A study of tonal attributes.

Originally published in The American Journal of Psychology, 30(2), 121-64, 1919

Gilbert J. Rich, Psychological Laboratory of Cornell University

Table of contents

Introduction
I. Historical Review
II. Observers, Apparatus and Procedure
III. Vocality

Preliminary Training
Method of Paired Comparisons
Vocal Limens
Discussion

IV. Pitch
V. Volume
VI. Brightness
VII. Tonality
VIII. Criticism of Previous Experimental Work
Conclusions

The pendular vibrations which form the simplest sound-waves of physics, and which are correlated with the tonal sensations of psychology, have the characteristics of amplitude and frequency. We were formerly taught that the amplitude of the wave corresponds, on the side of sensation, to the single attribute of intensity, and the frequency of the wave to the single attribute of pitch. But if we examine tonal sensations closely, we find a number of psychological characteristics. One may say, for example, that a given tone is high or low, large or small, bright or dull; that it is the musical note c or d, or that it resembles the vowel O or the vowel U. Is every one of these judgments based on a separate attribute of the tonal sensation? Do some among them represent different attitudes taken up toward the same attribute? Or are certain of them made upon an integrative or associative rather than upon an attributive basis? These questions constitute the problem of the present study.

I. Historical review.

The problem, as such, is of recent date. The observations that give rise to it are, to be sure, much older. Stumpf[1] shows that the similarity of tones standing an octave apart is recognized both in music and in the earlier psychologies. The similarity of certain tones to vowels also receives early recognition. Willis[2], in 1828, says that "vowels are a different affection of sound from both pitch and quality, and must be carefully distinguished from them." Hensen[3], in 1891, is another observer who notices the specific vowel-qualities of certain tones. It is a common observation that low tones are large and massive as compared with higher tones. Mach[4] holds that all tones are composed of varying proportions of two elements, the one bright and the other dull.

The systematic treatment of these characteristics in relation to attributes starts with Stumpf. In the first volume of his Tonpsychologie, he discusses the characteristics of volume[5] and brightness (Ibid., 221), denying that either is an attribute, and holding that both are matters of association only. But in the second volume of the same work (Ibid, 2, 1890, 56; 336; 535; 539), some seven years later, he takes the position that tones possess an attribute of extension or volume, parallel to pitch. Volume, pitch, and intrinsic intensity (with which we are not here concerned) form together his Tonfarbe. Brightness, however, he does not consider a separate attribute. Nor does he admit any attributive basis for the similarity of the octave, which is for him based on degree of fusion[6].

McDougall[7] separates pitch into two attributes. The one of these, quality, is common to the given tone and to all its upper and lower octaves; so that all the qualities of tonal sensation are contained within a single octave. The other attribute, which distinguishes the same tone in different octaves, is "of the same order as differences of extensity in the case of visual, tactual, or temperature sensations."

M. Meyer[8], in 1903, postulates two attributes of tones, that change with the physical frequency. These he calls Tonhöhe and Tonfarbe (pitch and quality, in English). Tonhöhe is lacking in noises. In the following year, he enlarges upon the difference between the two attributes.[9] The difference between tones and noises, he holds, can be understood only if we assume that one attribute, namely pitch, is lacking in noises; for if we can say that one noise is higher than another, we cannot name the interval between them. Similarly, very high and very low tones, which are often called noises, can be judged only in terms of quality. Music, then, depends upon pitch, to which unmusical persons are deaf. The similarity of the octave, Meyer further says, can be explained by the assumption of two attributes of tone; but the details of such an explanation are not worked out. Later, after Révész and Köhler have published their work, Meyer[10] insists that his pitch and quality are identical with Révész' Qualität and Höhe respectively, and his quality with Köhler's Vokälitat.

Dunlap[11] (1905, amplified 1912) calls attention to the common observation that low tones are large or voluminous. "Differences in pitch," he says, "are directly comparable to differences in planar linear extent." He therefore designates pitch as the extensive attribute of tone, excluding any attributive multiplicity.

Brentano[12] (1907) posits two tonal attributes. The one, Qualität, recurs at every octave; the other, Höhe, is composed of bright and dull factors, which unite in continuously varying degrees to form every tone in the scale.

In 1908, Titchener[13] distinguishes two Qualitätive attributes of tones, pitch and volume. Tones vary in volume, the low tones being large and massive, the high tones shrill, thin, and sharp. This difference is not spatial. Volume is not an intensive attribute, but a Qualitätive attribute, moving between the extremes of mild and shrill. Volume and pitch, moreover, are independently variable, in the sense that at the two ends of the scale volume changes more quickly than pitch, while over the middle region it changes more slowly.

The next contribution to the problem is that of Köhler (1909, 1910, and 1913), who deals with vocality. We are not ourselves concerned with the vowel-theories with which he principally deals. In his first paper[14], Köhler records the observation that the tones of certain tuning-forks sound like the different vowels. His second paper[15] reports a continuation of experimental work along the line thus suggested. In the preliminary experiments the observers are required to report what vowels the tones of various tuning-forks resemble. They find that some resemble the pure vowels U, O, A, E, and I, while others stand between two of these vowels. This similarity appears to be something given directly in the tones and not due to association; but the introspective data are scanty. In the main experiment, the observers make similar reports of the vocality of 30 forks presented 15 times in haphazard order. The reports show, on the average, a regular progression of the vowel qualities up the scale in the order U, O, A, E, I, though sometimes an Ä is found between A and E. Tones lying between two of the pure vowels are like both of the adjacent vowels. On the basis of these results, Köhler postulates a Qualitätive attribute of tones, alongside of pitch, which he calls Qualität, Vokalqualität, and later Vokalität (vocality). He next attempts to find the turning points (die ausgezeichneten Punkte) of the phenomenological system of vocalities. Working with pure tones, he starts with a "mixed" vowel and changes the frequency of vibration until the observer reports a pure vowel, continuing until a trace of the vowel next beyond is heard; a number of series is taken in both directions. The whole set of turning points from the semi-vowel M, which Köhler finds below U, to I are in almost exact octave relations. In a third paper[16], Köhler considers the vocality of very high tones. At succeeding octaves above I he hears S, F, and Ch, and insists that these sounds are tones, not merely noises.  (It would seem that Köhler means by "tone" any sensation aroused by a regular periodic sound wave, and not a particular form of experience.)

