A new classification of tonal qualities.

Originally published in Psychological Review, v.36, pages 172-80, 1929.

Christian A. Ruckmick, University of Iowa

Diagrams and schema showing the classification and relationship of qualities within each sense department have at least a two-fold usefulness. Even though they may simplify too much our current scientific knowledge, they render a distinct service, especially to elementary students, in affording a visualization of the present status[1]. If the scientist has learned to regard such diagrams as not necessarily factual and final per se, they furnish furthermore a basis of discussion and a point of departure for theoretical considerations. The main source of danger lies in the presumption that figures, in either sense of the term, photographically or accurately reproduce undeniable facts. Schematic outlines and statistical data are both probably allied to portraiture in the sense that the scientist as well as the artist frankly admits that relations between things are interpreted as best he knows how.

The sensory group that has been most persistently schematized in terms of a visual diagram is the visual group itself. Here we find that the double pyramid, or octahedron, is quite generally adopted[2]. Because of the outstanding work of Henning the olfactory qualities have recently received schematic attention and from the same source increasing reference has been made to the taste tetrahedron. Titchener is responsible for the newest arrival in this field, the touch pyramid[3]. But the figure requires further investigation and corroboration.

While several attempts have been made to organize the auditory qualities, apparently at the present writing there is no general acceptance of any one diagram. It is a remarkable situation in view of the fact that auditory phenomena have been under long and continuous scrutiny. Certainly no other group of sensations, save the visual sensations, has had so protracted a period of study. Although the visual qualities are thus fairly uniformly recognized and named, we do not have a similar state of affairs in regard to the auditory qualities. This is in part due to the practice of using descriptive terms for the auditory attributes which have not as yet become standardized.

The earliest attempt to depict the auditory qualities known to the writer was made by Drobisch in 1846[4]. In this scheme the chief principle was a spiral which gave the octaves the position of closest proximity in each return sweep of the curve. Ebbinghaus objected to this on two counts: (1) the relationship of the octave is excellent but the relation of the perfect fifth, the next best degree of fusion, is diagonally opposite; (2) tones most closely allied on the ascending spiral, i.e., the diminished second, are most unlike in terms of the tonal character of fusion. He claimed, furthermore, that the octave could be reached on the spiral only through a gradual approach by means of intermediate and totally dissimilar tones. In 1897 Ebbinghaus himself proposed a unidiiuensional or serial arrangement which took cognizance of the pitch character of the tone, as its principal quality[5]. He added, however, that a spatial envisagement of the tonal series which could also take account of other qualitative likenesses, though much to be desired, was impossible (op.cit. 280).  To meet the accumulating observations concerning the qualitative attribute of volume Titchener in 1909 proposed the tonal pencil.[6] In this diagram the attribute of size or diffusion, which is called "volume" only because languages are full of spatial symbols, is represented by a second dimension making the scheme now for the first time a plane surface. The attribute of diffusion is relatively great in the bass notes, less marked and without much variation in the middle register, and then rapidly disappears in the high treble giving the pencil its point. The diagram has not gained wide currency in our texts, but it did contribute to further experimental work on the attribute of diffusion, or what has become known as "volume." Although in some quarters the attribute of volume is beginning to be seriously questioned we are now rapidly approaching the situation in which many psychologists have practically accepted the attribute of volume in the non-spatial significance.

The point here raised concerns usually some description distinctive between the sensation and the percept. In assigning attributive names to qualities in any sense department, there is always a suspicion of dealing with perceptual material. The most difficult problem in classificatory work is to remain absolutely naive. This of course has been the outstanding development in connection with the fate of the so-called "vowel" quality. Were we not linguistically minded we would undoubtedly never think of classifying certain auditory qualities by their suggested vowel names. How heavy this latent task or self-instruction weighs upon trained laboratory observers only careful students of systematic psychology can understand (Cf. Rêvész, G., "Zur Grund. legung der Tonpsychologie," 1913). In the last analysis this may be reduced to a level of a difficulty to be met rather than to the point of an irremovable obstruction in the path of research.

