UC-NRLF B M En Ifib IThe Effect Discrimination FRANKLIN ORION SMITH t^ Reprinted from Psychological Review Monograph No. 69 The Effect of Training in Pitch Discrimination FRANKLIN URION SMITH I Reprinted from Psychological Review Monograph No. 69 The Effect of Training in Fitch Discrimination FRANKLIN ORION SMITH A thesis submitted to the Department of Philosophy and Psy- chology of the Graduate College in the State University of Iowa, in partial fulfillment of the Requirement for the degree of Doctor of Philosophy. Ml- &^ BERKELiY MUSIC LIBRARY UNIVERSiTV OF CALIFORNIA 1 THE EFFECT OF TRAINING IN PITCH DISCRIMINATION BY FRANKLIN ORION SMITH CONTENTS Method of procedure Effect of instruction Effect of practice Factors in the development of pitch discrimination The psychological limit Correlations General conclusions The present investigation forms a part of a series of researches in the Iowa laboratory/ upon the tonal hearing. The problem was to determine the effects of training in tonal hearing, considering age, sex, musical education, general intelligence, and kinship. The investigation consisted of a preliminary training series, a ten days' practice series and the correlation of the results with those of other researches. The experiments were conducted in the Univer- sity and in the public schools of Iowa City and Cedar Rapids in 1908- 19 1 2. Method of procedure The tuning forks and accessories which were employed in this re- search are fully described' by Professor Seashore in his report for the American Psychological Association on the standardizing of pitch discrimination tests.- The experimental precautions, both subjec- tive and objective, were observed as set forth in that report. The only change made in the apparatus consisted in using two resonators instead of one, which is a decided improvement because one resona- tor alone does not speak sufficiently well at the extremes where in- crements as large as 23 or 30 v.d. are used. The methods of pro- cedure recommended in the above named report were followed, as ^ The writer wishes to acknowledge his manifold indebtedness to Pro- fessor Seashore for his supervision and cooperation, which have made this research possible. To Dr. Mabel C. Williams and to companions in research who are working upon related problems in the laboratory, he expresses his grateful appreciation for assistance. ^ Psychol. Monog. No. 53. ^y-^iBO 68 FRANKLIN O. SMITH described on pages 39-43 of that report. The "heterogeneous" method was used in all preliminary experiments and with unclassi- fied groups. This consists in presenting the increments 30, 23, 17, 12, 8, 5, 3, 2, I, and .5 v.d. in the order named a number of times and finding at what level in that series the threshold falls in from ten to twenty trials. The mean variation of the records for all such sets is then computed by the method described on page 42 of the above named report, as follows : "For ordinary work we threfore recommend as a measure of variation in the record the use of the mean variation (m.v.) com- puted as follows : Regard the difference between successive steps as equal psycho-physic steps and, with the increment which is nearest to the median as a base, multiply the number of cases which are one step from this base by i, the number that are two steps away by 2, the number that are three steps away by 3, etc. : divide the sum of these products by the total number of cases (sets)." The homogeneous method is the ordinary method of right and wrong cases or constant stimuli, counting the threshold at 75 per cent, corrected cases. This method was used in dealing with indivi- duals or groups formed on the basis of preliminary tests. The preliminary training consisted of two tests which are desig- nated as the first and second preliminary tests respectively. The ob- servers consisted of pupils in the elementary and high schools, and students in the University. The ages vary from nine years to ma- turity. Most of the observers were unmusical in the sense that they had received no special training in music. These tests were made in the schoolrooms under good conditions. The temperature and ventilation were regulated by automatic systems (except in two small grade schools). The regular teacher remained in the room during the experiment maintaining normal conditions of order and school spirit. These general conditions did not differ materially among the schools nor among the different rooms of the same school. The tests were carried on in the morning between nine and twelve o'clock, each test lasting twenty to twenty-five minutes. Since it was not practicable in all cases to employ the homogeneous method, all the group tests were made by the heterogeneous method In figuring the results the nearest whole vibration (except 0.5 v.d.) was taken. The increments in the series of tones used (0.5, i, 2, 3, 5, 8, 12, 17, 23 and 30 v.d.) are referred to as units and are con- EFFECT OF TRAINING IN PITCFI DISCRIMINATION 69 ■sidered equally difficult to distinguish. That is, 23 to 30 v.d. is assumed to be as difficult for one whose threshold is 23 v.d. as i to 2 v.d. is for one whose threshold is i v.d. In case of defective hearing the pupil was seated where he would be certain to hear; or, if the deafness was serious, he was excused from the test. The rhythm of the work period was not so easily con- trolled. The tests were comparatively short and every effort was made both by the experimenter and the attending teacher to keep the effort up at a high pitch throughout the test. Indifference is perhaps the largest source of error in the few cases where it was manifest. This could be recognized directly at the time of the test and usually also by the distribution of errors in the records. One of the most striking and yet perplexing facts about pitch dis- crimination is that there is often no relation between the feeling of certainty and the correctness of the judgment. The judgment is often based upon a clear illusion. This illusion of hearing in the case of wrong judgment aids much in the encouragement to sus- tained effort. Anticipatory judging is a fruitful source of errors. Under the influence of expectant attention the observer anticipates the second tone the moment he hears the first. The experience is analogous to the illusion of lifted weights. With a strong expectation of hearing the second tone high, or low, the organism is set to make the ap- propriate response and this has marked influence upon the judgment. Closely related to anticipatory judging is the tendency to compare the present tone with the preceding pair. In fact this tendency often leads to anticipatory judging especially when the first tone of the present pair is compared immediately with the last tone of the pre- ceding pair. The confusion of pitch and intensity is a troublesome source of error, particularly with unpracticed observers. Making the tones actually objectively equal in intensity does not always allay the diffi- culty as disturbing associations may tend to create confusion. High tones are intrinsically louder than low tones. A slight difference in intensity is often interpreted as a difference in pitch. In computing the characteristic figure of a record it is necessary to take account of internal evidences and make a "correction" as is explained in the report of this test referred to above, pages 45-48. This must always be a matter of "good judgment" and can not be 70 FRANKLIN O. SMITH done mechanically. Certain