“Boundaries” and “thresholds”: Conceptual models of the musical mind in the history of music psychology

Boundary, phrase structure, and the cognitive mind

The most visible keyword in early music-psychological writings in the late 19th and early 20th centuries is Tonvorstellung(en), and I wish to investigate here the use of its parent word Vorstellung (Vorstellungen in plural) as a technical term in 19th-century German psychology. For a better understanding of the notions underlying the technical use, however, it is first necessary to explore the various implications of the term. In English, the term is often rendered as “presentation,” “representation,” “idea,” “ideation,” “imagination,” and “imagery.” The verb vorstellen can have a wide range of possible uses, ranging from the concrete sense of “to present” and “to place before the eyes” to the metaphorical sense of “to place the image before the mind,” “to introduce,” “to represent,” and “to imagine” (see Grimm & Grimm, 1854–1961, s.v. “vorstellen” and “Vorstellung”).

While carrying these various meanings in everyday life, the noun form, Vorstellung, has also been used as a central term in philosophy. As with the parent verb, a range of English words is used in translation because the German word itself has such a wide spectrum of meanings. Kantian Vorstellung, for example, was rendered as both “presentation” and “representation.” Recent scholarship adopts both “representation” and “presentation” in translating Schopenhauer’s Die Welt als Wille und Vorstellung (1819) – hence The World as Will and Representation (Schopenhauer, 1966) and The World as Will and Presentation (Schopenhauer, 2008) instead of the turn-of-the-century translation of The World as Will and Idea (Schopenhauer, 1907–1908).

A detailed philosophical account is beyond the scope of this article, but we should note here that Vorstellung was also a widely circulated technical term in the psychological discourse of the 19th century and that even within that realm, it had a variety of connotations. Historians of psychology use “presentation” and “idea” as the standard equivalent to Vorstellung in the psychological discourses of the late 19th century. Particularly relevant to the present discussion is the program proposed by Johann Friedrich Herbart (1776–1841), which came to be known as the “psychology of Vorstellungen” (See Boudewijnse, Murray, & Bandomir, 1999). Like Wilhelm Wundt (1832–1920), Herbart attempted to establish psychology as a scientific discipline, but far earlier, as early as 1816/1891 (Lehrbuch zur Psychologie), and in a different way. Herbart denied the possibility that psychology could be an experimental science, because according to him, “there are no general facts” regarding the human mind that can be tested by experiments, and “the true psychological facts lie in the momentary states of individuals” (Dunkel, 1970, p. 127). Instead, he sought to establish the “scientificity” (Wissenschaftlichkeit) of this new psychology by adopting models from physics. For him, the task of scientific psychology was to discover the quasi-mechanical laws governing interactions among the psychological elements that constitute the human psyche, elements that he named Vorstellungen. Just as physical things can be dissected into smaller parts and finally into atoms, mental states and processes can also be reduced to “psychic atoms,” as aptly described by Wolman (1968, p. 36), to characterize the basic building blocks of the human psyche as units of force that continually complicate, inhibit, and merge with one another. A passage from Herbart’s 1824 treatise Psychologie als Wissenschaft (Psychology as Science) succinctly expresses this belief:

Psychology has a certain similarity with physiology. Just as the latter builds up the body out of fibers, psychology builds up the mind out of series of Vorstellungen (Die Psychologie hat einige Aehnlichkeit mit der Physiologie: wie diese den Leib aus Fibern, so construirt sie den Geist aus Vorstellungenreihen). (Herbart, 1824/1890, p. 180) ²

Thus, psychology, the study of the mind, adopted its model from the natural sciences in order to achieve the status of an independent discipline.

Herbart used the term Vorstellungen to refer to simple and basic concepts or sensations, such as red, blue, sour, and sweet (Herbart, 1816/1891, p. 370). We cannot know the intrinsic properties of each of these Vorstellungen directly – only through their relationships. Whenever a new Vorstellung is presented to us, either in the form of sensation or as reproduced within the inner mind, the mind assimilates a newly presented Vorstellung by incorporating it within the larger set or mass of Vorstellungen that it already possesses, so that it can be comprehended as a part of the whole. In short, Herbart’s Vorstellungen are the fundamental units that together constitute the human psyche. Most thoughts (and sensations) presented before our minds are therefore compounds of multiple Vorstellungen, or simple ideas.