In the case of pitch we designate in all languages a quality which has no inherent spatial attributes through words that are steeped with spatial connotations. The meaning has here transcended the original import. We may be approaching the same situation with regard to the "volume" of tonal sensations. In our experimental work in this laboratory the reports of the Os designate "volume" as a rule only metaphorically.

In the light of this more recent research by Rich and others, Ogden suggested a tonal manifold in which intensity, pitch, pitch-brightness, and volume each found its place[7]. The fundamental principle of this diagram rested upon a proposal by Watt that not only pitch but tonal masses must be considered (Watt, H.J., op.cit, 62-73). The base line in the schemes of both Ogden and Watt indicate the relative thresholds for volume at successive pitches, the lowest in the series having a volumic spread inclusive of those assigned to each subsequent pitch. The chief criticism of these diagrams lies in the pronounced fact that for the first time in the history of spatial classifications we are including quantitative distinctions, e.g., thresholds of intensity in otherwise qualitative diagrams. Even the color pyramid with its thousand different pure grays is considered essentially a qualitative schema. What the fate of pitch-brightness as distinct from pitch or volume will be no one knows, but it still continues to be generally discussed.

A substantial amount of consideration has been given, chiefly by Köhler, Meyer, Révész and Watt[8], to a double usage of the terms pitch and "tonal quality." That there is a gradual change of pitch from one end to the other analogous to the change in the gray series from white to black among the visual qualities is quite generally admitted. But as these and other investigators indicate, a peculiarity in the tonal series exists which, with respect to the auditory sense department, is unique.

The double qualitative aspect of tonal sensations is further exemplified through numerous studies on absolute pitch consciousness and in colored hearing. In his elaborate study Baird discovered the difference between what he called "note-response" and "octave-response."[9] He found that these "were usually separated by an appreciable interval; and the degree of subjective assurance attached to the octave-identification was usually very much less than that attached to the note-identification. The octave-error was common to the identifications of all nine of our observers; and it was present in the identifying of notes of every variety of clang-tint." He calls this one of the most striking features of his study and he terms it "the illusion of the octave." Révész arrives at the same result from his study which leads him to a similar double classification of tonal quality[10]. The only dissenting note in a long series of experiments in the field is that of Mull[11]. She says explicitly: "There is no objective evidence which necessitates the postulating of an attribute of quality, or tonality, which recurs in successive octaves and upon which all judgment of absolute pitch rests; nor do the introspective reports disclose the existence of any such attribute." In this study it must be noted however that the principal part of the investigation was confined to a single octave and that the possibility of octave confusion did therefore not really exist for these observers. Thorough though this experiment was, work ought to be continued throughout the musical range of pitch. If under those conditions introspections did not reveal the octave quality, then we certainly should have to take notice of such a result, history notwithstanding.

A somewhat similar situation occurs in the field of colored hearing. There are very few cases on record which show an absolute change of color for a single note from one octave to another. Most observers report when these colors are definitely seen that the notes an octave lower or higher differ mainly in tint or saturation or both; but a neighboring tone will have a radically different color ranging again in tint, saturation, or both tint and saturation in successive octaves. Recalling in that connection how definitely these colors are experienced and how fixed they are, even for a term of years as Langfeld has shown[12], we ought to recognize the significance of a synaesthetic change in hue for the change of note as different from the change of tones an octave apart in tint and saturation.

From another source of investigation comes a corroborating argument. Brues would lead us to believe that the octave relationship in terms of simplicity of its vibration ratio must be excluded entirely from the field of fusion as a phenomenon of a different nature[13]. In a more recent study by Guernsey the distinction is made between fusion and consonance and the octave again is made to follow a separate sensory path[14]. This is somewhat in agreement with Stumpf's distinction between consonance and concordance. The upshot of all of this presumptive evidence is that the octave relationship is more intimately bound up with our perception of unison than with perceptions of consonance and in general supports the doctrine of a secondary tonal quality.

