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 sychological Review Monograph No. 69 
 
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 uracy of the Voice in Simple 
 Pitch Singing 
 
 BY 
 
 WALTER R. MILES 
 
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Reprinted from Psychological Review Monograph No. 69 
 
 Accuracy of the Voice in Simple 
 Pitch Singing 
 
 BY 
 
 WALTER R. MILES 
 
Reprinted from Psychological Review Monograph No. 69 
 
 Accuracy of the Voice in Simple 
 
 Pitch Singing 
 
 I M^SiC LIBKARV j 
 I UWVbHSlTY 0»^ i 
 
 BY 
 
 WALTER R. MILES 
 
 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. 
 

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 1 SB 
 
 ACCURACY OF THE VOICE IN SIMPLE PITCH SINGING 
 
 BY 
 WALTER R. MILES 
 
 Contents 
 
 Historical 
 The tonoscope 
 
 Experiments Series I : accuracy and the voice range 
 Experiments Series II : intensity of standard 
 Experiments Series III : volume of the voice 
 Experiments Series IV: timbre of standard tones 
 Experiments Series V : vowel quality and accuracy 
 Experiments Series VI : accuracy in singing 
 
 Apparatus and method : standards, observers, the charge, the test. 
 
 Justification of procedure : voice level of test, forks for standards, 
 many standards vs. one standard, sounding the two tones, order 
 of standards, time intervals, other factors 
 
 Tables of data. 
 
 Comparison of the abilities of men and women 
 
 The mean variation 
 
 The constant error 
 
 The group constant error 
 
 The best cases 
 
 Correlation of singing with pitch discrimination 
 The test of 1910 
 Recommendations 
 Summary of conclusions 
 References 
 
 The experiments here reported deal with two phases of simple 
 pitch singing: (i) the ability of the voice to reproduce the pitch 
 of a tone, and (2) the ability to matce faint shadings in pitch, sharp 
 or flat. The aim has been to formulate, if possible, a standard 
 test for the measurement of each, to establish norms, an3 to investi- 
 gate some of the underlying psychological factors.^ 
 
 ' The extensive measurements made would have been impossible were it not 
 for the previous labor of Professor Seashore in perfecting a recording appara- 
 tus, the Tonoscope. Dr. Seashore has furthermore proved himself an unfail- 
 ing source of inspiration and suggestion throughout the experimentation. 
 The author is also under heavy obligations to Assistant Professor Mabel C. 
 Williams, Dr. Thomas F. Vance, Messrs. Bruene and Malmberg, and the 
 many observers for their kind and prolonged assistance. 
 
 ^i^4iV8 
 
HISTORICAL 
 
 The first investigator to employ the experimental method in 
 attacking the problem of the accuracy of the voice in singing pitch 
 was Kliinder (ii) 1872.- He used a manometric flame with two 
 connected speaking tubes, an organ tone sounding in one while the 
 observer sang simultaneously in the other. The difference in 
 vibration number between the standard and sung tones was de- 
 termined by counting waves. The average rh errors found on three 
 tones, 128, 192, 256, v.d. are 0.761, 0.434, and 0.257 per cent. 
 (of standards) respectively. The difference between 0.761 and 0.257 
 was thought to be due to the vocal cords and not to hearing. 
 
 Kliinder was not satisfied with his method or his results and con- 
 tinued working on the problem, publishing a second time in 1879 
 (12). Again he used organ tones as standards and had his ob- 
 servers sing simultaneously with them, either in unison or in speci- 
 fied interval. The recording was done on smoked paper by means 
 of two phonautographs. The two records were compared directly, 
 that for the organ tone being used as a standard, and deviation in 
 the pitch of the voice from that of the standard was computed in 
 terms of .25 v.d. That Kliinder was primarily interested in the 
 physiological side of the problem is indicated by the questions 
 which he set himself: 
 
 (i) Does our ear control the voice or is it controlled by the 
 feeling of tension in the larynx? (2) How firmly does the voice 
 attack tones? (3) Are the fluctuations of the voice such that give 
 proof of control by the ear? (4) How many stress degrees of 
 muscular tetanus are we justified in accepting through the perform- 
 ance of the muscles of the larynx? 
 
 Kliinder found that for the pitches 96, 128, 192, 256, v.d., respect- 
 ively, he himself as observer made the following ± errors : .32 v.d.,^ 
 .47 v.d., .62 v.d., and .59 v.d. This however was somewhat better 
 than any of his other observers could do. 
 
 From this Kliinder concludes that the voice is very accurate in 
 reproduction of pitch and he answers his questions in substance as 
 follows : 
 
 ■Previous to this time Scott (17) and Blake (3) had developed phonauto- 
 graphs for registering voice curves. 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 15 
 
 (i ) The vocal cords are held in labial tension by muscular tetanus. 
 (2) The musculature allows from 40 to 170 different tensions in the 
 tetanus. (3) The regulation of the pitch of the voice takes place 
 directly through the sensation of tension in the larynx. 
 
 Seashore (19) in 1910 published in a very condensed form the 
 results of experiments carried on in 1905 by himself and E. A. 
 Jenner. Previous to that time, however, much work had been done 
 in perfecting a registering apparatus, the tonoscope, which is fully de- 
 scribed by Professor Seashore in the foregoing article in this volume 
 of the Studies. Some preliminary experimenting also was done in 
 1 90 1 -'02 with the help of Edward Bechly, the results of which have 
 never been published. Seashore and Jenner in their work sought to 
 answer two questions : ( i ) Can we facilitate development of control 
 in the pitch of the voice by using an aid to the ear in training? 
 (2) May the ordinary limits of accuracy be exceeded by training 
 with such an aid? In attacking these problems they used three 
 measurements: (i) accuracy in reproducing a given tone, (2) ac- 
 curacy in singing a required interval, and (3) the least producible 
 change in the pitch of the voice. The standard or fundamental 
 tone was 100 v.d., produced by a large tuning-fork ; the intervals 
 were the major third, the fifth, and the octave above this. The 
 least producible change was determined for each of these four tones 
 (i) in the least producible sharp and (2) in the least producible 
 flat from the note as actually sung. Each period of practice con- 
 sisted of one hundred and sixty trials, which took about forty-five 
 minutes. The tests continued twelve days, approximately succes- 
 sive. During the first five days the singer depended entirely on the 
 ear as in ordinary singing: then followed five days of singing with 
 aid, i.e., the observer was informed of the result of each trial imme- 
 diately after it was made. The records of the eleventh day were 
 taken without aid, while on the twelfth day aid was again given. 
 Six men acted as observers. The conclusions of this investigation 
 are quoted as follows: 
 
 "(i). The aid enhances the ability to strike a tone which has 
 been heard. The superiority of the aided series over the unaided 
 amounts to 42 per cent. (2) The aid enhances the ability to sing 
 an interval. The superiority of the aided series over the unaided 
 amounts to 50 per cent, for the major third, 50 per cent, for the 
 fifth, and 60 per cent, for the octave. (3) The voluntary control 
 
i6 WALTER R. MILES 
 
 of the pitch of the voice is improved by the aid. The average 
 superiority of the aided series over the unaided for all intervals 
 amounts to 26 per cent. (4) There is probably some transfer of 
 gain from the aided training to following unaided singing. (5)' 
 There is no evidence of transfer of the gain in the accuracy of the 
 memory image. This is undoubtedly due to the fact we have here 
 to do with memory rather than discrimination and the acquisition 
 of accurate memory images is a slow process — too slow in this 
 short series. (6) The gain in the discriminative control of pitch 
 of the voice is fully transferred. (7) Improvements in the ability 
 to sing a tone or an interval, and the ability to produce a minimal 
 change, are very much more pronounced and more rapid in the 
 aided than in the unaided series. (8) The second question is not 
 answered absolutely by our records, but it seems probable (a) from 
 the radical and immediate improvement of the aided series over the 
 unaided, and, (b) from the introspection showing a tone which 
 without the instrument seemed entirely satisfactory to the ear could 
 be corrected by the ear after the error had been pointed out by the 
 instrument, that a higher degree of accuracy of pitch in singing 
 may be attained by aiding the ear in the training than would be pos- 
 sible to attain without such aid. No matter how keen the ear of 
 a trained musician, it can be shown in a single test that his ear has 
 been "too generous" — too easily satisfied, for when the error is 
 pointed out objectively he can recognize it. We thus find cumu- 
 lative evidence to show that the singer can not reach the physio- 
 logical limit of accuracy by the ordinary methods of voice culture, 
 because he has no objective criterion by which he can check up the 
 accuracy of his ear. (9) The major third, the fifth, and the octave 
 are approximately equally difficult intervals to sing. If we express 
 the average error in relative fractions of a tone ( 1/25 of a tone) 
 instead of in vibrations, the ratio is 1.4, 1.5, and 1.4, for the three 
 intervals named above. The average error expressed in terms of 
 vibrations shows that the difficulty of a natural interval varies ap- 
 proximately with the magnitude of the interval. (10) The minimal 
 change is a relatively constant fraction of a tone within the octave. 
 This is true for both the aided and the unaided series. If we 
 reduce the records from vibrations to twenty-fifths of a tone, the 
 minimal change is 3.1, 3.1, 3.6, 2-3, for the fundamental, the major 
 third, the fifth, and the octave respectively. This is surprising, 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 17 
 
 because within this part of the tonal range the pitch discrimination 
 is normally measured by a constant vibration frequency instead of 
 by a constant part of a tone." 
 
 Cameron (4) 1907, varied somewhat the conditions of the ex- 
 periment as performed by Kliinder. In the first series the subject 
 was asked to sing any tone of medium pitch, a second tone of low 
 pitch, and a third of high pitch, and to sustain the pitch selected 
 in each case as uniformly as possible throughout the singing. The 
 second series was like the first except that each tone was inter- 
 rupted by the insertion of short pauses of .3 second duration. In 
 a third series, somewhat longer than those previously mentioned, 
 the ability of one observer to imitate organ tones in the range 94 
 v.d. to 303 v.d. was tested. The tones were reproduced in sequence 
 and, in chance order, partly simultaneously with the standards and 
 partly by singing the tones immediately after the organ had ceased 
 sounding. In a fourth series various distracting tones, (i) harmo- 
 nious or inharmonious with the standard tone; (2) of greater or less 
 interval from the standard; and (3) higher or lower than the 
 .standard, were introduced either at the beginning or just preceding 
 the beginning of the reproduction by the observer. The more im- 
 portant results of the study are here summarized : 
 
 "(i) In the singing of a tone a sudden marked rise in pitch 
 usually occurs near the beginning of the tone. This rise in pitch 
 is so general as to seem to indicate a universal tendency. (2) No 
 tone is sung entirely uniformly. It oscillates in pitch from period 
 to period throughout its length in a somewhat irregular rhythmical 
 fashion. (3) Very marked differences exist in different individuals 
 with regard to their ability to imitate a standard tone. The subjects 
 tested varied in degrees of accuracy in imitation of standard tones of 
 different pitch from a small fraction of i per cent, to 13 per cent, 
 of error. (4) There is manifest throughout a tendency to sing 
 a tone higher than it should be sung. Thus the end of a tone is 
 usually higher than the beginning and the sung tone (as a whole) 
 is almost invariably Higher than the standard tone. (5) Distrac- 
 tions when causing disturbances may affect the whole of the sung 
 tone or only the beginning of the tone. In either case the effect of 
 the distraction may be to cause the sung tone to vary from the 
 standard (a) in the direction of the distracting tone; or (b) in the 
 opposite direction from the distracting tone. (6) Sung tones vary- 
 
i8 WALTER R. MILES 
 
 ing from the standard under the effect or distraction are usually 
 harmonious with the distracting tone. When the distracting tone 
 is inharmonious with the standard tone, distraction is more likely 
 to occur than when the two tones form a harmony. (7) A person 
 may more or less closely imitate a tone which he has heard when his 
 attention was engrossed in singing another tone of a standard pitch." 
 
 An important contribution to the general problem of control of 
 the pitch of the voice in singing was made by Berlage (2) in 1910. 
 During the summer of 1907 Berlage carried on a series of experi- 
 ments in which definite time intervals were inserted between the 
 breaking off of the standard tone and the beginning of the reproduc- 
 tion by the observer.^ These intervals were of the following 
 values stated in seconds: i, 2, 3, 4, 5, 7, 10, 15, 20, 25, and 30.' 
 The tones were all sounded as "a" ('a' in *ah'). This series is 
 an amplification of the methods of Kliinder and Cameron, and was 
 undej-taken for the purpose of finding the time interval most favor- 
 able for the imitation of tones, which when found became one of 
 ■the conditions of further experimentation. 
 
 In the winter of i907-'o8 Berlage's general problem was to de- 
 termine the influence of articulation and hearing in the vocal repro- 
 duction of tones. In this series (second) as in the third series by 
 Berlage the standard tones to be imitated are voice tones. The 
 variation of conditions consisted in having the standard tones sung 
 part of the time by the observer and part of the time by the experi- 
 menter thus showing the immediate influence of hearing and of loud 
 articulation in tone-reproduction. It seemed desirable to determine 
 to what extent the influence of articulation is due to the larynx, and 
 to the mouth cavity. For this purpose, in a third series of experi- 
 ments, all the standard tones were sung by the observers, the 
 vowel quality being varied under control. The standard and repro- 
 duction were sung, sometimes to the same vowel as "i", "i" , or 
 "u", "u", and at other times to different vowels as to "i", and "u" 
 or "a" and "u". The chief conclusions reached from Berlage's 
 experiments are the following: 
 
 (i) "Accuracy in the reproduction of a "strange" voice tone 
 decreases rather regularly with the increasing time interval of 
 from I to 30 seconds. Accuracy is greatest with an interval of from 
 
 ' Berlage designates these tones as 'foretone' and 'aftertone'. 'Standard' 
 and 'reproduction' are used throughout this study. 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 19 
 
 I to 2 seconds. The values found here, for the variable 
 average error, in the case of the observers amounted to only .5 v.d, 
 and .6 v.d. (2) Observers reproduced their own voice tones more 
 accurately than those of another (time interval 3 seconds). (3) 
 The increase of precision shows itself chiefly in a decrease of the 
 constant error. In the reproduction of outside standards and es- 
 pecially when they are near the boundaries of the voice range there 
 is a tendency toward a constant error near the middle of the voice 
 range. (4) In the reproduction of one's own tones vowel change 
 works a disadvantage upon precision. With the standard tone sung as 
 "u" and the reproduction as "i" there is a tendency for the latter 
 to be lower, and vice versa when the vowels are changed. (5) In 
 the reproduction of an outside standard the variable average error 
 expressed in vibration frequency becomes larger with rising pitch, 
 while if expressed in per cent, of vibration frequency it diminishes. 
 (6) In the reproduction of one's own tones the variable average 
 error expressed in vibration frequency remains rather constant with 
 rising pitch. (7) The amount of departure of the individual tone 
 sections (measured off in .1 second periods) from the general 
 average of the reproduction shows no tendency, in the variations 
 carried out in these experiments, to change according to the ordinal 
 number of the tone sections in the course. (8) Only in the first 
 .1 second is the reproduction regularly lower than the rest of the 
 tone course. (9) Reproductions after the time intervals of from 
 3 to 10 seconds, in the case of two observers, show a sudden raising 
 or lowering of the tone after the tone has progressed some .4 
 to 1.2 seconds. (10) The average departure of individual tone 
 sections from the average for the tone is greatest in the repro- 
 duction of one's own tones. (11) The total amount of departure, 
 expressed in vibration frequency grows with rising pitch so that — 
 not considering rather marked irregularities with the individual 
 observers — the amount of variation expressed in per cent, of a 
 tone remains about constant." 
 
 The latest published study of this general problem to come to 
 our attention is that of Sokolotvsky (22) 191 1. His apparatus con- 
 sisted of a combination of the Einthovan string-galvanometer and 
 the Weiss phonoscope. The organ tones, which were used for 
 standards, acted on the string-galvanometer and the sung tones on 
 the phonoscope. Both tones were registered in a convenient way 
 for comparison by means of the Blix-Sandstrom photokymograph. 
 
20 
 
 WALTER R. MILES 
 
 Sokolowsky secured the cooperation of seven professional opera 
 singers, three men and four women. The observers w^ere allowed to 
 choose the vowel to which they sang the tones. The musical "a" 
 was chosen most frequently. There were three short series of ex- 
 periments : ( I ) singing a given tone simultaneously with the 
 sounding of the tone by the organ (unison) ; (2) allowing a time 
 interval between the organ tone and its reproduction. (The inter- 
 vals used were 30, 60, and 120 seconds, during which the observers 
 were instructed not to hum or sing to themselves) ; and (3) singing 
 a specified interval from a simultaneously sounding organ tone. The 
 musical intervals selected were the third, fourth, fifth, sixth and 
 octave. 
 