The derivative word Tonvorstellung(en) is closely related to the meaning of Vorstellung, which is defined as “the inner operations which are independent from perceptions in their emergence” (inner vorgänge . . . die in ihrer entstehung von wahrnehmungen unabhängig sind; Grimm & Grimm, 1854–1961, s.v. “Vorstellung”) because it often refers to imagining music without the presence of audible sound; in this sense, recent music-psychological discussion on inner hearing and the earworm phenomenon can be considered as relating to Tonvorstellung or auditory Vorstellungen. ³ Discussions of Tonvorstellung are found in several early music psychological writings, including the first volume of Carl Stumpf’s (1848–1936) Tonpsychologie (1883/1965). Stumpf differentiated the tones felt through sensation (empfunden) and those conceptualized and imagined (vorgestellt), and further discussed these psychological notions in detail afterward (Stumpf, 1918). The term Tonvorstellung was also brought into play in the psychological writings of Richard Wallaschek (1860–1917), referring to the psychological processing of individual musical elements, which was considered to be at a lower level than a more holistic Musikvorstellung (Wallaschek, 1894; see Graziano & Johnson, 2006, for a discussion of Wallaschek’s psychological view). Even though the precise term is not used, the meaning of a mental conception of music is present in an essay on tonality by Heinrich von Herzogenberg (1843–1900), who writes,

on an instrument tuned with pure thirds, [the comma difference] can be heard quite clearly, though it must always be an intentional object of consciousness (Auf einem mit näturlichen Terzen gestimmten Instrumente . . . sehr deutlich zu hören, immer muß er aber gedacht werden). (1890, p. 571) ⁴

The case to be examined here is Hugo Riemann’s (1849–1919) theory of Tonvorstellungen, which is often translated as “imagination of tone” in present-day music-theoretical discourse (e.g., Wason & Marvin, 1992) and “musical imagery” in the psychological context (e.g., Schneider & Godøy, 2001). In this regard, we can refer to Riemann’s well-known essay on the topic of Tonvorstellugen published in 1916 (Riemann, 1916; see Wason & Marvin, 1992, for the English translation). The syntonic comma, aforementioned in discussing Herzogenberg, is one of the instances cited as Tonvorstellung in this essay, which in fact revolves around Riemann’s harmonic theory (for a helpful discussion on Riemann’s Tonvorstellungen in the realm of harmony, see Hyer, 1995; see also Mehner, 2001; Mooney, 1996; Rehding, 2003). Nonetheless, there are a few references pointing to the relationship of this notion to rhythmic theory (for the discussion of Riemann’s theory of phrase structure, see Caplin, 2002; Krones, 2001; London, 1990; Waldbauer, 1989). Above all, “the complete theory of phraseology and the theory of musical period structure,” according to Riemann, “rest upon the logic of Tonvorstellungen,” and “the boundary-articulations of motives and phrases” are nothing other than segments “of a theory of Tonvorstellung applied to the area of rhythm” (Riemann, 1916, p. 24; Wason & Marvin, 1992, p. 107; see also Riemann, 1918). The connotations and implications of the Herbartian psychological idea examined above were carried over and translated into the realm of music, manifesting themselves in Riemann’s conceptualization of rhythmic structure.

Riemann’s inauguration of the new theory of Tonvorstellungen in this essay does not mean that the notion of Tonvorstellungen was suddenly revealed to him only in the late stage of his life. Riemann himself admitted developing this stance and coming to its realization only slowly and gradually. In fact, his position in the first two paragraphs of the article is somewhat ambivalent. On the one hand, he declares the beginning of a completely new theory; at the same time, he emphasizes the gradual evolution of that theory throughout his career. Riemann had used the term in his earlier writings as well; noteworthy among these was his short essay published in the little booklet called Max Hesse’s Deutscher Musiker-Kalender in 1900. The main topic of the essay is not the notion of Tonvorstellungen per se but the symmetry of musical rhythm. Nonetheless, the essay is relevant to our discussion because it illustrates how his conceptualization of phrase structure resonates with the psychological notion of Vorstellungen.