Révész, in 1912 and 1913[17], observes that there are two ways of taking the tones which stand an octave apart. If we take them in the one way, they are the most dissimilar tones within the octave; if we take them in the other way, they are the most similar. This latter similarity he calls "octave-similarity." He therefore presents to his observers series of pure tones, asking them which are the most similar, and finds that the octaves are so judged. Treating these phenomenological observations on the systematic side, Révész posits two attributes of tonal sensation. That which recurs at every octave he calls Qualität (quality) ; that which is different in different octaves he terms Höhe (pitch). He then proceeds to show that these two attributes are independently variable. In the first place, two tones can be judged as different when their physical frequencies differ so slightly that the direction of the difference cannot be stated, Since such a judgment is a judgment of quality but not of pitch, the differential limen is lower for quality than for pitch. Secondly, the same quality occurs with different pitches in the case of two tones standing an octave apart. Thirdly, Révész has discovered a pathological subject for whom quality is displaced in the one ear for a certain range of the scale, without any corresponding displacement of pitch. Fourthly, tones near the upper and lower limits of hearing, as well as the sensations of melody-deaf persons, lack quality though they possess pitch; for it can be said that one such tone is higher than another, but not that it is the octave of the other. Révész accepts Köhler's attribute of vocality, but does not identify it either with his pitch or with his quality.

Stumpf reviews the work of Révész and Köhler before the Sixth Congress for Experimental Psychology.[18] He accepts Révész' distinction of quality and pitch as attributes of tone, and specifically identifies the impressions of pitch and brightness. But he criticizes a number of the proofs brought forward by Révész in the attempt to show independent variability. The conclusions drawn from the pathological case, as well as the statement that the differential limen is lower for quality than for pitch, go further than the facts justify. Other interpretations are possible; for an observer should be able to tell the direction of a quality-difference as well as the direction of a pitch-difference. Stumpf tries some of the experiments of Köhler for himself, and fails to find a regularity of judgment. Some of the observers cannot distinguish any pure vowels in tones, while others can hear only U and I. As all of Köhler's pure vowels come at the note c, Stumpf thinks it possible that Köhler's observers came to call the quality c a pure vowel, a turning point in the tonal system. The different vowels, then, are simply the same quality with different pitches or brightnesses; O is a bright U, and so on. Thus Stumpf declines to admit vocality to his list of attributes, of which he now has three: namely, Qualität, Helligkeit (brightness), and volume.

Watt[19] (1914) is unwilling to accept Köhler's work on the vowel-qualities, which he considers as apart from the tonal series. He does, however, accept Révész' distinction of two attributes, which he calls pitch and volume. His pitch is equivalent to the Qualität of Révész; his volume is an attribute which changes continuously over the scale, and which he identifies with the Hdhe of Révész. He supports it by citing the usual phenomenological observations of the voluminous character of the tonal series. In his last paper[20] (1915), Köhler takes up the problem of the tonal attributes as such, and starts with a series of definitions. Tonhöhe (which we shall translate as "musical pitch") is that attribute by which tones are named and intervals judged. "Brightness" is used for auditory phenomena which give the impression of brightness; a further characterization is not possible. "Vocality" is used as in his earlier works. Brightness and vocality taken together are designated as Tonkörper (tone-body). Volume and intensity also belong to the tone-body, but are irrelevant to the discussion. Köhler now cites instances to show that musical pitch and tone-body are independent. In the upper range of the musical scale judgments of interval are displaced, while the turning-points of the vocality-series are not. In the pathological subject on whom Révész experiments, the octave-relation of the pure vowels is normal within the affected region, so that only musical pitch (and not tone-body) is displaced. Moreover, very high tones, very low tones, and the tonal sensations of unmusical subjects lack musical pitch, while tone-body is present.

Köhler's main experiment (1910) on vocality is repeated by Modell and Rich[21], with the variation that a serial instead of a haphazard order is used for presentation of the stimuli. The results are similar to those of Köhler, save that the exact octave-relation between the pure vowels is not found. Weiss[22] reports similar experiments with variable results. He attempts to identify vocality with Titchener's attribute of volume.

In 1916, Rich[23] publishes a study of the attribute of volume. His method of attack is a determination of the differential limen for volume-judgments at six points on the tonal scale. The results show that judgments of volume can be made with ease and readiness, and that they appear to be made upon an attributive basis. The limen for volume is everywhere higher than the pitch-limen; moreover, it tends to follow Weber's Law. Volume, therefore, satisfies the two criteria of inseparability and independent variability. The results, however, are obtained with tones from variators, and require verification with pure tones.