 The results from these three series of experiments may be sum- 
 marized as follows : ( i ) Curves for 8 tones were secured in series 
 I. The average pitch was 251 v.d. (range 165 to 296 v.d.), the 
 average error was ± 0.44 per cent. The average pitches for men 
 and women respectively were 197 and 286 v.d., with average ± 
 errors of 0.51 and 0.40 per cent. (2) The introduction of a time 
 interval increases the average error to ± 0.99 per cent, as compared 
 with ± 0.44 of the previous series. Errors are usually larger with 
 an interval of 60 seconds than with 30 seconds. (3) The average 
 error in series III is ± 1.51 per cent. The largest errors, average 
 dr 3.28 per cent, are on the fifth, while the smallest, average 
 ± 0.78 per cent, are on the third. (4) Of the entire number of tones 
 counted (46) 36 are sung flat and 10 sharp. The errors on the side 
 of sharping are divided among three women and one man ; those on 
 the side of flatting between three men and three women. 
 
 Giittmann (6) 1912, in his consideration of the psychophysics of 
 singing gives some attention to the problem of accuracy in reproduc- 
 ing pitch and states that recently he has been engaged in an 
 extensive research in this field. The results are to be published 
 shortly in one of the psychological journals, but in a preliminary 
 way he says that they agree in general with those secured by 
 Kliinder and Sokolowsky, but he thinks that the results of the 
 latter (unison curves) are "too good". 
 
 Other investigators, among them Hensen (10) and more recently 
 Marbe (14), Griitsner (5) and Scripture (18) have developed 
 methods for recording the pitch of the voice, but these seem not to 
 ha,ve been used in gathering data on our problem. 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 21 
 
 THE TONOSCOPE 
 
 In the investigations of Kliinder, Cameron and Berlage the 
 vibration frequency of the tones was recorded in tracings on smoked 
 paper. Sokolowsky photographed his records ; after these had been 
 rendered permanent the waves were counted and the pitch deter- 
 mined by comparison with a time or standard hne. This method, 
 commonly known as "graphic recording" has been used with various 
 refinements by many investigators in the field of phonetics. While 
 reliable, it is at best indirect and very laborious. 
 
 Seashore and Jenner in their research made use of an early model 
 (20) of the tonoscope. This instrument as lately improved was 
 used by the author in the present experiments.* It has several 
 advantages which recommended it as an instrument for the measure- 
 ment of the pitch of tones. In the first place readings are made 
 quickly and directly. The instant a tone is sounded the vibration fre- 
 quency is indicated by a row of dots. The experimenter has simply 
 to note the number of this row and to record it. He is, therefore, 
 enabled to secure a large number of observations in a relatively short 
 time. It is not difficult to take two hundred records in thirty minutes. 
 In the second place the experimenter has the advantage of knowing 
 how the test is progressing. If a preliminary practice series is de- 
 sired to acquaint the observer with some procedure we have in the 
 direct readings from the tonoscope an index to the observer's un- 
 derstanding of the test. The observer must be kept actively trying 
 throughout the experiment. In psychological tests, such as the 
 imitation of tones by singing, there is so much repetition in the pro- 
 gram for the observer that his attention easily wanders. Large 
 and unnatural errors are therefore likely to be found in the records. 
 Here the tonoscope as a recording instrument has an advantage 
 over other methods as it provides for detecting these errors as 
 soon as they occur. The experimenter as he takes each reading 
 notes roughly the attack, the steadiness, and the degree of success 
 with which the reproduction approaches the standard. He thus easily 
 becomes acquainted with the unusual range of variability and forms 
 an estimate of the observer's power to control his voice. When a 
 
 * The instrument is fully described in the preceding article in this volume 
 of Studies, "The Tonoscope", by Professor Seashore. A reading of that 
 article is essential for an understanding of the present report. 
 
22 WALTER R. MILES 
 
 tone of unusual divirgence is given he therefore immediately recog- 
 nizes it and can take cognizance of it, asking for introspection or for 
 a new trial, and all with scarcely any loss of time. He may thus 
 check up and to some extent control the observer, — keep him at 
 his best. Furthermore the possibility of encouraging the observer 
 or even of giving him full information regarding the success or 
 failure of each trial is in itself a most important asset. 
 
 The tonoscope has been criticised as giving only an approximate 
 result, because the pitch of the singing voice is not uniform and it 
 is therefore necessary in reading the instrument to select the pre- 
 dominating pitch. This criticism stands or falls according to 
 the needs of the problem to be attacked. If one were studying the 
 oscillations of the voice, or the variations of the individual sections 
 of a tone, as for example the difference in pitch between the first 
 tenth and the fifth tenth of a second of a tone, it would be better to 
 use a graphic method. But even in such problems as these the 
 tonoscope is not without its possibilities. The characteristics of 
 tonal attack in singing are easily discernible in the configurations 
 on the screen. With many of the problems which lie in our field 
 there is no need for so detailed a record. The predominant or 
 modal pitch of a tone of from one to two seconds in length is all 
 that is needed for much of the work in the psychology of pitch 
 singing. The tonoscope can of course meet this condition admir- 
 ably, as it is this modal pitch which stands out clear and distinct, 
 forcing itself upon the attention of the experimenter. 
 
 Tonoscope reading test. — The method of reading the tonoscope, 
 and the various sources of error having been fully treated by Pro- 
 fessor Seashore in the accompanying article, there is no need to 
 repeat them here. 
 
 In order to determine the degree of accuracy in the reading of 
 the tonoscope the following experiment was performed. A set of 
 ten large, movable-disc, tuning forks ranging from 128 to 131 v.d. 
 was so tuned that no two forks had a pitch difference of over 3 v.d. 
 and in the great majority of cases the differences were much 
 smaller. A revolving shutter, rotated by the tonoscope shaft, was 
 so arranged as to expose the mouth of a resonator connected with 
 the sensitive light for the following time intervals : .25, .50, .75 and 
 1. 00 second. In this way a tone sounded before the shutter was 
 registered by the tonoscope for just the period during which the 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 23 
 
 resonator was exposed.^ The presentation of the tones and the 
 recording of the observations were in charge of two helpers. The 
 experimenter did nothing but watch the moving screen and call out 
 the readings. He had no way of knowing the real reading in any 
 case. Five trials were given on each fork with each exposure 
 interval. The order of the forks was determined approximately by 
 chance. There was an interval of about five seconds between tones. 
 
 After the fifty trials with the .75 second exposures were finished, 
 the pitch of each fork was carefully determined with the tonoscope, 
 counts being made by the stop-watch during periods of from 6 to 
 15 seconds. These records formed the basis from which to compute 
 the errors in the first test. The assistant then changed the pitch of 
 all the forks and the above procedure was repeated with a .50 
 second exposure. Again the forks were changed and the same pro- 
 cedure was followed for the i.oo second and the .25 second expos- 
 ures in turn. Thus fifty records v/ere obtained for each of the four 
 exposure periods and the conditions were such that the reader could 
 have no accessory clue. The record is summarized in Table I. 
 
 To test the reading ability for tones one octave higher, i.e. 
 256 v.d., where it will be recalled the tonoscope reading, and hence 
 the errors, must be doubled, a set of seven small forks was pro- 
 vided. These were weighted so that no pitch difference between any 
 two forks was greater than 3 v.d. The test was made with the 
 exposure interval of .75 second. 
 
 In making the pitch difference between the forks come within 
 a range of 3 v.d. we approximate the condition presented when 
 working with voice tones that require accuracy in reading. If an 
 observer is asked to reproduce a tone or to sing an interval the 
 experimenter knows approximately the point on the scale where the 
 reading should occur. He is watching this point. Should the 
 reproduction be nearly correct and the tone fairly constant for, say 
 .50 second, he can read according to our result (see Table I) within 
 an error of less than ± .2 v.d. If however the reproduction goes 
 wide of the mark, for example to the extent of 6 v.d. there is no 
 need of reading in fractions smaller than halves. 
 
 " This arrangement is not ideal in that, as the tone is turned on and cut off 
 by the disc, slightly disturbing waves are set up and show on the screen. 
 In test No. 4 where the tone sounded for .25 second this was felt to be very 
 disturbing. The real time given for the reading of the tones in all these 
 tests was thus slightly less than that represented by the several discs. 
 
.12 
 
 v.d. , 
 
 m.v. 
 
 .lO 
 
 V.( 
 
 •15 
 
 a 
 
 a 
 
 .12 
 
 u 
 
 .19 
 
 li 
 
 a 
 
 .17 
 
 t( 
 
 .18 
 
 a 
 
 . ** 
 
 .11 
 
 (( 
 
 .65 
 
 ti 
 
 a 
 
 .27 
 
 a 
 
 24 WALTER R. MILES 
 
 TABLE L The degree of accuracy in the reading of the tonoscope 
 
 Exposure i.oo sec. Ave. error 
 
 .75 " (128 v.d.) 
 
 .75 " (256 v.d.) 
 
 .50 " (128 v.d.) 
 
 .25 " (128 v.d.) 
 
 EXPERIMENTS SERIES I: ACCURACY AND THE 
 
 VOICE RANGE 
 
 In the first five series of experiments the purpose was to answer 
 questions concerning some factors which must be considered in any- 
 adequate test of voice control, (i) How does accuracy of control 
 vary with the range of the voice? (2) How does the intensity of 
 the standard tone affect the pitch reproduction? (3) What is the 
 relation of voice volume to voice control? (4) Are the reproduc- 
 tions aifected by the timbre of the standard tones? (5) Do vowel 
 changes (timbre changes) in the reproductions cause changes in 
 the pitch of the reproduction? The sixth series represents an 
 effort to combine into a single test the results of our previous ex- 
 periments, together with those of other investigators, and to give 
 this test to a sufficiently large group that we might be enabled to 
 determine from the results some of the norms of voice control.*' 
 
 Seventeen men with splendid enthusiasm gave their services as 
 observers in the experiments of Series I. From among this number 
 several were selected to serve as observers in Series II, III, IV, 
 and V. The observers were all of mature age and more than half 
 their number had had some training in the methods of experimental 
 psychology. P, the only professional musician in the group, is a 
 teacher of "Voice" and a thoroughly trained tenor soloist. H, a 
 baritone of extensive special training, has for some time been the 
 leader of a large choir. He is a soloist of ability. Ma., W, and 
 V. Z. have all had special training in singing, and much experience 
 in solo, quartette and glee club work. S, C. Mi., Ro., An., Wi., 
 and V. H. all have had considerable experience in general singing 
 but are without special training. Ri., Ab., Mc, Br., D, and Bh. 
 very seldom sing in public but they enjoy music. 
 
 'Gutzmann (7) and Sokolowsky (22) suggest some of the above problems, 
 especially Nos. i and 5 as being important. These articles and suggestions 
 however did not come to the attention of the writer until the experimentation 
 was completed. 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 25 
 
 For Series I the standard tones were provided by a set of twenty 
 tuning forks tanging approximately by the chromatic scale from 
 Q, 64 v.d., to and including a', 426 v.d. The first fourteen forks 
 beginning with 64 v.d. were large and carried discs. All the tones 
 were of good quality and their duration of tone was more than 
 ample. Some of the forks were of different vibration frequency 
 than that indicated by the notes of the chromatic scale ; for example, 
 the pitch of the fork that corresponded to G was 182 v.d. in place of 
 192 v.d. These differences were made in order to check the ob- 
 servers from judging and singing the various steps as musical 
 intervals. 
 
 An independent selection of five forks was made for each ob- 
 server after a preliminary determination of his voice range. These 
 forks covered approximately one and one-half octaves in the middle 
 of the range and were fairly distributed. In giving the test the 
 experimenter presented the tones to the ear of the observer, who, 
 after listening for 1.5 seconds and allow-ing a time interval of i 
 second, reproduced the pitch of the tones as accurately as possible. 
 Proceeding from the lowest to the highest and then in reverse order 
 back to the lowest, each tone was given twice in succession, the test 
 consisting of twenty trials on each standard tone. 
 
 The results of these experiments are present in Table II. O 
 denotes the observer ; P, the pitch of the standard tone ; E, average 
 error; m.v., mean variation; and C.E., constant error. These five 
 successive columns give the record of the respective standards for 
 each observer. The footings in the table show the averages of the 
 figures above stated, first in terms of vibration (absolute) and 
 second, in terms of percentage of a tone (relative) at the respective 
 levels. The average C. E. in the footing is the average of C. E. 
 regardless of sign; in the second the sign is taken into account 
 giving group tendency of the constant error, or group constant 
 error (G. C. E.). These footings are represented graphically in 
 Fig. I. 
 
 Taken as a whole these records show that accuracy in the repro* 
 duction of the pitch of a tone, as measured by the average error 
 (E) with its mean variation (m.v.) the average of the constant 
 errors (C. E.) and the general tendency of the constant errors 
 (G. C.E.), tends to be a constant in terms of vibration frequency. 
 This is shown in Fig. i (A) by the fact that the four curves, for 
 
26 WALTER R. MILES 
 
 the absolute variation tend to remain horizontal lines whereas the 
 four curves for the relative variation (B) tend to fall in inverse 
 ratio to the rise of the pitch. The slight tendency to deviate from 
 the constant in terms of vibrations is in the direction of decrease in 
 accuracy with rising pitch. This, in the case of the highest tone, 
 
 TABLE n. Accuracy and the voice range 
 E. 
 O P m.v. P 
 C.E. 
 1.6 
 P. 128 I.I 160 
 
 —1.5 
 
 1.4 
 H. 95 .6 120 
 
 + 14 
 
 i-S 
 
 Ma. 95 -7 120 
 
 —1.5 
 
 •9 
 W. 120 .9 144 
 
 + .2 
 3.1 
 
 V.Z. 120 I.I 144 
 
 +3.1 
 
 2.6 
 
 S. 120 .8 144 
 
 —2.4 
 
 •9 
 
 C. 95 1-2 144 
 
 + .2 
 2.9 
 Mi. 86 2.3 120 
 
 +4.0 
 
 2.3 
 
 Ro. 95 4-5 144 
 
 + .1 
 
 5.0 
 An. 95 2.3 120 
 
 +Z-7 
 
 3-5 
 V.H. 107 1.7 128 
 
 +2.7 
 
 2.3 
 Ri. 95 1-9 144 
 
 +2.5 
 
 E. 
 
 
 E. 
 
 
 E. 
 
 
 E. 
 
 m.v. 
 C.E. 
 
 P 
 
 m.v. 
 C.E. 
 
 P 
 
 m.v. 
 C.E. 
 
 P 
 
 m.v. 
 C.E. 
 
 1.2 
 
 .6 
 
 — 1.2 
 
 182 
 
 .9 
 .8 
 
 + .4 
 
 256 
 
 1.9 
 
 1.6 
 
 —1.6 
 
 320 
 
 1.2 
 1.2 
 
 + .4 
 
 3.1 
 I.I 
 
 +3-1 
 
 160 
 
 .7 
 
 .7 
 
 — .1 
 
 213 
 
 2.9 
 
 14 
 —2.9 
 
 286 
 
 2-7 
 1.4 
 
 —2-7 
 
 .8 
 
 .8 
 
 + 4 
 
 160 
 
 3.0 
 I.I 
 
 +2.9 
 
 240 
 
 3.7 
 
 1.0 
 
 +Z.7 
 
 286 
 
 3.1 
 
 1-3 
 
 +3-0 
 
 1.0 
 
 .8 
 
 + .4 
 
 182 
 
 1.7 
 
 1.6 
 
 — .2 
 
 256 
 
 2.5 
 
 1.5 
 
 +1.9 
 
 320 
 
 1.8 
 
 1.7 
 — .1 
 
 1.6 
 
 .7 
 + 1.6 
 
 182 
 
 1.7 
 .9 
 
 + 14 
 
 256 
 
 I.I 
 I.I 
 
 + •3 
 
 341 
 
 2.7 
 
 1.4 
 +1.7 
 
 1.8 
 .9 
 
 — i.S 
 
 182 
 
 1.0 
 
 .8 
 — .3 
 
 240 
 
 2.1 
 
 1.2 
 
 — .9 
 
 286 
 
 7.1 
 1.8 
 
 +7.1 
 
 .7 
 ■7 
 
 — .0 
 
 I.I 
 
 .8 
 
 +1.0 
 
 182 
 182 
 
 .8 
 
 .6 
 
 — .3 
 
 1.6 
 
 1-9 
 
 — .1 
 
 256 
 
 256 
 
 1-3 
 1.9 
 
 + .8 
 2.7 
 2.7 
 
 + 1.0 
 
 341 
 
 341 
 
 17 
 
 1.5 
 
 — .9 
 
 3.5 
 
 1.8 
 
 +34 
 
 2.9 
 2.2 
 
 +2.5 
 
 182 
 
 2.1 
 2.0 
 
 + 1.3 
 
 240 
 
 4.5 
 1.8 
 
 +4.3 
 
 320 
 
 2.5 
 2.0 
 
 + .2 
 
 1.6 
 
 1-5 
 + -8 
 
 160 
 
 2.5 
 
 2.8 
 
 — 1.0 
 
 213 
 
 4.5 
 
 2.6 
 
 —4.1 
 
 256 
 
 4.6 
 
 3-5 
 
 —3-1 
 
 4.2 
 
 1.4 
 
 -3.6 
 
 160 
 
 2.0 
 
 1-7 
 —1.0 
 
 182 
 
 1.2 
 1.0 
 
 + .1 
 
 240 
 
 4.2 
 2.2 
 
 +3.9 
 
 2.9 
 -1.6 
 
 182 
 
 2.1 
 1.9 
 
 + .2 
 
 240 
 
 4-5 
 1-5 
 
 — .5 
 
 320 
 
 2.5 
 2.1 
 
 +2.7 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 
 
 27 
 
 TABLE II. (Coiitirmed) 
 
 Ab. 95 
 
 Mc. 95 
 
 Br. 
 
