be directly aware of the rate of vibration as such, for we hear it as musical pitch. This is one of the wondrous transformations "from matter to mind.5' Out of mere vibration is built a world of musical tones which do not in themselves suggest vibration at all. Yet the human ear may be so keen as to detect in nature a difference of a fraction of a vibration in frequency. It is fortunate that we can live in a world of music without thinking at all of the physical counter- part; still, for the science of music and for the study of musical talent, such reference is necessary.
The ear is a most wonderful mechanism with its membranes, levers, and liquid conductors carrying the vibration to the harp structure, its means of analysis of all pitches in that structure, and its means of transmission of each pitch over
S3
54 PSYCHOLOGY OF Music
its particular line to the brain. We cannot here undertake to discuss the structure of the ear, its physiology, and the numerous technical problems or theories of hearing. The reader who is interested in this phase of the subject must turn to books on the anatomy and physiology of the ear. But, for psychological pur- poses, it is necessary to make certain assumptions, of which the essential one is that there is a pitch-differentiating mechanism in the ear, capable of serving as a physical basis for the sensory phenomena with which we deal in the psychology of hearing; namely, pitch, loudness, timbre, volume, fusion, and consonance, and their derivatives or variants. For pitch, the harp theory furnishes at least a good analogy. Seashore.131
LIMITS OF AUDIBLE PITCH
Lower limit. The lower limit of pitch is that frequency which gives us the lowest sensation of tone. The lowest audible tone is usually said to be about 16 ~, but it varies with a large number of factors. There are two primary factors that determine the lower limit, the strength or intensity of the sound wave, and its form. If low tones are to be heard at all they must be relatively very strong. Therefore, the lower limit will vary with the intensity of the tone within a very wide range. The most favorable form of the wave is that smooth curve which gives us a pure tone. Under most favorable conditions, a good listener can get tonal fusion as low as 12 ~, whereas if the wave comes in the form of more and more acute puffs, as, in an extreme case, the sound waves coming from electrical sparks, the lower limit of tonality may be as high as 100 ~.
Upper limit. The average upper limit for an unselected group under the age of forty is probably about 1 6,000 ~, but this limit varies greatly with a number of important conditions, such as advanced age, and various types of defects and diseases of the inner ear. Even in the so-called "normal" ear, there are very large individual differences in the upper limit. These differences may have far-reaching significance for the character of what one hears. Reliable measurements still are not available for determination of the upper limit under the most favorable conditions and in sufficient detail for classification of types. It seems possible that the upper limit for human hearing in youth may rise to the height of 25,000 ~ in the most sensitive ear under the most favorable conditions. Yet, many people with apparently normal hearing can- not hear above 5,000 ~. In an unselected population, there is
PITCH: FREQUENCY 55
probably a large percentage of persons who cannot hear tones above 10,000—.
The average frequency in the chirp of a cricket is about 8,000 ~, but cricket tones as high as 32,000— have been recorded. Certain birds are also known to produce tones higher than those produced by voice or musical instruments. It is probable that such animals, capable of producing high tones, can hear tones at least as high as those they produce.
Sounds in nature as high as 40,000— have been recorded and artificially produced. Supersonic frequencies have been recorded as high as 2,000,000—. In brief, we are living in a world in which physical tones may exist within a very wide range, but each human being or animal can hear only a short section of these frequencies because the limits of audible tones for man or animal are set by the character of the receiving instrument, the ear. This normal limita- tion of the pitch range is a great blessing, in that it saves us from bombardment by the masses of higher frequency in nature which would serve but little purpose in auditory orientation.
Decline of the upper limit with age and disease. When Madam Gadski and her daughter were visiting the psychological laboratory, we tested them for upper limit of hearing and found that the famous prima donna could not hear any tone or overtone above 12,000— ', whereas the young daughter could hear up to about 20,000—. This was a shocking discovery for the mother, but certainly no discredit to her as a musician. The simple explanation was that the mother was older. The upper limit of hearing suffers a normal and predictable drop owing to the fact that, as age comes on, the highest pitch mechanisms in the ear progressively become nonfunctional. Since this loss is a function of the intensity of the sound, further consideration of this matter will occur under that head.
PITCH DISCRIMINATION
The ability to hear small differences in pitch is called "pitch discrimination" and determines what is generally called the "sense of pitch." It is a measure of the capacity for using pitch in musical hearing and tone production. We shall use interchangeably the terms "pitch discrimination" and "sense of pitch."*
* The sense of pitch, pitch discrimination, sensory discrimination for pitch, threshold of pitch discrimination, differential pitch hearing are all more or less synonymous terms. It is usually abbreviated as Af.
56 PSYCHOLOGY OF Music
Measurement. Pitch discrimination is measured by sounding two pure tones in quick succession and gradually reducing the difference in frequency until the observer is unable to tell which of the two tones is the higher. The steps usually employed in such a series are 30, 23, 17, 12, 8, 5, 3, 2, 1, 0.5 ~, at the level of interna- tional A, 435^. The standard procedure has been to use tuning forks with resonators, but various forms of electrical oscillators are now available and more convenient.*
For group measurements, the test material from the best avail- able instruments is recorded on a phonograph record which is economical, standard, durable, and relatively foolproof in use.
There are two fundamental methods of procedure. One is to begin with the smallest differential and take about 100 trials on each step up to the step in which 80 per cent of the answers are right. This step is regarded as the threshold of pitch discrimination, which is a measure of the sense of pitch. This is the best method to use in individual testing. The other method, better adapted for group testing, is to take a block of the 10 steps named above, mak- ing 10 trials for each step, and, using the 10 units as a single block, determining what per cent of right judgments can be made in all of these 100 trials as a block. This is the method used in the phonograph record.125
Norms. On the basis of thousands of trials by the above method, norms have been established in terms of centile rank. This method is convenient in that the same scale can be used for all kinds of measurements that are made and for which sufficient data are available to determine norms. According to the scale, rank 50 means average, rank 1, the lowest or poorest 1 per cent found, and rank 100, the highest 1 per cent found, intervening ranks being proportional to the numbers.
The average threshold for an unselected group of adults is about 3~ at the level of international pitch, 435 ~. This is % 7 of a tone, but a very sensitive ear can hear as small a difference as 0.5 ~ or less, which, at this level, is less than 0.01 of a tone. Some persons who pass in a community as having normal hearing may not
* These tuning forks with resonators may be obtained from the C. H. Stocking Com- pany, Chicago, but anyone desiring to do so can take forks of 485^ or 440~ and tune them by filing near the tip of the prongs and counting beats. Resonators may also be improvised by partly filling a half-pint cream bottle with water until it " speaks" to the fork. For a full account of the standardization of this measurement see Seashore.1*1
PITCH: FREQUENCY 57
be able to hear a half-tone or even a whole-tone difference. In ex- treme cases we may have pitch deafness.
Stucker1** examined the discrimination of 16 professional musicians in the Royal Opera in Vienna and found that for A3 in international pitch, they had the following thresholds in terms of vibrations: 0.1, 0.2, 0.2, 0.2, 0.3, 0.3, 0.4, 0.5, 0.5, 0.6, 0.8, 0.8, 0.9, 0.9, 1.1, 1.1. At this level one whole-tone step represents 54~. Therefore, the keenest of these musicians could hear )ls4o of a tone, and the poorest ^9 of a tone. These exceptionally fine records are not to be attributed significantly to training. They are probably due primarily to the principle of selection, in that persons with unusu- ally fine ears have sought and received this high order of training and recognition.
Physiological limit. The physiological limit of any sense organ is that limit for sensation and perception which is set by the struc- ture of the sense organ and the brain. In measurements of this kind we do not always reach this limit but attain what is called a cognitive limit of discrimination. A good test in the hands of an expert may properly establish the physiological limit of pitch dis- crimination in the first trial for a majority of the subjects in a group test, whereas in an individual test the physiological limit may be determined with a high degree of certainty for practically all. The difference between these two limits, the physiological and the cognitive, is an indication of the uncertainty and the unreliability of a test. It usually is due to a lack of understanding of the test requirements, or a lack of mental development, or of good will, or of general power of application on the part of the subject tested. This margin may be reduced or eliminated by a repetition and by indi- vidual testing by an expert.
Relation to intelligence. The physiological limit for the sense of pitch does not vary significantly with intelligence. The moron may have as keen a sense of pitch as the philosopher. Measurements on children and adults in which pitch discrimination is compared with intelligence show no significant correlation. The slight correlation that is found is due primarily to lack of the capacity for under- standing the test conditions and not to the capacity for pitch hear- ing as such.