Watt, in 1917[24], attempts to build up tonal psychology on a new basis. He rejects vocality, as lying outside the tonal series, and octave-quality as being unnecessary for purposes of explanation. He accordingly postulates but two attributes that vary with the physical frequency, pitch and volume. Neither of these is a Qualitätive attribute; for all sounds have one and the same "quality." Watt conceives of pitch as an ordinal attribute, an attribute of position, and of volume as an extensive attribute. Every phenomenological tone (except the very highest) is the sum of a large number of orders. The tonality of these orders constitutes the volume of the tone, while the predominant order gives the tone its characteristic pitch. The volume of any tone includes the volumes of all tones above it, for the volumes are planar and have, longitudinally, a common starting-point at the order of the highest audible tone. In support of his admission of volume as an attribute, Watt quotes the common observation that low tones are large and high tones sharp and thin; notes that the discrimination of pitch is finer than that of volume in the middle of the scale and coarser at the extremes; cites the implication of an extensive attribute inherent in his concept of pitch as order; and states the need of such an attribute for the explanation of fusion. Watt further holds that the judgment of intervals is based on the ratio of the volumes of the two tones. In particular, a given tone has twice the volume of its octave, so that as we go up the scale by octaves the volumes of the tone do not decrease by equal amounts, but are approximately halved.  (The idea that the volume of a tone decreases by halves as the tone becomes an octave higher implies, mathematically, that volume cannot follow Weber's Law: a direct contradiction of the results obtained by Rich. It is worth noting that the whole of Watt's treatment of the attributes is in the interest of their explanatory value for fusion, not in the interest of tonal analysis.)

Table I shows how the attributes postulated by the various writers fit together, those attributes which are similarly defined being listed in the same column. In the first column are to be found the attributes resulting from the judgments "brighter" and "duller," or identified with such judgments. The second column contains the attributes described by the terms "higher" and "lower." The attributes listed in the third column are typified by the judgments "larger" and "smaller." In Column 4 are attributes characterized by the similarity of their tones to some vowel or vowels, as well as proposed attributes later identified by their author with this characterization. Finally, in the last column is the attribute which has been defined only as being constant for a given note in different octaves. In recent works in English this characteristic has been called tonality.[25]

II. Observers, apparatus and procedure.

Nine observers took part in our experiment: Dr. R. M. Ogden (O), professor of education; Dr. H. P. Weld (W), assistant professor of psychology; Dr. K. M. Dallenbach (Da), instructor in psychology; Mr. F. L. Dimmick (Di), assistant in psychology; Miss J. M. Gleason (G), Miss C. L. Friedline (F), Mr. P. T. Young (Y), and Mr. C. M. Clark (C), graduate students in psychology; and Mr. E. de Laski (L), an undergraduate "majoring' in psychology. Of these observers, O, W, and Da were highly trained in psychological observation; Di, G and Y were relatively well trained; while the remaining three, F, C, and L had had comparatively little training. O, W, Y and C were markedly musical; the others, except F, were sufficiently musical to play some instrument or to sing. F turned out to be a typically "unmusical" or "pitch-deaf" subject. This fact was not discovered for some time. Special work was then undertaken, but unfortunately could not be completed. The results obtained with F in the regular series are, of course, valueless: most of the differences employed were considerably below her limen for any form of tonal discrimination. L was peculiar in that he seldom gave judgments of equality, even when the stimuli were objectively equal. The results obtained from him are valueless for our purposes, since they do not fit the phi-gamma hypothesis; they were therefore discarded. All the observers knew the general nature of the problem and were acquainted with earlier theories on the subject. Not all were utilized in every set of determinations; considerations of time frequently prevented.

As sources of tone we had three Stern variators: No. 2, 150-300 vs; No. 4, 300-600 vs; and No. 7, 650-1200 vs. The bottles were blown from a compressed-air system kept at a pressure of 14.6 mm. of mercury. This pressure was too great for use at the mouths of the bottles, and was reduced by a system of valves and pinch-cocks. The actual pressure at the mouths differed from time to time, as it was found necessary to reset the mouths and the pressures (accompanied by a retuning) to meet the needs of different parts of the experiment. The variators were tuned, by comparison with standard Koenig forks, for a temperature of 25° C. The maximal deviation of the experimental room from this temperature was only 5°, giving a maximal temperature-error of 1%. The average error was, of course, much smaller.

To obtain pure tones a set of 24 interference-tubes was employed. Krueger[26] has shown that maximal interference is obtained when the interference-tubes are so placed along the conducting tube that they stand at the nodes of the tone to be eliminated, an integral number of half wave-lengths apart. Most interference-tubes are built to satisfy this requirement only for one region of pitch and its octaves. We desired, however, a more generally serviceable piece of apparatus, that could be adapted for any pitch by adjustment of the distance between the interference-tubes. Accordingly, every interference-tube was mounted separately on a short section of conducting tube (10.1 cm.). Any length of pipe could then be laid between two of these units. The junctions between the sections of the conducting tube were formed by hardwood blocks, bored exactly to accommodate the pipe. The blocks ran upon a hardwood track, and could thus be set readily in the required positions. The conducting tubes and interference-tubes were of brass, of the same diameter, 19 mm. The interference-tubes were fitted with pistons, the maximal length obtainable being 55 cm.  (The apparatus was made to Dr. Titchener's specifications by the C. H. Stoelting Co., of Chicago.)

In setting up this apparatus, we tried at first to use only two rooms, but found it impossible to do so because the brass piping tended either to absorb or to give out sound-waves. When the interference-tubes were placed in the same room with the variator, they absorbed sound-waves from the air of the room; so that a tone eliminated by the earlier tubes might be picked up and transmitted by those further along. On the other hand, when the tubes were placed in a separate room from the sources of sound they gave off sound-waves to the air of this room; so that it was impossible to keep the observers and the tubes in the same room.