 95 
 
 D. 95 
 
 Bh. 
 P 
 
 bc-o 
 
 ^ .J 
 
 u > 
 
 > G 
 
 120 
 103.0 
 
 E 
 
 m.v. 
 
 C.E. 
 
 G.C.E. 
 
 3-2 
 i.o 
 
 +3.1 
 
 1-7 
 
 •5 
 
 —1.6 
 
 2.9 
 
 2.2 
 
 +2.7 
 
 1-7 
 
 •9 
 
 —1.4 
 
 1.6 
 
 I.I 
 
 —1-3 
 
 E 
 m.v. 
 
 CO 
 
 7. ^ c C.E. 
 > (u -"G.C.E. 
 
 2.3 
 
 1-5 
 2.0 
 
 + .8 
 
 .18 
 .11 
 
 .15 
 
 +.06 
 
 128 
 
 120 
 
 144 
 
 128 
 
 144 
 
 5.5 
 
 1.4 
 
 +S.5 
 
 3.9 
 
 1-3 
 
 +3.8 
 
 5.6 
 1.0 
 
 +5.2 
 
 3-3 
 
 31 
 
 — -3 
 
 2.4 
 
 1.6 
 
 + .9 
 
 135-0 
 
 160 
 
 160 
 
 182 
 
 160 
 
 182 
 
 172.9 
 
 2.6 
 
 1-3 
 
 2.0 
 
 + 1.0 
 
 .15 
 
 .08 
 
 .12 
 
 +.06 
 
 3-1 
 •9 
 
 +3.1 
 
 182 
 
 1-3 
 .8 
 
 + 1.7 
 
 1.9 
 
 .8 
 
 —1.7 
 
 213 
 
 1.0 
 
 •9 
 + -4 
 
 6.4 
 
 I.I 
 +6.4 
 
 256 
 
 3-7 
 1.0 
 
 +3.6 
 
 5-9 
 
 2.4 
 
 182 
 
 6.3 
 6.6 
 
 —5-9 
 
 
 —34 
 
 3.0 
 I.I 
 
 +3-0 
 
 240 
 230.6 
 
 5-1 
 1.8 
 
 +S.I 
 
 2.4 
 1.3 
 
 1.7 
 
 + .5 
 
 
 2.8 
 1.8 
 
 2.1 
 
 + .5 
 
 .11 
 .06 
 
 .08 
 +.02 
 
 
 .09 
 .06 
 
 •07 
 +.02 
 
 256 
 
 256 
 
 384 
 
 256 
 
 286 
 
 1-4 
 
 •9 
 
 + -9 
 
 2.6 
 
 1.2 
 +2.0 
 
 2.7 
 
 2.8 
 
 +1.3 
 
 1 1.2 
 
 5-4 
 
 2.5 
 
 1-4 
 
 +1-5 
 
 299.4 
 
 3-5 
 2.0 
 
 2.5 
 + .8 
 
 .10 
 
 •OS 
 .06 
 
 + .02 
 
 '09 
 
 Fig. I. Accuracy and the voice range. (Table II) 
 
 is to be accounted for mainly by the fact that some observers were 
 erratic on this tone, probably because the tone was higher than the 
 observer commonly sings. As a matter of fact only half of the ob- 
 servers, nearly all of whom would be classed as bass or baritone in 
 their range, show any tendency to decrease in accuracy at this 
 
28 WALTER R. MILES 
 
 point; five show the tendency to increase in accuracy and the re- 
 maining four tend to remain constant. 
 
 This result is in harmony with results found by Preyer (i6), 
 Luft (13), Meyer (15) and Vance (26) on the sensory side, that 
 pitch discrimination is approximately constant in terms of vibration 
 frequency within this range. It is in harmony with the finding of 
 Berlage (2) as quoted above: item 5 (second part), that average 
 error diminishes with rising pitch if expressed in per cent, of vi- 
 bration frequency ; and item 6, with reference to the reproduction 
 of one's own tones. 
 
 It is interesting to compare and to contrast these records with 
 those of Seashore and Jenner (19), item 9, showing that the average 
 error in the singing of a natural interval (third, fifth, and octave) 
 varies approximately with the magnitude of the interval; (see also 
 Sokolowsky's results above) and, item 10, showing that the mini- 
 mal change is a relatively constant fraction of a tone within the 
 octave. 
 
 The tendency for the C. E. to be in one direction (-|-) will be 
 considered in a later section in connection with the constant errors 
 in our other series of experiments. 
 
 EXPERIMENTS SERIES II: INTENSITY OF STANDARD 
 In the experiments of Series I, as stated above, two successive 
 trials were made on each fork. Occasionally upon the presentation 
 of the tones for the second trial at reproduction the observer would 
 say ''Let me hear that again; it sounds higher (or lower) than be- 
 fore", or "Is that the same fork?" Such remarks by careful ob- 
 servers led to this consideration of the intensity factor. 
 
 The same forks were used with the respective observers as in 
 Series I. The tones were presented to the ear by the experimenter 
 as before. But with half of the trials the standards were made 
 about as strong as possible by striking the forks a heavy blow and 
 presenting them near the ear. The other standards were made as 
 weak as could be heard with distinctness. The observers were en- 
 couraged to sing with a medium volume of voice and not to imitate 
 that of the forks, as is the natural tendency. Twenty records 
 were made with each fork, ten on the "weak" and ten on the 
 "strong" in the double fatigue order, as regards pitch and intensity. 
 No successive trials were made on the same fork except on the 
 highest and lowest. Having sung the tones from the highest the 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 29. 
 
 observer would sing them in reverse order from highest to lowest; 
 but a short pause was introduced between such successive repro- 
 ductions. Of the eight observers tested, P, Ma., V. Z., C, An., 
 V.H., S and Mi., the first six had no definite knowledge of the 
 object in view. 
 
 The results are shown in Table III and graphically represented 
 in Fig. 2. "W" denotes weak and "S" strong, while the other 
 notation is the same as that previously used. It will be seen that the 
 intensity of the standard tone has a decided effect upon the ac- 
 curacy of reproduction. 
 
 (i). Increase in intensity causes a lowering in the pitch of the 
 reproduction. The G. C. E. for S on each of the five levels is less 
 than that measure for W., the minimum amount of difference- 
 being 1.4 v.d., the maximum 4.1 v.d. and the average for the five 
 pitches, 2.3 v.d. In all the forty individual constant errors with the 
 exception of two (see V. H.'s lowest tone and C.'s highest; in this, 
 latter "W." and "S/' are just the same) the reproductions of the 
 "strong" standards are lower than those of the "weak". If we 
 compare these averages (C. E.'s and G. C. E.'s) with those of the 
 previous series of experiments we find not only that the "strong" 
 C. E.'s and G. C. E.'s are lower in the majority of cases than those 
 of Series I, but that these measures for the reproductions made 
 from the "weak" standards are somewhat higher than those of the 
 former series. The effect of intensity in other words, is evident in 
 both "weak" and "strong" standards, the former heightening the 
 seeming natural tendency to sharp and the latter overcoming this 
 tendency with a more powerful one to flat.'^ 
 
 (2). Strong standard tones cause general inaccuracy of voice con- 
 trol. Most of the observers stated that they were less sure with the 
 "strong" standards. Others complained that the test made their ears 
 tired. Reference to the mean variations and also to the E.'s and 
 C. E.'s will show that in the majority of cases these amounts are 
 
 ^ When the conditions of this experiment (Series II) were explained to 
 P., the professional musician, he remarked off hand as he began the test : 
 "Loud tones would make your nerves more tense and would in general tend 
 to make you sharp." He was asked then and at other times during the test 
 to let any conscious tendency to flat or sharp take care of itself e.g. not 
 knowingly to correct for it. At the last P. said : "I am equally satisfied with 
 my reproductions of weak and strong.'' Cf. P.'s record in Table III. 
 
30 WALTER R. MILES 
 
 TABLE in. Intensity of standard tones 
 Ave. P. 105 v.d. 135 v.d. 174 v.d. 237 v.d. 301 v.d. 
 
 
 W. 
 
 S. 
 
 W. 
 
 S. 
 
 W. 
 
 S. 
 
 W. 
 
 S. 
 
 W. 
 
 S. 
 
 
 E. 
 
 E. 
 
 E. 
 
 E. 
 
 E. 
 
 E. 
 
 E. 
 
 E. 
 
 E. 
 
 E. 
 
 0. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 m.v. 
 C.E. 
 
 p. 
 
 1-3 
 
 I.O 
 
 — •/ 
 
 2.1 
 
 .6 
 
 —2.1 
 
 .7 
 
 .5 
 
 + -3 
 
 1.2 
 
 ■9 
 — 1.0 
 
 2.3 
 
 1.2 
 
 +2.3 
 
 1-4 
 1.4 
 
 + -3 
 
 I.I 
 
 .7 
 + 1.1 
 
 .7 
 
 •7 
 
 + .2 
 
 3.0 
 1-3 
 
 +2.9 
 
 1.0 
 
 .8 
 
 + .5 
 
 Ma. 
 
 I.I 
 
 •9 
 
 +1.0 
 
 I.I 
 •9 
 
 1.0 
 1.0 
 
 — .2 
 
 1.4 
 .8 
 
 —1-4 
 
 3-2 
 
 .8 
 
 +3.2 
 
 1-7 
 
 1-7 
 
 + .8 
 
 3-1 
 .6 
 
 +3.1 
 
 2.1 
 1.0 
 
 -)-2.0 
 
 2.1 
 
 ■7 
 +2.1 
 
 1.4 
 
 1.0 
 
 —1.4 
 
 V.Z. 
 
 3.8 
 
 ■7 
 
 +3.8 
 
 1.6 
 
 •9 
 
 +1.2 
 
 2.9 
 1.3 
 
 +3.1 
 
 I.I 
 
 •7 
 +1.0 
 
 3-2 
 
 .5 
 +3.2 
 
 •7 
 
 •7 
 
 1.9 
 
 I -5 
 
 — 1.2 
 
 4.8 
 
 1.2 
 
 -4.8 
 
 2.0 
 
 1.7 
 + -3 
 
 1.8 
 
 1-3 
 —2.1 
 
 c. 
 
 1.2 
 
 •5 
 + 1.2 
 
 •7 
 
 •7 
 
 + .2 
 
 1.9 
 
 •5 
 +1.9 
 
 I.I 
 I.I 
 
 + .3 
 
 1-7 
 .8 
 
 + 1-7 
 
 •7 
 
 ■7 
 
 — .1 
 
 3-0 
 
 I.I 
 
 +3.0 
 
 2.4 
 
 •9 
 
 +2.4 
 
 2.8 
 2.0 
 
 +2.6 
 
 2.6 
 
 1.0 
 
 +2.6 
 
 An. 
 
 6.4 
 
 6.4 
 
 +6.4 
 
 5.4 
 
 2.8 
 
 +4.8 
 
 1-9 
 1-3 
 
 + 1.9 
 
 I.I 
 
 I.I 
 
 — .1 
 
 1.9 
 1.9 
 
 — -5 
 
 2.3 
 
 1-3 
 
 —1.9 
 
 3-2 
 1.2 
 
 —3.1 
 
 7.8 
 1-7 
 
 -7.8 
 
 3-7 
 1.8 
 
 —3.4 
 
 8.1 
 
 1.2 
 
 —8.1 
 
 V.H. 
 
 3-1 
 1.6 
 
 +2.6 
 
 2.9 
 
 1-7 
 
 +2.9 
 
 3-9 
 1.0 
 
 +3.9 
 
 3.5 
 1-5 
 
 +2.9 
 
 1.0 
 .8 
 
 1-9 
 
 1.8 
 
 — 1.2 
 
 2.2 
 1-9 
 
 + -8 
 
 2.1 
 
 2.1 
 + .3 
 
 2.9 
 3.0 
 
 — .5 
 
 8.0 
 
 3-4 
 —8.0 
 
 S. 
 
 1.8 
 
 .5 
 —1.8 
 
 4.2 
 
 .7 
 —4.2 
 
 1.0 
 
 •5 
 + 1.0 
 
 •7 
 
 .6 
 
 — .4 
 
 .8 
 
 .8 
 
 — .2 
 
 3.6 
 
 1.0 
 
 -3.6 
 
 2.1 
 
 1.2 
 
 —1.8 
 
 4-7 
 .9 
 
 —4-4 
 
 5-3 
 1-3 
 
 +5.3 
 
 5-5 
 
 1.4 
 
 +5.5 
 
 Mi. 
 
 9.3 
 
 1.9 
 
 +9.3 
 
 8.5 
 4.1 
 
 +8.5 
 
 1-5 
 .9 
 
 + 1-5 
 
 1-7 
 •9 
 
 + -5 
 
 2.2 
 2.0 
 
 — .8 
 
 5.4 
 
 2.9 
 
 —5-4 
 
 4.0 
 
 3.1 
 
 +2.4 
 
 4-5 
 
 4.1 
 
 — 2.1 
 
 7.8 
 1.9 
 
 +7.8 
 
 4.7 
 
 2.9 
 
 -4.6 
 
 Av.E. 
 
 3-5 
 
 3-3 
 
 1.9 
 
 1.5 
 
 2.0 
 
 2.2 
 
 2.6 
 
 3.6 
 
 3-7 
 
 4.1 
 
 Av. m.v. 
 
 1-7 
 
 1.6 
 
 •9 
 
 1.0 
 
 I.I 
 
 1.4 
 
 1-4 
 
 1.6 
 
 1.7 
 
 1.6 
 
 Av. C.E. 
 
 3.4 
 
 3-1 
 
 1.7 
 
 1.0 
 
 1.6 
 
 1-7 
 
 2.1 
 
 3.0 
 
 3-1 
 
 4.1 
 
 G.C.E. 
 
 +2.7 
 
 + 1-3 
 
 + 1.7 
 
 + .3 
 
 -fi.o 
 
 —1.4 
 
 — .5 
 
 —1.8 
 
 +2.1 
 
 — 2.0 
 
 larger with strong standards, thus indicating conditions that operate 
 against the best vocal control. 
 
 The matter of intensity has been considered in the field of pitch 
 discrimination, where it must really be worked out. Seashore (21) 
 makes the following statements concerning it: 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 
 
 31 
 
 "Extensive experiments show (i) that both trained and untrained 
 observers may be influenced by intensity in their pitch judgment; 
 (2) that although there is a tendency among the untrained, espec- 
 ially the ignorant, to judge the loud tone the higher, it may work 
 either way; (3) that the same individual may show one tendency 
 at one time and the reverse at another; (4) that for trained ob- 
 servers the two tendencies are about equal; and (5) that the 
 tendency is more serious for large than for small intensity differ- 
 ences. Introspection shows that this confusion rests largely on 
 motor tendencies, or motor images. We associate high and strong 
 with strain — the reversal can in some cases be traced to a correc- 
 tion, conscious or unconscious, based on knowledge of this danger. 
 
 S.S.(3J 
 
 — 7- /^ 
 
 r;z::.:^-'*^—"im.d(^J 
 
 Fig. 2. Tne influence of intensity of standard tones. 
 
 "Experiments show that the just perfectly clearly perceptible tone 
 is most favorable for accurate results. It is ordinarily purer than 
 a stronger tone and favors concentration. Experimenters must 
 guard against a very common tendency, usually unconscious, to 
 facilitate the discrimination by making the tones loud ; and untrained 
 observers usually desire (unwisely) a loud tone." 
 
