Let us imagine an aesthetics of music grounded in the notion of compression. Audio file-compression locates the point at which the granularity of the signal is of sufficient density to recreate sound, to give the illusion of an original indistinguishable from that of a higher-resolution reproduction. We might stipulate that the efficiency of perception is an aesthetic desideratum: the beautiful or well-formed is that which transmits musical information without waste, locates a “sweet spot” in the density of information. The flattened dynamics of commercial music could be said to be well formed, locating the ideal point in the dynamic range or the place of maximum efficiency. Should we be catholic in our definition of music, we could assert that the clarity of the cinematic soundscape (wherein everything is completely audible) is likewise efficient or ideal. From this a corollary: sound designed or rendered is to be preferred to “natural” sound. By extension, we might imagine a sociology, one wherein the beautiful is that which is coded by timbre or genre or the like so as to allow internal soundscapes to be optimized; or to allow even for an optimized listening, one locating an ideal point between attention and disattention.

What is interesting here is not the exercise itself (admittedly facile) but the almost automatic rejoinders it provokes. Rejoinders epistemological: Would not neuroscience, perhaps, provide a more solid ground for an aesthetics, one whose development rested less on suggestion and more on things empirical, testable? Rejoinders moral: Would not an aesthetics grounded in efficiency sacrifice a richness of experience? Is there not something important captured by lossless encoding, or vinyl? Rejoinders ethical or disciplinary: Given that the desideratum of such a theory would be a set of covering laws governing music, could the end result be anything but mechanistic, prescriptive? And even were we to come up with a satisfying set of covering laws, need these award any special privilege to music? Or need music be but a special case in a general aesthetics of sound?

Have we even need for an aesthetics? The aesthetics of music survives as a technical project within philosophy, analytic and otherwise, a subdiscipline of a subdiscipline. In the musicologies proper, though, it is something deferred, particularized, historicized. If it at times seems to motivate certain areas of music theory, it does so covertly, or is explained away with a degree of embarrassment. It does not walk in daylight under its own name, or when it does, it dons the mystic's motley or the widow's weeds. This being said, much or even most of the interesting work in theory and historical musicology is aesthetic in all but name, weaving its way delicately around old arguments and well-seated prohibitions. One can argue that the absence of an explicit positive aesthetics is a sort of liberation from some conception of absolute music. But is the ideology of “absolute music” itself sufficiently powerful to engender such deep anxieties?

The introduction to Alexandra Hui's text recounts (with musical examples) a lecture given by the physicist Ernst Mach in 1871 to an audience in Prague. Mach grounds the notion of aesthetic pleasure in the repetition of sensation, and particularly in the repetition of sensations across axes of symmetry. This is an established dictum of visual aesthetics, a survival from the classical tradition. He then sits at the piano, plays through several short passages (chord sequences in one hand, melodies in the other). Next, through the use of mirrors, reorienting the notation in different ways, he plays the examples upside-down and backwards. Symmetry destroys the aesthetic experience—with one exception. Sequences of major harmonies come out sounding like minor. Here, Mach asserts, there is a symmetry for the ear, and a fine one at that, as it demonstrates some sort of mental functioning, the workings of an aesthetic faculty. Here, Hui notices something more fundamental than the harmonic dualism. Without any sense of it being outlandish, Mach proposes (and the audience accepts) music as a scientific instrumentality and aesthetics as something empirically demonstrable. From this epiphany (so simple, so profound), Hui spins a carefully wrought account of a complex intellectual motion, a narrative told from the standpoint of the history of science, to be sure, but partaking of the contemporary musical discourse. Indeed, if the musical readings often run through what is for us familiar territory, this is more than recompensed by the richness of the telling as a whole. Music is not subordinated to the history of science, treated as an invited guest, but itself becomes part of the history of science, even briefly its driver.