factors may however be quite clear and exact. The distribution of the records in the heterogeneous test with respect to the operation of the laws of chance is one of the most tell- ing. A record of, e.g., 8 v.d. may on examination of the distribution of the errors be found to contain indisputable proof of a threshold of 2, or I, or .5 v.d. as the case may be. Sometimes when a source of error has been noted a study of the distribution may show where it operated and where it did not oper- ate. A small mean variation, e.g., i.o or less is almost certain proof of the reliability of the actually computed median. The study of the internal evidences therefore has its principal use in cases showing a large mean variation. All our records were examined with reference to internal evidence of error in the computed median and, it must be frankly admitted, wherever such evidence was found the correction was made. All the records here used in the heterogeneous method are therefore "corrected" records. Fig. i shows, it will be seen, that the tendency of the correction is to lower the record and that most of the corrections are made for those who have poor records. «*^-* ' 2 y y 5 — a — 79 — 73 — Iff Fig. I. Distribution of 476 pupils for one day's practice before and after the records had been corrected. The effect of instruction As a preliminary to the training series two tests of about 25 minutes each were given to 1980 pupils by the heterogeneous method in their regular class divisions. In the first period the test was begun without any explanation beyond what was necessary to direct them about reporting "higher" or "lower". The second period was opened with simple and diversified explanations and illustrations of what pitch is. This explanation was based upon a previous study of the kinds of difficulties encountered. Pitch was differentiated EFFECT OF TRAINING IN PITCH DISCRIMINATION 71 from intensity, duration, volume, timbre, etc. in familiar talk and by different instruments. Unfortunately the two factors of instruction and experience, or direct observation resulting in a growing familiarity with the prob- lem, are not isolated. We have simply the records for the two periods and must interpret the gain as due to both of these factors, which are, of course, inseparably associated. To facilitate comparison the observers were divided on the basis of these tests, into A, B, and C grades in accordance with the posses- sion of a good, medium, or poor ear. Grade A includes those who TABLE I. D istribh '.tion of ■ those ' who improved in the p reliminary te St 30 23 17 12 8 5 3 2 I 0.5 A B 30+ II II 10 15 6 3 2 I 59 23 17 12 8 5 3 2 / 0.5 30 13 13 II 17 7 3 64 II 17 12 8 5 3 2 I 0.5 23 13 \2 15 2 3 45 24 12 8 5 3 2 I 0.5 17 17 8 38 5 14 3 4 2 I I 0.5 I 76 36 12 25 5 30 3 16 3 / I 0.5 75 55 8 103 3 43 2 15 10 0.5 171 lOI 5 126 2 35 8 0.5 8 177 159 3 122 45 0.5 13 180 197 2 44 0.5 7 51 177 I 9 9 147 Italics designate increments; the other figures give the number of cases for each of the respective degrees of improvement; thus, of those who had a record of 304- in the first test, 11 went to 30—, n to 23, 10 to 17, i5 to 20, 6 to 8, 3 to 5, 2 to 3, and i to 2 in the second tes't. A shows the total number of cases at each increment in the first test ; B same in second test. hear differences of less than 3 v.d. ; grade B those who hear differ- ences of 3 to 14 v.d. ; and grade C those who hear differences of 14 to 30 v.d. or above. The records show that 54 per cent, made no improvement in the second test; 46 per cent, of all observers made better records in the second preliminary test than in the first. The amount gained varies from I to 8 units. The average amount gained varies from 3.8 v.d. at nine years of age to 0.3 v.d. at maturity. Table I analyzes the distribution and the amount of gain by the 72 FRANKLIN O. SMITH cases (46 per cent.) which improved with the instruction. Of the 46 per cent, who improved, only 7 per cent, changed from grade C to grade A in the second test. Of the 425 pupils (22 per cent.) who improved and were in grade B at the beginning, 225 (60 per cent.) changed to grade A in the second test. Measured by the first test 26.5 per cent, of those who improved were in grade A. Measured by the second test 70 per cent, were in grade A. Of the changes to grade A, 96 per cent, were from grade B ; and 91 per cent, of the changes to grade B were from grade C. Fig. 2. The effect of instruction. Distribution of 907 pupils who made improvement from the first to the second preliminary test. .fJret fesM, OS f a J s o iz 17 23 30 yj* Fig. 3. Distribution of entire group, 1980 cases, in preliminarj' tests. n 13 lb f ^fe io 11 /2 /5 /9 7s ie Fig. 4. Distribution of improvement in the preliminary tests by age and sex, 417 boys and 490 girls. EFFECT OF TRAINING IN PITCH DISCRIMINATION 73 The efifect of the instruction and experience thus gained from the first to the second test is shown in Fig. 2 which represents only the 46 per cent, of cases in which improvement was made. Fig. 3 shows the efifect upon the whole group of 1980 cases. Fig. 4 shows the distribution of improvement by age and sex. TABLE II. Distribution of forty-seven out of fifty-four university students who improved with individual instruction ^3 17 12 8 5 3 A B 30 I I I 2 I 6 17 12 8 5 3 2 ^3 I I 2 I 12 8 5 3 2 I 17 4 I 2 8 I 8 5 3 2 / 0.5 12 2 2 I 2 8 I 5 3 2 0.5 8 3 3 6 2 2 I 0.5 12 5 5 4 I 4 2 II II Below 5 28 Notation and pi an of this table same as in Table I. A similar test of the efifect of instruction was made in a class of 200 adults. After two preliminary tests, one heterogeneous and one homogeneous, the poorest one-fourth of the group were taken and instructed individually as to the actual nature of pitch hearing. An effort was made to find out what particular difficulties they were encountering, and explanation and illustration were based progress- ively upon this information. As a class these had made but little improvement in the second preliminary test, both the first and the second having been given "without i'nstruction". But as a result of this personal instruction all but 7, i.e. 47 out of the 54 made rapid improvement. The change in the record for the group is shown in Fig. 5 by giving the distribution at the begiYining and at the end of the period of individual instruction. The distribution of the gain is analyzed in Table II. The fact that these were adults familiar with the class room and trained in many psychological experiments, yet made such marked response to the instruction and individual help, doubly emphasizes the i'mportance of thoroughness and individual attention in the in- structions if the records are to be entirely reliable. One of the best experimental proofs that we have showing the efficacy of individual care and instruction is found in the un- 74 FRANKLIN O. SMITH Second fej* Fig. 5. Distribution of 54 university students in individual tests (Table 11). published experiments of Dr. H. S. Bufifum, which have been sum- marized in the above mentioned Psychological Association report by Professor Seashore, as follows: Dr. Buffum experimented on twenty-five eighth grade pupils in a grammar school room. He first made a fifteen minute individual test of each pupil and classified them on this basis into three groups with modes at 3, 8 and 17 v.d. respectively. The object was two- fold : (i ) to determine the effect of practi'ce and (2) to determine the success of the preliminary