 These conclusions are found on tests made by Anderson (i) at 
 the level of 435 v.d. Our results just stated led to a re-examination 
 of the effect of intensity on pitch. Hancock (8) found that as 
 
32 WALTER R. MILES 
 
 measured in terms of hearing alone the tendency to hear a relatively 
 low strong tone as low is greater than is shown in this series for 
 singing. All these facts make clear that in singing from a standard 
 tone greater care must be exercised to keep the tone constant and 
 at a most favorable strength. We have no adequate quantitative 
 data to show what strength is best but the facts available tend to 
 support the statement made by Seashore (21) that the just per- 
 fectly clearly perceptible tone is most favorable for accurate results.* 
 
 EXPERIMENTS SERIES III: VOLUME OF THE VOICE 
 
 The effect produced by varying the intensity of the standard 
 tones suggested a parallel question concerning the relationship of 
 voice volume and accuracy of reproduction. This problem was 
 attacked in the following manner. The forks selected were the 
 same for each observer as in the voice range test. Series I ; they 
 were presented to the observer's ear by the experimenter who 
 endeavored to keep the intensity as nearly constant as possible, and 
 the observer was instructed to reproduce the tones in three degrees 
 of voice volume, "loud", "medium" and "weak". Ten trials were 
 made on each fork with each of these three degrees of loudness of 
 voice, the order being as follows : one trial on each fork from lowest 
 to highest and after a pause from highest to lowest with "medium" 
 intensity; from highest to lowest and back to highest with "loud" 
 intensity ; from lowest to highest and back to lowest on "weak" ; 
 highest to lowest and back on "medium" and so forth until the 
 150 trials were made. 
 
 These records are summarized in Table IV and represented in 
 part in Fig. 3. In this table L, M and W represent respectively 
 loud, medium, and weak, other notation is the same as in the fore- 
 going tables. 
 
 Here we find again, as in the foregoing series, the tendency for 
 accuracy in singing to remain a constant in terms of vibrations, ex- 
 cept for the extreme notes, at which there is a decrease in efficiency, 
 especially at the high note. The form of the average error curve (E) 
 
 'The force of the blow changes the pitch of a fork, (See Winkelmann's 
 Akustik, Vol. 2, p. 358) lowering it slightly, but this change in these forks 
 could hardly be detected and certainly fails to account for the error in 
 reproduction. See also Seashore (21). 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 33 
 
 here is entirely analogous to the form of the curve of pitch discrimi- 
 nation referred to above (16, 13, 15 and 26) but it represents a 
 shorter range, as the voice has a shorter range than the ear. 
 
 The constant error for men here, as in the foregoing series, is in 
 the direction of sharping. It is a relatively constant fraction of a 
 vibration for all pitches except the highest. The records for the 
 medium and the weak tones practically coincide,'' and compare very 
 favorably with those of Series I., but there is a uniform tendency 
 to sing the loud reproduction highest. The average difference be- 
 tween the loud and the weak (see the G. C. E.'s) is here .6 v.d. 
 . This is not a contradiction, but the reciprocal of the results found 
 in Series II: namely, that the loud (or strong) standard is re- 
 produced low. 
 
 It will be remembered that in Series II the standard was made 
 strong, the observer tried to produce a tone that subjectively seemed 
 the same in pitch, and that practically all of his reproductions were 
 flat. This result in the light of Series I, where sharping was the 
 rule, seemed to warrant the conclusion that the strong tone is 
 judged low. Now in Series III we have a confirmation of this ; here 
 the standard is of medium intensity while the reproductions are 
 varied : loud, medium and weak. It seems therefore that the in- 
 stant the observer commences his loud reproduction he is subject to 
 the same error in judgment as was revealed in Series II, and that 
 to make his reproduction subjectively equal in pitch to the standard, 
 he thinks it necessary to raise. This brings about abnormal sharping: 
 the average G. C. E. of Series III is -{-1.3 v.d. as against -\-.y v.d. 
 for Series I, where intensity differences were at a minimum. 
 
 The agreement of the errors (G. C. E.'s) in these two series 
 (II and III) at once offers an explanation for them: the error is 
 primarily one of hearing which is basal and the chief cause for the 
 error in singing.^^ This is in harmony with the contention of Kliinder 
 
 ' Medium and weak tended to be confused by the observers who would 
 frequently have to be reminded that they were not making sufficient differ- 
 ence between them. This would imply that they each seemed more natural 
 and less distinct than the loud, which is borne out by the fact that the 
 average G. C.E. for weak (Series III) is identical with that for Series I, 
 i.e. -i-.7 v.d. However it should be noted that the curves for weak are less 
 regular than in Series I. 
 
 ^^ It is interesting to note that in Series II the high strong is flatted most, 
 while in Series III the high loud is sharped most. 
 
*>. "00-<S- Tj-rofO roqf^ '^. "?^ °9'^. "^ Q'^Q 9^^ ". '*'^'^'> 
 
 !> -^"i-; NMOJ H^Mi-; i/jMirj oii-^ci r^oioi rocs" coi-Ioii-H 
 
 + + + + + I + + 
 
 QOi^ cvii-ioi MMM wi-h' tOMiT) r'^HHf-^ -tC^'-^ fOi-<fO rOi-Hro>-< 
 
 g + I I + + I + + 
 
 ..^••.,-cs'-ioq Ti-o)N ooio \oq\tr) \o"/io mu^co "?"?"? ". J^oq Ov 
 
 ^|ii>li|^^' |_;^^^ Mi_;' r<."t<. ir)Mio oin'i-' Cn<^0\ TJ-i-;ro<N 
 
 EU + I I 4- + j + + 
 
 !> w ■ M M M w oj ' oi • • • ^i ^^ f^' r^ oi ' (N c^' M _; ^h' M ■ 
 
 + + I I + I + + 
 •d 
 
 >M f^fO"? 00"^ lOOfO TtOiO VOxf-tO <NcqoO corj-tv. Qif^JfOOv 
 
 ^ '^ Ml-;' mm' M i-I rj _;■►«■ ro ' r^ oi d ' M w ■ M w i-i' ■ 
 
 ^ 1 + + I + 4- + + 
 
 5" .-.cjNi-it^ NOPi NNiN. O\oq '^ oosO \qtN.T}- i-;f9'-: '-'. ^ <^0Q 
 
 a hJW^W'^'^''^ oii-Ioi CS^w '--t f^'p^ mm' roc^ro (Nwoi' 
 
 s Su I I I + + + + + 
 
 s I^ w'l-I c«o'rr) >-i'i-I oi'ts '"' ■^<~6cs Mi-ii-i rji-Hj-I' 
 
 « ^ + + + I + I I + 
 
 § ^ OvOics. q<7q q o\oq ^\q -^ ^^^ '^. Q ^ '^ ^ ^ '^'^'^'l 
 
 '^ "^S • ' • f^^^ro csi-h'm oi'cj ••■ tvic4i-< 01 f^"' mmm" 
 
 ^ ^ I + + I I I + + 
 
 O , ... 00 00 ^ lO CO ^ rovo O ^i.-.^ li^iom 0\rOt-' i-HTfin covo r^ a\ 
 
 •— 'riJ>W''' ^^l-JN oit-Ioi cok^co h^^H'* cioiN r6c^i-< cii-H*h4* 
 
 s su I + + + I I + f 
 
 ►^ J> '?"?'^ rxvovo vO"^<^ ■-;0\D r^OOI-% \OMDO f>q f^" " °*? '^ "^ "^ 
 
 1^ ... „•,_;• t^j ,^ 5vj M i-i ' M ' M M M c^' oi IN (vi w w M i-H 
 
 ^•. +I+ + + + + + 
 > 
 
 ty § ^MOi '*'^'-: "?^"? ^°Q "? "^"^ "I" •> "?°Q ^.^ '^ •> ^i ^. "? 
 
 ^ - I + + I + I + + 
 
 i-'M'tWcoiotN. o\o-Ln qiwoq <^^. "-; <^'-:'7 '^^'^ '>"?'> ^. ^]<^'> 
 
 S U f^ ' ci oi i-H w (vj M oi i-h' i-I ■ !_; hH i-< oi w N N !-<' t^' N i-H iM ■ 
 
 I I + + + + + + 
 
 I I + I I + + + 
 
 '•g qcoq\ ooqio lo^Hup co-^n '^i^N c\«. q\ ^"poi "?"^'> 
 
 2^ I + I + + + + 
 
 '— 'W-*. Wqvqi-; qi>q q\qq\ rooqiN -t-iort qoqq\ f^vqoj 'f9"1"'7 
 
 S U "^ ' <^ oi ' ^i r^ i-i <r> oi ' ci .-; " m d> i-i oo <n ^-" oi r<S « fo w 
 
 I I + I + + + + 
 
 6 . • . . . . 
 
 Oh" 1^ >■ >• '^ > Suq 
 « < >• >u 
 
 < << 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 
 
 35 
 
 
 'M/lffj 
 
 .._ ^ mv. ivij 
 
 . —^•'^ i-nUlM-/ 
 
 103 /J7 176 Zl-/ 30G 
 
 Fig. 3. Volume of the voice and accuracy (Table IV). 
 
 (12) that the ear is the chief criterion for regulating the voice. But 
 the result quoted from Hancock (8) : that the hearing error is 
 greater tan the singing error (when dealing with a low, strong 
 tone), together with the fact (Series III) that there is relatively 
 more flatting with a strong standard than there is sharping with a 
 loud reproduction, would conform to the conclusion reached by Stern 
 (24) that the kinaesthetic sense of the singer is also an important 
 factor. 
 
 One would expect a larger mean variation (m.v.) for the tone 
 that has the largest error, but the table shows the mean variation 
 to be practically equal for all three intensities of sound. This may 
 be taken as a mark of the relative constancy of the motive for the 
 intensity error. 
 
 The agreement and the remarkable uniformity in these two laws 
 as shown in Series II and III would indicate that we are here 
 dealing with an important factor of which we must take cognizance, 
 both in the hearing and the producing of musical tones. 
 
 EXPERIMENTS SERIES IV: TIMBRE OF STANDARD 
 
 TONES 
 
 Kliinder (11 and 12), Cameron (4) and Sokolowsky (22) in 
 their researches used organ tones for standards, while Berlage (2) 
 made use of tones from the voice. Having ourselves used tuning 
 forks it seemed advisable to ascertain if timbre differences in the 
 standards affect the accuracy of reproduction. 
 
36 WALTER R. MILES 
 
 The standards selected for the test were : a large disc tuning fork 
 (144 v.d.) sounded before a resonator, the dichord (137.5 v.d.) 
 energized by bowing, and an organ pipe blown by mouth. In using 
 the latter, because of the variability of the blow and hence the 
 uncertainty of the pitch sounded, the vibration frequency of each 
 standard tone was read on the tonoscope and entered in a parallel 
 column with the reproductions. The tones were so far as possible of 
 uniform intensity, they were sounded for approximately 2 seconds 
 and after the interval of i second reproduced on a, as in "law" with 
 medium volume of voice. Twenty trials were made on each 
 standard, and because the effect of timbre was the point of interest, 
 the reproductions were in groups of five successive trials, the 
 standard of course being sounded before each attempt. 
 
 TABLE V. Timbre of standard tones and accuracy 
 
 0. 
 
 Fork 
 E. 
 
 144 
 
 m.v 
 
 v.d. 
 C.E. 
 
 St 
 E. 
 
 ring 
 m 
 
 137 
 .v. 
 
 •5 v.d. 
 C.E. 
 
 Pipe 
 E. 
 
 Av. 150 
 m.v. 
 
 v.d. 
 C.E. 
 
 p. 
 
 s. 
 
 Ma. 
 V.Z. 
 
 Mi. 
 
 2.5 
 
 I.O 
 
 1.2 
 
 1-3 
 2.0 
 
 .6 
 
 .9 
 
 1-3 
 
 •5 
 .6 
 
 +2.5 
 - .8 
 + 1.2 
 +1.2 
 +2.0 
 
 1.8 
 1.9 
 1.2 
 2.1 
 .6 
 
 
 •5 
 .8 
 
 •5 
 •4 
 •5 
 
 —1.9 
 —1.9 
 
 +1.2 
 —1.9 
 + -3 
 
 •9 
 I.I 
 
 1-3 
 .6 
 
 •5 
 
 
 •4 
 
 •5 
 .8 
 
 •5 
 •4 
 
 — .1 
 
 — -3 
 + .6 
 
 — 5 
 
 — .2 
 
 Av. E. 
 Av. m.v. 
 Av. C.E. 
 
 G.C.E. 
 
 1.6 
 
 .8 
 
 1-5 
 
 +1.2 
 
 1.5 
 
 
 .5 
 
 1-4 
 — .8 
 
 .9 
 
 
 •5 
 
 •3 
 — .1 
 
 The results of this series of experiments are summarized in 
 Table V. Judging by the magnitude of the average error and the 
 constant error, the record is in favor of the organ pipe. This is 
 probably due to the fact that this tone is most nearly like that of 
 the human voice in tone-color, or timbre. The introspections of our 
 observers, all of whom have good musical ability and were practiced 
 in observation, are however not in accord with this. Four of the 
 five stated that the string was the easiest standard to imitate. P, 
 the one professional musician in the group, felt that he did best on 
 the fork. But reference to the table shows that it was here that he 
 made his largest errors and even the largest made by any observer on 
 that standard. S. stated that the string was by far the best as a 
 standard but made his smallest errors, and the smallest made by 
 anyone, on the fork. It must be noted also that S. has had more 
 practice with forks -than any other member of the group. Practice 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 37 
 
 is undoubtedly a factor and the value of it for a particular observer 
 depends chiefly on what associations are awakened by a given tone- 
 color. Purity, for example, may be thought of as thinness, and 
 secondarily as highness of tone. While tuning forks, being relatively 
 pure and free from over tones, are at a disadvantage on the side of 
 richness, it is also true that in most groups the observers are about 
 equally unpracticed in singing with forks, which is an advantage 
 from the standpoint of measurement. The forks also are decidedly 
 more constant in pitch than any other type of standard tone. Two 
 of the observers noticed a tendency to imitate the timbre of the 
 standards. 
 
 From the above observations it seems fair to conclude that rich- 
 ness of tone favors accuracy in the reproduction of any particular 
 standard." 
 
 EXPERIMENTS SERIES V : VOWEL QUALITY AND 
 
 ACCURACY 
 
 Berlage (2) introduced the problem of the influence of vowel 
 quality (or change in the timbre of the singing voice) upon accuracy 
 in imitating pitch, and made measurements on this point for the 
 purpose of determining the effect of mouth resonance upon the 
 pitch of the reproductions. In considering the problem there 
 is no thought of discrediting the results found by Berlage. The 
 tonoscope method of recording has enabled us to take many more 
 records than were used by him in computing his results and the 
 matter is of such far reaching importance that it seemed worth while 
 to include in our study a series on this factor, limiting our measure- 
 ments to the following vowels : 
 
 u as 00 in "toot" 
 o as o in "no" 
 a as in "ah" 
 ^ as e in "there" 
 i as i in "machine" 
 
 In addition to these, humming the tone was introduced in the test 
 as the "hum" seemed to have no marked vowel quality. 
 
 " Starch (23 p. 52) in his conclusions on the effect of timbre in the locali- 
 zation of sound makes this statement : "The richer and more complex a 
 sound the more accurately it can be localized." 
 
^ C^ ■ (vj mm' ri h-I oi CO M ro • • • ^ ^ ^ cj i-i 01 ci 
 
 + + + + I + -h 
 
 — q ^ q ■^ q t> ro ^ q q ms q m3 ro -+ oq cq oq oj oj q q 
 
 ■^■^ mhh' f6i-<rr) ^M-rj- WMM '^i-i-rj- r<-3i-ir0<0 
 
 + + + + + + + 
 
 "O M ' _; M M ' 01 i-< r4 oj w oi ' ' ro i-' ro oi m" >-< w 
 
 > + I + + 1 + + 
 o 
 
 rt ^ OOO ■*<N>-; ioq\-i- irsMM 1-; CfvM:> "?"."? "^ ^ " '^ 
 
 01 i-l oi M M I-.' 01 ' cN 01 M o5 hh' ■ ■ Tt 0) Tj- 01 w 01 !-<■ 
 
 + I + + I + + 
 
 l-iMI-; l-I,.;' f^M(\j r^n'oi WI-h' Oll-Hoi OlMl-HW 
 
 + I + + + + + 
 
 3 . vqoivo -^MrN. loNc^ '^".P ""PI" oi>-;\0 -rj-rt-CNr^. 
 
 • > oii-Hoi Mh-!' oii-ioA oqi->'oi oii-i" rooioi oiwi-HH-i 
 
 ? W gu + I + + + + 
 
 "3 - 
 
 %. j; ^ ■^ "1" P °Q "^ '>'>". P °Q "^ Q R* '^ ". " ■* P^''9 "? *? 
 