. . . in the case of music hearing we are actually dealing with an accumulation. For the musician, listening to a piece of music is by no means only something temporally flowing, which is over once the final cadence arrives; rather, if he has listened correctly, it is a finished whole within a kind of spatial existence that stands before his soul/mind at the end. Everybody uses the metaphor of construction of a musical piece, speaks of the piling up of motives, etc., and in doing so sets up no mere futile comparison. Rather, the motives grasped by the skilled listener are building blocks, nay, the smallest self-enclosed units of the art work, which he does not stack up in his memory one behind another, rather, which after he has understood them as they flow by temporally, he collates one to another. He actually first constructs as a whole from these parts a number of smaller wholes (thematic patterns), which are collated with one another yet again and that which has come into being temporally finally stands as an actual spatial thing, for which the use of the term symmetry appears not inappropriate. (Riemann, 1900b, pp. 149–150; see Appendix [1] for the original German)

This passage illustrates the essential aspects of Tonvorstellungen as a psychological notion in three ways. First, listening to music is actively imagining and representing musical images in the mind, not just passively receiving (erleiden) stimuli of sounds. The mind is the agent that has the function of demarcating motivic boundaries. Riemann’s use of the phrase Lehre von den Tonvorstellungen may have been meant to refute Hermann von Helmholtz’s Lehre von den Tonempfindungen (theory of sensations of tone). ⁵ Vorstellung as a product of mental activities is distinguished from Empfindung, the passive reception of external stimuli. The activeness that gave rise to Vorstellung, as opposed to the passiveness underlying Empfindung, is one of the crucial aspects by which we may differentiate Riemann’s from previous theories of the perception of music.

The second aspect to be noted is the visual factor in music cognition. A composer, according to Riemann, hears the music inwardly prior to his actual writing down of the notes, just as a painter gazes inwardly and sees the picture that he wishes to paint. The verb vor-stellen has the concrete sense of “to place before the eyes,” and the psychological notion maintains this visual, even theatrical, implication in its representation of our cognitive activities (Hoffman, Cochran, & Nead, 1990, p. 180). Space-image (Raumvorstellung) and tone-image (Tonvorstellung) together are among the topics widely discussed by late 19th- and early 20th-century psychologists: Carl Stumpf, for example, published his study on space-image well before he began his research on sound perception (1873). In addition, it is well known that Riemann explored the capacity of space to represent harmonic motions between chords and keys (e.g., Tonnetz). Interestingly, this essay on symmetry ends with a similar topological attempt to represent the transformation of the passage of time into a spatial shape (“die Umwandlung des zeitlichen Verlaufs in ein räumliches Gebilde”), in which the aural perception of an 8-measure period is represented by the shape of a rectangular prism, as shown in Figure 1. ⁶

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Figure 1.

Riemann’s spatial representation of the aural perception of an 8-measure period. Measures 1, 2, 3, and 4 are represented as lines forming a four-sided face, and the antecedent and consequent phrases as two identical square sides, which then form the rectangular prism of an 8-measure period (Riemann, 1900b, p. 150).

Third, the compound nature of Tonvorstellungen should be noted. What Riemann argues for is not some generalized or hazy fantasy, but a very concrete and detailed sonic representation of tonal structure. A skilled listener grasps the minutest building blocks of music (the motives) and their correct relationship with each other, and only then is the “ultimate identification of the essence of visual and aural imagination” achieved (Riemann, 1916, p. 12; Wason & Marvin, 1992, p. 93). This third aspect, namely Tonvorstellungen as a compound of discernible units, offers good reasons for the use of Tonvorstellungen in plural form in designating the theory.

If we take only direct references and explicit exchanges into consideration, Herbart does not seem to bear as apparent and strong a connection to Riemann in terms of his general psychological stance as Helmholtz or Stumpf does. Certainly, Riemann did mention Herbart’s works on occasion, but mostly in connection with the latter’s discussion of the physiological basis of musical rhythm, ⁷ and not with regard to his psychology of Vorstellungen. Nonetheless, there are distinct parallels between the ideas of these two scholars, and such parallelisms comprise the common mode of thinking that determined the ways they thought and wrote. ⁸ Note that in such theories of musical hearing, a profile of the musical mind emerges in which it is seen as cognitive, rational, and conscious. To Riemann, musical imagination operates with concepts (die Begriffe) (Riemann, 1917, p. 1). In his theory, identifying cognitive units and establishing relationships among them is accomplished by means of concepts, categories, and logic. This idea finds correlations in the Herbartian psychology of Vorstellung, where the object of study was something that we may call the mind, rather than the traditional notion of soul.

This is sharply contrasted to the 18th-century “old faculty psychology,” which assumes a set of innate psychic faculties that are given by God as different manifestations of the soul. The German word Seele originally meant “the breath” and “the life-principle” (Baldwin, 1901–1902/1998, p. 680), and was sometimes interchangeably used with another term, “pneuma.” “Soul” in this sense designated the human mind as a whole, in contrast to more confined terms, such as Geist in German, or “mind” in English. ⁹ The soul remained the focus of psychology for a long time even when it began to be allied with physiology in the 18th century as a guiding power, irreducible to mechanics, under whose direction living matter operates.