There are three significant issues with which we must not con- fuse this negative finding about intelligence: (1) It has no bearing upon the opprobrious question often heard, "Are musicians
58 PSYCHOLOGY OF Music
dumb?'' We have no evidence to show that the distribution of intelligence among musicians differs from the distribution in an unselected population. Our best guess is that the distribution is approximately the same. The common observation that musicians live more in the realm of feeling proves nothing in regard to the distribution of the capacity for intelligence. There also may be such a thing as a f eelingf ul intelligence. (2) It does not imply that intelli- gence is not essential to a high degree of musicianship. Music is a learned occupation. Like lawyers and physicians, the musician must show a high order of intelligence in order to gain professional distinction. (3) It does not depreciate the necessity for employing intelligence in the use of pitch in all phases of musical performance.
Relation to age. In the absence of disease, the physiological limit for the sense of pitch does not vary with age. A standard group test can be made on children as low as the fifth grade. The average achievement of children in the grades is not so high as for adults. As we have seen, there are different age norms. The reason for this lies, of course, in the relative cognitive immaturity and not in the capacity of the sense organ. However, an expert working with intelligent children may reach this limit in individual tests as early as at the age of five.
It seems probable that just as the physical eye of the child at the age of three is as keen as it ever will be, so the pitch sensitiveness in the ear probably reaches its maximum very early. Development in the use of the sense of pitch with maturation consists in acquiring habits and meanings, interests, desires, and musical knowledge, rather than in the improvement of the sense organ.
Relation to training. The physiological limit for hearing pitch does not improve with training. Training, like maturation, results in the conscious recognition of the nature of pitch, its meaning, and the development of habits of use in musical operations. Training probably does not modify the capacity of the sense organ any more than the playing of the good violin may improve the quality of its tone.
Fortunes have been spent and thousands of young lives have been made wretched by application of the theory that the sense of pitch can be improved with training. It is the cause of the out- standing tragedy in musical education. On the other hand, ear training is one of the most neglected elements of musical education. However good the sense of pitch may be, it demands training in
PITCH: FREQUENCY 59
proportion to the natural capacity in this sense. The training is significant not only for the appreciation of "pitch play'* in music, but even more significant for the control of performance. The trouble with flatting, -slovenly intonation, inability to sing inter- vals, poor timbre control of voice or instrument by a person with a good sense of _p itch, may Ibe a slovenly ear, an uncritical ear, or an untrained ear, not motor 6F muscular trouble.
Limit elemental. The physiological limit is elemental in the sense that it indicates a specific capacity in one sense attribute which is relatively independent of intelligence, age, and training. It is a moot question whether any psychophysical capacity can be elemental, in view of the fact that a certain amount of knowledge and experience is necessary in order to make the test. It is probable that in this particular measurement of pitch discrimination we come as near to securing an elemental measure as can be found in any of the senses. However, we must always bear in mind the possibility and probability that we may be dealing with the cognitive limit instead of the physiological one. Nevertheless the concept is a use- ful one. We should not think of the physiological limit as fixed, because within a small range it in itself can vary with factors which either raise or lower the functions of the nervous system, such as fatigue, rest, the action of either depressive or stimulative drugs, or disease.
Inheritance. There is good evidence to show that a musical ear, by which we mean primarily an ear with good sense of pitch, is inherited to considerable extent and that with this inheritance follows variability in the tonal capacities which depend upon pitch discrimination, such as tonal memory, the sense of timbre, the sense of consonance, and auditory imagery. This topic will be discussed in a later chapter.
Frequency level and sensation level. Pitch discrimination varies in a systematic manner with the frequency within the tonal range and with the intensity of the tone. This is shown graphically in Fig. 1. In brief, the figure shows that (1) pitch discrimination is poorest for low tones and best above 1,000~; (2) this variation with fre- quency holds for all sensation levels from 5 to 60 db; and (3) it is keener for strong tones than for weak.
Figure 1 is based upon measurements with pure tones. It is well known that discrimination is finer for rich tones. It varies with both degree and kind of richness.
60
PSYCHOLOGY OF Music
Number of just -noticeable differences. How many differences in pitch can the average person hear? This is determined by start- ing with the lowest audible pitch and proceeding step by step in terms of just-noticeable differences (j.n.d.). Figure 2 is a typical record. It has been found that the average ear can hear approxi-
0.07
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125 250 500 1000 2000 4000 600011,700 Frequency, f
FIG. 1. — Variation with frequency level and sensation level. The numbers at the bottom denote frequency; at the side, the increment in per cent of frequency. The numbers within the figure denote sensation level, that is, number of db above the threshold of audibility. For example, for the frequency of 125-^', the increment must be 6 per cent for a 5 db tone, 4 per cent for a 10 db tone, and between 2 and 3 per cent for 20, 40, and 60 db tones, respec- tively. (Shower and Biddulph.161)
In music it is helpful to think of the data in Fig. 1 in terms of fractions of a tone rather than in terms of per cent of the fundamental frequency. Since a whole-tone step is 9/8 of
the fundamental frequency f -v J i we may convert the figures at the left of the table into
hundredths of a whole-tone step by multiplying each by 8. These numbers would then read, from top downward: 0.56, 0.48, 0.40, 0.32, 0.24, 0.16, and 0.80.
mately 1,400 steps of difference in pitch of a medium-loud pure tone. However, it must be remembered that this is an average figure and that this number varies with several factors, among which four are outstanding: (1) individual differences — one person may hear more than a hundred times as many pitch differences as another; (2) intensity — more steps in pitch can be heard in strong tones than in weak tones; (3) duration — the most favorable dis- crimination occurs when there is an abrupt transition from one
PITCH: FREQUENCY
61
pitch to the next within a tone; (4) timbre — more steps in pitch can be heard for rich tones than for pure tones. This concept of the number of perceptible steps in pitch is a very important one because it is an index of the extent to which hearing differences function in daily life.
Binaural versus monaural discrimination. Binaural is finer than monaural discrimination by about 10 per cent for most musical tones. The difference decreases gradually to about 2 per cent for tones at or above 500^.
Duration. There are three types of musical situations which may be recognized in the measurement of pitch discrimination: (1) going
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FIG. 2. — A scale of just perceptibly different pitch steps (j n d ). (Lewis.77)
from one note to another with a complete break between them, as in the standard test where we sound two notes, each of which is one second in duration but differing in pitch and separated by a very short interval of time; (2) legato rise or fall in pitch or pitch vibrato; and (3) sudden shift in a single note without break in tone, as in erratic intonation.
The discrimination is different for each of these three, the neces- sary increment being about twice as large for the first type as the third, and the second falling between these two. These differences are related to the differences in total duration of each tone.
The minimum duration necessary in order to identify the pitch of a tone clearly varies with the frequency and to some extent with
62 PSYCHOLOGY OF Music
the loudness. It has been found that in order to be heard clearly as of definite pitch, a tone at 128 ~ must have a duration of 0.09 second; for 256 ~, about 0.07 second; for 384 ~, about 0.04 second; and for 512 ~, about the same.
Masking. The damping of one tone by another is called "mask- ing." This is due to interference of vibrations in the basilar membrane of the inner ear. A low pure tone tends to "drown out" a higher tone of any frequency, but a high tone has but little effect upon a lower tone. It is much easier to talk or sing against high noises than against noises of low frequency. The low partials in a rich tone tend to dampen the higher partials. Therefore, as a piano tone is made stronger and stronger, the timbre of the tone changes because the low partials become more and more effective in drown- ing out the higher partials.
This is a phenomenon which plays an exceedingly important role in the determination of tone quality. In the past the artistic composer and performer have taken facts of this kind .into account more or less intuitively, but experiments by Fletcher*1 have estab- lished definite laws of masking which now can guide the composer in producing certain effects. Stewart1** gives a good account for musi- cians. Likewise, these laws guide the performer in the modifying of tone quality by control of intensity and in the balancing of chords for the same purpose, with knowledge of masking effects.