 J " T " + ""+ ""+ ""+ " + 
 
 5> na M ■ _; • • • J, ■ • • . . „• ■ „• „• ►J • H^ ■ • • 
 
 - >■ i i I + + I I 
 
 H^ n! 'S "^^Q t P *> '> ". P^^ ^ ''P "1" "^ P" "^i ^! '^ "^ ". °° <-o oq 
 
 O HHt— (I— I ^H l-<)-((-HI— l(-H 
 
 I I I I I I I 
 
 • ••» 
 
 "3 o "^ Q "^ '^ Q^°9 ^ '>oQ **^. 'n' 9 "^ Q "? ^ '^'-^ ■■; Q '^ <^ 
 
 S |-IHH)-H * I— ll-HHHl-l'l-HI-l i-HH-l 
 
 ^ i I I I [ I I 
 
 B 3 [xi > bj '>°^ "? P^ *> P' *"> •> "^. O^ 't "^ ^ ". ". ^! '^! •> P °9 ^ "^ 
 
 O " • . • • • ... ... ... ^ „■ „■ ^ ^ ' M ' 
 
 ^ Su I I I I + I I 
 
 ■— i' : "?'^ ^7 p^t^ •> '7^. ". "T "i" ^! ^. °o '^ °0. P^ *> "? P* P* P^ 
 
 ^•C ... ... ^'m' .-■ ^ ' ^ ^^ f^ ' ^^ ' ' ' 
 
 ^ ' I + + + + I + 
 
 D3 .« \q tN. '^ p\0 -^ ^. "? ^. "? "^ "? '> f> '> '>^. ^. P^o°. ^. ^ 
 
 s + + + + + + + 
 
 V ^ oqinp "oqcq cqcq<rj "+'7<7 "^P*" '>'>"7 '^. °Ovqvp 
 
 ^ KH 01 01 ^ >^ I"" 
 
 i + + + + + + 
 
 rt *^ '^'^'^. oqin>o q\t-^io inLooi Onooon <^oi^ qi^^Dsq 
 
 1 + + + " + ""+ " + 
 
 O vq vq I-; oq CO 1-; p\ '^^p pf>"1' 0<Nm 'Oiopi t-H OvMD i- 
 
 ^^ I I + + + I + 
 
 O PlJ iy;i (J N -^ ■^' W >.KtJ 
 
 > > ^ ^ SuU 
 
 < > >^ 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 39 
 
 Three forks of the large disc variety were used as standards, the 
 pitches being: 144, 182 and 240 v.d. and each of these three tones 
 was reproduced to the five vowels and the "hum" twenty times, a 
 total of 360 trials for the individual observer. The test was divided 
 between two equal periods. The order of reproducing was two trials 
 on each fork to each vowel in the double fatigue order, illustrated as 
 follows: 144 to u, 182 to n, 240 to u, pause, 240 to u, 182 to u, 
 and 144 to u; then 240 to o, 182 to 0, etc., followed by 144 to a, 182 
 to a, and so on throughout the test, the order of the vowels being 
 u, o, a, e, i, and "hum." All standards were presented to the ear for 
 a duration of approximately 2 seconds and an interval of i second 
 was allowed before the singing. 
 
 That the vowel quality is a factor influencing the accuracy of 
 reproduction is borne out by the results of the series as shown in 
 Table VI. The average error (E) and the mean variation (m.v.) 
 are given merely for an index to the reliability of the record. They 
 are both large as compared with the constant error (C.E.) which 
 is the factor in terms of which we desire to measure the effect of 
 vowel quality on reproduction. 
 
 Although there are characteristic differences for the three pitch 
 levels and for the different individual observers, the results in 
 Table VI may be fairly represented by a single curve (Fig. 4). This 
 
 u 'V a ' 'c ' c ' 'H 
 
 Fig. 4. Vowel quality of the voice and accuracy (Table VI). 
 
 shows graphically the algebraic average of the records (G. C. E.) 
 for each of the vowels and for the three levels, 144 v.d., 182 v.d. 
 and 240 v.d. There is a tendency for the vowels to fall into three 
 groups: namely, (i) sung the lowest, (2) a, e and possibly u 
 sung moderately sharp and (3) i sung decidedly sharp. These facts 
 would seem to point to the general conclusion that the higher the 
 dominating overtone in a vowel clang, the higher that vowel will 
 be sung. In Fig. 4, u offers the single exception to that rule. 
 
40 WALTER R. MILES 
 
 The hum was supposed to be neutral as it was moderately weak 
 and the record was made from the nasal breath. This assumption is 
 confirmed by the record which gives the hum a middle place with 
 a and e. 
 
 It must be remembered that there is, in the foregoing records 
 which were sung on a, a tendency to sharp by about the amount of 
 sharp for a here. That tendency is probably due to some other cause 
 than timbre. It may therefore be suggested that a and e, the vowels 
 usually sung when one is free, are fairly neutral; o (and possibly 
 u) are sung relatively flat and i relatively sharp. This view, it 
 will be observed, is confirmed by the hum. 
 
 Our results seem to differ radically from those of Berlage (4), 
 second part of item 4, in the observations which are common to 
 both. But our method also was radically different ; moreover, his 
 conclusion (item 4) is somewhat modified when we read in his 
 article p. 76 where the results of the vowel experiments are dis- 
 cussed. "Accordingly one may look upon a slight increase in the 
 variable error as probable with vowel change" (i.e. when the ob- 
 server tries to reproduce his own pitch but on a different vowel) . . . 
 "other generalities cannot be deduced for the table ..." 
 
 These results in reference to vowel quality are of so far reaching 
 significance for speech and song that we may not venture further 
 discussion for the matter must be made a special object of investiga- 
 tion for verification of the empirical data and in search of an inter- 
 pretation. It seems safe however to proceed in our work using "a" 
 as the vowel quality for reproductions. 
 
 EXPERIMENTS SERIES VI : ACCURACY IN SINGING 
 
 Having gained some insight concerning the influence of voice 
 range, standard tone intensity, *voice volume, standard tone timbre, 
 and voice timbre, on the accuracy of voice control, we now turn to 
 the main problems of our research. These may be restated as 
 follows : ( I ) What is the average error of the human voice in 
 reproducing the pitch of a tone? (2) What is the average minimal 
 producible change of the voice? (3) Is there any general tendency 
 to sing sharp or flat? (4) How does the average performance 
 of men and women compare on the above three points? All the 
 studies referred to in the historical account contain results which 
 cast light on some of these problems. But in almost every case these 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 41 
 
 results and problems are secondary to the main interest of the study; 
 and moreover the number of observers and observations is usually 
 quite limited. In Series VI therefore, we have made these problems 
 the central issue on a large group of persons to give our results 
 significance as norms. 
 
 Apparatus and method 
 
 Standards. With the aid of the tonoscope, eleven large disc forks 
 were tuned to the following pitches: 128, 128.5, 129, 130, 131, 133, 
 136, 140, 145, 151, and 158 v.d. The series of pitch increments be- 
 tween the forks was therefore: .5, i, 2, 3, 5, 8, 12, 17, 23, and 
 30 v.d. as measured from 128 v.d. This series of tones was used for 
 men. For the women a second set was provided on 256 v.d. as a 
 basis, namely, 256, 256.5, 257, 258, 259, 261, 264, 268, 273, 279, 
 and 286 v.d. In this second set it will be noted that the same pitch 
 increment (absolute) were used as in the 128 v.d. set instead of the 
 relatively equal increments. In this respect the procedure was based 
 upon the conclusions reached in Series I. 
 
 Koenig resonators were provided for each set of forks. As the 
 increments were small it was found that one resonator would speak 
 sufficiently well to several tones. In the case of the 128 set three 
 resonators were used: first, 128 v.d. to and including 136; second, 
 140 and 145 v.d.; and third, 151 and 158 v.d. For the higher set 
 two resonators were found sufficient : first, 256 v.d. to and including 
 268 v.d. ; and second, 273, 279, and 286 v.d. Both series of forks as 
 reinforced by the resonators gave tones of pleasing quality and 
 medium intensity. 
 
 Observers. Two hundred and one individuals, ninety-four men 
 and one hundred and seven women, took the test which is about to 
 be described. This number comprised those enrolled in the elemen- 
 tary psychology courses in the University of Iowa, 1912-1913. Of 
 these about one hundred fifteen were sophomores ; the remaining 
 were upperclassmen. None of them had had any practice in this 
 test. Among them were some excellent vocalists and some others 
 who claimed never even to hum or whistle and to have difficulty in 
 recognizing old and familiar tunes if unaccompanied by words. No 
 one was excused because of his inability and no one was selected 
 because of ability, for it was desired in so far as possible to secure 
 what might be considered an average group. A previous lecture on 
 
42 WALTER R. MILES 
 
 the measurement of musical capacity had successfully aroused the 
 interest of the observers so that they entered into the experiment 
 with zest, many of them desiring to secure their individual results. 
 
 The charge. The instructions were given by word of mouth to 
 each person, although the appointments were so arranged that one 
 observer was present while another was taking the test and so be- 
 came familiar with the procedure before he actually entered upon it. 
 Supposing the observer to be a man the instructions would be as 
 follows : 
 
 "Mr. , we have here a series of eleven tuning forks. This 
 
 one (striking the 128 v.d. and presenting it before the resonator) 
 is c below "middle c", it is a tone of 128 v.d., the lowest tone in the 
 series ; we will call it "o". This one (striking and presenting the in- 
 crement fork 30, 158 v.d.) is considerably higher than o as you 
 easily notice, and is the highest one in the group. These other forks 
 all represent pitches between the two which we have sounded. The 
 test to-day consists in singing these eleven tones one after the other 
 as they are given. They will be presented in pairs. First we will 
 sound the o, the lowest one of the tones; you will listen carefully 
 to it and then sing a tone of the same pitch. Immediately after your 
 singing, the highest tone in the group (30, 158 v.d.) will be sounded; 
 you will listen and sing that one. Then the o will be sounded again 
 and, after you sing it, there will come the next to the highest tone 
 (23, 151 v.d.) ; and so on we will come down one step at a time 
 always reproducing the o before each of the interval forks. When 
 you have tried all the tones in the series you will go back over them 
 in the reverse order. Simply imitate as nearly as possible the pitch 
 of each tone as it is given, always remembering that the o is the 
 lowest one in the series. Sing all the tones with a natural voice 
 volume and use the vowel "a" (a as in "ah") and whenever you 
 feel dissatisfied with any trial ask for a repetition." 
 
 Following these instructions, in order to put the observer at ease 
 and to satisfy his curiosity, the experimenter gave a brief explanation 
 and demonstration of reading on the tonoscope. 
 
 The test. The forks were presented to the resonator by a helper 
 who gave his attention solely to the task of sounding the tones in the 
 right order and with as nearly uniform intensity and duration as 
 possible. The tones w^ere sounded with medium intensity varying 
 towards the "weak." The observer sat on a high stool or stood at 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 43 
 
 the side of the instrument in a position which kept him from seeing 
 his own record. He sang the tones into a metal speaking-tube 
 placing the lips lightly against the fingers of the hand which grasped 
 the mouthpiece. The arm was supported by an adjustable rest and, 
 so far as could be, strain and unnaturalness were avoided. 
 
 A few preliminary trials were given on increment 0-30 in order 
 that the observer might find himself becoming somewhat familiar, 
 not only with the tonal range covered by the standards but with the 
 experience of taking pitch from a tuning fork. The series was then 
 given in pairs in the following order: 0-30, 0-23, 0-17, 0-12, 0-8. 
 0-5, 0-2, o-i, 0-.5; 0-.5, o-i, 0-2, etc., back to 0-30. The complete 
 test consisted in singing the series thus five times. This gave one 
 hundred reproductions of the 0, and ten on each of the increment 
 tones, a total of two hundred tones for each observer. This series 
 therefore contains forty thousand records. The test as outlined 
 could not be performed with care in less than 30 minutes. In 
 some cases and especially with non-musical persons a much longer 
 time was required than this. 
 
 Throughout the test we endeavored to keep the observer seriously 
 trying to sing the exact pitch of the forks. To this end it was deemed 
 desirable to ofi^er some encouragement, especially during the first 
 fifth of the experiment, no matter how poor or good the record. 
 It was observed that encouragement did not cause the singers to 
 be self-satisfied or careless but rather served to make them try the 
 harder. It helped moreover to create an atmosphere of ease and 
 naturalness. But while there was encouragement there was also 
 some criticism. If, for example, the observer was singing the o 
 flat 5 or 6 v.d. regularly he was told to listen more carefully to the 
 standard and to make sure that he had the right pitch but no intima- 
 tion was given as to the character of the error. Little rest periods 
 of twenty seconds were rather frequent and were found to be of 
 much service. Many times it was noted that after such a period the 
 errors were decidedly smaller than before. 
 
 A few questions concerning the observer's musical education, 
 voice range, and ability to play and sing were asked during or fol- 
 lowing the experiment and the answers together with some com- 
 ments regarding his performance of the test were made matters of 
 record. 
 
44 WALTER R. MILES 
 
 Justification of procedure 
 
 Before considering the results of this series it remains to justify 
 the form of procedure as outlined above in the light of the sources 
 of error revealed by our previous experiments and by those of other 
 investigators. 
 
 Voice level of test. Our experiments (Series I) on the accuracy 
 of pitch singing within the voice range demonstrated that the errors 
 are relatively smaller on the higher tones. Unpracticed observers 
 however, will much more readily try a tone that is medium or low 
 than one that is high. It therefore seemed best for general testing 
 to choose a voice level which all would recognize as being well within 
 range. The selection of 128 to 158 v.d. for men and of 256 to 286 
 v.d. for women is thus the result of considerable experience in test- 
 ing groups of individuals, and seems further justifiable on the 
 grounds of pitch discrimination as previously stated. 
 
 Forks for standards. Tuning forks were retained for standards 
 even though the records of Series IV indicate that the organ pipe 
 and dichord can be imitated more accurately. Forks are very sim- 
 ple, easily manipulated, of practically constant timbre, and at the 
 same time reliable in pitch. And if, as in our test, a series of tones 
 differing from each other by slight degrees of pitch is desired to be 
 sounded in rapid succession, tuning forks are the most reliable 
 apparatus. Furthermore they are used so little for general musical 
 purposes that in testing with them no group of observers is given 
 undue advantage. 
 
 Many standards vs. one standard. Berlage (2) found that his 
 observers could reproduce their own voice tones more accurately 
 than tones given by some one else, the increase of precision show- 
 ing itself chiefly in a decrease of the constant error. We have fre- 
 quently noticed a tendency, which is a corollary of Berlage's con- 
 clusion. Observers when making successive trials on the same 
 standard very often reproduce their own reproductions rather than 
 make new efforts at imitating the real standard. The observer finds 
 it much easier to reproduce his own previous tone, duplicating the 
 muscle tension and mouth resonance which he experienced at that 
 time and felt to be satisfactory. Indeed, even though he conscien- 
 tiously work against this tendency, he can not overcome it entirely if 
 engaged in making successive trials where the pauses between are 
 brief. This is confirmed by the fact that frequently when observers 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 45 
 
 for some cause or other have been dissatisfied with attempts and de- 
 sired new trials giving them immediately they would in the new trials 
 unconsciously repeat the identical pitch given before. This same 
 tendency has sometimes been evident even in large and unusual errors 
 which the experimenter might rule out, asking for new trials. In view 
 of these considerations it seemed best in our general test to adopt 
 the principle of many standard tones and no successive trials on the 
 same tone. 
 
 The increments between the forks were made small and of vary- 
 ing magnitudes for two reasons : first, in using these small increments 
 we do not complicate our work with the factor of musical intervals, 
 and second, in using a series of small increments we make possible 
 the measurement also of the ability to make faint shadings (sharp or 
 fiat) in the pitch of the voice. The selection of increments is arbi- 
 trary. These particular steps were chosen because they have been 
 found satisfactory in work with pitch discrimination (21) at the 
 level of 435 v.d. and, as stated before, extensive research by Vance 
 (26) and others shows that pitch discrimination is practically con- 
 stant in terms of vibration frequency in the middle range of tonal 
 hearing here covered. This is also the ground for making the in- 
 crements for the women the same number of vibrations instead of 
 the relative parts of a tone, in which case they would have been 
 doubled. 
 
 Sounding the two tones. Seashore and Jenner (19) employed the 
 method of "least producible, or minimal, change". The observer 
 sang the standard or a tone at a given interval from it and then re- 
 produced his own reproduction, save that he made it "the least pos- 
 sible" sharp or flat according as the experimenter might direct. 
 While this will undoubtedly become a standard method in extensive 
 work with an observer it is not suited to tests of a single sitting, 
 first, because ability is rapidly improved by practice and, second, 
 because the observer tends to be easily satisfied with his effort. The 
 better way is not to rely on the changing subjective standard of the 
 observer but to provide a series of constant objective increments 
 and give him the opportunity to find his own level as by the method 
 of constant stimuli in lifted weights or pitch discrimination. Such 
 a series has been provided in the standards and increments men- 
 tioned above. 
 