By way of contrast, there was no room for such spiritual forces in Herbart’s psychology of Vorstellung. It is not that the terminology of soul (Seele) is completely absent in Herbart’s works on psychology; on the contrary, Seele appears frequently throughout his treatises (as is the case with many of the so-called “founders” of scientific psychology, including Fechner and Wundt). Nevertheless, Herbart makes it clear elsewhere that the object of study in his program of psychology is something that we may call the mind, rather than the traditional notion of soul: “A simple definition of the soul is completely unknown and will remain so forever. It is no more a subject for speculative psychology than it is for empirical psychology” (Herbart, 1816/1891, p. 364; see also Appendix [2]).

Hence, the psychology of Vorstellungen marks a critical transition in the history of psychology. Psychology, once called “the science of the soul (pneumatology),” then became the “psychology without soul (Psychologie ohne Seele)” as expressed by Lange (1865/1950, p. 168), who wrote extensively on the history of materialism. Herbart’s connection to materialistic thinking is worth noting at this point. Herbart’s notion of psychic atoms harks back to the early materialistic interpretation of the soul by Democritus, although the Greeks’ “atoms” are of different nature (see Copleston, 2003, p. 252). Herbart’s analogue drawn between physiology and psychology calls to mind the ideas proposed by the early 19th-century French physiologist/philosopher Pierre Jean George Cabanis (1757–1808), which were succeeded and further fortified by the German scientific materialist Carl Vogt (1817–1895): “all those capacities that we understand by the phrase psychic activities (Seelenthätigkeiten) are but functions of the brain substance; or to express myself a bit crudely here, that thought stands in the same relation to the brain as gall does to the liver or urine does to the kidneys” (cited in Gregory, 1977, p. 64).

After the mid-19th century, the term soul (Seele) gradually disappeared from the scientific literature and was replaced by notions such as consciousness (Bewußtsein) and mind (Geist), which are characterized by thought, intellect, and reason. Thus, psychology underwent a change during the course of the 19th century, not only in terms of its methodology – i.e., in moving from pure observation to experiments – and its interdisciplinary alliance – i.e., moving from a close connection with metaphysics to one with physiology – but also, and more important, in terms of the object of its study, in that it gradually narrowed down its focus from soul to mind. ¹⁰

Riemann’s music-psychological arguments reflect similar conceptions of the musical mind as a cognitive agent.

Once again I must emphasize the fact that understanding a large complicated composition requires both practice and good will. Both a grasp of detail and a conscious ability to trace the way in which the whole work hangs together, i.e., a good memory and synthetic activity of the mind are needed if the work is not to disintegrate into a series of loosely connected single impressions, none of them very powerful, instead of each supporting, highlighting, and intensifying the other either by analogy or by contrast. (Riemann, 1888, p. 42; Appendix [3])

In such theories of how we hear music, there appears to be no room for the spiritual activities of the soul. Or is there?

The music-psychological aspect of Riemann’s theory examined up to this point exhibits the notion of musical comprehension as purely a product of the conscious mind. Nonetheless, different viewpoints or even contradictions can be found within the writings of the same author, and this is precisely the case for Riemann’s writings. The next section examines these somewhat opposing concepts through the lens of Riemann’s and his contemporaries’ discussions on rhythmic values of tones and rests.

Threshold, values of rests, and the soul

Here, I would like to invoke the discussion of music by one of the most famous pioneers of psychology: Wilhelm Wundt. Wundt’s connection to the study of music is not widely known to contemporary scholars, and even when it is, only in part (see Gjerdingen, 2002). However, he was deeply interested in and engaged with the study of music, and his works were well known to late 19th-century music theorists, especially to Riemann. His most significant treatise, Grundzüge der physiologischen Psychologie (Principles of physiological psychology, 1873–1874) contains substantial chapters devoted to music, and many of these discussions concern the subject of time and rhythm. ¹¹ Some parts of his writings echo the conception of rhythm in Akzenttheorie, which was supported by theorists such as Johann Philipp Kirnberger (1721–1783) and Moritz Hauptmann (1792–1868), who viewed the rhythm of music as an alternation between accents and non-accents (see Hauptmann 1853; Kirnberger, 1771–1779). In the section on the “rhythmic connection of the sound images (Rhythmische Verbindung der schallvorstellungen),” for example, Wundt speaks of the “intensity of sound” as being strong (stark) and weak (schwach), which may be graphically represented as shown in Figure 2.