Three rooms were therefore used in the experiment. The variators were placed in the first room, before the open end of the tube, over which was fitted a paper funnel, 17 cm. in diameter and 21 cm. long The sounding variator was about 2 m. from the wall through which the tube passed, and about 1.5 m. from the nearest side-wall. On both the side-wall and the wall behind the variator curtains were hung to minimize reflection. The conducting tube ran from this room through a stone wall approximately 55 cm. thick to the middle room, which contained the interference-tubes. The track mentioned above was placed on long tables, and the interference-tubes were set in blocks running along the track. Beyond the interference-tubes the conducting tube passed through a double plaster wall to the room in which the observers sat, and ended flush with the further surface of this wall. Since it was desirable to work with several observers at the same time, three booths were built in the observers' room. The observers sat facing the wall through which the pipe came. A three-way distributor, set in a rubber stopper, was placed in the end of a conducting tube, and the sound was led to the observers by rubber tubing, which terminated in pairs of ear-tubes of the type furnished with the dictaphone. The "ready" and "now" signals were given by a muffled bell, fastened to one of the booths, which was readily heard by the observers when the ear-tubes were in position.

All the stimuli of the experiment were drawn from three regions whose limiting tones were octaves of one another. If, now, the interference-tubes were so placed along the conducting tubes as to lie an integral number of half wave-lengths apart for the overtones of the lowest region we were using, then they must also be at the same time an integral number of half wave-lengths apart for the overtones of octaves of our lowest fundamentals. It was, therefore, not necessary to change the distances between the interference-tubes during the course of the experiment. The first interference-tube was 244.5 cm. from the end of the conducting tube next the variators (these measurements are from center to center of the interference-tubes). The first twelve interference-tubes, set alternately to cut out the second and fourth partials, were 16.2 cm. apart. They were followed by six tubes, 21.7 cm. apart, set for the third partial. The remaining six tubes, set for the fifth partial, were 21.6 cm. apart. From the last interference-tube, the pipe ran 242.2 cm. to the rubber stopper in which was set the three-way distributor.

TABLE II.
Lengths of interference-tubes in cm.

We took advantage of the finding of Köhler[27] that it is possible to set a series of interference-tubes in such Wise as to secure pure tones over a considerable range. To accomplish this result, six interference-tubes designed to absorb the same partial were set at slightly different lengths. Our tubes were set to give pure tones throughout the three ranges: 235 to 295 vs., 470 to 590 vs., and 940 to 1,180 vs. The various lengths of the interference-tubes are shown in Table II. (The zero-point for these measurements is the point at which the flat piston-head of the interference-tube is flush with an element of the inner surface of the conducting tube.) The method of their determination can best be shown by an example, e.g., the second partial of tones in a range 235 to 295 vs. The second partial ot 235 vs. is 470 vs. A tone of this frequency was sounded, and one of the interference-tubes was shifted in and out until the point of maximal absorption was found. A number of trials was made, and the results were averaged. The same procedure was followed with a tone of 590 vs., the second partial of 295 vs. The two lengths thus found were 18.1 and 14.3 cm. The distance between them was then divided into five approximately equal parts (equal to the nearest integer). The four values thus obtained, together with the two extreme values experimentally determined, constituted the lengths at which the six interference-tubes for this partial were set. A similar procedure was followed for the fundamental in the other two regions, and for the third, fourth and fifth partials. All the sixth partials were also eliminated, since their frequencies were odd multiples of the frequencies of the second partials.

Some difficulty was found in keeping constant, throughout any one of these ranges, the intensity of the tone heard by the observers. There are two principal causes of variation. In the first place, the intensity of the tone produced by the variator may not remain constant. We were able to eliminate this source of error, over the relatively small ranges used, by careful adjustment of the air-pressure and the position of the mouth-pieces of the bottles. A second possible cause of differences in intensity lies in the existence of reflected waves, either in the apparatus-room or in the conducting tube, which would intensify certain frequencies and weaken others. Standing waves in the same room with the apparatus were eliminated by curtains hung on the walls of the room, and by the placing of the variators as far from the surrounding walls as conditions would permit. Reflection inside the tube was not stopped; but the conducting tube was made of such a length that reflection did not affect intensity within our range of frequencies. This length (between the last interference-tube and the rubber stopper) was determined empirically.

The sounding of the stimuli was automatic. The supply of air to the variators was controlled by a pinch-cock operated by a solenoid; it was thus possible to regulate electrically the turning on and off of the air. This was done by a rotating commutator, which also made connections for the "ready" signals, single strokes of a muffled bell. The commutator made three revolutions in a minute. The "ready" and "now" signals were separated by 5.2 sec. The first tone came 1 sec. after the "now" signal, and lasted 2.4 sec. After a pause of 2.0 sec., the second tone followed, also with a duration of 2.4 sec. (These times are not exact. They are the times during which the electric current operating the solenoid was flowing. There was undoubtedly some lag in the starting of the variators after the opening of the pinch-cock.) The complete cycle occupied 9 sec., and the observer was allowed ix sec. to record his judgment before the signal for the next pair of stimuli.

The observers all gave written reports. Every observer was furnished with a board-clip containing a mimeographed sheet with space for 90 reports, and blank paper for introspective records. He was also furnished with typewritten instructions.

Our general procedure was a differentiation of the attributes on the basis of their difference-limens. The plan was to put the observer under instructions to judge now one, now another, of the characteristics postulated as attributes, and to determine in every case the least noticeable difference. We hoped by this method to discover, first, whether the various characteristics of pure tones could be admitted to the attributive classification on the basis of independent variability, and secondly, whether the judgments of these characteristics were made upon an attributive or an associative foundation.