examination. For this purpose he gave them twenty forty-five-minute periods of training. The results show (i) that for no group is there any evidence of improvement with this practice, and (2) that all except two chil- dren remained throughout the whole practice series within the. group to which they had been assigned. Of these two, one who had been assigned to group III was immediately found to belong to group I as there had been a failure to understand the pre- liminary test; and the other, although retained in group II, proved really to be near the dividing line and could have been classified in group III. Evi'dently the physiological threshold had been reached in twenty-four of the twenty-five cases in the preliminary test." In Dr. Buflfum's experiment the fifteen-minute preliminary classification was so efficient as practically to eliminate poor records due to ignorance of the test. The significance of instruction is further proved by the records in successive classes in the university for a period of years. It is found that the average record has improved slightly from year to year. There is no reason for believing that this is due to anything EFFECT OF TRAINING IN PITCH DISCRIMINATION 75 but improved skill and technique and increased care in the instruc- tions and charge to those about to be examined. In the above records we have conclusive evidence that effective instruction is of the greatest importance in making records on pitch discrimination. It is not a poor ear, but ignorance that accounts for the bulk of poor records in a first test. Those who made a fine record in the first test are, of course, not subject to this source of error; and those who have poor records but show no improvement after instruction or prolonged training may also be free from this source of error. It is a safe rule to say that all tests should be pre- ceded by efficient instruction ; if this can be made individual, so much the better; and all who show poor records must be subjected to more intensive and searching instruction before the record can be accepted for serious purposes. The effect of practice The first of the two extensive experiments in practice was a series of group tests by the "heterogeneous" method covering a period of ten days. The second was a series of individual tests on adults by the "homogeneous" method. In addition to these certain special training series will be described. The group tests were made on 476 pupils (215 boys and 261 girls) in two elementary schools selected from those in which the pre- liminary tests had been made. These practi'ce tests were conducted in the same manner and under the same conditions as the prelimin- ary tests except with regard to instruction. Each test was preceded by a brief warming-up exercise in which the pupils answered orally. This also helped to keep interest alive. A short rest period was taken at the middle of each test. At this time opportunity was given the pupils to ask questions about the test. Running parallel with the class tests were certain individual tests which were carried on in the afternoon foUowi'ng a given set of class tests. At the noon intermission the records of one or two grades were checked up and pupils whose threshold for that day was be- tween 20 v.d. and 30 v.d. were given individual practice. The object of these individual tests was to give special assistance to backward pupils, aiding them to distinguish different tone qualities and to form right habits of attention. These tests include 71 boys and 35 girls constituting the poorest in the group tests. 76 FRANKLIN O. SMITH With regartl to the general musical preparation of these pupils it may be said that music was taught systematically in all the grades, and that the schools were provided with Victor graphophones in which high grade selections were played regularly. For comparison the cases under observation may be divided as follows : Group I, those who made no improvement either with instruction or practice ; Group II, those who made no improvement in the practice; Group III, those who made little (1-3 v.d.) improve- ment in the practice; and Group IV, those who made marked im- provement (3 v.d. +)• The records of these practice series on children are set forth in Tables III-IX and Figs. 6-10. Table III gives the daily average threshold for the twelve days of training by ages, section A showing those who do not improve with training and B those who do im- prove with training. Table IV gives the daily average threshold for those who improve with training regardless of age for the four Fig. 6. Daily average, by groups, of those in the practice series (Table VI). .3c oj/a _J_Lj_i__ :r-u:i:u' aj/s Z 3 1 S 6 •+'--1 Fig. 7. Daily average by sex (Table V). EFFECT OF TRAINING IN PITCH DISCRIMINATION 77 Fig. 8. QS '~i 2 5 J a 11 Tj 73 30 Jor Distribution of 270 pupils who improved with practice (Table VI). Fig. 9. Daily average record of those who were given special individual help (Table VII). '->-s.. .....CHrfe '3 If 15 16 17 '/6 le^ Comparison by ages of the average (median) abilities of boys Fig. 10. and girls. groups. Table V gives the averages of the same separately for the boys and girls, Groups II, III, and IV combined. Table VI gives an analysis of the distribution of those who improve with practice. Ta- ble VII (Fig. 9) contains the record of those who were given indi- vidual tests or help during the practice, showing the daily record and the record of two individual tests in the average for the group. Table VIII gives a compari'son of the mean variations with reference to sex and age. Table IX gives the distribution of those who attain the approximate physiological threshold in different days of the practice. FRANKLIN O. SMITH TABLE III. Daily average threshold, by age A. Group I : those who made no improvement with training Age J 2 3 4 5 6 7 8 9 10 II 12 : Number 9 6 6 6 6 8 7 8 10 9 8 7 8 29 lO 6 6 4 7 8 8 6 7 7 8 6 8 31 II 8 4 6 7 5 7 6 7 5 6 7 8 47 12 8 8 8 5 7 8 7 7 8 8 8 5 23 13 5 5 5 5 4 5 5 5 4 4 5 5 29 14 6 5 5 5 4 4 5 4 4 4 4 5 32 15 5 6 5 5 4 4 4 4 4 4 4 4 15 B. Gro\ ups //, ///, , IV comb ined: f/;oj^ w/; made impro t'^m^nf Age I 2 3 4 5 6 7 8 9 10 II 12 Number 9 7 5 5 5 4 4 4 4 4 3 3 2 16 10 7 7 5 5 4 4 5 3 3 3 3 3 43 II 10 10 8 7 8 5 5 5 6 5 4 5 43 12 7 5 4 3 3 3 2 2 2 2 2 2 53 13 8 8 5 5 6 4 4 4 3 2 2 2 51 14 7 7 5 s 5 5 4 3 4 3 3 3 34 15 787555433343 30 Ave. 7.5 7-1 5-7 5-0 5-0 4-3 4-1 3-4 3-5 3-0 3.0 2.9 % gain 9 30 15 o 15 4 I5 o 9 o 2 TABLE IV. Daily average by groups I 23456789 10 II Group I 5-9 4-8 5-2 5-8 5-i 5-5 5-4 S-O 5-4 5-2 5-1 Group II 8.5 9-0 3-3 4-6 7-6 5-3 4-7 4-0 4-0 3-5 3-0 5-0 Group III 6.9 6.2 5.4 5-1 5-0 5-8 4-5 3-5 3-5 3-4 3-1 Group IV 15.0 lo.o 8.2 5.5 5-1 5-i 3-i 3-4 2.5 2.9 2.6 TABLE V. (Fig. 7) Daily average by sex for Groups II, III. and IV Number i 2 3 4 5 6 7 8 9 10 n 12 Boys. 215 8.1 6.5 6.3 5.8 5-6 5-2 5-3 5-2 5.0 4-6 4-6 4-7 Girls: 261 6.3 5-3 5-2 5-2 4-9 4-8 4-7 4-7 4-5 4-0 3-5 4-5 12 Number 5-4 206 5-0 52 30 172 2.7 46 TABLE VI. Distribution of those who improve with practice 30+ 30 23 17 30 23 17 12 5 5 i? 2 / 0-5 I I 2 2 I I 23 // 12 8 5 3 2 I 0.5 3 2 4 I 2 I I 17 12 8 5 J 2 / 0.5 4 5 4 4 2 I I 12 5 5 3 -? / 0.5 5 7 3 2 I ,S* 5 ? 2 / 0.5 8 10 8 3 I I 5 3 2 I 0.5 14 26 15 6 6 3 2 / 0.5 15 26 10 4 2 / 0.5 12 16 14 I 0.5 4 8 18 8 31 14 67 25 53 33 42 55 12 59 Below 2 73 Notation and plan of this table same as in Table T. EFFECT OF TRAINING IN PITCH DISCRIMINATION 79 TABLE VII. Daily average record of those who were given special individual help Days 12 34 5678 9 10 II 12 Boys: 17.3 12. 