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Figure 2.

Representation of 3/4 and 4/4 meter in Wundt (1873–1874, p. 514).

Riemann would not agree with this view. In referring to the “values” (Werte) of rhythmic units, Riemann deliberately adopts the expressions “light” and “heavy” as opposed to “strong” and “weak,” as if to refer to the weight of a physical object. In opposition to such a mechanical theory, Riemann’s theory of “dynamic shading” (dynamische Schattierung) conceives of rhythmic units with gradual changes (see Caplin, 1983). Abrupt changes in tone intensity, such as those implied in Akzententheorie, would yield something “tasteless and contradictory to the practice of all good artists” (Riemann, 1895/1967, p. 76). ¹² In view of such statements, William Caplin suggests that Riemann’s theory is “clearly a theory of musical performance, one rooted in a Romantic aesthetic of ultra-expressivity,” like Mathis Lussy’s theory, and that “the crescendo and decrescendo notations were meant as actual indications of tone intensity is obvious from much of Riemann’s discussion” (Caplin, 2002, p. 684; see Lussy, 1874; for discussions of Lussy’s theory, see Dogantan, 2002; Green, 1994). Indeed, most of his writings point in this direction, but there is another possible way to interpret Riemannian values of tones as a theory of the musical mind. We gain insight into these possibilities when his discussion of the value of rests is viewed in light of the psychological writings of his contemporaries.

Note that in Wundt’s and other theorists’ representations in the tradition of Akzenttheorie, the intensity of sound “runs through all possible grades between zero and the (highest) limit that we can sense” (Wundt, 1873–1874, p. 514). The lowest limit, which would be at or near the value of zero here, would be a rest, signifying the absence of sound. For Riemann, however, the rests as well as the tones would have their values. ¹³ What is being considered here is neither the absence of sound nor the notational signs used for them: rather, a rest is defined as “the negation of the musical life, of the tone” (Riemann, 1884, p. 137; see also Appendix [4:1]). The value of a rest is contingent upon its position in relation to a motive. A rest is “the negative equivalent of the tone-value for which it stands” (Riemann, 1887, p. 735; Appendix [4:2]; see also Riemann, 1903, p. 130). It is then considered to have different effects, depending on the positive value of the corresponding tone that it negates (Riemann, 1895/1967, p. 42; 1900a, p. 152). These terms are used here to denote particular qualities of rests, which can somehow be measured in opposition to the positive values of tones. Rests are conceived of as “not zero, but of a minus value” (Riemann, 1903, p. 130), thus pointing to something present rather than absent, and thus a positive definition rather than a negative. In fact, the following statement by Zofia Lissa (1964) very much echoes that of Riemann: “Silence is one of the structural elements of the sound fabric, though in itself silence is the very negation of a sound fabric” (p. 445).

Riemann even attempted to represent visually what is perceived and understood during pauses. These representations strengthen the connection between the theory of rests and Tonvorstellungen, given the strong visual connotation of the terms vorstellen and Vorstellung. ¹⁴ Figure 3 shows a prototypical graph representing the values of tones and rests within a motive. The horizontal line (a–b) represents the “level,” and the rise and decline of values are represented above and below this line, respectively. The white and gray areas each represent the values of tones and rests, and together take the shape of a “symmetrical pathway” around the axis of the middle “dynamic zero.” In the figure, tones have positive, plus values, whereas rests have negative, minus values. ¹⁵ The point c marks the highest point within the motive; the (a–c) part and the (c–b) part, therefore, stand for the upbeat and ending of a motive, respectively. Figure 4 represents the values of two different types of rests that can appear in relation to this kind of motive, with Figure 4 a) illustrating the value of an inner-rest (Innenpause) located in the middle of a motive, and Figure 4 b) representing the shape of an end-rest (Endpause) marking the end of a motive or unit.

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Figure 3.

Dynamic values of tones and rests (Riemann, 1903, p. 130).

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Figure 4.

Dynamic values of rests (Riemann, 1903, p. 132).

In musical literature, inner-rests would be much less common than end-rests. Example 1 shows such rests located within motives. Riemann’s eccentric phrasing marks transform rests originally written as end-rests into inner-rests. These rests within motives carry a cognitive function different from that of the boundary-marking motives, and their effect is felt as “growing in depth” and “increasing in the force of negation” (Riemann, 1903, p. 132).