The method of constant stimulus differences was used to determine the limen. The instructions, and the pitches employed as stimuli, will be stated under the various attributes. Five comparison stimuli were used in every case, objective equality and two steps above and below. Fifty series (in addition to the preliminary series) were taken for every determination, except with the observers Da and W, who completed thirty-three series only. The stimulus-pairs were given half in each time-order, and the results for the two time-orders were computed together. The order of the stimuli, as well as of the time-orders, was determined by chance; but the same order was followed for all determinations. The limens were computed from the crude data by the phi-gamma hypothesis, Urban's tables being used and the computations checked. Six values were found for every determination, three for the upper limen and three for the lower limen. These were the limen proper (L), the measure of ptecision (h), and the value c h X L, This latter value, since it is independent of the units employed, forms a measure of relative precision, comparable to the "coefficient of variability" of statistical work. L and h are, of course, in terms of vibrations. In addition, the mean difference-limen (half the "interval of uncertainty") was computed for every determination, as average of the upper and lower limens (L) ; as well as the relative difference-limen, which was obtained by dividing the mean difference-limen by the standard stimulus.

III. Vocality.

Preliminary Training. Most of our observers had never made judgments of vocality before this experiment was undertaken. It was therefore necessary to train them in vocality, to teach them what they should look for when they observed the vowel-qualities. The training was accomplished by requiring the observers to give absolute judgments of the vocality of single tones-- much as Köhler did in his early experiments. For this preliminary work, variators were used without the interference-apparatus. The observer sat in the same room with the experimenter, a few feet away and with his back to the variators, and gave his reports orally. A series of 35 tones was made up, ranging by half-tones from 150 to 1,200 vs. During the first few hours of work with every observer, these tones followed one another in ascending or descending serial order; toward the end of the practice a haphazard order was used. Two, three, and occasionally four series were run in the course of an hour's work.

The first set of instructions was as follows:

You will hear a relatively simple tone. Report any resemblance to any vowel or vowels (or semi-vowels), and roughly the degree of that resemblance. This is your main task: but if anything else that is relevant catches your attention, report it also. A tone will be repeated if necessary.  The successive tones will run in order up or down the scale, as announced by the experimenter.

We found that under these instructions the observers tried to fit different vowel-sounds to a tone, and to determine which vowel was most appropriate, rather than to listen for a characteristic of the tone. After a few days, the following instructions were therefore substituted for the original formula:

You will hear a relatively simple tone. Regard it as singing or speaking a vowel (or vowel-like consonant) to you. Report what vowel or vowels you thus hear. This is your main task: but if anything else that is relevant catches your attention, report it also.

The practice was continued until the observer was able to recognize and name the vowel-qualities of the tones with a fair degree of consistency. The time required to reach this stage varied from observer to observer.

One observer, W, was not given any preliminary practice. He had been a subject in the experiment of Modell and Rich, and was able to give vowel-judgments very readily.

Two other observers had had some practice with vowel-qualities, and gave consistent judgments from the first. Di had set up apparatus for the demonstration of vocalities in Dr. Titchener's lecturecourse often enough to be familiar with this character, and to have no difficulty in hearing the vowel-qualities in the tones. He found the pure O and U lower than we had expected from previous investigations, but remained consistent in his reports through some four hours' practice. He says in his reports that "the vowels are very self-evident." C, on the other hand, was acquainted with vowels from the practical rather than the theoretical point of view. Although he had little psychological experience, he had been trained in singing vowels, and was thus able to give judgments that were consistent; they were also in accordance with the findings of Köhler.

Y was also able to make fairly consistent judgments from the first, so that three hours of practice were sufficient in his case. His success in this form of observation was due not so much to his previous training as to the manner in which he went about the task set him. He reports: "I retain the tone, and then catch myself trying to shape my lips and throat so as to form a vowel. Sometimes I hit upon it; sometimes I am very doubtful. When I think of vocality, I think of a spoken vowel, E, I, etc., a voiceness." He had thus followed the instructions implicitly, and had come immediately to the correct method of observing vocality.

Three observers, Da, G, and O evidently relied to some extent upon their theoretical knowledge of vowels. They knew the order in which the vowels should come, in an ascending or descending series; and having given the first judgment, they would report successive vowels less than an octave apart, sometimes only a few notes apart. G, for example, would start with a judgment of M (in an ascending series), and report successively the vowels to I in a little over an octave. Her difficulty is explained in the following report: "Vocality does not 'mean' to me. I judge the vowel spatially by pitch ...I keep unintentionally falling back on what I know from the lectures." It was necessary to demonstrate to her, through speaking and singing the vowels (Professor Weld was kind enough to assist us in demonstrating the vowels to the observers), what is meant by vowel-quality, before her report became even moderately consistent. 0 also seems to have made use of his theoretical knowledge; but as he is musically trained, he judged the octave-relations correctly in the majority of cases, so that his reports were on their face consistent from about the second hour of practice on. Da started to judge in about the same manner as G, but corrected himself when shown by the experimenter what he was doing.

F and L, the two observers whose results are utilized only in the preliminary work, at first gave scattering judgments; they reported practically every vowel in every part of the scale. Neither had any notion of vocality; and even after some hours' practice it was possible to get consistent judgments only after the vowels had been demonstrated afresh by singing and speaking.

Method of Paired Comparisons. Our next step was to determine the pure vowels, the turning-points of the system of vocalities. Köhler (Ibid, p.111), it will be remembered, had in his experiment determined these points by a limiting procedure. He started with the tone on the one side of a given vowel, and varied it by small steps until the observer first noted a trace of the next vowel beyond. We desired, however, to avoid the errors of expectation which are inherent in such a method, and to make it as difficult as possible for our observers to judge some particular tonality as representing the pure vowel in each octave. In order to overcome this possible tendency (to call a certain tonality the pure vowel), we used the method of paired comparisons with a haphazard arrangement of the pairs. The observers were instructed as follows:

After two bells as "ready" and "now" signals, you will hear two tones near U in vocality. Report whether the second tone is nearer to U or farther from U than the first. Record your reports in order upon the sheet provided, indicating a report of 'nearer' by + and a report of 'farther' by -.  Any further observations you may care to make should be written out at the end of the series on the blank paper provided.