With this situation in mind and with a close perusal of other auditory investigations for the last few decades before him, the author tentatively proposes a figure that for lack of a better designation may be called a "tonal bell" (The author has consulted a number of mathematicians and they are agreed that there is no technical term which fits this type of geometrical figure. If there is one the author would be glad to learn it).  The pitch character of tonal sensations is represented by a continuous gradually ascending spiral line (painted red in the laboratory model). Adopting Drobisch's idea of the spiral, at each successive octave the ascending line brings these pitches into what may be called "note relationship" or "tonality". These note relationships are indicated by lines running generally in a vertical direction (painted blue in the laboratory model). The spiral starts somewhat below the lower auditory limit for tone (painted very dark red in the laboratory model) and continues beyond the upper tonal limit (painted very light red in the laboratory model). The interval relationships, since they are phenomena resulting from a complex situation partly sensory, partly perceptual, and partly ideational, are indicated in the middle register by cross lines (painted yellow in the laboratory model). These are inserted simply for the convenience of the student but are not important in the classification of sensory qualities as such Similar cross lines could be inserted, of course, in other octaves and for other intervals if desired.

The tonal bell.
Reproduced from the author's The Mental Life through the courtesy of Longmans Green & Co.

The attribute of volume in one form or another originally indicated in the Titchener tonal pencil still has a large place in the literature. Just what its thresholds or differentiae are must be further investigated[15]. By adopting the suggestions of Titchener the tonal bell follows in general the principle of Titchener's diagram. Volume, or what the present author prefers to call "breadth," consequently demands a broad base which gradually diminishes until the middle registers are reached, stays approximately uniform through this region, and then diminishes rather rapidly in the high registers. A cross-section through the tonal bell would therefore give an approximation to the tonal pencil. The length of the radius of each successive spiral roughly indicates, then, the breadth of that particular pitch attribute.

One other factor is represented in the tonal bell. It will be seen that the spirals rise with varying pitches Putting it in another way the spirals are closer together in one region than in another. Assuming the vertical direction to be in general that of increase of pitch, the author has taken this means to show that according to our present data on pitch discrimination a tone may go the rounds of an octave without rising much in pitch in the lowest and highest regions of the scale. Investigators are in general agreed that pitch discriminations are most acute in the middle register. For the lowest and highest regions, of course, we have nothing at hand but estimates based on approximate geometrical continuations of the curve showing pitch discriminations. Boring has recently also raised the issue whether or not classifications of sensory qualities should be based solely on the data obtained from judgments of discrimination.[16] But since this has been heretofore our general practice the author has made allowance for the large number of discriminable qualities on the basis of units calculated from the accompanying table. This is therefore responsible for the uneven rise of the spiral line.

* Estimates based upon continuations of the curve for determined discriminations.
**Calculated from the compass of each octave in terms of d.v. within that octave. Pitch discriminations in terms of d.v. multiplied by the respective units equals approximately the compass of each octave in terms of d.v. The above units were used to establish the amount of rise in the spiral above the base line at each successive octave level.

The author has put this diagram to the test of criticism in an attempt to clarify the present situation with respect to the tonal qualities. The diagram is essentially a qualitative figure. While still a considerable amount of work is required in order to stabilize and standardize our knowledge, experience dictates the advisability of presenting this diagram to a still larger group of critics for comment. It may serve the purpose not only of concretely presenting the issues which punctuate our present discussions but also of serving as a point of departure for future theoretical considerations.

Footnotes

1.  The author has put his convictions into practice in his recently published book, The Mental Life.  So far as he knows this is one of the few texts that have made extensive use of diagrams in connection with the various sensory qualities. At the present stage of our qualitative analysis no classificatory schemata have been proposed for the kinaesthetic and organic sense departments.  [Return to text]

2.  The writer has recently consulted some twenty text-books and systematic treatises on this point. All but four authors definitely refer to the color pyramid while a few, like Warren, prefer to call it a spindle in view of its proportionally long axis. Two texts fail to mention any diagram, while one presents the visual scheme as a hexahedron, and another illustrates the qualities in terms of a circle.  [Return to text]