12.5 12.5 14.5 15.5 12.5 114 1 1-3 1 1.2 9-5 9-8 12. 8. Girls 17.7 11.8 9.5 11.5 1 1.4 10.5 10.5 8. 8.5 8.4 7-9 7-8 8.2 5.3 Italics, average record on the first and the second individual tests re- spectively TABLE VIII. Average mean variation from the individual records in the preliminary and final tests. Boys (215) Girls (261) Age Prelim. Final Prelim. Final 9 1.82 1.93 1.99 1-97 10 1.66 1.81 1.76 1.60 II 1.63 1. 7 1 1.68 1.82 12 1.70 1.53 1-51 1-68 13 147 1.52 I.S4 i-6o 14 145 1.48 1. 6s 1.65 15 1.64 1.59 1.53 1-38 Total 1.61 1.65 1.65 1.69 TABLE IX. Distribution of those who reach the approximate physiological threshold ( on different days of practice. Days I 2 3 4 5 6 7 8 9 10 Per cent. 689 9 9 13 12 13 8 7 Of the 476 children 206 (43%) fall in Group I; i.e., so far as the instruction and practice are concerned, these made no improve- ment that could be traced in the records, due allowance being made far daily variable errors. The number of those who do not improve with practice is relatively greater for the younger than for the older children. Classifying these 260 on the basis of record into Grade A, those whose threshold is 4 v.d. or less ; Grade B, those whose threshold is between 4 v.d. and 14 v.d. ; and Grade C, those whose threshold lies above 14 v.d., we find 40 per cent, in Grade A, 51 per cent, in Grade B, and 9 per cent, in Grade C. Of the 270 cases (57 per cent.) which show improvement with practice 19 per cent, are in Grade A, 64 per cent, in Grade B and 17 per cent, in Grade C. Relatively the largest number of cases of improvement occur among those who start out with a very inferior record. This can be shown by comparing the distribution of cases which make improve- ment for each of the increments as set out in Column A, Table VI with the normal distribution of thresholds for the entire group. Of those who did not improve ten were unable to hear any of the increments used and judge as required. It was however found upon 8o FRANKLIN O. SMITH making private examination of the seven of these who were avail- able that they could hear tone differences. Two of these could distin- guish between A and B on the piano. Two of them seemed unable to grasp the concepts "high" and "low" with reference to the naming of pitch. One of these — a scatter-brain — could, however, sing a half-tone correctly when played on the piano. The other — re- tarded about five years — could sing a fifth fairly accurately with the piano. Three were able to imitate a pitch difference in the forks of 3 v.d. by singing enough to show whether the second of the two tones was sharp or flat. The other three were, unfortunately, not avail- able for special tests. Thus, of the 476 cases not a single case of so-called tone deafness was found. The last line in the footings of Table III, B shows that the gain of those who do improve is most rapid in the first part of the train- ing series, 54 per cent, of the gain being made in the first three steps. The further analysis of these figures in Table IV, illustrated by Fig. 6, shows that this principle is true for all three of the groups which show improvement. All the observers included in Table VII took the first individual test which occurred on different days, from the third to the seventh day. Most of these tests were given early in the practice series. The second test began on the fifth day and extended over the remainder of the practice series. Only 26 boys and 9 girls needed to take this test. A very few were given a third test near the end of the prac- tice but the results were not included in the table. Not only does the individual test yield a lower median than the group test in a majority of cases, but the individual test often influences the later results of group practice. In this experiment 6 boys and 4 girls made immediate and permanent improvement after the first individ- ual test which it will be remembered was accompanied by instruc- tion. In one case the gain was from 30 to 9 v.d. ; in another from 23 to 5 v.d. and in a third from 24 to 10 v.d. In some cases im- provement did not begin until after the second test, and in the case of 29 boys and 13 girls no improvement was made. Of these only 2 (both girls) made better records in the individual tests. The average amount of improvement for all cases at each incre- ment decreases with the diminishing of the increment. This is seen in Table VI, and may also be seen graphically in Fig. 8. It must be remembered that this figure does not represent the whole group but only those who improved. EFFECT OF TRAINING IN PITCH DISCRIMINATION 8i The series is not long enough to guarantee that any or all reached the physiological threshold.^ The main difficulty in determining this lies in the fact that persons often come to a "plateau" in the record which is due to some motive or condition which may be re- moved by instruction or training. This, however, gives trouble only when it continues to the end of the training series. Classifymg the cases roughly on internal evidences of the records we find that what may be approximately the physiological limit is reached in successive days as set forth in Table IX. From the variations in the records it is quite clear that the data in this table are quite problematical. To get the actual physiological threshold it is necessary to have more favorable conditions for isolation of the observer and the elimina- tion of disturbances. Undoubtedly there may also be several who remain on a "cognitive" plateau throughout this series and would improve under the proper impetus. Yet, due allowance being made for these sources of error, the table shows that there is a "rapid maturing" in this training ; 6 per cent, reach their bed-rock level on the first day, 8 per cent, on the second, 9 per cent, on the third, etc. After the preliminary tests the number who reach the approxi- mate physiological threshold increases gradually to the fourth day. On the fifth day the number increases suddenly from 24 to 41 (9 per cent, to 15 per cent.) and then gradually decreases to the eighth day after which there is a rapid falling off to the tenth day. (Table IX.) The results show that 47 per cent, of those who improve reach the approximate physiological threshold by the fifth day of practice. The mean variation as given in Table VIII conveys the signi- ficant items — the result of practice, the variations with age, and the "The term is here used in the sense defined by Seashore (3) page 49-SO. "The Cognitive vs. the Physiological Threshold. In sensory discrimination of this sort we may speak of two thresholds: the physiological, which is set by the Hmits of capacity in the end organ; and the cognitive, which is set by cognitive limitations. Theoretically we always aim to reach the physio- logical threshold, but practically we often fall short of this and find a cog- nitive limit; i.e., a higher threshold due to lack of information, best form of attention, interest, effort, etc.; or to disturbances of some sort. Usually inspection of a record or observations made in the test enable us to tell whether or not we have reached the physiological threshold. It cannot be judged by a single rule, although a small m.v. and a well defined mode are pretty sure indications. This distinction is of greatest importance in classification, and in the theory of training." 