These instructions were varied for the other vowels by inserting O and A in place of U.

The stimuli were pure tones obtained through the interference-tubes ifi the manner described. In the regular series there were 90 pairs. These gave all the possible combinations of ten tones in both time-orders. The stimuli were as follows: for U, 240 to 280 vs. by 5 vs. steps; for O, 480 to 570 vs. by 10 vs. steps; and for A, 960 to 1,140 vs. by 20 vs. steps. The order in which the pairs were given was arranged by lot, and was the same for the three regions. In making up these series, we were guided by Köhler's figures. The stimuli cluster about the values obtained by him for the pure vowels, and spread over as large a range as the interference-tubes would permit. With a view to equalizing the effects of practice, parts of each one of the three series were given in every observation hour. These parts varied in length from 30 to 40 pairs. With observers Da and W, however, halves of each of two series were given in every hour. Every observer had two hours of preliminary practice, with short series of 21 pairs, to accustom him to receiving the stimuli through the ear-tubes and to making written reports.

The results of the experiments by this method are the frequencies with which the different stimuli were judged as "nearer" to the pure vowels. These can be treated mathematically by averaging the stimuli, multiplying every one by the number of times it is judged as "nearer" (judgments of = being counted as a frequency of one-half for each stimulus). The values so obtained, together with their mean variations, are shown in Table III. It would seem from these figures that an approximate octave-relation obtains between the pure vowels: an approximation which is very close if we average the values (and also the my) for the individual observers. But the averages obtained by experimentation also approximate equally well the averages that may be obtained by applying the laws of chance to these stimuli.

TABLE III.
Positions of the pure vowels by paired comparisons.

If, as Köhler holds, the turning-points for vocality are sharply defined, we should expect that a curve showing the frequency with which every stimulus is judged as "nearer" would come to a sharp peak at the pure vowel, and fall away regularly on either side.  The curves did not, however, behave in this way. Eleven of the 24 curves obtained showed two distinct peaks. We might remark, parenthetically, that these curves are not curves of any mathematical functions, since every stimulus is compared, not with the same set of stimuli, but with a different set of stimuli. It seems possible that these double predominances may be due to a shift in the attitude of the observer from day to day. We therefore considered separately the two halves of the results obtained from Da and W for the vowel 0: results which, it is to be remembered, were obtained at two sittings. The fractionation showed that for Da the point of maximal judgments shifted from 500 vs. on the first day to 540 vs. on the second day, while for W the shift was from 560 vs. to 510 vs. Since these changes were in opposite directions, they cannot be due to any unnoticed variation in the stimuli, but clearly show a change in the attitude adopted by the observer in judging a pure vowel. The other cases are doubtless similar.

In 8 of the 13 curves which did not exhibit bimodality, the frequency of judgments of "nearer" increases steadily toward either the upper or the lower end of the series of tones with which we worked. This fact would imply that the purest vowel lay either at or beyond the end of our series. Yet the averages for such a set of judgments are still well inside our range. This result was to be expected. It proceeds from the fact that the stimuli throughout the middle of our range are naturally preferred to tones still further from the pure vowel than they are themselves. These preferences, of course, operate to pull the average away from the point of purest vocality and toward the center of the region in which we are working.

Our mathematical averages, therefore, are of little value. The close octave-relation between the averages of eight observers for the three vowels is a result, not necessarily of the positions of the pure vowels, but more directly of the octave-relations existing between the stimuli used. A very similar result would have been obtained had the judgments been scattered among the pairs by mere chance, as is shown at the bottom of Table III. We were getting out of the experiment only so much of an octave-relationship as we had previously put into it.

On the other hand, the very variability of the results is significant. We were not using a serial procedure in which the observers could stop when they came to a certain tonality. It would have been far more difficult in our experiment for the observers to pick out such a tonality, and to call it the pure vowel, than it was under the procedure followed by Köhler. His subjects may have noted some particular change, and have continued to report that change as the turning-point; while our observers could not do this, because the stimuli varied continuously throughout the region, instead of passing the significant point in regular progression; and because this significant tone, even if it actually were one of the tones of our series, occurred in only one pair out of ten. But if the figures obtained by Köhler were in reality the results of judgments of change of vowel-quality, then there is no reason why equally regular results should not have been secured by our method. Our observers had less opportunity than Köhler's to judge anything save vocality; and the very regularity of Köhler's figures would seem, therefore, to show that they are not the results of purely vocal judgments.

Vocal Limens. We next desired to find the differential limens for vocal judgments of the pure vowels. The method of paired comparisons did not furnish us, as we had expected, with definite values for this purpose. It was therefore necessary to adopt another method of determining approximately the turning-points. A single tone, repeated several times, was presented to the observer, who was asked to report whether or not it was a certain pure vowel; and, if it was not, to give the direction in which it differed from the pure vowel. On the basis of this report, the experimenter then sounded another tone, slightly different in frequency; and this process was continued until a tone was found which the observer was willing to accept as a good vowel. A short series of liminal judgments was then run (under the instructions given below) ; if the observer reported differences on both sides of the pure vowel, we considered that an approximation sufficient for our purposes had been attained. The same position was not always found by a given observer on different days. A tone that was, for instance, reported on a certain day to be on the A side of O would be reported the next day on the U side. Nor was it always possible to obtain a good vowel within the limit of tones produced by our apparatus. We were unable to get tones high enough to give a good A for Da, Di, and W, or a good O for C and Y. In these cases we went as near to the pure vowel as we could. The positions for pure vowels obtained by this method constituted the standard stimuli for the determination of the vocal limens. These standards are given in Table IV. The comparison stimuli differed by 5 vs. for U, by 7.5 vs. for O, and by 15 vs. for A. The general procedure described in an earlier part of this paper was followed.