 Order of standards. Manifestly the standards might be presented' 
 
46 WALTER R. MILES 
 
 to the observer in any one of a number of different orders. After 
 trying out the matter thoroughly with the help of three good ob- 
 servers we selected the order of presentation above described for the 
 following reasons: (i) to give the tones in pairs (0-30, 0-23, etc.) 
 takes direct advantage of all the latitude which the series provides. 
 Most observers can easily detect the difference 0-30, while many 
 (theoretically about 25 per cent.) would be baffled to find a differ- 
 ence between 23 and 30; (2) to begin with the largest increment 
 and work towards the smallest has the double advantage of es- 
 tablishing confidence in the attitude of the subject and of stimu- 
 lating effort; (3) to give the increments in a series and in double 
 fatigue order rests the voice from the unusual strain of making 
 the least producible change, and (4) to explain definitely at the 
 beginning of the test that all the increments are in one direction, 
 i.e. above the o, simplifies the problem and puts it more definitely 
 under control than if uncertainty as to change of direction in stand- 
 ards were allowed. The test is therefore not to measure the judg- 
 ment for direction of pitch difference but the judgment and expres- 
 sion of the amount of pitch difference between two tones. In pitch 
 discrimination it is well known that much depends upon the direc- 
 tion of the expectant attention.^- And should we present the stand- 
 ards of our test in a chance order we would complicate it exceedingly 
 at the critical point of the smallest increments. 
 
 Time intervals. At the very beginning of the test the intention 
 was to allow an interval of i second between the breaking off of the 
 standard tone and the singing by the observer. But the method 
 
 ^An idea of the influence of this same source of error operating in the 
 field of singing may be gained from the following illustration. The author 
 in instructing a very fine observer thoughtlessly said, (the error was alto- 
 gether unintentional) ; "We have here two forks, the first, 128 v.d., and the 
 other one 3 v.d. higher, 131 v.d. You will please sing them one after the 
 other. I will give the lower one first." Then the forks were presented and 
 reproduced as directed. When we came to the twelfth trial the observer 
 remarked : "I seem to feel strain to bring the 131 v.d. up". In the moment of 
 reflection following this remark the writer recognized that he had made a 
 mistake in instructing the subject, as the so-called "131 v.d." was really 3 v.d. 
 " lower than 128 v.d., or 125 v.d. We find in the twelve trials made that the 
 average reproduction of 128 v.d. is 123.6 v.d. while the average pitch given for 
 the supposed 131 v.d. (really 125 v.d.) is 124 v.d. The misunderstanding 
 and therefore expectant attention changed the direction of the reproductions, 
 and brought in much larger constant errors than are usual for this indi- 
 vidual. It should also be noted that the errors are minus. 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 47 
 
 was soon given up as, in this case, cumbersome and unpractical, and 
 furthermore we did not care to compHcate our test with the factor 
 of tone memory. (See Berlage (2) and Sokolowsky (22) ). 
 The observers in their usual singing with musical instruments make 
 no such perceptible time intervals. They sing with the tones of the 
 instrument, perhaps holding them somewhat longer than is done by 
 the instrum.ent. When the standard has been sounded the atten- 
 tion is centered, the muscles of the larynx almost involuntarily 
 assume a particular tension and it is unnatural to wait for the 
 beating of a metronome or some other signal to begin singing. 
 If the unpracticed observer is told to make his own interval, un- 
 less checked up diligently, he will very soon be making intervals 
 that are exceedingly short, if indeed he is not singing simultaneously 
 with the standard tones. The method followed therefore was to 
 sound the forks for approximately i second, encouraging the ob- 
 server to begin his tone during the sounding of the fork and to hold 
 it longer than the fork. 
 
 It may be objected that one might sing fairly accurately judging 
 simply on the secondary criterion of beats between his voice and the 
 standard tone. Helmholtz indeed (9 p. 326) suggests this as a 
 convenient method for the singer to use for checking his own accu- 
 racy in practice exercises. While it would be possible for a highly 
 practiced observer it can hardly have much influence in our test. The 
 author made it a point to question frequently regarding the way 
 observers judged of their success in reproducing tones and was not 
 able to find any one who knowingly made use of this criterion. It is 
 however quite possible that the roughness of 6 or 8 or more beats 
 per second may occasionally have caused some observer to be dis- 
 satisfied with his attempt. But the tonal fluctuations and adjust- 
 ments which are necessary to bring about a lessening of the fre- 
 quency of beats between the voice and an outside standard are 
 easily recognized with the tonoscope; no such "finding" process 
 was observed. 
 
 Another time interval which must be considered is that between 
 the o (128 or 256 v.d.) and the increment fork of any particular 
 pair. In order that the standards for minimal change of voice may 
 have their greatest value the interval indicated must be as short as 
 possible admitting of a quick, direct comparison of tones; other- 
 wise the test practically resolves itself into the singing of a single 
 
48 WALTER R. MILES 
 
 tone. Hence the presentation of the increment fork followed 
 immediately upon the close of the observer's reproduction of o, 
 the subject being encouraged to make the reproduction about i 
 second in length. The increment forks were struck while the o was 
 being reproduced. This was, however, no distraction as only a 
 slight blow on the practically noiseless sounder was necessary, and 
 the forks could not be heard until presented before the resonators. 
 Following the reproduction of each increment fork there was a 
 period of about 2.5 seconds before the next sounding of o. 
 
 Other factors. In the matter of intensity of standard and in- 
 tensity and vowel quality of the voice we took direct advantage of 
 our previous work and adopted such conditions as would give the 
 most normal results according to those findings. By the use of 
 resonators at a considerable distance from the observer's ear w'e 
 found a satisfactory means of controlling the intensity of the 
 standards, ^^ while the intensity of the voice had to be judged sub- 
 jectively and watched by the experimenter. And in the selec- 
 tion of "a' we are using that vowel quality which according to 
 Berlage and our own results afifects least the constant error of the 
 reproductions. 
 
 Tables of data 
 
 The constant error (C. E.) and mean variation (m.v.) were found 
 for the ten trials on each fork of the ten pairs given in the test. 
 These twenty C. E.'s and twenty m.v.'s for each individual tested 
 are embodied in Table VII, which has been divided into two parts, 
 A. and B., for the men and women respectively. In the first column 
 of the table, at the left, are given the numbers which stand for the 
 individual observers. This numbering is in no sense a ranking, but 
 simply for convenience in handling the data and aid in identifica- 
 tion. Odd numbers are used throughout to refer to women and 
 even numbers to men. The second column from the left shows the 
 C. E. and m.v. (the latter is under the former) for the ten trials 
 on o. when used in the pair 0-30. The same measures for the ten 
 trials on variant (or interval) tone 30 are given in column three, 
 and each of the successive smaller increments are represented in 
 the same manner. The arithmetic averages for the constant error 
 
 " It is possible that the pitch of a standard is not only varied by its intensity 
 but also by its position when held near the ear. 
 
: 1 
 
 5 „ 
 
 
 I I 
 
 T +"+"T"?-?"T"+"7"+"T-i-T-T + + ? V^ +' 
 
 3^=23 
 
 T"T" 
 
 I I + 
 
 + + 
 
 + + 
 
 
 + + 
 
 ^■ssn^S'?^ 
 
 Tf f^T 
 
 
 ■'+''+''+"l"i"?'^:"+"+'|"+"+''" ■■"?'?" ■ 
 
 5 +-;-;-+ °-?'j-7-T-|-+-+ :?-+"+-+-? + i ° + +"t ?. + + + ? + + + i i 
 
 « ^3J-JS3.;j»j~j-jp-}«j-j-4:-|-^:^|-:|;-5^"j"Y-'^-|-.|--.:f":f-=;'-jj:-5™f-5.":f-f ■■^-+-jf-4;";f-j"!f''5.-'4:-':f'J-|-:^~j ^ + + + ? + + + + + + ? + + + + + + + j + + + J ? + | +" + "+ + + +"+"+ ?*?'+'?"* :f + * + + + + + + + + + + + ? + + ?.T + + 
 
 T + + T + I 
 
 . ., -, :■:-.-;;-■■ T 3»;'g -TJT joj^e- ^^=3 :;7'S'S 32 2 
 
 +"? r 
 
 
 * |'j'$=}'i-t-t'?-:f'-+"?"*-?-r +"+ 4: + t *"* + '"*" +"* +T- + * + + + + * + + i"r+ + + » + ? + + ? + * + * + + +"+"+: |'|"$'$"j ? t + + + + •"ijf-y-:;-^-'^:"^-^-'^":?. :fjt + + + + + ^-+ + + t + + ?:f + + jf + 
 
 
 ? ?:! 
 
 + + + 
 
 + + + 
 
 
 rrr 
 
 I) «c^ii?fl -^c cc (if. T«!a5»; 1 
 
 
 I 
 
 
 fliip«q isoNQujq-o. 
 
 i"*" 
 
 q TOS'JSQq iTfl f^ "f 
 
 "+"4'* 4^" + "?" + "+" + "' 
 
 "'-° ;^"+"^^-+-+''+"+ T + ■?■ +"+"■¥"! +"+"+" "+"+"+ 
 
 T"?- 1 "+"+'■ 
 
 -r-r-^ ■»«'fla)T«<* Ro«« 
 
 1-« TleflB-fl* TO T^'0«i23'^* ""^ "^ 
 
 
 ?SS'S*3S3 
 
 1-1 T>>-7«rTS0.«ia«o«((!»i'iB-'O,*;«TP>oqc««*Qq T-It1 
 
 + 4-+T+ + + + tT T+ + + f + + 
 
 ,,.^.,„ 
 
 +"!"+"+ +-^"T"^ f-i-^-f^+'T +'+"+"+'+ ""+"?"+"? ?"t"T''-?"+"*"+"? + + t"+"T"^~t"+ + ?-~+"T"+"+" +"+ + + + +"+ + + +"+"+ +"+"+ + + + ^ + 
 
 ■+"j"^~T +"+"7*'^ f-+"+-f + T + +"?"+ +" +"T" T"T"'r"'T ?'"r'"+'"+"H^ ^_---_«^-^-,|-^-- +"+"h^ ?*■■?■"+ +"?"■?■ +"+ + +"+ i + + +"1"'+ + + + + + ■+ + + 
 
 ^ 4- WIS-*" 
 
 ? §■ f ^ 
 
 ll=? 
 
 f 
 
 ? 
 
 + 
 
 <•>? 
 
 S-"-5 
 
 s 
 
 3»-S 
 
 : o<s 
 
 ?^"? 
 
 t 
 
 5e«-? 
 
 
 + 
 
 1 
 
 sa ft" i;« 
 
 e 
 A 
 ■? 
 
 + 
 
 3B3-«K 
 
 
 + 
 -+ 
 
 s. 
 
 l«'°f| 
 
 s 
 
 ^^"'B 
 
 - 
 
 
 
 
 5 
 
 ^rtij 
 
 1- 
 
 f*-3| 
 
 " - - I 
 
 « - ~+ 
 "+ 
 
 ^'■S>? ^-s>? 
 
 - T"? 
 
 : ? 
 
 + + + + + + | + + + + +l+ + + + + + + +T+ + + f7+4:+ + + + + + +T+ + + + + + + + + + + + + + + + + + + + + + + +T+ + 
 
 + ti-f + + +ffTTtT'+?+T + ?TTTi+ + + T + T ' ' i44+ifTTf7iiT + + + +T+i i7++iT'+TTii iTTT7''++' I'^i'f+i |-TitTTT++7+TT+T 
 + 1+^ +-fi Ti7iT+i+TT+rTri+++l + iTTl+ + + +ri iTTlTi +^ ^ + T*TTi+Tl I ill ii 
 
 V\ T * + ^ + 
 
 
 "T'^ f * ^n 
 
 '^^B*^3*-'"y^°''' '''^'^"' ''" 3'"'2'^2*'' ^T". •?■ 
 
 r^-rri-'r^ v^-vrv 
 
 I T"T''T"7 T'"?"+ + T T + T 
 
 
 +''+"T'?'' 
 
 -r+-t T-T T T-ri" 
 
 ,„j..„.. 
 
 «^c.^«^««-,;| _jn2-,y«_,,« 
 
 -•fl «lllf«.«! T 
 
 ''S5S!£)J2'*'SI!JS25 2S?5S!22JA5"3^riS'322.S'i^?3S'S;^;:;'3J?2S53J^"'^S2'^f -JRI-^T^a 2q'*>«!'P'fit;VJ-'»«3iy-)'q q'^«!r"^'>5'J'^T'l')PT«!'?'^33<*'-'iq»-a! o<i-r>-.!f "rTS>e'"5t?Toj"! q-- -^-n" '-qoo a 'jo?fi.nuj-->n>?-tj'nTPoqo?<!t>r»«!.qi^uj-^-»-T.5q>ni><ji?oqs^tii^'7uii;oq -■>>«- ««>«<>! 
 
 ?-rrrrnTP!'rr?'fTF*''rtTrr?-rn7-T^I'rn-r11'rT^fTrT-T-T=^^ 
 
 + + + + + + } + + + + + + + + + + +Tf + +-:^ + + + + 3. + 3. + + + + ? + + 3 + + + + + ?- + + ?T + + T + 4-3- +T _"|";:";f"jf 2»a»:p 41 ^»^,jp™^™^ .,|.;j.-^».«»»^,^.--.-;^ + + + ^"«~i +-^ + 3 + 3 + 3 
 
 qq Tjj^i^'D 
 
 f'''^*q P '^^'S P 'J'T'O'^'^ ""^P^-t^jq"-*! f 7 f> 5 =? 5 '2'^ 525q=flTa^1P1 "7^ T-t*- fP TI ^t?* 1 '^--qs^" n ■n<.«>*9)<J n-- CT.ir.-i. .-ininqq(-.oOio-IT'>'>ortici-fmi. « ^TT-'Q^'^'-tTn'o- ";"iq>o-t'»-«'r ")T»io " ^o o « n o o r. o»o - - -rnni-.OHtMn-ioon ono ptio-MS- cote i^—soe« in- TiO •) - fl« "i>>0 tfJTOO h-no n-fliq 
 
 rrri 
 
 T-J-yqqqi^"? 
 
 frt- 
 
 ^...j.f... 
 
 T + +T + 5L + + 3 + + I + + + + + + + +-+ +I+ + + 3- + + +:t + + "•■+ :^"+ J + :f + ? + + + + +"+"^'+"1 3;"j"j _».~«™,jj,,n«-,^»«.^„^, -„„ 
 
 r,.?<^»i^Qq.^l^.BqFtB;-n-.vi--»u>-;<>^>|.q-74q>qqK^q'ir} 
 
 "n^i'iT-n-q-q"-*q''« 4w «q>n-.^^»q- — '5.>o^-t'»>^ 
 
 + i-f + + + :j + +™ T + T + + I + + + 
 
 f-r° I ^ i r^ rrVrrl 1-1-""-+ 
 
 ? T"T''T'i% ^ i"fTT-rT T + +"+ rri rrrvvrrri ^ v^"\~i r 
 
 ■>'fl'^31'2SSSS?^ .^t^(,-r.^Bi«?«-Q-5(>^r,^(iq-^q,,<^q.;5q<9~t>Tqq<>«yq-T5-7>>t»»'n'7qqh.'n--r,ino.«n 
 
 ITI+ + T+I + ITI 
 
 ■Yi^i^f 
 
 m 1 ' 
 
 ■f"t"T 1*7 4"+ ?"7 +-f-t-7^ T" 
 
 T "-3<>!'P-7' 
 
 "% T" 
 
 + 'rt f-t-rf"T"t 
 
 T I I + + + t 4 + + + TV jp T-| T":f t t + + ^ + ^"hL 5: ^^"5 3 3 +-?-+''+-f 3 + T 3 
 
 "t~+"T"r 
 
 =?Tqq'P"5i?«iP'^ti<! 3'ii"">'ot-<?'if>5 3*S'5f^'>;*"'''^ 
 
 !" * T-fT''T-T"+ T"'^-T"+'+ T 
 
 f •*!•** ri-fr*- 
 
 +T+++++++++ 
 
 ?r^:j-J-'f|3fps'spi|ipi''^5pps'='j'5^spppj-3-jj;::p^'j:p8=j333j:'f;pp|S3:a=!jp^^ 
 
 ■^f-i-r^^i^f 
 
 c 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 49 
 
 (C. E.) and the mean variations (m.v.) on both standard and 
 variant are presented in the two columns headed O. V. (Arith- 
 metic). The algebraic averages for the constant errors (C. E.) on 
 both standard and variant are given in the two O. V. columns at the 
 extreme right of the table.^* 
 
 The consolidated footings for Table VII, section A and B, are 
 given in Table VIII. The top notation is thus the same as in 
 Table VII. A contains the final footings for men and B for women. 
 The footings are set out as follows : Ave. m.v. is the average 
 mean variation for the respective points in terms of vibrations ; 
 C. E. % -f-, the per cent, of individuals who made a constant error 
 in the direction of a sharp ; ^ — , the per cent, of those who flatted ; 
 % O, the per cent, of those who made no appreciable constant error 
 in the ten trials; C. E., v.d., the average magnitude in vibrations of 
 the constant errors, without regard to sign ; and G. C. E. v.d. the 
 tendency of the constant erors for the group, the algebraic mean. 
 At the right, the grand averages for both groups are presented under 
 the headings designated above. 
 