82 FRANKLIN O. SMITH variations with sex. It must be borne in mind that the unit of the m.v. is not the vibration but the increment, as was described above. That is, the increments increase in a geometric ratio of the second order; therefore, e.g., the increment 17-23 v.d. counts one unit just as do the increments 5-8 v.d. or 1-2 v.d. It follows that as the threshold is lowered the mean variation unit remains relatively constant. Equal power of application of those who have high and those who have low thresholds should therefore show in about equal mean variations; and, conversely, unreliability in judgment wall show in increased mean variation equally for the one who has a fine ear and the one who has a poor ear. The mean variation is slightly larger in the final training test than in the preliminary. The difference is not large— only .04 units — but it is fairly constant for all ages and for both sexes. This is rather remarkable as, in the nature of the test, one would look for evidences of increasing familiarity in the lowering of the mean variation. On the other hand the fact that the procedure does not reduce the mean variation is a most telling proof of the elemental nature of the test. The test is so stripped of conditions for varia- bility that it is possible to be as consistent in the preliminary trial as in trials after practice. The variability is a trifle larger for girls, both in the preliminary and the final tests. This is true for all the ages except 12 and 15 in the preliminary and 10 and 15 in the final. Were it not that this has a bearing on the much mooted question of sex difference on this point and that the data here given represent such a large number of cases (1980 in the preliminary and 476 in the final) no signifi- cance would be attached to this difference. The second decimal figure is of doubtful value in an average of this kind and, as stated, the variation is in one direction for five ages and in the opposite for two both in the preliminary and the final. On the whole our in- terpretation is, therefore, that practically there is no significant difference in the variability of the boys and the girls in pitch discrimination. There is a general, though not great, tendency for the mean variation to decrease with age. This is the measure of growing reliability with age which we are accustomed to find in records of this kind. In this practice series in the elementary schools there are two EFFECT OF TRAINING IN PITCH DISCRIMINATION 83 items that count distinctly in favor of the girls. One is that of the 215 boys and 261 girls who took the practice series, 71 boys and 35 girls were considered, on the same basis, poor enough to need in- dividual instruction and drill. This is a distinct mark of superiority in the girls. The other is that the girls in the training series, quite uniformly for all ages, have a lower threshold than the boys by from one to two vibrations. (See Table V, and Fig. 7). This superiority of the girls over the boys is evidenced also in the preliminary tests with remarkable uniformity as is seen in Fig. 10 where a fairly constant difference is maintained throughout all the ages. The same fact is illustrated from another point of view for the elementary school in Table X and Fig. 11. This difference, however, disappears when we come to the higher ages. Fig 12, for the high school, and Fig. 13 for the university, based on Table X reveal no recognizable superiority of either sex in the preliminary tests. — fi. - .-.-i-r t -i~r ->•••? -I ^ _/ ZJ Possibly there was a greater effort to center attention on the two sounds when my eyes were open. In both of these tests there were times when T seemed to notice a difference in pitch, but could not tell which sound was. higher. This difficulty seemed to disappear with the maze test." N. E. G. "I felt that it was much easier to decide with my eyes closed^ than with the maze. However, my third record shows fewer errors with the- maze." P. H. H. "In the test using the maze it seemed easier to concentrate the mind ; that is, the mind was concerned with two definite things : the maze and the tones, as opposed to the free associations. There was less inclina- tion to drift to other things. The decisions in the maze test involved less conscious effort and seem to be 'felt' rather than consciously formed. Errors in the maze test often followed the effort to locate the end of the pencil line, after it was lost through the recording of the introspection. I gained better success by starting the maze line ahead of the trial." T. F. V. "I found in this experiment that everything depended upon my attitude towards it. If I had my attention in high strain to perceive the difference between the tones and to give a correct judgment my results would be very poor. However, if I fixed my attention upon something else and gave almost passive and indifferent attention to the forks my judgments were far more certain. When my eyes were closed I attempted to focus my attention upon the retinal light and also attempted to complicate matters by means of eye-movement. That is to say, I was endeavoring to center my attention on something other than the forks. In the maze, the more intensely I worked with respect to accuracy and speed, the more clear seemed the distinction between the forks. This focusing of my attention on something else than the thing in hand was very hard to do, especially after I made one or two mis- takes in close succession. If I had not been so desirous of getting correct judgments I am sure my discriminative ability would have been better." 94 rRANKLIN O. SMITH L. E. W. "My preference is for the maze, eyes open, next and last of all eyes closed. In the latter case my mind is ever full of visual and auditory imagery, rich and prolific. One moment I am in my room and can hear the clicking of my typewriter, the next I am singing some haunting air, then I see a paper on my table I should have brought with me this morning. Sometimes I recall in auditory imagery just what the order of the last two forks was and I feel sure that I was wrong though I had unconsciously made the wrong reply. The main difficulty with keeping the eyes closed is that in so doing I can't keep a constant image or position before me; my mind refuses to remain a blank. Now, with eyes open I can fixate my eyes on some particular object and as long as this does not waver and my thoughts and attention are on the business at hand I feel secure — am so, in fact. With the maze I direct my attention to one thing continuously." E. D. S. "Yesterday I was interested in the maze and hence was distracted by it. To-day I felt no such interest in the maze. In the test with eyes closed I became interested in the method of presenting the forks and was thinking about certain possibilities of modifying the method. This became a distraction or rather a constant object of attention and source of error." The second function of training in pitch discrimination is the acquisition of skill in listening to musical tones. Four factors are involved. First, skill means raising the level of non-voluntary atten- tion. The power to concentrate upon the characteristic acuteness or gravity of the tones v^ithout conscious effort usually favors correct judging and is the end to be sought in ear training. Swift found that strained attention results in distraction, and a number of observers make similar statements regarding their own experience in distinguishing tones. Second, skill means mechanizing the conscious factors