Hui's thesis is that the discipline of psychophysics in mid- to late nineteenth-century Germany was, over the course of its short span, inseparably bound to the corresponding post-Romantic musical aesthetic. A first chapter focuses on the work of Gustav Fechner, that strange and straying professor of physics whose conception of a science transcending crude materialism prompted him to reformulate mathematically the work of Ernst Weber on tactile sensitivity. His reformulation, wherein the relation between the intensity of a stimulus and its perception can be expressed as a logarithmic function, has come to be called the Fechner-Weber law and was the foundation of his Elemente der Psychophysik (1860).1 Fechner consistently disclaimed any expertise in music and rarely wrote of it (referring only to experiments in pitch discrimination). Yet Hui makes a strong case that his was an intensely musical world. More important was Fechner's specific interest in aesthetics, culminating in the Vorschule der Aesthetik of 1876.2 He maintained that the aesthetical, in so much as it almost short-circuits the distinction between sensation and higher mental functions, constitutes a bridge between inner and outer worlds, and allows a unique access for the experimental investigation of the former. Hui's second chapter introduces the new musical aesthetic of the latter part of the century, tracing a path from A. B. Marx to Hanslick, and hence to Hugo Riemann. This material will be familiar to musicologists, but Hui gives it a twist. Fechner's project demanded something new, a sort of methodologically rigorous subjectivity, the test subject becoming the monitor of his or her own response. This, she asserts, is bound up with the new musical aesthetic, which in putting forward a semantically empty and autonomous music as an ideal made corresponding demands on the listener, privileging sensation over emotion, pathologizing passive reception. She ties this also, in ways we might expect, to the theoretical world of Riemann, whose focus on hearing (and its extension into a musical logic) drew authority from the psychophysical. A third chapter turns to the singular figure of Hermann von Helmholtz, whose magisterial Die Lehre von dem Tonempfindung als physiologische Grundlage für die Theorie der Musik (1863) came almost immediately to stand as the emblem of an aesthetics that was both scientific and artistic.3 That Helmholtz himself did not think of his work as a psychophysics is beside the point for Hui, who argues that his deep musical background, classicist taste, and fascination with (in particular) keyboard instruments allowed him to focus on the materiality of sound, and thus to draw music in as a privileged case of sensation, one peculiarly amenable to empirical study. Her fourth chapter explores the collaboration of Mach and the Viennese critic Edward Kulke. Specifically, she addresses the way in which the former's work on the mechanisms of accommodation, the ability to alter a global perception by attention to the particular detail, led to a historicized conception of listening, one that could embrace Wagnerian and post-Wagnerian composition. A final chapter recounts the controversy over experimental method between Carl Stumpf and Wilhelm Wundt towards the close of the century, one that led to the divorce of musical aesthetics from psychophysics, and indeed the displacement of the psychophysical project itself by the modern psychological laboratory.

Benjamin Steege's study of Helmoltz is of a different temperament, shading more to the critical and theoretical than the strictly historical; it is latitudinal rather than longitudinal. His text moves out and around the narrative spine given by Hui with an interpretive delight and a virtuosity, drawing in a wide range of subjects and interlocutors—the politics of the post-1848 generation, educational theories, and a range of modern authorities, from Gadamer to Benjamin, Max Weber and the like. His argument, unfolding in six chapters, tracks the three great divisions of Die Lehre von dem Tonempfindung, moving from physical and physiological acoustics through the psychophysical to the doctrines of music theory. Received history would locate the beginnings of Helmholtz's project in methodology, as it is he who applies Fourier's equations to the world of sound (as a way of resolving an argument over whether sound is perceived as singular or multiple, the Seebeck-Ohm controversy). Steege holds this until his second chapter, taking pains in his first to point out something less obvious. It is not for nothing that Helmholtz fastens on sensation, that term so beloved of eighteenth-century empiricists. What motivates Helmholtz's work is the desire to wrestle the discourse of mind away from idealism in any of its varieties—Kantian, Hegelian, even perhaps Fechnerian. His concern with sensation, with micro-sensation at that—phenomena such overtones and combination tones previously noted but always left at the margins—shifts the focus to ordinary hearing, democratizes the discourse, binds the project to its own popularization, to public demonstration. This is most notable in the form of Helmholtz's famous resonator, wherein the upper partials of a generator (the almost imperceptible strike of a tuning fork) are almost magically made audible.