\i ABSOLUTE PITCH
/•
(The term "absolute pitch" is used with various meanings. It is common practice to say that a person has absolute pitch if he can name instantly any key that is struck on the piano. This capac- ity is rather common) The term probably should be restricted to possession of the ability to identify tones by much smaller steps than those of the musical scale, for example, from 0.01 to 0.1 of a tone. If the violinist is right when he says, for example, that a given violin is tuned 0.05 of a tone above international pitch, or any other recognized standard, without having had any chance for comparing the tone to any audible standard of reference, then he has absolute pitch. Such capacity is very rare. The possession of absolute pitch to any degree is a safe guarantee of a good sense of pitch and of ear-mindednessv
To measure absolute pitch, it is necessary to make only one trial at a time and to make that just after waking up and before
PITCH: FREQUENCY 63
any comparison of tone has been heardJThe measurement can be made by a series of tuning forks differing in small steps as in the discrimination test. It is generally believed that the musical ear acquires a standard reference tone, perhaps C3 or A3, and that any tone that is sounded in the musical continuum is placed with refer- ence to that in the musical scale. That answers the question as to how it is possible to identify all the audible tones. A more important question pertains to the basis of the reference tone. It is quite generally agreed that the identification is not only in terms of pitch, but also in part in terms of timbre or tone quality, particularly in relation to a similar instrument.
THE SIGNIFICANCE OF INDIVIDUAL DIFFERENCES
Since pitch is the fundamental character of a tone, and pitch discrimination is a measure of the capacity of this sense, it ordi- narily may be regarded as the most basic measure of musical capacity that we have. It determines not only what we shall hear, but fundamentally what we shall remember, imagine, and think, and, most important of all, it determines in large part what emo- tional reaction we shall have for the tone. These differences, often enormously large, must therefore be taken into account in selection and guidance for musical education, in musical criticism, in choice of instruments, and in judgment concerning extraordinary capacity or incapacity, for musical purposes.
NORMAL ILLUSIONS OF PITCH
"Things are not what they seem." As was pointed out in Chap. 2, the ratio of 1 : 1 between the physical fact, such as frequency, and the mental fact, pitch, is not always exact. Thus 440 ~ does not mean always the same pitch. The pitch would vary in predictable ways with differences in intensity, duration, and harmonic constitu- tion of the tone, that is, with amplitude, duration, and form of the sound wave. In a predictable way, we speak of the deviation as a normal illusion. An illusion is said to be normal when all persons under similar circumstances tend to get the same result. It is called illusion because the perception does not correspond to the physical object to which it refers. The illusory perception is always positive; that is, it represents a genuine perception and may be just as strong and clear as the perception in which no illusions are involved. The normal illusions often represent short cuts to meaning and an
64 PSYCHOLOGY OF Music
economy in our response to nature and art. A single illusion may be due to half a dozen causes or motives, some cooperative and some inhibiting. Since illusions are measurable and play a very important role in our hearing and rendition of music, the future psychology of music will be expected to state the fundamental laws of illusion of pitch as well as other sensory characteristics.
A beautiful example of the measurement of illusion of pitch due to the varying of the intensity of the tone has been made recently by Fletcher.™ Indeed, his measurements reveal several normal illu- sions of pitch governing the relation of pitch to intensity. The reader who is interested in good examples of law in illusion of tone should consult this authority.
In general it has been found that tones having frequencies below 2,000^ become lower in pitch while those having frequencies above this level become higher when the intensity of a pure tone is increased.
Three general problems were suggested by his experiment. (1) Would the same be true of rich tones? It was found that for rich tones, such as violin tones, the illusion is only one-fifth as large as for pure tones. (2) Will two such tones of different intensity sound discordant when produced together? It was found that they will not. (3) Does the violinist make correction for these illusions in his playing of intervals? Lewis and Cowan7* conducted a series of experiments on this and found that he does not. Knowledge of this illusion, is, of course, of very great interest and significance to the musician, and it explains many of the well-known inconsistencies between pitch and frequency.
Six illusions were illustrated in Chap. 4. The entire field of "subjective tones" falls largely within the realm of normal illusion.
SUBJECTIVE TONES*
A very large number of the tones which play leading roles in music are purely subjective; that is, the frequencies represented are not present in the physical tone but are supplied by the individual in hearing. When two or more tones are sounded together, the trained listener can hear not only these two generators but a con-
* The content of the remainder of this chapter overlaps with Chap. 8. Therefore, those readers to whom this material is new will do well to coordinate the reading of thia •ection with that chapter.
PITCH: FREQUENCY 65
siderable number of subjective tones which may be quite conspicu- ous and always play a very important role in music. In order to illustrate the character of subjective tones, we shall draw upon the following experiment.
A subjective-tone experiment. Wegel and Lane211 devised a very fine illustration of the existence of four kinds of subjective tones. They used two strong pure generating tones. To detect the presence of subjective tones, they employed an "exploring tone" which could be varied through a large range of frequencies. This could be set so as to differ 1 or 2~ from a theoretical subjective tone. If
TABLE I. SUBJECTIVE TONES DETECTED IN A TWO-CLANG TONE COMPOSED OF 700~ (A) AND 1,200~ (B) PURE TONES AT 80 DB SENSATION
LEVEL
(Adapted from Wegel and Lane*11)
1. 600 (B - A)
2. 200 (*A - B) ; 900 (3 A - B) ; 1,700 (2B - A); 1,000 (2£ - 2,4); 2,900 (35 - A)
3. 1,900 (A + B)
4. 2,600 CU -f B) ; 3,800 (2,4 -f SB), 3,100 (A + 2B); 4,300 (A + 3#) ; 3,300 (SA + B)
6. 1,400 (*A) ; 2,100 (3,4) ; 2,800 (4,4)
6. 2,400 (2£) ; 3,600 (3B)
1. First difference tone
2. Other difference tones
3. First summation tone
4. Other summation tones
5. Harmonics of the lower generating tone
6. Harmonics of the higher generating tone
the subjective tone was sufficiently loud, it would beat with the exploring tone.
This was a very simple and strategic device for the securing of objective evidence for the existence and location of subjective tones. Naturally many of the weaker subjective tones would be too faint to cause a perceptible beat, but a sufficient number of them were strong enough to present a most formidable array of the sub- jective tones that can occur in such a simple situation.
They used two pure tones, 700 and 1,200^^, each 80 db above a standard, as generators. Let us call the first A and the second B. These tones were sounded together and a search was made through- out the audible range for subjective tones which would beat with the exploring tone. The location of these was, of course, predictable according to theory. By this method they were able to demonstrate that, in this two-clang combination, 17 subjective tones were pres-
66 PSYCHOLOGY OF Music
ent and sufficiently loud to cause beats. The results are expressed in Table I, which is very illuminating and helpful in the classifica- tion of these phenomena. The black-faced numbers denote the pitch of each of the 17 subjective tones recorded. The structure of each tone may be seen at a glance in the formula given in paren- theses where A denotes 700 ~ and B 1,200~.
This table is a revelation to the student of music, showing that in this very simple situation 17 distinct subjective tones could be heard clearly enough to have their pitch measured with precision. Incidentally, it may be said that they also were strong enough so that their actual loudness could be measured. Theoretically, more are predictable and may be identified with further refinement of measuring technique.
But it is even more baffling to realize that the complexity of the situation increases in geometric ratio with the addition of one or more tones to the chord or discord and that again it increases vastly with the utilization of rich generating tones, such as those of stringed instruments which have prominent harmonics, since each harmonic may act as an independent generator.
Fortunately, in musical hearing we do not ordinarily hear these subjective tones individually. Like overtones, they fuse into the complex tone which we hear and are, in large part, recognized as the determinants of timbre and tone quality. But by numerous forms of experiment, they may be classified, isolated, and studied one by one. Let us here give some consideration to each of the three main groups.
THE FIRST DIFFERENCE TONE
The most conspicuous and best known of the subjective tones is ordinarily the first difference tone (B — A) in the first line of the table. If we use two pure tones, keeping one constant and varying the other, we may produce as many difference tones of this order as there are differences in the frequencies ranging from the lowest audible up to the highest audible tones. For example, the first difference tone for the clang 200 and 300~ is 100~; for 200 and 800 ~ it is 600 ~; for 200 and 1,000~ it is 800 ~.
The identification of these difference tones throughout the audible range furnishes a most excellent exercise in ear training. The best technique is to use vacuum tubes for producing pure tones. The old method was to use glass whistles, called Quinke's
PITCH: FREQUENCY 67
tubes, which produced relatively pure tones. These Quinke's tubes can easily be made by the student himself from the description in some textbook of physics.
OTHER DIFFERENCE TONES
As is shown in the second item of Table I, other difference tones are present, at the frequencies of 200, 900, 1,000, 1,700, and 2,900~, respectively. These are all equivalent to a number of pure tones added to enrich the clang. None of them belong in the harmonic series, and they contribute by the introduction of more or less discordant elements in the quality of the clang.