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Example 1.

Examples of Riemann’s inner-rests: Beethoven Sonata op. 31/3, the first movement (1917–1919, p. 427). ¹⁶

What is growing and increasing here, then? The values of the rests do not stand for the mere durations of acoustical silence but for the perceived quality of the rests: rests are indicative of “perceived silence” rather than “acoustical silence.” ¹⁷ Of course, these values, as originally conceived by the composer, ought to be realized in performance, if not consciously, so that the dynamic shading becomes clear to the listener. In the case of rests, the agogic can replace the dynamic so that the value of the rest can be expressed in performance: “Perhaps the rest placed in the position of the stronger tone becomes lengthened” (Riemann, 1884, p. 149; Appendix [4:3]). Nevertheless, writes Riemann, “undoubtedly, many things become a matter only of imagination (Vorstellung), not of execution” (1884, p. 148; Appendix [4:4]). He is speaking not of the acoustical property of a thing, but of the subjectively felt property of the rests – the qualia, to adopt a term from the philosophy of mind. ¹⁸ In his 1916 article, Riemann goes a step further and refers to this experienced quality of a tone as its “size” (Grösse) or “measure” (Maβ): “Most important to absolute hearing – what it recognizes – is merely the consciousness of the quality of a tone that we could call its size or measure, which is dependent on its frequency or wavelength” (Riemann, 1916, p. 14; Appendix [5:1]). Intensive musical imagination contains “all the attributes of actually sounding music” (1916, p. 3), and this would include not only pitch, timbre, and duration but also the metrical weight and aesthetic value of tones as well as rests. The word “conscious” appears frequently and with importance in his 1916 essay, declaring the beginning of his new theory of Tonvorstellungen. In addition to the passage cited above, he writes in the same essay “for the imagination of tones, the conscious realization (Das Bewußtwerden) of the distinctions of single tones in each of these areas implies the emergence of more complicated formations” (Riemann, 1916, p. 10; Appendix [5:2]).

Such a psychological interpretation of Riemann’s values of rests and the idea that individual tone-images “become conscious” yet again find resonance in psychological writings. Interesting analogical sentences are found in the writings of Wundt when he speaks of “the sinking of one of the ideas and . . . the rise of the other” and of an “empty time interval” in which “attention is not sufficiently accommodated either to bring a distinct perception”; or “While we are hurrying from one [idea] to the other, everything between them vanishes in the twilight of general consciousness” (Wundt, 1873–1874, p. 263, as cited in James, 1902/1981, p. 599).

More specifically pertinent here is the psychological program proposed by Herbart. As previously pointed out, Herbartian Vorstellungen (i.e., the psychic atoms) are the fundamental units constituting the mind. Additionally, these are units of self-activity rather than static contents, and in this regard are distinguished from “Ideas” in British associationist psychology, rooted in John Locke (1632–1704), continued by David Hartley (1705–1757) and David Hume (1711–1776), and developed further by James Mill (1773–1836) and Alexander Bain (1818–1903). As noted by many later-generation scholars, ¹⁹ Herbartian Vorstellung resembled the associationist notion of Idea in that both are fundamental units that together constitute the human psyche, and Herbart was certainly familiar with the German translation of Locke’s Essay Concerning Human Understanding. ¹⁹ Nevertheless, Herbart did not consider his Vorstellung as an equivalent to Locke’s Idea because his Vorstellungen, as dynamic units, facilitate or inhibit each other. Herbart’s psychology is none other than “the statics and mechanics of mind” (Statik und Mechanik des Geistes), in which these Vorstellungen float near the surface of consciousness unless they sink or are suppressed by other ideas (Hoffman et al., 1990, p. 185). In fact, Herbart introduced the term Schwelle (threshold) or Schwelle des Bewusstseins (threshold of consciousness) into the psychological discourse in order to explain the detection and discrimination of a given stimulus, and more generally, to refer to the boundary between lower and higher mental faculties (Herbart, 1816/1891, 1824/1890).