Thus, in Steege's second chapter, Helmholtz invents the modern ear. The application of the Fourier equation to sensation joins his work with that of psychophysics. More, though, the logical entailments of this move force a displacement. Traditional physical acoustics cedes its place to a physiological acoustics. The study of the structure of the ear itself takes center stage, as it is the material portion of an engine of analysis, a machine for determining all of the components of the musical sound. (Musical sound is privileged as the most transparent of stimuli, and thus the one that provides the greatest payoff for study.) The körporliche Ohr, though, cannot be all. It requires a counterpart, a geistige Ohr, and here is the crucial move. For Helmholtz, the notion of the geistige Ohr cannot rehabilitate the philosopher's vital force, cannot become the agent of a backdoor metaphysics. It too is part of the mechanism. The geistige Ohr processes the information given by the körporliche Ohr. Yet then it conceals the workings of the analytic engine, packaging and coding what is heard as a single thing, a sign. The sound of a violin, once named as the sound of a violin, is always the sound of a violin. Fortunately for the researcher, this coding is never completely efficient. It is but a clouding-over, and what remains outside its reach is the marginalia of sensation. These marginalia are the evidence for the workings of the engine. And thus, as Steege would have it, the modern ear doubles on itself. The object of investigation becomes the instrument for investigating itself. One learns how hearing works by listening.

Or better, by listening closely. The ear becomes an analogue of the Helmholtz resonator, sensitized to the point that it can bring out that which is barely heard. For example, in addition to the partial series, Helmholtz is drawn to such psychoacoustic phenomena as acoustic beating and combination tones (summation and difference tones). This last becomes the basis for a theory of dissonance. The combination tones of the constituent pitches of any simultaneity, being more or less in accord with each other (as are, to a second degree, the combination tones of combination tones) provide for a simple algebraic computation of degrees of dissonance. That these calculations exceed the threshold of conscious perception is not a problem. The ear will perceive dissonance as a sort of roughness (and consonance as a smoothness). Thus, Helmholtz's definition of dissonance is more fine-grained than the crude divisions of the theorist, positing a scale of dissonance. It requires no reference structure, no triad (though triadic sonorities are the smoothest, and other sonorities rapidly become too complex to calculate). It is registrally sensitive: for Helmholtz, the root-position triad is far from the “smoothest” or most consonant of triadic sonorities. How, then, are the workings of sensation and perception to be tied to a theory of music? Steege's third chapter argues how central attentiveness is to Helmholtz's project. There is a temporal gap between the experience of a sensation and its perception. The consignment of experience to the sign is not simply incomplete but also belated. Theory comes into being not as a mechanical derivation from sensation itself but from this belatedness. To think of this another way, Helmholtz spreads his discourse. As discussed, this involves opening a discursive space between the analyses of whole-number acoustics and music theory, a structure that had governed the latter since Rameau. Physical acoustics gives over to physiological acoustics; and in turn the analytic workings of the körporliche Ohr give over to the mental representations of the geistige Ohr. Between these, though, appears a different epistemological entity, a “third ear” (to use Steege's coinage). The traversal of domains is also a traversal of different degrees or sorts of empiricism. This is not a unified system but a construction held together through a series of pragmatic methodological compromises, evidencing a willingness to accept different sorts of arguments as applying to different domains. (Steege's fourth chapter situates Helmholtz's theory within the context of liberal politics.) Attentive listening makes the mechanisms of hearing available to investigation. But the relation between this listening and that of music theory carries with it a reciprocity. Musical training makes for the optimally attentive listener. This casts attentiveness is a learned faculty. If one follows the argument further, music theory itself can be taken as a sort of learning to be attentive, the exploration of the affinities of the tones and their partials becoming a sort of ongoing collective revelation. Musical theory is evidence of historical process.