 Comparison of the abilities of men and women 
 
 The most striking general feature of these experiments is the 
 the fact that women show the same ability as men, vibration for 
 vibration, although the women sang an octave higher than the men. 
 
 The data on which this assertion is based may be traced most 
 readily in the curves, Figs. 5-8, 10. In Fig. 5 C. it is seen that the 
 curves for the average constant errors on the standard as well as 
 on the variant practically coincide. On the standard they are 
 almost straight lines, the variation for the men being from 1.36 v.d. 
 to 1.66 v.d. with an average of 1.54 v.d., while in the case of the 
 women the variation of this measure is from 1.52 v.d. to 1.81 v.d. 
 with an average of 1.65 v.d. The curves for the variants do not 
 come so near coinciding; they are of the same form, but the 
 women have the advantage, their range of C. E. falling between 
 1.69 v.d. and 6.71 v.d. with an average of 4.86 v.d., while that for 
 the men lies between 2.59 v.d. and 7.15 v.d. with an average of 
 5.32 v.d. As further confirmation of the fact that the average con- 
 
 " There would be little gained by placing E., the crude error, in our table as 
 this measure is something of a cross between C. E. and m.v. and serves 
 simply to indicate the distribution of the constant errors. 
 
50 
 
 WALTER R. MILES 
 
 
 
 0.5 O.d, 
 
 Fig. 5. The data in Table VIII. If there had been no errors all curves 
 would coincide with the base line. The amount of deviation is indicated at 
 the left in terms of vibrations : the increments on the base line. O denotes 
 the standards (128 v.d. for men and 256 v.d. for women); V the variants; 
 C. E. average (arithmetic) constant error; G. C. E. the algebraic constant 
 error or general tendency of the group ; and m.v. the mean variation. 
 G. C. E. above the base indicates plus or sharp and below minus or flat. 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 
 
 51 
 
 
 0-30 0Z3 on 0-iz oB ft? 03 c*2 or 
 Fig. 6. Intervals as sung. (Table VIII). The distribution of the group 
 constant errors ( G. C. E. ) for the standards (128 and 256 v.d.) and the 
 variant in each interval. The intervals represented by the forks are shown 
 in the heavy solid curves with which the other curves would coincide were 
 there no errors in singing. 
 
 '6 
 
 14 
 IZ 
 10 
 6 
 6 
 <} 
 
 Z 
 
 -Men 
 
 Women 
 
 
 1 i m\ \/ •■•'-'^ 
 
 1 I 
 
 ../ I I V I \|— I— f— i---l 
 
 u 
 
 — . -f- ''*-• 
 
 x^d 10 1.5 20 15 3.0 JJ W 45 50 5.5 6.0 65 7.0 7.5 80 
 
 Fig. 7. The distribution of the average constant errors of all intervals 
 for each observer with reference to the magnitude of the error. The data 
 for this figure are found in the columns headed Arithmetic Average in 
 Table VII. O, the standard tone: V, the variant. 
 
52 
 
 WALTER R. MILES 
 
 Standard 
 Variant 
 
 ^ k 5 i^.-^ 9.5 5 S5 6 65 7 75 Q 05 9 35 lO lOSIt 
 
 Fig. 8. Distribution of constant error, flat being denoted by 
 the base and sharp by -|- above. 
 
 — below 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 53 
 
 stant errors for both men and women represent approximately equal 
 magnitudes attention is called to Fig. 7 in which is presented the 
 distribution of the average constant errors of all intervals for each 
 observer with reference to the magnitude of the error. The men have 
 a slightly better record on the O. but the women have a more than 
 compensating advantage on the V. 
 
 A corresponding agreement in the records for men and women 
 is seen also in the constant tendency for the group (G. C. E. Fig. 
 5 A and B, 6, and 8 A and B). While the women tend to sharp and 
 the men to flat on the standard (see Fig. 6) the amount is not far 
 from equal in the two cases. (Cf. Table VIII, 65 per cent, of men 
 flat on O while 67 per cent, of women sharp). In view of the 
 general tendency of both men and women to sharp on the variant 
 this difi^erence in the tendency on the standard gives an advantage 
 to the women as regards accuracy in the singing of the interval. 
 An advantage which amounts to an average of over 2.0 v.d. 
 
 Women 
 
 O.d 10 1.5 Z.0 Z5 3.0 JS W f.5 SO dS 6.0 6.5 7.0 
 
 15 
 
 Fig. 9. The distribution of the mean variation (m.v.) for individuals 
 (Table VII, average m.v. at right) with reference to the magnitude of the 
 variations. O, m.v. of the standard tone; V, m.v. of the variant. 
 
 In the mean variation (Figs. 5 and 9), which is an important 
 criterion, the advantage is more clearly in favor of the women, 
 particularly in the singing of the variant. There are more men than 
 women with a relatively large variation : but the mode in the case 
 of O is slightly better for the men than for the women. The averages 
 
54 WALTER R. MILES 
 
 of the men (Table VIII) are 1.54 and 3.05 v.d. as against 1.29 and 
 2.21 v.d. for women. 
 
 Taking all the data into account the general balance of all scores 
 results practically in a draw :^^ men and women sing with equal 
 accuracy (in terms of number of vibrations of error) although 
 the former sing at 128 v.d. and the latter at 256 v.d. If on the 
 other hand we count the error in lelative parts of a tone instead of 
 vibration for vibration, the women sing twice as accurately as the 
 men. It may, however, be shown that the former statement repre- 
 sents the more logical point of view. 
 
 This result is in harmony with the results found in Series I with 
 reference to accuracy within the tonal range. It was there found 
 that so long as the singer was certainly within his natural range the 
 man could sing the two tones here considered, 128 v.d. and 256 v.d., 
 with nearly equal accuracy, in terms of vibrations and that, there- 
 fore, he tended to sing the higher twice as accurately as the lower. 
 The difference here discussed is therefore not peculiarly a sex 
 difference, but distinctly a matter of psycho-physic law of voice 
 control within the tonal range. Men and women have equal ability 
 in pitch discrimination (reference 21 p. 44), so also in voice control 
 they have equal ability level for level within the tonal range. The 
 fact however remains that women's voices are pitched in a higher 
 register than men's voices and therefore, from the musical point of 
 view, they can sing their tones relatively more accurately. 
 
 This result is, after all what we should expect for the principal 
 limit upon accuracy in singing is accuracy in hearing and we know 
 that both men and women can hear a difference of, e.g., i v.d. as 
 easily at 256 v.d. as at 128 v.d. 
 
 The mean variation 
 
 Fig. 5 shows that the mean variation is larger for the variants 
 than for the standards. This is because the former are more 
 difficult. It should be noted that this difference in the mean varia- 
 tion is a measure of the relative difficulty of the two tones as felt 
 
 "The following facts are significant: (i) there are fewer poor observers 
 among the women ; (2) women have smaller mean variations than men ; and 
 (3) women more nearly reproduce the intervals. It seems quite likely that in 
 a mixed college group such as we have here, the women give more attention 
 to vocal music than do the men, which may account for their superiority 
 in this test. 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 55 
 
 and would also be a measure of the relative degree of accuracy 
 in the singing of them were it not for the operation of the two 
 motives for sharping the variant about the middle of the series of 
 the increments. The fact that the mean variation is unaffected by 
 the operation of these two motives is an indication of their fairly 
 rigid operation. 
 
 The constant error 
 
 Figs. 5 and 6 show that the singing of the standard tone is not 
 affected by the magnitude of the increment to be sung. The constant 
 error is small and uniform. This is due partly to the fact that the 
 standard tone was the same in all trials and therefore tended to 
 become more or less automatic, and partly to the fact that the 
 standard was sung first and that therefore the difficulty in marking 
 off the interval would tend to crop out in the variant tone. 
 
 The singing of the variant follows the law that ( i ) all these small 
 increments are overestimated and that (2) this overestimation in- 
 creases gradually from the largest interval (0-30) and reaches a 
 maximum in the cases of both men and women (Fig. 5, A and B) 
 at the 5 v.d. interval from which it gradually again diminishes. 
 
 There are probably several motives operating to produce this 
 overestimation; the fact that the maximum falls in the increment 
 5 v.d. points to a relationship between the hearing and the singing 
 of the interval. The median for the least perceptible difference in 
 pitch for this same group of individuals falls on 3 v.d. The incre- 
 ment 5 v.d. in singing would therefore represent one of the smallest 
 increments actually heard. The distribution around this would be 
 analogous to the distribution of the records in pitch discrimination 
 for this group. 
 
 It is probable that, as in visual perception of space, all small 
 angles are overestimated, there is in hearing of pitch a tendency to 
 overestimate the smallest increments perceived. If we represent the 
 uniformly increasing series of increments of pitch difference as a 
 sharp wedge the apparent magnitude would be represented by a 
 wedge blunted and thickened. 
 
 The operation of such a principle has been demonstrated for hear- 
 ing in the matter of localization of sound. Starch (23) found that 
 when a correction is made for the least perceptible change in the 
 direction of the source this correction is always overdone. 
 
 The lack of fine control of the voice to reproduce the smallest 
 
56 WALTER R. MILES 
 
 differences that are heard is another element involved. This factor 
 is partly due to lack of knowledge and practice in this kind of voice 
 control. The small differences which are actually heard larger than 
 they really are, are sung still larger on account of this general lack 
 of control for the making of fine shadings in pitch. This overdoing 
 of a difference may perhaps be regarded as another phase of the 
 same principle as the overestimation of small differences in pitch in 
 hearing. At any rate the enlarging of the small discriminated in- 
 crements is without doubt much increased in the singing. These 
 small increments are overestimated in hearing (when heard) and are 
 again overdone in the singing; and that this enlarging is propor- 
 tionate up to the threshold for pitch discrimination. 
 
 In applying these principles to the interpretation of the relative 
 magnitude of the errors in the singing of these increments we must 
 bear in mind that where the small differences are not heard there 
 would be a tendency to repeat the standard in trying to sing the 
 variant — this happens not only because the difference is not heard, 
 but even when an effort is made to sing an imperceptible sharp 
 theoretically known to exist there is a tendency for the voice to 
 "fall into the groove" of the standard tone which has been sung im- 
 mediately before. 
 
 On the other hand it seems reasonable to take account of the 
 fact that in this test we are asking the observer to do something 
 with which he is almost entirely unfamiliar. In the larger intervals 
 he recognizes differences but overestimates and oversings them. 
 This overestimation increases regularly from the largest interval, 
 0-30, to 0-5, as was above noted. At 0-3 most of the observers fail 
 to hear the difference because the conditions of the test do not 
 provide the immediately successive presentation which is most fav- 
 orable for the discrimination of pitch differences. Therefore, at 
 0-3 failing to hear the second fork higher, recognizing that he has 
 not yet reached the smallest possible interval, and knowing that the 
 second fork is higher than the O, our observer concentrates his 
 attention, trying harder and harder until the last interval is sung. 
 He is in large measure freed from the factor of overestimation in 
 hearing for he hears no difference. He will very likely tell you 
 that the forks sound just alike, but he knows and is reminded that 
 the second one of each pair is higher. This knowledge forms the 
 basis of his control of the voice. Quite naturally under the circum- 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 57 
 
 stances he resorts to the tendency (noted above) to take his cue for 
 the second tone not from the fork but from his own previous tone. 
 He "falls into the groove", however, just long enough to get his 
 bearings, then sharps from this point, the magnitude of the sharp 
 being governed roughly by the subject's pitch discrimination ability. 
 In about 8 per cent, of the individual records of 0-.5 the records on 
 the .5 v.d. are not sharp or may be slightly fiat; in other words, the 
 observers took the risk of making no sharp. 
 
 Applying these factors in the interpretation of the error in the 
 singing of these small intervals of different magnitude, we find that, 
 ( I ) the average overestimation is relatively small for the smallest 
 increments because in many cases the difference is not heard and in 
 singing a very small interval the voice uses its previous reproduction 
 as the standard, sharping from it, and (2) the overestimation of 
 the small increment is greatest for the smallest increments per- 
 ceived and gradually diminishes as the increments grow larger so 
 that it tends to disappear on the average when the magnitude of a 
 half-tone is reached. Therefore, our test seems to have met the 
 conditions for measuring the minimal producible change in the 
 pitch of the voice. The increments from 0-30 to 0-5 serve to work 
 down the voice, to make clear to the observer what is to be done, 
 and to center his attention for most careful control. The four 
 smaller increments, 0-3 to 0-.5 are the place where the "ability to 
 make faint shadings" is really tested and under usual conditions 
 the reproductions on the smallest increment, 0-.5, would seem to 
 give the best measure. 
 
 If from the records on 0-.5 (algebraic C. E. or G. C. E.) we 
 compute the magnitude of the smallest interval as actually produced 
 by the individual observers and distribute these magnitudes accord- 
 ing to their frequency, we have the curves of Fig. 12. The median 
 value of the measures represented in Fig. 12 is 4.0 v.d. for women 
 and 4.5 v.d. for men. There are more extremely poor observers 
 among the men so that the average smallest intervals produced are 
 5.6 v.d. and 3.7 v.d. for men and women respectively.^'' These median 
 values are in harmony with the results for pitch discrimination and 
 may be taken as measures of the ability to produce minimal changes 
 sharp or flat in the pitch of the voice. 
 
 '°A part of this difference between men and women is to be accounted 
 for in the fact that on the average the men flatted the O. 
 
58 
 
 WALTER R. MILES 
 
 Dr. D. A. Anderson made a test on "minimal change in the pitch 
 of the voice" in the Iowa Psychological Laboratory in 1909. His 
 observers imitated the pitch of one standard fork and then sang 
 the tone the least possible sharp or flat according as directed, making 
 ten successive trials in each direction. There were 115 women and 
 65 men in the group tested. From the unpublished results of this 
 test we learn that the average minimal producible change for men 
 was 5.5 v.d. and for women 4.6 v.d as against 5.6 v.d. and 2)-7 v.d. 
 in our test. In comparing these results it must however be noted 
 that 45 of Professor Anderson's poorest observers, most of them 
 men, made no records which entered into his averages. 
 
 Seashore (19) reports the results of some tests of "minimal 
 prpducible change" given to a small group of observers. The 
 average records for six men on five successive days are as follows ; 
 3.4. 3.5, 3.0, 2.6, and 2.7 v.d. Evidently the factor of practice entered 
 here. However, the average of these results, which represents 
 the only other available data on this ability in voice control, falls 
 on the mode of our curve (Fig. 12) for men. 
 
 /O II IZ /J 14 15 
 
 Fig. 10. Distribution of the magnitudes of the smallest interval actu- 
 ally produced by men and women. The method of computing the average 
 magnitude of the smallest interval produced by each observer is illustrated 
 in the following example: if the C. E. on O is —.9 v.d. and on V is +1.4 v.d. 
 then the produced interval would equal the difference between —.9 v.d. and 
 +1.4 v.d. plus .5 v.d. (the real step between the forks) = 2.8 v.d. If the 
 C. E. on O is plus it is of course subtracted from the sum of C.E. on V 
 and .5 v.d. Men dotted line; women broken line. 
 
 The average constant error (C. E.) on the standard is small and 
 uniform, as is also the mean variation and the constant tendency 
 for the group, (G. C. E. on the standard). Accuracy in the stand- 
 ard is not influenced by any difference in the magnitude of the in- 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 
 
 59 
 
 crements. This is chiefly because the standard tone was sung before 
 the variant was sounded, and partly because a sort of "rut" was 
 formed for the singing of the repeated standard. 
 
 The researches previously reviewed contain scattered measures 
 on this ability. Kliinder (i) found that he could reproduce an 
 organ tone of 128 v.d. with an average crude error of .47 v.d. He 
 rejected however the records of some other observers who showed 
 larger errors. Cameron (4) worked with seven observers and tried 
 a number of organ tones. The records by three of these observers 
 gave an average error of about 6.6 v.d. Berlage (2), whose three 
 observers reproduced voice tones, does not give the pitch of the 
 standards. The average error for the three men, singing with an 
 interval of from i second to 2 seconds, is .50 v.d.^' Seashore (19) 
 gives 1.2 v.d. as the average error of 100 trials by each of six men, on 
 standard 100 v.d. Sokolowsky (22) with his seven professional 
 singers finds an average error of i v.d. at the average pitch of 
 251 v.d. 
 
 The group constant error 
 
 Throughout the previous pages there have been references to the 
 tendency of both men and women to sing sharp when reproducing a 
 tone. The difference in the direction of this error in the standard 
 for men and for women is so constant that, while small, it points 
 to some motive in the character of the tone, the mode of singing, or 
 some tendency characteristic of a given pitch level. The distribution 
 seen in Figs. 7 and 8 shows that the sharps and the flats are not far 
 from equal both in the number and the magnitude for men; for 
 women the sharps predominate in both magnitude and number. 
 