SUMMATION TONES
Items 3 and 4 in Table I give examples of summation tones, each represented by the sum of the frequencies of the two generators or the sum of some multiple of the two fundamentals. The most conspicuous of these is perhaps the first summation tone, A + B. None of these falls in the harmonic series and, therefore, their func- tion, like that of the second group of difference tones, is to increase the complexity of the clang by more or less discordant elements.
SUBJECTIVE HARMONICS
The reader who is not familiar with the harmonic structure of musical tones will do well to cast a preliminary glance at Chap. 8, which is devoted to that subject. In accordance with har- monic theory, a good rich musical tone is composed of a funda- mental and a series of partials, each being a multiple of the fundamental. In the experiment reported, pure tones were used. That means that no physical partials were present. If the tone from a stringed instrument had been used, the partials for the lower generator could have been 700, 2,100, 2,800, 5,600—, etc., each a multiple of the fundamental, and for the higher tone they would be 1,200, 2,400, 3,600, 7,200—, etc., depending upon the richness of the tone. Theoretically, in this experiment, if the tone had been weaker, no physical partials should have been present, but 80 db is a very strong tone, and the effect of such intensity upon the inner ear is to produce subjective partials; that is, partials which have a distinct pitch, loudness, and harmonic relation to the funda- mental but have no corresponding physical frequency. For the
68 PSYCHOLOGY OF Music
lower generating tone, Line 5, Table I, the second, third, and fourth partials were observed in spite of the faet that they came from a tone which generated no physical partials. Likewise, for the second generator, the second and third partials were present under the same circumstances. Here we have a third type of contribu- tion to the character of the clang as heard, namely, the presence of five partials, each of which contributed to the richness of the tone of each generator in spite of its physical purity. It should be noted, however, that these subjective harmonic partials are produced only for extremely loud tones, such as do not ordinarily function in musical performance. To what extent they are present in ordinary musical tones in a lower degree of loudness than that here measured remains to be shown by experiment.
In the interest of clarity, the illustrations here given have been carried in the simplest terms, namely, a clang composed of two pure tones. It is easy to see that if we add one or more pure generat- ing tones to the musical chord, we shall increase the complexity of the situation in geometric ratio but all in accordance with the prin- ciples here laid down for two generators. Again, if instead of pure tone generators in the chord, we use rich tones, such as those of orchestral instruments, we shall again increase the complexities of the situation to a most baffling degree, and yet one not defying analysis and experimental illustration.
THE DIFFERENCE TONE A SUBSTITUTE FOR A LOW FUNDAMENTAL
A rich tone from a musical instrument may be modified by introducing a filter, either mechanical or electrical. A filter is a means for eliminating completely the frequencies of any desired partial or group of partials in the musical tone. Suppose now that we have a tone of 200 ~ played on the G string of a violin, and we eliminate the fundamental frequency by filtering, without inter- fering at all with the partials above the fundamental. The musical listener may fail to notice any difference between this tone and the tone in which the fundamental is present and is absolutely certain to hear the pitch of the missing fundamental, namely, 200^. If, again, we eliminate the fundamental and the second and third partials, we still hear the tone definitely as of a pitch of 200 ~9 although there is no physical frequency present lower than 800^. Furthermore, as we shall see in Chap. 17, there is comparatively
PITCH: FREQUENCY
69
little energy in the fundamental of low tones in voices and instru- ments. But the fundamental not only gives the pitch to the tone as a whole, but often stands out as dominant, owing to reinforcement by the subjective tone.
The reason for these phenomena is that successive partials are always multiples of the fundamental; in this case 200— (first partial or fundamental) has 400, 600, 800, 1,000— etc., as multiples of it- self. The difference between the fundamental and the first overtone is, therefore, 200, and the difference of any two adjacent higher partials is always the same — 200—, which is the pitch of the
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90 60 70 60 |
f |
PIANO |
s |
\n |
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'\ RANGE OF FUNDAMENTALS |
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f |
CONCERT ETUDE-LOW-* |
0 |
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MARCH MILITAIRE-o |
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-y- |
CONCERT F.TUDE-HICH-o |
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•*n |
H |
Ch |
PAS 1 |
S F |
ILTERS |
LOW P, |
^SS F |
ILTl |
:R« |
I |
50
100 500 1,000 5,000 10,000
FIG 3 — Number of times filter condition was correctly preserved as function of cutoff frequency for the piano. Figures at the bottom denote frequencies; figures at the left, per cent of correct judgments. The instrument was the piano The range of the fundamentals for each selection is shown by the arrowed lines under the name of the selection. "High- pass filters" means that low frequencies were eliminated; "low-pass filters'* means that high frequencies were eliminated. Thus m the Concert Etude, symbolized by a dot, the range was from 82 to 800~. For the Afarche Mihtaire, symbolized by a circle, from 42 to 1,800~; and for the Concert Etude, symbolized by a square, from 192 to 2,500~. (Snow?.170)
fundamental. The result is that we get a difference tone of the pitch of the fundamental for each successive pair of partials; and, since this is always the same, the effect becomes cumulative and adds to the loudness of the subjective fundamental. This is equivalent to the sounding together of a number of pure tones of 200 ~.
The limits of effective frequency in the piano. Snow1™ performed a very interesting series of experiments to determine to what extent the highest and the lowest frequencies of the musical tone are negligible. He used trained observers under most favorable condi- tions in observing low and high tones in the three musical selections. His findings are summarized in Fig. 3 for the piano. Let us consider first only the low tones.
70 PSYCHOLOGY OF Music
His method was to compare the regular nonfiltered tone of the piano, which we shall call N9 with the same tone, F, which had various lower frequencies eliminated by filtering. He eliminated, in turn, all frequencies below 70, 80, 90 and 100~ to determine whether or not the fundamental below these limits would be heard, and whether or not the F tone could be distinguished from the N tone. His records were kept in terms of the percentage of right judgments on whether or not the two tones sounded alike. The result may be seen at the left side of Fig. 3.
We see that when all notes below 55 ~ were eliminated, the judgments were 50 per cent right, which is what they would be by chance. Therefore, the observers had no ability to distinguish the B tone from the A tone. When he eliminated frequencies below 65 ~, the judgments were 65 per cent right. When he eliminated all frequencies under 100^, the judgments were about 78 per cent right. When he eliminated frequencies below 130~, the judgments were 90 per cent right. To get judgments 100 per cent right, he would have to eliminate all below 165~.
What does this mean, then, in general terms? It means (1) that, although the fundamental frequency was completely eliminated in these low tones, it was still heard as the fundamental pitch of the tone; and (2) that a considerable amount of filtering could take place in tone B without altering the perceived character of the tone. This is a very impressive illustration of the role of subjective tones in the everyday hearing of piano music.
On the other side of the chart, we see what happens if we com- pare N and F tones when the F tone has certain higher partials eliminated. The conclusion from this is that, above the region of 5,000^, the high overtones gradually cease to be heard either as pure tones in themselves or as modifying the character of the tone perceptibly.
Audible frequency range for music, speech, and noise. Follow- ing the same method of experimentation, Snowm investigated the principal types of instruments and voices, with the result shown in Fig. 4. The whole solid line shows the normal frequency range of the instrument; the circle on a line shows the limit below which lower frequencies could be eliminated before the observers could make 80 per cent right judgments in distinguishing the F tone from the N tone. The same principle applies to the upper limit. The regions indicated by short bars at the right are the regions of accessory
PITCH: FREQUENCY
71
noises for each type of tone. Snow170 summarizes his findings as follows :
1. The piano was alone in producing tones with inaudible fundamentals.
2. Audible frequencies down to 40 cycles were produced by the musical instruments, but reproduction only to 60 cycles was considered almost as satisfactory.
AUDIBLE FREQUENCY RANGE
FOR MUSIC SPEECH AND NOISE
ACTUAL TONE RANGE
mmimt ACCOMPANYING NOISE RANGE
• -CUT-OFF FREQUENCY OF FILTER DETECTABLE IN 80% OF TESTS
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SNARE DRUM |
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FRENCH HORN- — |
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HAND CLAPPING KEY JINGLING |
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4 |
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0 100 500 |
1,000 5,000 1 |
0,000 2O.C |
FREQUENCY IN CYCLES PER SECOND
FIG. 4. — Audible frequency range for music, speech, and noise. (Snow.170)
3. It was found that transmission of the highest audible frequencies was needed for perfect reproduction of musical instruments, mainly because of the noises accompanying the musical tones. A 10,000 cycle upper cut-off had slight effect upon the tone quality of most instruments, but a o,000 cycle cut- off had an appreciable effect upon all except the large drums.