in learning to distinguish differences in the pitch of tones. The pupil has learned to image the tones as auditory, auditory-vocal, kinaesthetic, or motor qualities. In this process some one or two qualities have predominated, and the object of ear training is to form habits of listening to, i.e., of thinking musical tones in terms of their dominat- ing imagery. The third factor in the acquisition of skill is interest. One of the chief aims of ear training should be to enlist the pupil's interest in the appreciation of musical tones and the enlargement of the scope of apperception with reference to isolated tones. The physiological limit Tlie physiological limit is undoubtedly considerably lower than is indicated by the threshold which would give 75 per cent, right EFFECT OF TRAINING IN PITCH DISCRIMINATION 95 cases, as here used. To demonstrate this and, at the same time, to observe the significance of the choice of a particular increment in the homogeneous method, measurements were made on seven good observers whose threshold had been recorded as being in the neigh- borhood of I v.d. Four tests were made on each of the seven observers at i, 0.5, and 0.25 v.d. with 200 judgments at each unit in double fatigue order, or a total of 800 judgments at each unit. From the per cent, of right judgments the probable threshold with 75 per cent, right cases was computed by the Fullerton-Cattell formula. Table XIII shows the difiference threshold which was required to give 75 per cent, of right judgments for i, 0.5, and 0.25 v.d. respectively. TABLE XIII No. I ■ v.d. 0.5 v.d. 0.25 v.d. v.d. v.d. v.d. I .42 •44 .49 2 .40 .27 •23 3 1.30 3.33 1.30 4 1. 10 1.47 1. 10 5 1.75 1.47 1.30 Average .82 .74 .60 6 1. 00 1. 00 7 1.54 1.30 Average 1.24 1.17 The first five observers had more than fifty per cent, of right judgmients at 0.25 v.d.; hence the threshold is calculated for the three increments of the other cases. Number 6 got only 49 and number 7 only 46 per cent, right cases on the 0.25 increment. But the significant fact is that for both of these persons the number of right judgments on 0.5 v.d. was such as to give practically the same threshold as was found on i.o v.d. Only one important incon- sistency occurs in the above table. In the case of No. 3. the right judgments at 0.5 give a threshold of 3.33 v.d. while at i v.d. and 0.25 v.d. the threshold is exactly the same. Examination of the table therefore proves that in the region of the average physiological limit the conventional threshold may be com- puted on the basis of observations considerably below that limit (here in five cases out of seven) and that the actual physiological limit is always considerably below the conventional threshold. This is, of course, analogous to what we find in sight ; under exception- 96 FRANKLIN O. SMITH ally favorable circumstances we may see a small, well defined object at a distance which, from the nature of the dioptric system, repre- sents the physiological limit of acuity in vision but average records of acuity would ordinarily designate a point short of that distance. Correlations From the standpoint of musical training it is important to know how the ability to distinguish differences of pitch is correlated with other mental characters, as general intelligence and singing ability. In addition to these we wish to know whether brothers and sisters are more closely correlated in ability to distinguish differences of pitch than other children not related. These questions are dis- cussed in their order. For the purpose of the correlation between pitch discrimination and general intelligence and singing ability, the data for pitch dis- crimination were obtained from the final days of the practice series. No single absolute measure of general intelligence is possible. For the present purpose the teachers were instructed to mark general intelligence on the basis of two criteria, brightness and reliability, assuming these to be of equal weight. By brightness is meant quickness and accuracy of mental grasp, or, in other words, general wide-awakeness. Reliability is self-explanatory. It is the correlate of a small mean variation for daily work. For convenience of marking, these two factors may be considered as having equal weight and may, therefore, be marked independently on a scale of lo. It was explained that the markings should follow approximately the normal distribution for each age and for both sexes. The mean of the two marks was taken as the mark representative of intelligence. In order to facilitate correlation the ten units in the series of in- crements used in pitch discrimination were translated into corres- ponding values on the scale of lo, thus: 30 v.d. corresponds to i ; 23 to 2; 17 to 3 ; etc 0.5 v.d. to 10. The markings on singing ability were also based on the teacher's judgment of the pupil's ability to sing correctly in pitch scale and a melody. As regards kinship, three correlations were as follows: (i) be- tween younger and older brothers and sisters with practice; (2) the same without practice; and (3) between the younger members EFFECT OF TRAINING IN PITCH DISCRIMINATION 97 of the second correlation and other children of the same age and sex as the second members, but not related. The correlations were determined by the Pearson product- moments method. In order to show the relative distribution of individuals for each factor correlated, each group is subdivided into five grades. This is not a quintile subdivision as there is no attempt to have an equal number of persons in each subdivision. The distribution by grades serves the purpose of comparison quite as well as the quintile or quartile method and avoids the necessity of ranking, which is practically impossible on a scale of lO units. The method of subdivision is very simple. The scale of lO units is is divided into five equal parts, i and 2 = E. 3 and 4 = D. 5 and 6 = C. 7 and 8 = 6. 9 and 10 = A. An example will make clear the method. An observer gets 3 in pitch discrimination and 7 in general intelligence. He belongs to Grade D in the first factor and in Grade B in the second factor. The number who are in the same grade in each factor indicates the degree of correlation. The number who are in different grades in the two factors indicates lack of correlation or low correlation. The results show a relatively high coefficient of correlation between pitch discrimination and general intelligence, singing ability and musical training (Tables XIV and XV). It is higher for boys than for girls and highest for both boys and girls between pitch dis- crimination and general intelHgence. TABLE XIV. Correlation of pitch discrimination with general intelligence and singing ability Pitch discrimination with (i). General intelligence Boys r .70 p.e. .023 Girls r .62, p.e. .026 (2) Singing ability Boys r .71 p.e. .023 Girls r .51 p.e. .031 TABLE XV. A. Pitch discrimination and general intelligence Girls Intelligence 274 A B C D E A 6 14 14 B 12 51 27 3 Pitch C II 49 2,7 1-2 D 4 3 17 4 E 163 Boys II titelligence 234 A B C D A 4 15 16 3 B 6 31 29 3 Pitch C 3 25 2,2, II D 8 19 8 E I 4 4 9 FRANKLIN O. SMITH B. Pitch discrimination and singing ability Boys Girls Singing Singing 234 A B C D E 2/4 A B C D A 5 7 3 2 A II 21 12 I B 1/ 22 13 8 4 B 8 46 38 10 Pitch C 4 24 23 12 7 Pitch C 8 27 39 16 D 2 13 i6 8 6 D 3 8 16 2 E I 4 IS 8 II E The fact of a high correlation between pitch discrimination and general intelligence favors the conclusion reached