TABLE IV.
Standards for vocal limens.

 The observers were instructed:

After two bells as "ready" and "now" signals, you will hear two tones, both of which are near U. You are to report the vocality of the tones (disregarding their pitch) as same or different; if you judge different, you are to give the direction of the difference, i.e., to say that the one tone is nearer to O or nearer to M than the other. Your report will then take the form: 1 O, 2 O, 1 M, 2 M, or --. Enter your reports in order upon the sheet provided.  At the end of the series, you are to make an introspective report, upon the blank paper provided, covering the processes upon which your judgment is based."

Similar instructions were used for the other vowels. When judging tones in the neighborhood of O, the observers made their reports in terms of U or A, while tones near A were reported as towards O or E.

The numerical results are shown in the accompanying tables: V, VI and VII. An examination of these tables shows that, without exception, the limen increases with progress up the scale. The relative difference-limen, on the other hand, shows a decrease from the vowel U to the vowel O; from that point to A the change is less certain, there being an equal number of cases of increase and decrease, so that no general statement of direction is possible.

TABLE V.
Vocal limens:  Values of L, h, and c.

TABLE VI.
Vocal limens:  Mean difference-limens

TABLE VII.
Vocal limens:  Relative difference-limens

We may next inquire what sort of judgments our observers were making, as shown by their introspective reports. Statements that vocality is introspectively a part of the tone are rare:

"There seems to me to be no doubt that the vowelness is intrinsic to the tone" (Di).
"Vowels seem objective, i.e., not added by me but an intrinsic part of the tone" (Di).
"Vowelness seems an intrinsic part of the tones as they come. Often, perhaps usually, the two tones are distinctly diiferent as totals, but the same vowel sounds out from the different settings" (Di).
"The vocality is in the tone" (Y).

Slightly less positive are the reports which say that the tone seems to "sing" or "speak" the vowel.

"Listened passively; tone sang the vowel-quality" (Da).
"Attended passively; tones sang the vowels. ....The tones came as O, U-ish, or A-ish" (Da).
"Each of the tones seems to say its vowel to me" (Di).
"I hear the tone uttering the vowel, as vocalized" (O).
"Some tones shout A and others shout U" (Y).
"The tone says O or OU or OA; I record what the tone speaks" (Y).

Imagery of various types is frequently mentioned:

"The vowel quality of O lies around 70-80 series in my 'number-form.' I am vaguely aware of this 'number-form,' but do not use it in making judgments" (Da).
"This morning, for the first time, I had visual imagery. O was accompanied by a rough outline; A by a black streak. But I think that these did not affect my judgment" (G).
"In judging M, there is often an auditory image of the hum for comparison" (W).
"Kinaesthesis is accompanied in many cases by an auditory image of the vowel" (Y).

More important to the judgments, however, are the almost universal reports of kinaesthesis, either imaginal or actual:

"In listening for the vowel quality, I had distinct kinaesthesis when there was much difference. I suppose the thinking of the quality into the tone is the setting of the throat and other muscles to a position that gives the vowel-quality I am attending to" (C).
"I doubt if I have any kinaesthesis from the throat, but I have an image (kinaesthetic) of the sensations produced by the articulation process for the vowel I hear" (C).
"Repeated the vowel 'sung' in verbal kinaesthesis so as to 'fix' the image in mind. Judgment then made with •the sensation of second tone and image of the first" (Da).
"Passively attended to sounds; verbal kinaesthesis of pronouncing vowel quality" (Da).
"In making judgments, especially when the tones are close together, I often find myself forming the corresponding vowel in my throat. This is for the purpose of making the judgments more accurate; when the throat forms the same vowel for both, the judgment is "equal.' This method is not invariably applied" (Di).
"I judged the vocality on the basis of motor tendencies to form the vowels of the tones with my lips" (G).
"Tendency to form vowels of tones given, sometimes in lips, usually in throat. At other times merely a more widespread 'set' meaning E or A" (G).
"Here again I get different kinaesthesis for the pure vowel, i.e., I usually judge OU or OA when I get the unstable sensation. On the other hand, E often comes with its own kinaesthetic set, and I immediately get verbal-motor E" (G) (A-series).
"After the tone I form the vowel incipiently with my throat muscles, sensations of strain localized in the throat. Always this throat kinaesthesis is the surrogate. It retains the U-ness of the first tone for me, and comparisons are always made in terms of it. The kinaesthesis is accompanied in many cases by an auditory image of the vowel" (Y).
"A kinaesthetic complex from the set of my throat, together with an auditory image (noticed in some cases) is the basis of judgment" (Y).

For some observers, however, the kinaesthesis eventually dropped out, and the judgments came to be made immediately, though for the majority this change did not occur:

"Judgments made to a greater degree than previously on auditory impression; they come almost immediately, sometimes without the usual kinaesthesis" (G).
"Judgments more immediate than usual and based on auditory impression. Motor tendencies are less articulate than they have been, and play less part in my judgment, often not coming to clearness until after it is made" (G).
"The kinaesthetic feel in my throat is frequently there, but this morning the vocality judgment was immediate. I was often ready to write the judgment before the second tone was completed" (W).
"Verbal kinaesthesis played practically no part. Judgments were immediate; the one had an M or O or U quality" (W).

Our observers were not at all times sure that the judgments they gave were purely vocal and uninfluenced by other attributes, as the following reports show:

"Pitch has some influence on the judgment, I think" (C).
"Several times noted pitch. Once the pitch seemed equal and the vowel-sounds O and U'ish. Another time, the pitches were different and the vowel qualities seemed equal" (Da).
"A few times there was kinaesthesis only in my larynx, but in those cases I was not sure that my judgments were purely 'vocal,' i.e., that pitch was not also a factor" (G).
"I find a tendency to take the first tone as standard, modifying it subjectively to the utterance of the vowel. The second tone, then, because of its difference, is more apt to be judged less like the vowel. If it is higher, it becomes in this case A; if lower U. The A and U qualities are not so much recognized as inferred" (O).
"Judgments easier than usual. I fear that this is partly a result of recognition of the standard, and that pitch judgments cut across" (N).