4. The quality of reproduction of orchestral music continued to improve materially as the lower cut-off was extended to about
72 PSYCHOLOGY OF Music
80 cycles and the upper cut-off to about 8,000 cycles. Reproduc- tion of the full audible range was preferred to any limitation of band width.
5. Noises required reproduction of the highest audible fre- quencies. A 10,000 cycle cut-off caused appreciable reduction of naturalness on common noises. It was felt that this cut-off probably would never preclude recognition of a noise.
Phonograph and radio. Let us take an illustration from the situation with the phonograph and radio before the perfection of electrical recording. Little did the listeners realize in the early period of the phonograph records and radio transmissions that the recording instruments did not respond satisfactorily to low tones. These reproductions, therefore, furnished their own filters for low tones tending to eliminate the fundamental frequency and some- times even the second partial, and yet we heard with unquestioned certainty the fundamental pitch of these musical tones, fixed and unwavering. What we did hear as the fundamental pitch in these low tones was purely subjective.
Thus, we see that this purely subjective difference tone is psychologically and musically not only an impressive reality but frequently an indispensable factor in the determination of the pitch of musical tones. To the composer, the instrument-maker, the performer, as well as to the listener, they are stern realities and essential factors in the structure of musical tones. As to the physi- ological theory of all these subjective tones, we have but little to say at the present time, but in the last five years such progress has been made in the experimental work on the theory of the pitch- differentiating mechanism in the human ear that we may reason- ably soon expect to have a physiological explanation in terms of the function of the inner ear.
It should be noted that although we must deny the physical existence of frequencies corresponding to these tones, the oscillo- graph faithfully records wave patterns in terms of which many of the subjective tones may be identified. The theoretical existence may, of course, be predicted in purely mathematical terms, the only psychological problem being to determine to what extent they are audible.
Audible frequency range in voice and instrument. Each voice or instrument has its typical frequency range for acceptable tone
PITCH: FREQUENCY
73
74 PSYCHOLOGY OF Music
quality. This is illustrated in Fig. 5, which is a copy of a chart issued by the National Association of Musical Instrument Manu- facturers,101 1927. The chart is self-explanatory. The limits here indicated are merely approximations and can vary under a large number of circumstances.
PITCH PERFORMANCE
We have dealt with the ability to hear tones and to hear differ- ences in tones. There is a parallel on the side of tone production; namely, in the range of tone production of voice or instrument and the precision of intonation. Various aspects of this will be discussed in the chapter on Musical Skills.
Control of intonation. The ability to control the pitch of tones presents three types of situations: (1) the reproduction of a stand- ard tone; (2) the making of fine deviations from the standard; and (3) the production of intervals.
The capacity for reproducing a standard tone is relatively elemental. It depends primarily upon a good sense of pitch. Natu- rally one cannot control pitch any finer than he can hear it; but the control of pitch is frequently subject to considerable improve- ment by training, principally the type of discipline that makes the ear more critical. Ordinarily the fault is not in the voice or instru- ment but in the fidelity of the ear and auditory imagery. To exercise critical control, it follows that the capacity for pitch control in intonation varies in a way somewhat parallel to a variation in capacity for pitch discrimination. However, in stringed instru- ments and in wind instruments, a large element of skill is required, and that comes only with rigorous training.
The power of precision in controlling artistic deviation from true pitch is again primarily a matter of a sensitive ear, rather than muscular control, although in both voice and instrument a certain amount of experience and training is necessary. In Chap. 27, we shall see some exercises for training in this respect.
The control of intervals hinges primarily upon interval concepts. Some of the intervals are natural; others are more or less arbitrary. But a certain amount of training is necessary in order to standard- ize the concept of interval. Historically speaking, there has been a variety of scales, and even at the present time in modern music there is considerable dispute about minor differences in intervals which constitute scales. But, given the concept of interval, preci-
PITCH: FREQUENCY 75
sion in singing or playing intervals depends to a great degree upon precision in the reproduction of a tone and in the control of fine differences in pitch.
Interval. Melody and harmony are both built upon the con- ception of intervals, some aspects of which we shall discuss under the head of Consonance. There is a very extensive literature on this subject, particularly with reference to musical scales. Much of it awaits verification, criticism, and extension by means of laboratory experiments. As an example, we may mention the contest over the tempered scale and just intonation in violin playing.
LOUDNESS: INTENSITY
THE ROLE OF INTENSITY
WE have seen that there are four fundamental aspects of all music: the tonal, the dynamic, the temporal, and the qualita- tive. The tonal aspects are primarily the outgrowth of pitch and timbre; the dynamic are usually reduced mainly to intensity; the temporal rest basically upon time but are greatly modified by intensity; the qualitative rest primarily upon timbre, but this is greatly modified by pitch, intensity, and time in sonance. We see, therefore, that intensity plays one of the four basic roles in all music.
We are perhaps less conscious of intensity than any of the other three attributes in music, for several reasons. In terms of pitch, we have musical scales, melody, and harmony with exact quantita- tive determinations for each. The musical score shows pitch and time with precision but shows only very crude indications of inten- sity. Therefore, owing to the relative absence of definite concepts, their conspicuous absence in the score and, until recently, the ab- sence of units of measurement, little or nothing is said in musical literature about intensity or loudness, and yet this attribute of tone is comparatively conspicuous for musical hearing and musical expression.
In phrasing, for example, which is the very heart of musical interpretation for both the performer and the listener, the pianist can do comparatively little or nothing to modify pitch and com- paratively little to modify timbre. The pianist's musical interpreta- tion deals almost entirely with intensity and time. The singer expresses his musicianship primarily in two ways: in the control of
76
LOUDNESS: INTENSITY 77
the quality of tone and in phrasing. The quality of tone assumes a fairly fixed character at a given stage of training, but the musical phrasing is the most plastic unit in terms of which the singer or the violinist expresses personality and musical interpretation, and phrasing is largely a matter of time and intensity.
The builder of instruments, the musical critic, the teacher, and the scientist dealing with the art of music must develop a more conscious recognition of the role of intensity than that which now prevails in judging the beauty of music. The student must become aware, not only of principles of dynamics in music, but also of his own sensitivity and power of discrimination, and the countless devices which must be at his command in controlling, modifying, and utilizing loudness characteristics in tone production. Funda- mentally, there are two goals, effectiveness and agreeableness. The former pertains to carrying power and intelligibility of the sound, the second to the art of dynamic modulation as an element of beauty in itself and as a medium for the control of tone quality.
There are two measures which are basic to all dynamic aspects of tone, sensitivity and discrimination. The first is the measure of the natural capacity of the ear for becoming aware of sounds; the second is a measure of the capacity of the ear for hearing differences and, therefore, the power to use the ear in a musically significant way dynamically, that is, to assign musical meaning to loudness characteristics. On the motor side, we are correspondingly con- cerned (1) with the ability to control the intensity in intonation, and (2) with the ability to produce artistic deviations in intensity.
SENSITIVITY OR HEARING ABILITY
Audiometry. The art of measuring the sensitivity, usually called hearing ability or acuity of hearing, is just coming into the medical profession and into activities which are affected by keen- ness of hearing or hearing loss, such as music, speech, and various industries. This is largely because it is only within the last few years that reliable measuring instruments and units of measure- ment have been available in the fields of psychology, physics, and engineering.
Sensitivity is best measured with an audiometer, which produces pure tones at different levels of pitch in the tonal register. The measurement consists in determining the weakest sound that can be heard. This measure, as we have seen, is expressed in decibels.
78 PSYCHOLOGY OF Music
It usually is plotted in terms of the number of decibels of deviation from standards for normal hearing of persons not above forty years of age and is designated as "hearing loss." Thus, we say a per- son has so many decibels hearing loss for different levels of frequency.*
On the conventional hearing chart in Fig. 1, various types of hearing loss are represented. A word of comment in regard to each of these is in order.
Normal hearing. The straight line numbered 0 represents normal hearing for young adults and is taken as a base line from which hearing loss is measured. The ear is probably as sensitive to sound
* Very rapid progress is now being made in the design and marketing of audiometers. Dr. Scott Reger, specialist in matters pertaining to audiometry, lists instruments now available as follows:
A. Western Electric No. 2- A Audiometer. Battery operated: generates eight fre- quencies in octave intervals from 64 to 8,192 cycles.