above that pitch discrimination depends partly upon the ability to learn, i.e, upon brightness and reliability. If this is a correct view, training in pitch discrimination is essentially mental training. It is more than repro- ducing tones ; it is thinking tones. Another conclusion which is in harmony with what has just been said is that a child may possess a perfect ear for tones, and still be unable to distinguish differences in pitch. Musical training should begin with training in tone quality. The coefficient of correlation between pitch discrimination and singing ability is technically high. A high correlation between these factors means that the ability to distinguish differences in the pitch of tones is an essential factor in learning to sing. Table XVI shows that, for the groups compared, girls are superior to boys in pitch discrimination, since there are no girls in Grade E and relatively few in Grade D. But they are not shown to be essentially superior in singing ability. TABLE XVI. Correlations for blood relationship Correlation between pitch discrimination of (i). Brothers and sisters: (a) with practice r .48 p.e. .031 (b) without practice r .43 p.e. .035 (2). Children not related r .53 P-e. .030 The coefficient of correlation between brothers and sisters on the basis of ability in pitch discrimination is not higher than between other children. This is true both for records without practice and records after practice. Although the results are clearly negative, no sweeping conclusion should be drawn because several variables are involved, such as advantage of the knowledge which comes with age, differences in intelligence, the element of competition, etc. This is regrettable since it had been definitely hoped and planned EFFECT OF TRAINING IN FITCH DISCRIMINATION 99 that this large collection of data might contribute to tlie solution of this interesting question. Finally, the younger member of each pair in the second correlation was compared with another child of the same age and sex as the second member, but not related. The coefficient of correlation is practically the same for the three groups. (Table XVII). No conclusions can be drawn from these meager results as regards the influence of heredity on tonal hearing. XVII. Correlation of pitch discrimination /o; and older brothers and sisters [a) With practice Older 129 A B C D E A 7 5 I I B 9 2,2 12 5 I Younger C 4 17 7 4 2 D 9 2 3 E 3 2 2 I (2) Without practice Older 275 A B C D E A 2 13 12 7 I B 2 6 17 12 I Younger C 12 12 54 27 ID D 7 8 25 32 5 E I I 2 4 2 (3) Children not related and wi thout practice Older 275 A B C D E A 4 2 3 B 6 22 28 12 8 Younger C 6 38 2(> 15 9 D 2 15 22, 4 2 E 13 16 4 7 General conclusions The quantitative statement and analysis of data has been presented in such condensed form that a summary of conclusions from that point of view is scarcely necessary. There is, however, need of a statement of "general conclusions" from the point of view of inter- pretation and application of the experimental results in the light of the quantitative data, the introspections of the observer, the daily notes of the experimenter, and a general study of the problem with the collaborators in research. Such a statement necessarily involves something of a personal equation and I am glad to acknowledge in this the co-operation of Professor Seashore whose long and varied experience in this field of research makes this interpretation possible. 100 FRANKLIN O. SMITH The psychological limit in jiitch discrimination is always below the conventional threshold (75 per cent, right cases). Thus, a person whose threshold is i v.d. may, under extraordinarily favorable cir- cumstances, hear as small a difference as .25 v.d. ; and it is probable that in the normal unreflective and uncritical appreciation of music the automatic "impression" of tone differences comes freely through this region of increments which are below the conventional thresh- old. This conventional threshold which can not be further reduced by instruction or training we have called the "approximate" physio- logical threshold. This is the concept of threshold that must be employed for most purposes of research and in nearly all applications of the test for practical purposes. The three factors which differen- tiate it from the true physiological threshold are — the convention of counting 75 per cent, right cases, the physical variation in the organ of Corti, and the failure to keep all the conditions of the measure- ments under control. Success in making a true measurement on an unexperienced ob- server in a single sitting varies with the knowledge, keenness, and care of the observer and the many objectively favorable or unfavor- able conditions of the test as well as the experimenter; but, every- thing taken into account, it is safe to say that when an individual test is made under favorable conditions the approximate physiologi- cal threshold may be reached in a single sitting of less than an hour for more than half of the cases of adults or children who are bright and old enough to understand the test. Even in group tests by the heterogeneous method one may reach in an hour the approximate physiological threshold of nearly half of the observers who are old enough and bright enough to observe. A cognitive threshold, always above the approximate physiological threshold, may be due to failure in understanding what is required in the test, lack of information, defect in auditory imagery and memory, lack of application, confusions, objective or subjective disturbances, expectations, inhibitions in writing or speaking, etc. Most of these conditions are such that they may be removed by in- formation, by inducentent to use the best eft'ort, or by learning through some experience. There are means of determining when the approximate physiologi- cal threshold has been reached. Chief among these are the mean variation and the character of the distribution of the errors. But in EFFECT OF TRAINING IN PITCH DISCRIMINATION loi individual tests many direct observations on the character of the difficulties in judging may be helpful. In general, vi^here a record is low^ (good) the chances are that the observer has no "cognitive" difficulties. The uncertainty is, of course, always with reference to the poor record. Practical advice or recommendation should there- fore be cautious in the case of poor records for fear that the limit reached, although persistent, may be merely cognitive. One can not err on the side of getting too good a record ; the danger is always that something has prevented a fair test of actual ability. The sensitiveness of the ear to pitch difiference can not be im- proved appreciably by practice. There is no evidence of any im- provement in sensitiveness to pitch as a result of practice. When a person shows a cognitive threshold practice ordinarly results in a clearing up of the difficulties which in the way of a true measure of discrimination by information, observations, and the development of interest, isolation of the problem in hand, and more consistent ap- plication to the task in hand. This is, of course, not improvement in the psycho-physic ear but merely a preliminary to a fair determina- tion of the psycho-physic limit. It follows that instruction in regard to the nature of the test and individual help are all important for the lowering of the cognitive limit and that mere practice for this purpose is a poor and uncertain makeshift. It