 Cameron (4) noticed this tendency and called attention to it. 
 In his experiments it appeared especially in sustained tones. ^"^ We 
 have not worked with sustained tones but have found the same 
 
 ^' Berlage's tables are needlessly complicated by his using the signs with 
 opposite from the usual meaning. 
 
 ^'^ Berlage (2) did not find this tendency to sharp and was surprised, but 
 we must remember that he worked with voice tones for standards (the 
 richest tone possible) and our experiments seem to show that with rich 
 standard tones the sharping of the constant error is considerably decreased. 
 Sokolowsky's (22) results are also negative as regards any general ten- 
 dency for both sexes to sing sharp. The errors on the twenty tones sung 
 by women, however, shozv an algebraic average of +/.oj z'.d.. although 
 eleven of these tones were sung flat. 
 
6o WALTER R. MILES 
 
 tendency with reproductions of one and two seconds in length. 
 Reference to our tables (G. C. E.) will show that almost without 
 exception sharping is the predominant direction of the constant 
 errors in all six series of our experiments. The tendency to sing 
 sharp is not materially alTected by the level of the pitch so long as 
 the tone remains within the range of the voice ; it is increased by loud 
 volume of voice, weak volume of standard, certain vowel formants 
 such as are found in "e" and "i'", and by purity of the standard 
 tones. 
 
 The best cases 
 
 The question naturally arises, to what extent the presence of a 
 few cases of very large error affect the averages. To cast some 
 light on this and also to gain an idea of the performance of the best 
 observers in the group the author made a selection of twenty-five 
 persons of each sex. The selection was made chiefly on the basis 
 of a small Ave. m.v. in the standard (o). The size of the Ave. C. E. 
 of o and the Ave. m.v. for the increments, were used as secondary 
 criteria. There are some records, for example N. 9, which from the 
 standpoint of the constant errors alone are very near the ideal curves, 
 but because of rather large mean variations must be omitted from 
 these selected groups. The selection of women was as follows : 
 Nos. I, 3, 13, 15, 21, 55, 61, 63, 77, 85, 93, 97, 105, 107, 113, 117, 
 125, 153, 159, 169, 177, 181, 183, 201, and 209. The men's records 
 chosen were: Nos: 6, 8, 10, 12, 16, 28, 50, 62, 68, 72, 82, 88, 102, 
 106, no, 114, 120, 126, 128, 144, 146, 148, 154, 156, and 164. 
 
 The separate tabulation of these fifty supposedly best cases re- 
 veals the presence of the same general tendencies in these selected 
 groups as have been noted in the large groups, with the difference 
 that they are not so pronounced and that here the men in a relative 
 comparison make a better showing than the women, in that their 
 overestimation especially of the smaller pitch increments is less. 
 Therefore blame for the large errors (overestimation of intervals) 
 can hardly be shifted to a few individuals as indeed we might have 
 shown by referring to Figs. 7 and 8 which demonstrate that the 
 distribution of the errors forms fairly normal frequency curves. 
 
 Correlation of singing zvith pitch discrimination 
 
 Pitch discrimination records are available for eighty-two of the 
 men, and one hundred and four of the women V\^ho acted as observers 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 6i 
 
 in our tests. The well-known formula of the Pearson "Product- 
 Moments" was employed and resulted in the following correlations : 
 
 r P.E.r 
 Men: Size of ave. smallest interval produced with Pitch. Disc. +.21 .072 
 
 Women : 
 
 m.v. on 0. 
 
 
 u 
 
 il i 
 
 +.04 
 
 .074 
 
 C.E. on 0. 
 
 
 u 
 
 n > 
 
 ' +.08 
 
 .074 
 
 m.v. on V. 
 
 
 (t 
 
 it i 
 
 +.33 
 
 .066 
 
 C.E. on V. 
 
 
 it 
 
 ti 
 
 ' +.15 
 
 .073. 
 
 smallest interval 
 
 produced 
 
 n 
 
 it 
 
 " —.11 
 
 .065 
 
 m.v. on 0. 
 
 
 it 
 
 il • 
 
 +.27 
 
 .061 
 
 C.E. on 0. 
 
 
 ti 
 
 ti t 
 
 +.11 
 
 .065 
 
 m.v. on V. 
 
 
 « 
 
 it < 
 
 +.51 
 
 .048 
 
 C E. on V. 
 
 
 « 
 
 it 
 
 ' -.07 
 
 .065 
 
 It will be recalled that in order to be satisfactory a coefficient 
 "should be perhaps three to five times as large" as its probable error. 
 This rule liberally applied to our results leaves us the coefficients 
 -I-.33 and -(-.51 both of unquestionable reliability. These coefficients 
 represent the correlation between pitch discrimination and the aver- 
 age mean variation in singing the intervals, for men and women 
 respectively. 
 
 The Test of ipio 
 
 A series of musical tests, given by the writer in the Iowa Psycho- 
 logical Laboratory, during November and December of 1910, in- 
 cluded one on Accuracy in Reproducing Tones. There were ninety 
 men and one hundred and seven women, members of the elementary 
 psychology classes who took this test. 
 
 The apparatus besides the tonoscope consisted of five large forks 
 with pitches as follows: 128, 256, 320, 384, and 512 v.d. The ex- 
 perimenter instructed the observer to take the 256 v.d. fork, strike 
 it gently, bring it to his ear, listen carefully, and then to reproduce 
 the same pitch. This he repeated with fork 256 v.d. Then taking 
 the 320 v.d. fork he proceeded as described. The last four forks 
 were gone over five times in this manner, which gives ten trials 
 on each tone, forty trials in all. The test is thus very simple, the re- 
 production of four tones (two successive trials on each) which 
 are at the same time natural musical intervals: major third, fifth and 
 octave. No restrictions were placed upon the observer in the matter 
 of humming or singing with the standards. As the fork was in his 
 hand he sang with it or after it as seemed best to him. About one- 
 half the observers preferred to take the fork away from the ear 
 before beginning to sing. The men sang the tones one octave below 
 
62 WALTER R. MILES 
 
 the pitch of the fork. When it was difficult for them to commence 
 doing this, the 128 v.d. standard was used for orientation. 
 
 The results for this series of 8,000 reproductions are given in 
 Table IX. The notation is the same as in Table VIII. The test of 
 19 10 was complicated by the factor of natural musical intervals, it 
 was also considerably shorter and simpler than the one of 1913 but 
 in comparing it with the latter we find the results in practical agree- 
 ment on some points. 
 
 (i). There is a uniform tendency for the majority of observers 
 to sing sharp. Here again the tendency appears to be greater for 
 women than for men, the G. C. E, for men being +.26 v.d., for 
 
 TABLE IX. Accuracy of singing: test of 1910 
 
 90 men 128 v.d. 
 
 160 v.d. 
 
 192 v.d. 
 
 256 v.d. 
 
 Ave. m.v. 1.42 
 
 1.36 
 
 1.43 
 
 1.79 
 
 % + C. E. 47 
 
 63 
 
 51 
 
 63 
 
 % - C. E. S3 
 
 37 
 
 49 
 
 37 
 
 Av C. C. 1.62 
 
 1.62 
 
 1.72 
 
 2.70 
 
 G. C. E. + .26 
 
 + .65 
 
 — .06 
 
 + 1.06 
 
 107 
 
 
 
 
 women 256 v.d. 
 
 320 v.d. 
 
 384 v.d. 
 
 512 v.d. 
 
 Ave. m.v. 1.89 
 
 2.15 
 
 2.07 
 
 2.83 
 
 % + C. E. 81 
 
 90 
 
 84 
 
 86 
 
 % — C. E. 19 
 
 10 
 
 16 
 
 14 
 
 Av. C. E. 2.59 
 
 3-91 
 
 3-47 
 
 5 -90 
 
 G. C. E. +2.39 
 
 +3-36 
 
 +3.1 1 
 
 +4.76 
 
 women -|- 2.39 v.d., a difference of 2.13 v.d. as contrasted with 1.30 
 v.d. in the previous measurements. In the test of 1910, as mentioned, 
 the men and women used the same forks, the men singing the stand- 
 ards one octave low. Therefore the tendency for men to sing less 
 sharp than women in the 1913 experiments can hardly be attrabuted 
 to a timbre or sound volume difference between the sets of forks. 
 The men are must more evenly divided between the sharping and 
 flatting tendencies than the women, for example on 256 v.d. the one 
 tone which both sexes had in common, the percentages in favor of 
 sharping are 63 and 86 for men and women respectively. (2) The 
 average constant error (arithmetic) on 128 v.d. is slightly larger in 
 1910, 1.62 v.d. as against 1.54 v.d. The mean variation for 128 v.d. 
 are 1.42 v.d. (1910) and 1.54 v.d. These differences are rather 
 slight. (3) Men and women sing their one common tone (256 v.d.) 
 
ACCURACY OF VOICE IN SIMPLE PITCH SINGING 63 
 
 with equal accuracy: m.v. 1.79 v.d., Av. C. E., 2.70 v.d. (men) to 
 m.v., 1.89 v.d., Av. C. E. 2.59 (women). It would seem from a com- 
 parison of available norms for voice range in the sexes (Helm- 
 holtz (9) and Zahm (27) that 256 v.d. should be about as high for 
 men as it is low for women, and that it is well within the average 
 range of both. We have here therefore a confirmation of our 
 previous conclusion, i.e., that men and women sing with equal 
 accuracy vibration for vibration. However the errors in this case 
 under consideration (1910) are much larger than the results of 
 Series VI would lead us to expect. This is true of all the tones 
 sung by the women and renders them incomparable with the pre- 
 vious results. 
 
 Recommendations toward a standard test 
 The recommendations which follow must be considered as pre- 
 liminary and as applying simply to the two measures of singing 
 ability considered throughout this study, i.e., the ability of the 
 voice to reproduce pitch, and the ability to produce voluntarily 
 small changes sharp or flat in the pitch of the voice. 
 
 1. The two factors may be tested together with advantage. They 
 are closely related phases of the same thing. Neither of them should 
 be taken in combination with such factors as accuracy of tone mem- 
 ory, or judgment for musical intervals. 
 
 2. Use a graded series of standard tones similar to that commonly 
 employed in testing for pitch discrimination. Such a series has ob- 
 vious advantages over the use of a single standard; (i) If several 
 observations are to be made at a single sitting the efifects of practice 
 are not so great. (2) The small pitch intervals make clear to the ob- 
 server what he is expected to do with his voice. (3) The variety 
 of standards (and hence degrees of difficulty) reduce monotony 
 and fatigue. A graded series furthermore has advantage over 
 any other series : ( i ) it keeps the test comparatively free from 
 complication with the singing of musical intervals, and (2) when 
 the standards represent small steps of pitch difiference the observer 
 discriminates more carefully and is not so Hkely to be satisfied with 
 a mere approximation. 
 
 3. Use tuning forks for standards. They are very easily manip- 
 ulated, are not subject to certain sources of error commonly met in 
 the control of reeds, pipes and strings, and are readily arranged 
 
64 WALTER R. MILES 
 
 into a graded series as recommended above. Any disadvantage, if 
 indeed it may be so called, from the standpoint of the purity of the 
 fork tone seems more than compensated for in having a definable 
 quality and a standard on which all observers are equally 
 unpracticed. 
 
 4. Begin with the largest pitch increments and proceed to the 
 smallest and then in reverse order back to the largest. This will 
 economize effort, provide the best practice, and help to control tha 
 attention. For general testing ten intervals representing as many 
 degrees of difficulty, ranging from 0-30 to 0-.5 are not too many. 
 For extensive testing of one observer or in working with highly 
 practiced observers the increments which are distinctly above the 
 threshold for pitch discrimination may be omitted. 
 
 5. Give the tones in pairs, presenting the variant tone imme- 
 diately after the reproduction of the standard, thus securing a rapid 
 adjustment which favors discrimination in the kinaesthetic sensations 
 from the larynx. As an alternative procedure the two tones 
 might be presented in immediate succession as in the pitch discrim- 
 ination tests, the observer carrying the standard in mind while 
 listening to the variant, and then singing them in quick succession. 
 
 6. Control conditions : ( i ) The forks should be presented be- 
 fore resonators which are some distance from the observer and care 
 must be exercised to present them with uniform intensity. (2) 
 The observer should use a medium volume of voice in singing the 
 tones. (3) The experimenter should select the vowel to be sung 
 and insist on a good quality. (4) If time intervals are used be- 
 tween standards and reproductions they should be short, not longer 
 than two seconds at most. (5) Time intervals should be introduced 
 between pairs of tones. These should be at least 2 seconds in length. 
 Longer intervals would doubtless be better as the voice could the 
 more easily be kept out of a "rut" in reproducing the standard. 
 (6) Secure effort on the part of the observer who is too easily 
 satisfied with his own performance. 
 
 Our test is one of motor control. As a musical test it bears the 
 same relation to the motor side as pitch discrimination does to the 
 sensory side. In fact it is in a practical way for the motor pitch dis- 
 crimination of the singer, and as far as singing is concerned it is 
 more important than simple sensory pitch discrimination. 
 

 
 ACCURACY OF VOICE IN SIMPLE PITCH SINGING 65 
 
 SUMMARY OF CONCLUSIONS 
 Among others the following general conclusions may be gleaned 
 from the foregoing experiments. 
 
 1. The human voice is about equally accurate, in terms of vibra- 
 tion, at all points well within its range ; therefore, the high tones are 
 sung relatively (per cent.) more exactly than those which are low. 
 
 2. A strong standard tone (especially with low forks) is repro- 
 duced as decidedly lower than a weak standard. 
 
 3. The voice can most easily reproduce pitch for those standard 
 tones which have a rich timbre, such as the organ tone. 
 
 4. Measured in terms of average error the voice is less accurate 
 when its volume is large. 
 
 5. Vowel quality affects the accuracy of vocal reproduction of 
 tones. The "a'" (as i in machine) is reproduced the highest, "0" 
 the lowest, and "a" occupies a middle position. 
 
 6. Men and women sing in their representative ranges with equal 
 accuracy vibration of error. 
 
 7. Women show better relative voice control than men, if judged 
 on the basis of their mean variation. 
 
 8. With women there is a general tendency to sing sharp. Men 
 are about equally divided in this regard, sharping however being 
 slightly more frequent. 
 
 9. The average error of the voice in reproducing a tone given 
 by a fork is 1.5 v.d. for men at range 128 v.d., and 1.5 v.d. for 
 women at 256 v.d. in a representative group of students. 
 
 10. A small perceptible pitch difference between two tones is 
 overestimated in the singing. 
 
 11. The average minimal producible change of the voice for men 
 at 128 v.d. is about 5.5 v.d., and for women at 256 v.d. it is 3.5 v.d. 
 
 REFERENCES 
 
 1. Anderson, D. A. The Effect of Intensity on the Apparent 
 Pitch of Tones in the Middle Range. (In this Volume.) 
 
 2. Blake, The Use of the Membrana Tympani as a Phonauto- 
 graph and Logograph. Arch, of Opthal. and Otol., 1876. V. 
 
 3. Berlage, F. Der Einfluss von Artikulation und Gehor beim 
 Nachsingen von Stimmklangen. Psychol. Stud., 1910, VI, 
 39-140. 
 
 4. Cameron, E. H. Tonal Reactions. Psychol. Rev., Monog. 
 Suppl, 1907, VIII, 227-300. 
 
 5. Grutzner, Die Stimme. 1907. 
 
G6 WALTER R. MILES ^ 
 
 6. Guttman, A. Zur Psychophysik des Gesanges. Zsch. f. Psy- 
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 7. Gutzmann, H. A. K. Physiologie der Stimme und Sprache. 
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 12. Kliinder, Ad. Ueber die Genauigkeit der Stimme. Arch. f. 
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 19. Seashore, C. E. and Jenner, E. A. Training the Voice by the Aid 
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 20. Seashore, C. E. A Voice Tonoscope. Iowa Stud, in Psychol., 
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 22. Sokolowsky, R. Ueber die Genauigkeit des Nachsingens von 
 Tonen bei Berufssangern. Beitr. z Anat., Physiol., Path, usw. 
 von Passow u. Schaefer., 1911, V. 
 
 23. Starch, D. Perimetry of the Localization of Sound. (lozm 
 Stud, in Psychol., V, 1-55) Psychol. Rev. Monog.. IX. 
 
 24. Stern, H. Gesangphysiolgie und Gesangpadogogik ihren 
 Beziehungen zur Frage der Muskelempfindungen und der beim 
 Singen am Schadel und am Thorax fiihlbaren Vibrationen. 
 Monat. f. Ohrenhk., 1912, XLVI, 337-352. 
 
 25. Stumpf, C. Tonpsychologie. 1883. 
 
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 27. Zahm, J. A. Sound and Music. Chicago; McClurg 1892. 
 
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