B. Western Electric No. 6- A Audiometer. A.C.-D.C. operated: generates a con- tinuously variable range of frequencies from 128 to 10,000 cycles.
C. Western Electric No. 4- A Audiometer. Designed to test the hearing for spoken speech reproduced from phonograph records of as many as 40 pupils simultaneously. This instrument is used principally for the group testing of school children.
D. Western Electric No. 5-A Audiometer. A.C. operated: generates a single complex "buzzer" tone.
E. Western Electric No. 3-A Audiometer. Battery operated version of the Western Electric No. 5-A Audiometer. The Western Electric No. 5-A and 3-A Audiometers were designed for use in various industries where a rapid approximation of hearing acuity is desired. The Western Electric Audiometers may be obtained from the Graybar Electric Co., Graybar Building, New York City.
F. Sonotone Jones-Knudsen Model 1 Audiometer. A.C.-D.C. operated: generates seven frequencies in octave intervals from 128 to 8192 cycles. Also provides a continuous sweep of frequencies from 2500 up to 16,000 cycles in two ranges: 2500 to 7500, and 8000 to 16,000 cycles. Sonotone Corporation, 19 West 44th Street, New York City.
G. Maico Model D-4 Audiometer. Generates frequencies from 32 to 12,288 cycles. (Complete detailed information on this instrument is lacking.) The Medical Acoustic Instrument Co., 730 Hennepin Ave., Minneapolis, Minn.
H. Auragraph Audiometer. A.C.-D.C. operated: continuously variable from 64 to 8192 cycles. The Marvel-Clark Co., Grand Rapids, Mich.
I. Brenco 34-C Audiometer. A.C. operated, generates eight frequencies in octave intervals from 64 to 8192 cycles, plus the additional three frequencies of 12,000, 16,000, tnd 20,000 cycles. Physicians Supply Co. of Philadelphia, 116 South 16th Street, Phila- delphia, Pa.
Audiometers C, D, and E measure hearing acuity in terms of percentage loss; A, B, F, G, and I are so calibrated that the results are read in terms of decibels hearing loss; nothing is known about the intensity calibration of H. All of the above Audiometers except C, D, and E are equipped with both headphones and bone conduction vibrators for testing acuity for both air and bone conducted vibrations. Audiometers B and F are also equipped with microphones to enable conversation and the selection of hearing aids for the hard of hearing.
LOUDNESS: INTENSITY
79
in the first year of childhood as it ever will be thereafter. The change that takes place with maturation and education consists of the development of the ability to assign meaning, develop habits of selection, and give accurate account of it. There is, of course, a considerable latitude of variation around this normal, up to 10 db or more above or 10 db or slightly more below at all frequencies. -20
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64 128 256 PITCH C c c» C2 63 C4 ca C€ FIG. 1. — Audiograms showing types of hearing loss. Straight line at zero, normal hearing regarded as a base line; A, normal loss due to age; B, middle-ear lesion, advanced in impairment; C, acoustic neuritis, hearing loss approximately uniform; D, extreme form of acoustic neuritis. The dash lines show the average deviation from line A for persons above 60.
There may also be ups and downs of a minor sort within this range of about 10 db on each side.
Acoustic neuritis. Line B shows a typical case of acoustic neuri- tis due to some form of pathology in the inner ear. This, as the curve shows, is rather severe and usually does not respond to treatment.
Middle-ear lesion. This is commonly due to disturbances in the bones or membranes of the middle ear. Line C shows a mild type, in which the subject clearly recognizes that he is hard of hearing but does not ordinarily need a hearing aid; whereas, Line D is of a se-
80 PSYCHOLOGY OF Music
vere type in which it becomes advantageous to wear some hearing aid. In certain types of middle-ear lesions, the patient may obtain better results from a bone-conduction hearing aid than from the ordinary sound-amplifying (air-conduction) instrument.
The threshold of pain. The dotted line at the bottom represents the limits at which sounds are loud enough to produce a feeling of pain. This pain is located in the eardrum and serves as a protection for the ear.
DETERIORATION WITH AGE: PRESBYCOUSIS
There is a tendency for aged people to have some degree of loss of hearing. Such loss of plasticity is observable in other sense organs as well as in the muscles and glands; but in hearing we have a peculiar situation in that, while hearing in the lower register may remain normal into old age, there is always a very radical and progressive loss of hearing for the higher tones.
Line A in Fig. 1 is from Kelley's™ recent investigation. He selected only the cases of old persons between sixty and seventy- five years of age who had approximately normal hearing, at least up to 500 ~, in order to get cases which are unquestionably due to deterioration with age. This condition was certified by otological examination. The curve shows that, on the average, these people had a hearing loss of 8 db at 1,000—, 24 db at 2,000, 44 at 4,000, and probably would have about 60 at 8,000~.
The dash lines above and below the line A show the average deviation from this average in 70 cases. This close agreement with the average indicates that this type of decline follows a fairly fixed law. As we grow old, we may therefore have the comfort of companionship in this loss for high tones.
To verify this in actual music, he took a violin tone which had a rich spectrum of high tones and, by filtering, eliminated in different experiments those above 2,000, 4,000, and 8,000~. Careful re- measurements were made to see whether the aged person could tell the difference between the filtered tone and the full violin tone. What was predicted proved true: an aged person cannot hear any overtones above what is indicated by his hearing loss. Therefore, both music and speech are to him radically different from what they were in youth. These losses come on so gradually that the sound of the human voice or of a violin does not seem to be noticeably dif- ferent from what it was in youth.
LOUDNESS: INTENSITY 81
This state of partial deafness arising from senile changes in the ear is called "presbycousis." The term should be applied to that type of hearing loss which has been described in the preceding paragraph and should not be applied to the loss of hearing below the region of 1,000^ due to old age.
Kelley™ investigated seventy cases of persons above sixty years of age and found that about 75 per cent had normal hearing, that is, not more than 10 db hearing loss at 64 to 500^, and only a slight hearing loss at 1,000^. This shows that loss of hearing in the lower register does not necessarily come from age or occur with age. In the 25 per cent of the cases in which there was a loss in this region it could be traced to such specific causes as may operate at any age. This is a comfort to those who have fatalistic fear of loss of hearing. It has been shown that where the tympanic membrane is destroyed, a person can employ stronger hearing aids than otherwise, because the sense organs of pain that protect the ear are located primarily in this membrane. Lewis and Regcr82 have shown also that the hearing of subjective tones is not dependent upon the presence of the tympanic membranes.
CHILDREN'S HEARING
The measuring of hearing ability of school children has been grossly neglected on account of the absence of measuring instru- ments and the lack of realization of the deep significance of hearing loss in children. Many children are regarded as dull and become problem cases simply because they do not hear. It is typical of both children and adults, as a rule, to pretend to hear and to develop defense reactions. They also develop skill in drawing inferences from situations, in guessing from partly heard sounds, and especially in the art of lip reading, which in extreme cases may become an actual substitute for hearing.
In the public schools of today, it is found that from 5 to 10 per cent of the school children have some significant hearing loss. Many of these defects are unknown to schoolteachers and parents. In fact, only one out of five can be detected by ordinary methods. The audiometer permits a survey test that discovers all hearing- deficient pupils. Loss of hearing may be due to a great variety of causes, and many forms may be treated successfully, especially in a growing child, but most important is the provision of preventive
PSYCHOLOGY OF Music
measures and precautions which save the child from developing deafness.
It is evident that loss of hearing ability becomes an impediment to the hearing, appreciation, and performance of music. The person so affected lives in a different sound world from the person who has normal hearing. Many peculiarities in musical interpretation, likes, and dislikes are due either to hypersensitivity or to loss of sensitiv- ity to sound. Hypersensitivity is a very potent source of that type of
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irritation which shows itself in eccentricities of the musical temperament.
The field of hearing. There is an upper and a lower limit of hearing. How strong a sound can the ear endure? The solid line at the top in Fig. 2 indicates that at this point the sound becomes so strong that it arouses pain and cannot be endured above that level. This is the upper limit, in the region of 125 db.
How strong must a sound be in order to be heard? That is, what is the lower threshold of hearing? In other words, what does "nor- mal" hearing as represented by the base line (0) in Fig. 1 mean? The answer is given in the lower part of Fig. 2. This figure is only an approximation to the more recent measurements, but it shows the important fact that the ear is highly sensitive in the region of 500
LOUDNESS: INTENSITY
83
to 4,000 ~, which is the region most significant for music and speech. Above and below this region of frequency, sound must be increasingly stronger in order to be heard. The broken parts of the curve indicate high and low regions for which the curve is more or less hypothetical.