We also find a number of descriptions of vocal differences in terms that are ordinarily used to describe other attributes:

"Sometimes there is a more widespread kinaesthesis which seems to have the meaning 'more open' or 'more closed'" (G).
"The E is the most definite vocality; it shrieks" (G).
"The tones I judged as like A were more open and more like A in this sense. They seemed too open for O, but they have very little A quality (whatever that is) aside from the openness" (W).
"The tones I judged as E were 'harder' ...E has this 'hard' quality as compared with the softness of a good A" (W).
"Vowel is given immediately. E-ness is hard, small, cramped up, 0-ness is more diffuse, large, open, and soft " (Y).

At the opposite pole to the statements that vocality is intrinsic to tones, stand the reports that an observer found it necessary to "think' the vowels he heard into the tones:

"In judging the vowel, I seem to think the vowel into the experience" (C).
"The tone does not speak the vowel to me. I rather think the quality into the tone. I expect the vocality and interpret the tone as that, within the limits of suggestion" (C).
"The A and U qualities are not so much recognized as inferred" (O).
"Tried to try out on the first tone the peculiarities of O, UO, and OA, and reach a tentative judgment before the second tone" (O).

Discussion. We may now ask what evidence these facts adduce with regard to the status of vocality as an attribute. In the preliminary work it was found that only those observers who had had some sort and amount of previous training with vowels were able at once to give judgments of vocality. Of the others, several tried to make judgments on the basis of theoretical knowledge. When they did this, they were able to fit the complete vowel-series into a very short range, and to make vocal reports very different from those they learned to give later on. It was, it will be remembered, necessary to show three observers, by speaking and singing the vowels, which vocalities were to be heard at various parts of the scale. There are two possible interpretations of such teaching. We may have been pointing out to our observers what they were to look for in observing vocality; or we may have been building up perceptions of the vowels (perceptions that already existed for the observers accustomed to vocality) ; it was then to be expected that these perceptual judgments should, with practice, become as immediate as attributive judgments.

The outstanding results of our experiments by the method of paired comparisons were the extreme variability of the results and the lack of octave-relations between the pure vowels (save such octave-relations as were due to our choice of stimuli). The latter result is at variance with that obtained by Köhler with a limiting procedure. It echoes the suggestion made by Stumpf[28] that Köhler's observers were judging some particular tonality as the turning-point, a judgment which our observers were not so liable to make.

The quantitative figures for the vocal limens of themselves tell us little. They show a high degree of consistency between the observers with respect to the course of the limen, although the values themselves show considerable individual differences. The introspective views, however, exhibit a number of important features. Statements that the vowels seem to be inherent in the tones are balanced by reports that other observers have to "think" them there. It would seem that the latter are the more significant, since a report of inherence might have its roots only in the observer's adaptation to a particular type of perceptual judgment.

Kinaesthesis, together with verbal and auditory imagery, was prominent in most of the observers. It always tended to drop out, and in several cases completely disappeared. The presence of such surrogate imagery, however, is only a very weak implication that the judgments are not attributive. Those observers who lacked auditory imagery were forced to adopt some other means of remembering the first tone in order to compare it with the second.

Not only did our observers occasionally find pitch influencing their vocal judgments, but they give descriptions of differences in vowel-quality in terms of other attributes, speaking of vocalities as open, closed, hard, soft, cramped up, and shrieking. These terms seem more akin to descriptions of volume or brightness than of vocality.

On the whole, it would appear that vocality has not, in these experiments, shown its right to be classed as an attribute. The judgments of vowel-quality seem rather to be judgments of perceptions, perceptions which we found ready-made in some observers, and built up in others. A long series of studies in the theory of vowels has shown that a given vowel-sound always contains a predominating tone or tones in a certain region of the scale, and that the regions are approximately an octave apart. These predominating tones form the core of the perception of vowels. If, as in our experiment, the core is presented to an observer who is instructed to hear the vowel, the remaining elements are supplied in some individual fashion, and the vocal judgment is rendered.

IV. Pitch.

The experimental work on pitch consisted of a determination of the differential limen by the standard method. The instructions were as follows:

After two bells, as "ready" and "now" signals, you will hear two tones. You are to report the relative pitch of the tones, judging the second in terms of the first. Your report will then take the form: "higher," "equal," or "lower." Enter your reports in order upon the sheet provided. At the end of the series, you are to make an introspective report, upon the blank paper provided, of the processes upon which your judgment is based.

No provision was made in the instructions for "doubtful" judgments. The instructions used in determining limens for vocality were already so complicated that it was not considered wise to add any further categories; and since we wished to make the instructions for the different attributes comparable, we must needs omit mention of "doubtful" judgments throughout all the instructions. The observers did, nevertheless, occasionally give judgments in this category (as well as judgments of the "or" type). George[29] has shown that such judgments, when they occur, involve a shift in the attitude of the observer toward the impressions, and that they should, so far as possible, be eliminated in psychological work. We accomplished this end by discarding all "doubtful" or "or" judgments, and repeating the stimuli in a later series. We did not, of course, eliminate all judgments in which the observer was doubtful, for the instructions would tend to make him neglect to report as such judgments that were in reality of this type. Whatever bad effect our procedure may have had upon the psychometric functions was the same for all determinations.

TABLE VIII.
Pitch limens: Values of L, h, and c