A closer similarity to Riemann’s idea is found in the writings of Gustav T. Fechner (1860), a pioneer in experimental aesthetics and psychophysics, which he defines as “an exact theory of the functionally dependent relations of body and soul” (p. 8). ²¹ What seems to have a more direct bearing on the current discussion is Fechner’s notion of Bewustseinsschwelle (conscious threshold), which is adapted from Herbart’s psychology. In Fechner’s program, the threshold became primarily concerned with sensation, referring to the “point at which a stimulus or a stimulus difference becomes noticeable or disappears” (Fechner, 1860, Vol. 1, p. 238; Appendix [6:1]). In other words, the outer stimulus must reach this physical magnitude in order for the sensation to become perceptible and thus conscious. It is worth citing a passage from his Elemente der Psychophysik (Fechner, 1860) in its entirety here, because the parallel between this passage and Riemann’s explication of the rest is fairly obvious.

As long as the stimulus or stimulus difference remains below the threshold, its perception remains, as one says, unconscious. As the size of stimulus and stimulus difference descends further and further below the threshold, the unconsciousness is deepened further and further accordingly. Thus distant sounds, the stimuli of smells in the atmosphere, and the sensation awakened by these remain unconscious until the intensity of those stimuli exceeds a given magnitude, the threshold. From this, we are led to the designation of negative values for the unconscious sensation values, if we take the threshold value as zero and the value of conscious sensations as positive. (Fechner, 1860, Vol. 1, p. 246; Appendix [6:2])

The postulation of such negative sensations was necessary for mathematical reasons. The well-known Fechner’s Law, measuring the magnitude of a sensation in logarithmic relation to the strength of a stimulus (S = k log R, where S stands for sensation intensity, R for the magnitude of the stimulus, and k for a constant), presupposes the theoretical existence of negative sensations. This notion was apparently the source of frustration, and Fechner struggled with critics as a result throughout his life. Our interest is not in resolving the controversy surrounding negative sensations, which appears to be ongoing still, but in the way Fechner explains the notion. Even though a psychophysical process may fall below the threshold of consciousness and become unconscious, its value is “not zero” (nicht Nichts). Its psychical value is “determined by the distance from the point at which it becomes real for us” and is negative (Fechner 1879, p. 245, as cited in Heidelberger & Thomas, 2010, p. 228).

The concept of negative sensations refers neither to weak sensations nor to non-sensations but indicates the amount of psychological activity necessary to render unconscious sensation perceptible and thus raised to the level of consciousness. Although initially this explanation was not the central idea in his theory, the unconscious entered into Fechner’s psychological discourse through use of the metaphor of threshold, and the notion of the human psyche came to embrace the unconscious, or what is below the conscious threshold. These aspects of early psychology had once been marginalized, with only the features contributing to the “scientific” foundation of the discipline tended to stand out. In the history of psychology, increasingly frequent in 19th-century psychological writings is the discussion of such topics as the unconscious, volition, will, and drive. Even Wundt, who is often credited with being the discipline’s founder, and who disapproved of the idea of “unconscious mental states,” discussed the subject of volition and differentiated between different degrees of being conscious. ²² The process of the “focalization of some content in consciousness” was referred to as apperception, and was seen as a volitional process. It is a narrower form of consciousness characterized by selective attention and is thus set apart from the larger field that is less conscious. ²³

Such views on the human mind constituted the conceptual environment that acts upon Riemann’s notion of the musical mind and may have influenced his ideas. Riemann did not explicitly allude to the above writings on the unconscious. ²⁴ Nonetheless, the ideas of threshold and perceptual activity as bringing the unconscious into the consciousness lie at the center of Riemann’s theory of Tonvorstellungen. Riemann’s idea can be characterized as a theory of musical apperception, “conscious perception,” achieved by means of an activity of the perceiver in the form of attention given to the Vorstellung. Riemann also recognized the kind of music that is experienced beneath our threshold of consciousness, as illustrated by his theory of rests, which asserts that the dynamic values of rests are felt in cognition beneath the level of consciousness.

These intriguing examples – that is, the negative value of rests that can grow or diminish during the acoustical silent interim, the notion of tone-images as becoming conscious, and rests as a suppression of such tone-images below the conscious level – point to a conception of the human psyche different from what we have encountered in the first part of this article. Instead of the cognitive and conscious mind, we see traces of the old notion of soul, which had disappeared from the discourse of scientific psychology. In Riemann’s 1916 essay, which discusses most of the nuclear concepts of his harmonic theory in a psychological light, he uses the word “mind” (Geist) throughout, but one passage stands out notably in terms of its rhetoric:

Thus, as a result of the valuation of pitch-level motion as alternating rising and falling, striving and renunciation, will and resignation, a psychic experience emerges comparable to an ascent into the lighter regions and a descent into the darker [ones] – not as something viewed but as something actually experienced. The imagining (Das Vorstellen) of these motions is a true participation with the Will; the soul (Seele), the living human-spirit, carries these motions itself and through them rejoices in its existence and its efficacy. (Riemann, 1916, p. 15; Appendix [7]) ²⁵

The use of the word “soul” (Seele) here occurs in the context of a discussion of melodic motion, as has traditionally been so, and in resorting to a more metaphysical and philosophical language and analogies, this passage sets itself distinctly apart from the rest of the essay, which uses rigorous and controlled symbols for tone-relationships, such as T, Q, O, 1/T, 1/Q, and 1/O. ²⁶ The separation of the “lighter” and “darker” regions reminds us of the human psyche as configured by the notion of threshold and encompassing both conscious and unconscious. Furthermore, the evocation of “descent into the darker regions” bears a similarity to Hegel’s notion of the feeling soul (fühlende Seele) and a reference to the unconscious within the stage of presentation (Vorstellung): “. . . this night-like mine or pit in which is stored a world of infinitely many images and representation, yet without being in consciousness” (Hegel, 1971, p. 204). Riemann’s allusion to soul here may not be as deliberate as some of those “strategies of reenchantment” found in the world of science in late 19th-century Germany (see Daum, 2002). Nonetheless, it reveals the ambivalence between two seemingly contradictory modes of thinking that characterize modernity at the fin-de-siècle and the contemporaneous mind sciences.

Rethinking conceptual paradigms in early music psychology

In the second volume of Elemente der Psychophysik, Fechner (1860) refers to the rather modern concept of “modeling”: “the most general relations of the life of the soul allow a very simple and satisfying psychophysical representation [i.e., modeling], owing to the premise that the threshold concept is transferable onto the psychophysical movement” (Vol. 2, p. 435; see Appendix [8]). Analyzed in light of the mind sciences of his contemporaries, Riemann’s language and terms reveal much more than mere pretentious borrowings of (pseudo)scientific concepts: His thoughts on phrase structures and rests exhibit two different and even conflicting ways of modeling the musical mind. The boundary concept emphasizes the demarcation of temporal flow into recognizable units, and thus points to a conception of the cognitive and representing mind (Geist). On the other hand, the threshold concept distinguishes different levels of conscious, embracing the conception of the soul (Seele) that feels the sublime. Here, we find a flux between two different aspects of the human psyche in one theorist’s writings, which cannot be simply described as Musikpsychologie. Bujić (1988) would describe such inconstancy in Riemann’s theory as due to the general spirit of the time, embodying the clash between the romantic attitude, philosophical speculation, and positivistic, scientific rigor (p. 341). I would like to express these concepts more specifically in terms of their parallel to the models of the human mind in contemporary psychology, which provided the conceptual circumstances for Riemann. The pursuit of rigorous “scientificity” was a significant motivation, but it constituted only one part of the reason for the close liaison between music theory and the incipient discipline of psychology in the late 19th century. As a study on the human mind, psychology tended to construct its subject rather than to discover the raw truth, and cross-fertilization between psychology and music theory was thus achieved through terms and concepts. Even if they manifest incorrect usages and misunderstandings, the analysis of these music-theoretical terms against the background of contemporary psychology reveals conceptual implications that may not have been immediately apparent to the practitioners.

As the historian Edward Reed (1997) recounts, psychology emerged gradually from a science of soul, narrowing down to a science of the mind during its formative years from the early to the late 19th century. Nonetheless, the process was not constant but fluctuating. Even the scientific psychology at the end of the 19th century sometimes illustrates a more inclusive aspect, encompassing both the cognitive/conscious mind and the unconscious, possibly resurrecting the older idea of the soul. Music theorists with psychological orientations were influenced by such a notional environment, in which two contradictory modes of modeling the mind coexisted. Analyzing the specific uses of languages illuminates this undercurrent operating beneath the consciousness of individual theorists, possibly indicating an important paradigmatic mode of thinking in early music psychology, and such a line of enquiry points to a kind of approach that has not been widely adopted in the historical study of music psychology.

The preceding analytical exercise primarily aims to explore the origins of music-psychological ideas that were shaped out of the interplay across various forms of knowledge and to provide insight into patterns of thought that were characteristic of 19th-century music-psychological thinking. In light of the recent rise of academic interests in various modes of listening, including emotion and trancing, such a historical understanding is expected to render us more sensitive to the implications of our own position today as we venture to cross the boundaries between theoretical accounts of music and psychology.