There are very large individual differences in hearing ability from the supersensitive to the stone deaf, and this influences their activities in daily life to an extraordinary degree. The person who
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FIG. 8. — Loudness-level contours. (Fletcher.**)
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has an especially keen ear perceives and responds emotionally to countless sounds that his neighbors cannot hear. The person who is hard of hearing has the advantage of freedom from disturbing noises but also suffers a loss of power in his daily adjustments.
These limitations are, in a way, a great blessing because they save us from hearing a great mass of rumblings and roarings which occur in nature and also from the infinite variety of high tones which are ever present but are of little or no significance for music and speech. In other words, the ear is selective in that it is respon- sive to that region of sounds which is of greatest significance and use.
More significant than hypersensitivity in this respect is the mental set which centers consciousness upon sound rather than
84 PSYCHO LOGY OF Music
upon other stimuli. Keen hearing ability and vivid auditory imagery coupled with a dominating interest in sounds is what throws the musician under the spell of sounds. Harshness, discord, volume have meaning to him just as purity, harmony, and modula- tion have. It is therefore important to recognize that, although a musician may have just a normal hearing ability, he may be extra- ordinarily responsive to sounds which to the nonmusician pass unobserved.
Loudness versus intensity. Figure 2 suggests that there must be great disparity between the intensity and the loudness of a sound. However, this relation follows a definite law which is expressed in Fig. 3. The difference between the physical intensity and the mental experience, loudness, is greatest at the threshold of hearing and decreases gradually up to the upper limit of hearing. Figures 1, 2, and 3 may now be reviewed together.
Reference tone. It is now clear that the loudness of a sound varies with a great many factors involved in frequency, duration, timbre, and intensity level. It also varies with a great variety of conditions in the room and the relation of the source to the ear as well as with such factors as fatigue, attention, and alertness on the part of the listener. Therefore, in order to determine the loudness produced, it is necessary to define the intensity of the sound, its physical composition, the kind of ear receiving it, and the physiolog- ical conditions of the listener. For this reason, scientists have adopted as a standard reference tone a pure tone of 1,000~ and provided that the reference intensity for intensity-level com- parisons all be 10~16 watts per square centimeter. This furnishes us a fixed base from which intensity and loudness measurements can be made under all sorts of conditions.
DISCRIMINATION: THE SENSE OP INTENSITY
Intensity discrimination is measured with a special type of audiometer by determining the smallest difference in loudness that can be heard. For practical reasons 1 db is usually considered the magnitude of the just noticeable difference. This, however, is an arbitrary standard because the j.n.d. varies a great deal with the pitch level, the absolute loudness, timbre, and duration of the tone. It also varies in a large range with the individual differences of the listeners.
LOUDNESS: INTENSITY
85
Intensity discrimination measures the ability to hear differences in loudness and is therefore a measure of a person's capacity for using loudness differences in every dynamic aspect of music and in other hearing situations in daily life. For group measurement, the phonograph record, "The Sense of Intensity," No. 53003-D, from the Seashore Measures of Musical Talent, is satisfactory. The record by this method is given in terms of centile rank in the same manner as for the other measures, which makes such capacities readily comparable.
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FIG. 4. — The number of just noticeable steps in loudness (j n d ) between the threshold of audibility and the threshold of pain. (Rietsz.112)
There are very great individual differences in this capacity. When individual measurements are made with an audiometer, it is found that there is an approximately normal distribution of capac- ities, ranging from 0.2 to 20 db or more. These differences are fairly independent of age, intelligence, and training. They play a very important role in determining success or failure in ordinary inter- course and in vocations which involve discriminative hearing, particularly in music and speech.
NUMBER OF AUDIBLE DIFFERENCES IN LOUDNESS
How this capacity varies with pitch level is illustrated in Fig. 4, which shows that, at a pitch of 64^, the average ear can detect about 45 different steps in loudness, an octave above that, about 95 steps, and at C3, about 175 steps, etc.; the finest discrimination
86 PSYCHOLOGY OF Music
is found in the third octave above C3 at which the average ear can detect about 375 steps or differences of loudness.
But this curve is for an average ear. For a superior ear, it would rise much higher at all pitch levels, and for an inferior ear, it would fall far below the present curve.
Similar illustrations might be made to show that the capacity for intensity discrimination varies with absolute loudness, time, and timbre. In general, we may say that the ear is most discriminating for differences in loud tones and least discriminating for differences in soft tones, and that these differences for loud, medium, and weak tones are greatest in the lower octaves. The discrimination varies also with the duration of the tone and, in a very complicated way, with the timbre.
MOTOR CAPACITIES
Matching intensities. The first of the two basic measures of motor capacity for control of intensity of sound is to match or reproduce a tone of given intensity. The subject may be required to sing or play a tone of any intensity and then immediately repeat it with the same intensity, all other factors held constant. The two intensities may be read directly in decibels on the dial of a power- level meter, such as is used in every radio studio for regulation of the intensity of the radio sounds. We shall see later how this principle may be used in training exercises for the development of dynamic skill.
Differentiating intensities. This is measured in the same manner as above with voice or instrument. The capacity thus revealed is a measure of the ability to produce artistic deviation in loudness. It is the fundamental key to the art of interpretation, as in musical phrasing. While the loudness discrimination is a relatively ele- mental capacity, the motor skill involved in its artistic use is subject to marked refinement by training, and artistry consists largely in the development of fine and meaningful modulations of intensity.
Naturally the limits for matching intensities as well as for varying intensities are set mainly by the capacity for intensity discrimination. For two persons, one of whom can hear a difference of only 4 db under standard conditions and the other can hear 0.4 db difference, we should expect a corresponding difference in the ability to control the intensity. In general, however, a person can-
LOUDNESS: INTENSITY 87
not produce a given loudness so accurately as he can hear it, because there are various elements of motor skill involved. Measure- ments show that a fine pianist may be able to hear and reproduce differences as small as 0.1 db in the middle register. The pianist perhaps has the greatest responsibility for the mastery of intensity control since this is one of the two principal media under his con- trol, and the instrument responds favorably to fine shadings in touch. Performance on wind and percussion instruments is far less accurate. This topic will be discussed further in the chapter on Musical Skills, Chap. 27.
INTENSITY CHARACTERISTICS OF MUSICAL TONES
Beats. One of the basic determinants of harmony is the phe- nomenon of beats, which consists of the periodic pulsation of inten- sity. Below 12 or 15 pulsations we do not hear tones but distinct beats. The number of beats per second indicates the number of vibrations in the difference of the frequencies of the two beating tones. Above the threshold of tonal fusion the tones are character- ized as harsh or rough. The roughness decreases with the increase in number of beats up to certain levels. Thus, a minor third is rougher than a major third.
Beats are more conspicuous in pure tones than in rich tones. If two pure tones beat, they tend to cancel each other, so that for each beat +here is a moment of silence; but the richer the tone is, the more complicated the situation becomes.
Resonance. If we suspend a violin string between two solid supports without any resonance box, the string must be bowed hard before the tone can be heard at all. The real tone which we hear from the violin is caused by the sympathetic vibration in the resonance of the box. That is, what we hear is not primarily the vibration of the string but the vibration of the various parts of the resonance mechanism. The same is true in principle for all forms of instruments and especially for the human voice, in which the oscil- lation of air caused by the vocal cords alone is significant in com- parison with the oscillation which emanates through the mouth from the resonating cavities.
It is this differential modification in the loudness of partials which governs the timbre of tones.
88 PSYCHOLOGY OF Music
Reverberation. Another factor which plays a large role in modifying the character of the tone by changes in intensity is that of reverberation. The ordinary music room or music hall is in effect a resonance box. Every sound we have goes out to the walls, the ceiling, the floor, the furniture, and the occupants, and is reflected back in a mass of sound waves of increasing complexity. Therefore, a violin tone may be radically different in one room from what it is in another, or different in one part of the room from what it is in any other part, because of these characteristics of reverberation. By taking basic measurements in the dead room, which eliminates the element of reverberation and transmission of sounds from the outside, we can determine the character of the instrument or the voice in itself, and then by taking corresponding measurements in any music room or any part of the music room we can determine exactly what it is that the room contributes. The adoption of scientific principles in the construction and sound treatment of auditoriums and music rooms is one of the most recent triumphs of architecture and is destined to contribute much to the refinement and mastery of musical performance.