also follows that a "cognitive" threshold is no measure at all but rather a confession that the measurement has not yet been successfully made. Training in pitch discrimination is not like the acquisition of skill, as in learning to read or to hear overtones. It is in the last analysis informational and the improvement is immediate in pro- portion to the effectiveness of the instruction or the ingenuity of the observer and the experimenter in isolating the difficulty. Reduced to its lowest terms the question of variation with age may be interpreted to mean that we have no evidence of improvement in the psychological limit of pitch discrimination with age ; a young child of school age and even younger, can hear pitch fully as keenly as an adult. The amount in favor of the adult shown in all group statistics is amply accounted for by the difficulty in making a re- liable test on the young and by their lack of information. This statement is based primarily on two lines of evidence. — the common occurrence of fine, irreducible records among young children, and the character of the conditions which are ordinarily overcome by instruction and training. 102 FRANKLIX O. SMITH Pitch discrimination does not vary with sex to any significant- extent. In the records here reported and in the many hundreds of other records in this laboratory in which comparisons may be made for sex, certain tendencies are shown in groups of records, sometimes in favor of one sex and other times in favor of the other sex, but on the whole, it seems certain that such differences, except so far as they are due to grouping, may be accounted for as due to the conditions of the test rather than to the sex difference in the psycho-physic capacity of pitch discrimination. Thus one of the most consistent and striking differences reported above, that of the superiority of elementary schoolgirls over elementary schoolboys may probably be fully accounted for by the prevailing trait of aloof- ness of the preadolescent boy toward music. These boys often regard music as a sort of frill for girls and, therefore, enter the test with less fervor than do the girls. Such interpretation is sup- ported in part by the fact that in the high school and in the univers- ity, where the girls have had far more advantage of training than the boys, the records reveal no appreciable difference for sex. Not a single case of tonal deafness was isolated in any of the records here reported. This would indicate that if tonal deafness exists at all in a "normal" ear, it is no so common as has usually been supposed. We have found a high correlation between pitch discrimination and ability in singing, as judged by teachers. In the collective records there is also a high correlation between pitch discrimination and "general intelligence." This is undoubtedly due to the presence of so many "cognitive" as opposed to physiological thresholds. Under the conditions of this test the records of members of the same family do not correlate more closely than do members of dif- ferent families. This test is elemental, i.e., when applied under favorable condi- tions it calls forth a relatively simple and immediate sensory dis- crimination which does not improve appreciably with practice. It is like the minimum visible angle in visual space — the limit is set by the sense organ. We say "under favorable conditions" because the cognitive factors which condition a fair test must be recognized. As has been seen in a large per cent, of cases, we can get only a cognitive threshold in the first attempts. As elemental, this test is contrasted with, e.g., a test of ability to isolate overtones EFFECT OF TRAINING IN PITCH DISCRIMINATION 103 in a violin tone which represents a skill that can only be acquired through practice. It must be recognized that the test is a true and successful test, the results of which may be applied with safety, only as it is actually elemental. The basal character of pitch discrimination in the appreciation and expression of music has become evident in many ways. Keen recognition of pitch difference is a condition of auditory imagery, auditory memory, singing or playing in true pitch. This is true as well for the affective attitudes with reference both to pitch and to timbre, for timbre is in the last analysis simply a pitch complex. It would therefore seem to be most fundamental of all tests of musical talent, although, of course, no one test by itself can be considered an adequate rrieasure of such talent. The educational value of this test has been strongly impressed during this work. It is unquestionably the isolation and measuring of one specific, basal factor in musical talent. It may be under- taken individually or in groups and commends itself particularly as one of the tests that should be made in schools for the purpose of vocational guidance in music, in the music studio for the pur- pose of learning where to place the emphasis in instruction and in adapting the course to the natural capacities of the student, and as a recurrent exercise in the schools and in the studio for the purpose of developing keenness in attention to detail of tone in ear training. The instruments, i.e., the tuning forks and resonators as here used, and the method, both the heterogeneous and the homogeneous procedure, have proved eminently satisfactory. THE LOWER LIMIT OF TONALITY BY THOMAS FRANKLIN VANCE An accurate determination of the threshold of the lowest audible tone involves a consideration of the variables which condition it. The area and the amplitude of the wave and the distance of the vibrating body from the ear of the observer are the principal objec- tive variables. Individual differences, due largely to innate capacity, degree of practice, and ability to concentrate attention, and varia- tions within the same individual which may be attributed to changes in physical tone and mental content, are obviously the most influen- tial subjective variables. These variables, both objective and subjective, present particular problems which must be considered in their relation to the general problem of the lower tonal limit before the latter can be accurately determined. No attempt will be made here to review the history of investiga- tion on this problem. A good summary is found in Titchener's Instructor's Manual, Quantitative. Mr. Misao Imai made a careful study of this problem in this laboratory in 1907. Inasmuch as his results have not been published and the present study is essentially a repetition of his work for the purpose of verification it is necessary to report his work in brief. Mr. Imai's first problem was to determine the relation between the threshold and the amplitude of the wave. He produced the tones by an electro-magnetic fork 460 mm. in length and 10 mm. by 20 mm. in cross section of a prong. By differential weights five tones could be produced, namely, 35, 25, 22, 19, and 17 v.d. By varying amount of resistance different amplitudes could be secured. The test ir«. each caise'coiisiisted in determining the smallest amplitude that would produce an audible, tone at a given pitch. The measure- m,enfsrwere made -on: ten laboratory students. With this apparatus, he obtained the results shown in Table I. TABLE I. The relation of threshold to amplitude v.d. ampl. in mm. m.v. 30 1.30 .IS 25 1-73 .30 22 2.20 .45 19 2.95 .50 17 345 .50 1 TKTR BOOK TS DUE ON THE LAST DATE 4 p\V TT<^F comoiDDbs Music Library University of California at Berkeley