3.  Titchener, E. B., "Models for the demonstration of sensory qualities," Amer. J. Psychol., 1920, 31, 253. See also Burnett, N. C., and Dallenbach, K. M., "The experience of heat," Amer. J. Psychol., 5927, 38, 418-431; "Heat intensity," ibid., 1928, 40, 484-494.  [Return to text]

4.  Drobisch, M. W., "Über die mathematische Bestimmung der musikalischen Intervalle," 1846; also AM. d. kgl. sachs. Ges. d. Wiss. math.-phys. Cl.B. II, 1855, 35. [Return to text]

5.  Ebbinghaus, H., "Grundzüge der Psychologie," Leipzig, 1902, 278.  [Return to text]

6.  Titchener, E. B., "A Text-Book of Psychology," 1909, 94. The study of "volume," which followed upon the presentation of this diagram is an indication of the theoretical utility of such diagrams. (v. Rich, G. j., "A preliminary study of tonal volume," J. Exper. Psychol., 1916, I, 33-22; "A study of tonal attributes," Amer. J. Psychol., 1919, 30, 121-164; "A note on "vocality"," Amer. J. Psychol., 1921, 32, 446-447; Ogden, R. M., "Hearing," N. Y., 1924, 66-75; Ruckmick, C. A., "Recent acoustic research," Psychol. Bull., 1924, 21, 606; Watt, H. J., "The Psychology of Sound," Cambridge, 1917, 27ff.)  [Return to text]

7.  Ogden, R. M., "The tonal manifold," Psychol. Rev., 1920, 27, 136-146. See also "Hearing," 69-75.  [Return to text]

8.  Köhler, W., "Akustische Untersuchungen III," Zsch.f. Psychol., 1915, 72, 1-192. Meyer, M., "On the attributes of the sensations," Psychol. Rev., 1904, 11, 83-103; "Vorschläge zur akustischen Terminologie," Zsch. f. Psychol., 1914, 68, 115-119; Review of Révész's "Zur Grundlegung der Tonpsychologie," Psychol. Bull., 1914, 11, 349- 351. Révész, G., op. cit., 16ff. Watt, H. J.,op. Cit., 3-12. [Return to text]

9.  Baird, J. W., "Memory for absolute pitch," Studies in Psychology, Worcester, 1917, 69.  [Return to text]

10.  Op. cit., 16-19. Révész has further illustrated his dichotomy through the description of a pathological case in which the octave of the tone was correctly given but its pitch placement was defective in terms of a constant pseudotone of g#.  [Return to text]

11.  Mull, H. K., "The acquisition of absolute pitch," Amer. J. Psychol., 1925, 36, 469-493.  [Return to text]

12.  Langfeld, H. S., "A note on a case of chromaesthesia," Psychol. Bull., 1914, 11, 113-114.  [Return to text]

13.  Brues, A. M., "The fusion of non-musical intervals Amer. J. Psychol., 1927, 38, 624-638.  [Return to text]

14.  Guernsey, M., "The role of consonance and dissonance in music," Amer. J. Psychol., 1928, 40, 173-204.  [Return to text]

15.  In some recent investigations of Gundlach, reported at the last meeting of the Midwestern Psychological Association, doubt has been cast on the attribute of "volume." If further research should lead us to believe that volume like vocality is perceptual in character and not an attribute of auditory sensation, the figure would lose its "bell" shape and become cylindrical without any definite significance to the length of its radius. This would leave its top and bottom surfaces uninhabited. But so at present are Henning's triangular faces without the recognition of triplex odors! This may nevertheless be a fault which points to the inadequacy of our present knowledge in the auditory field. At any rate it would do away with the criticism that in our diagram one set of attributes (pitch, and tonality) are represented by position on lines, while another set (volume) are shown in terms of distance from a central axis.  [Return to text]

16.  Boring, E. G., "Auditory theory with special reference to intensity, volume, and localization," Amer. J. Psychol., 1926, 37, 157-188.  [Return to text]