AMPLIFICATION OF SOUND
The engineering development in the control of the dynamics of tone in recording, reproducing, and broadcasting is one of the most important contributions that has ever been made to the populariz- ing of music. In recording a sound film, for example, not only can the man at the instrument change instantly the loudness of the tone as a whole, but he can deal with any particular element of the tone selectively in such a way as to improve upon the perform- ance of the instrument or the voice. This is called building up the tone. As a result of this, we hear over the radio voices which are much better balanced through the radio rendition than in the actual delivery of the voice. One of our most famous baritones has a voice which is naturally weak in the lower registers and, therefore, im- presses one as thin and top-heavy. But in the radio rendition, and to some extent in the phonograph, this voice is rebuilt so that it approximates an ideal distribution of the loudness for each register and for each partial in the complex tone. This phenomenon can easily be observed when one has the opportunity of hearing the singer in person and hearing one of his latest recordings so that a comparison can be made between the record and the sound in the
LOUDNESS: INTENSITY 89
performance of the voice. This does not imply, necessarily, that in every respect the recording of the tone is better than the natural voice, but is emphasizing the fact that it is possible to make a voice sound better than it really is. We are familiar with the analogy to this in painting and photography.
A scale of musical dynamics. To most of the readers of this book the term "decibel" is new. As yet it has a very slight place in musical language; but it must be recognized that the appearance of this term, or its equivalent, was a condition for the scientific dis- cussion of dynamic expression in music and for the application of exact terminology in musical composition, performance, and criticism. When Stokowski directs his orchestra over the radio control board, he has before himself an intensity meter which shows the loudness of the orchestral performance from moment to moment. He can, therefore, adopt and enforce specific standards.
It will not be long before there will be in music studios meters which will register loudness in decibel readings for any voice or instrument so that the terms will have a fixed value in the score and can assume specific and permanent values in the conception of the composer and the performance of the artist. It will require a great deal of experimenting to standardize such norms.
At the present time we can only make a rough estimate. Dr. Scott Reger, who is an expert in this field of measurement, sug- gests that tentatively we may adopt the following scale: For a 75-piece orchestra in decibel equivalence above the threshold, ppp, 20 db; pp, 40 db; p, 55 db; mf, 65 db; /, 75 db; /, 85 db; ///, 95 db.
The intensity of an average whisper when the mouth of the speaker is 4 feet from the ear of the listener is about 20 db above the threshold. The loudest sounds of average conversational speech are about 60 db above the threshold under similar conditions. There is an intensity-level range of about 73 db in a crescendo from the average level of the softest violin playing to the peaks in the heav- iest playing of a full orchestra. If the intensity of the softest violin were 20 db above the threshold, the heaviest playing of the orches- tra would be about 95 clb above the threshold.
Measurements of this kind will, of course, be of very great value in the determination of such features as carrying power of voice and instrument, the acoustic characteristics of each and every part of an auditorium, discussion of the volume of voice or instrument, and scientific statements of principles of dynamic expression.
DURATION: TIME
NATURE OF THE PERCEPTION OF TIME
rriHERE are two aspects of the sense of time; namely, that con- JL cerned with fine distinctions of short intervals of time and that concerned with the judging of the flow of time in longer periods, such as seconds, minutes, or days. Individuals differ extra- ordinarily in their abilities and habits for judging sustained inter- vals of time. The judgment depends largely upon an appraisal of the net result of the flow of events which occur within a time period, such as the speaking of a sentence, the delivery of a speech, or the work of the day. Every moment of time is filled in some way, and an infinite variety of clues are used in judging the progression. For example, an undesired visitor may engage in small talk for an hour without noticing the flight of time, whereas the host may be very restive and overestimate the duration. In other cases, the estimate may be based upon observed events which take a fairly even, cus- tomary course. For example, a man can get some idea about what time he has arisen in the morning by observing the length of his beard in shaving. There are definite, established principles of overestimation and underestimation of time, for example, an inexperienced after- dinner speaker always underestimates the time that he has talked. But we need not say anything more about the judgment of the flight of time, because that plays only a secondary role in music. Everyone will, however, think of how differently the time passes in a boring musical program from the way in which the time passes in which the listener is on the verge of ecstasy in the appreciation of music.
90
DURATION: TIME 91
Sensitivity to time differs from sensitivity to pitch, intensity, and timbre in that there is no evidence to show that it depends upon the structure of the ear under normal conditions. There are very great individual differences in the capacity for hearing time, but these differences are due to a large number of factors, such as the capacity for differential attention, or, ear-mindedness, that is, the tendency to live in a tonal world in which significance is at- tached to the temporal aspects of sounds. This is characterized as perhaps the most important factor in the capacity for imaging the time value of tones and for remembering the time value of sounds. We, therefore, attach no great significance to the measure- ment of sensitivity to time but make large use of the discrimination for time which we usually call the sense of time.
DISCRIMINATION: THE SENSE OP TIME
"The Sense of Time" record, in the Seashore Measures of Musical Talent, illustrates a method and furnishes the means of measuring this capacity. A series of time intervals are marked off by clicks in which the differences of two compared intervals vary from 0.02 to 0.20 second, and the subject is asked to say which of the two intervals is the longer. From the percentage of right answers the centile rank is established, showing norms for adults and for fifth- and eighth-grade children.
A common method in the laboratory is to vary the difference in time intervals by increasing the magnitude and determining the length of interval for which about 85 per cent of the answers are right. This is spoken of as the threshold, or the limit for time dis- crimination. It is found that a very fine musical ear may detect a difference in the length of two notes as small as 0.01 second, whereas another ear may require as much as 0.10 or 0.20 in order to hear the difference. It is perfectly evident to anyone that these differ- ences in the sense of time are very important determinants of what a person can hear in music and the accuracy with which he can per- form. Tempo rubato is one of the most important means that the artist has for interpretation of music, and this depends upon the ability to hear and the ability to produce fine shadings in time in order to produce the desired modulation.
It is evident that these individual differences in the capacity for hearing time are at the base of the capacity of feeling for time, which plays such an extraordinary role in the enjoyment and the
92 PSYCHOLOGY OF Music
production of music. A person with a fine sense of time tends to feel the musical value of fine shadings in time corresponding to his capacity for hearing them. The feeling aroused may be agreeable or disagreeable. It tends to give rise to attitudes of attraction or repulsion. In piano playing, for example, where time is one of the only two media that the artist has for interpretation, we may say roughly that half the feeling value for or against the musical rendition hinges upon the role played by fine distinctions of time, as, for example, in the asynchronization of chords, in the overlap- ping of notes, and in all forms of artistic deviation from rigid time or fixed tempo.
This is about all we need to say about time as a sensory capac- ity. Of course, this capacity functions throughout music in countless forms of perception, memory, imagination, feeling, and action. Tempo, synchronization, rhythm, and all other forms of precision or artistic deviation in terms of temporal aspects constitute at least a good fourth of the content of the musical medium.
NORMAL ILLUSIONS OF TIME
The perception of time in music is subject to a great variety of normal illusions. Aside from cases of mere incompetence and errors, these subjective variables tend to follow natural laws and are, therefore, predictable. In psychological measurement involving time, such factors must be controlled. Psychologists have measured scores of these illusions. But the significant thing for music is that a very large part of the artistry in music lies in the utilization of these principles. Without them, accent, rhythm, and phrasing would be hopelessly sterile.
MOTILITY
Temporal activity will be discussed under various heads, such as Rhythm, Tempo, and Time, which are analyzed in the actual musical situations; but the problem of motility, which involves various aspects of speed and accuracy in movement, underlies all these. A person may be quick and accurate, quick and inaccurate, slow and accurate, or slow and inaccurate in various degrees and combinations.
In instrumental music, there is a natural limit to the speed a musician can exhibit, and in this limit there are large individual differences. The real significance for music, however, does not lie in
DURATION: TIME 93
the upper limit for speed of action, but rather in the fineness of the control of time and action which is involved in musical interpreta- tion. The problem for the musician is not so much, "How fast can I move my fingers?" but rather, "How accurately can I make fine time distinctions in the movement?"
Music is a form of "serial action"; that is, the time value of a note depends upon its integration in the melodic and harmonic progression. Therefore, measurement of skill and talent for time must be validated in relation to the types of function that actually occur in music. These may take countless forms. All our perform-