Here I need to take a breath. Steege's arguments are more subtle and involved than my summary would indicate. He reads closely and reads well. As a theorist, his discussion of Helmholtz's recuperation of the discipline is acutely sensitive to its logical entailments, to the latter's delicate wrestlings with the concept of affinity and the function of memory. But to turn away briefly, it is worth remarking that there is a counterpoint between his reading and Hui's discussion of Mach. The engagement between psychophysics and music was as brief as it was intense, its main dialogue falling between Fechner's Elemente der Psychophysik of 1860 and the final volume of Stumpf's Tonpsychologie of 1890.4 It was always a conversation. Mach, three years after the publication of Die Lehre, authored a reworking of Helmholtz for musicians, and his conception of accommodation takes as its point of departure the former's discussion of attentiveness.5 (Mach—physicist, psychologist, philosopher, sometime musicologist, confidant of Einstein, correspondent of Schenker—is perhaps the most fascinating figure in Hui's account.) It is in their respective moves to historicism, though, that the differences emerge. As Hui explains (pp. 105–14), by the publication of his magnus opus in 1886 (Die Analyse der Empfindungen und das Verhältnis des Physischen zum Psychischen),6 the idea of directed attention—accommodation—has for Mach given way to an almost Lamarckian understanding of aesthetic evolution, one in which the attentiveness to particular features in one generation becomes an inherited trait in the next. (This, Hui indicates, is one product of Mach's engagement with the Wagnerian Kulke.) Helmholtz's historicism, by contrast, takes an oddly different turn. Throughout, Steege's readings seem almost overly sensitive to the social and political tonalities of Helmholtz's writings—and for good reason. Recall Helmholtz's theory of the perception of consonance and dissonance as the perception of degrees of smoothness/roughness. What should be obvious is that this perception must be most clear to the ear when harmonies are voiced in terms of just intervals. Needless to say, just temperament was at odds with the equal temperament integral to chromatic harmony. It was this which prompted Riemann's later rejection of psychophysics, equal temperament being crucial to his musical logic; and we would be sympathetic, particularly as those who advocate for just temperament do so in strangely moralistic tones. Yet given Helmholtz's ideation of music history as a materialization of attentiveness (a strategy that Riemann appropriates for his own history of theory), it is as plausible for him to conceive just rather than equal temperament as the goal of a music-historical teleology, a goal that might, in fact, be promoted a sort of Herbartian pedagogy (pp. 121–22). Thus Steege's fifth chapter culminates in an odd but rewarding excursion into Helmholtz's engagement with the Tonic Sol-fa choral movement (one of those meekly authoritarian attempts at the moral development of the Victorian working class).

To close the story, Helmholtz's fascination with micro-sensation was coming to seem dated by the 1880s. Far more appealing was Carl Stumpf's theory of the perception of consonance as Verschmelzung (fusion), a synthetic and wholly psychological function. This was indicative of a deeper shift. Hui focuses the denouement of her narrative on a notorious dispute between the two great figures of the younger generation, Stumpf and Wilhelm Wundt (see her chapter 5). The stakes in their contest were still musical, involving the mechanics of pitch discrimination. The argument began over the proper application of the now sacrosanct Fechner-Weber law to pitch sensitivity, a student of Wundt presenting results that challenged Stumpf. The technical details are interesting for the theorist, as they turn on the perception of arithmetic and harmonic means; yet the consequences are more so. As the exchange intensified, Wundt weighed in on the part of his student, and the focus shifted to methodology. The question came to turn on who constituted the best test subject in the psychological laboratory. For Stumpf, it was those with musical training—with a “music-infected consciousness” (musik-infinizierten Bewusstsein)—those whose refined senses offered the sort of attentiveness needed to pierce the veil of the ear. Wundt came to argue the opposite. Musical training, to turn Stumpf's formulation on its head, could be seen as introducing bias, and the valuable test subject was one who was uncontaminated, possessed of the innocent ear. Real results were to be obtained not from the services of the gifted few but rather through the testing of large numbers. Thus an inflection point. Music remained, to a certain extent, an object of study in psychological circles into the next century. Yet it was Wundt's views that ultimately prevailed in the laboratory. Stumpf moved on to become one of the founders of the discipline of comparative musicology, whereby sound recording usurped the practical function of the trained listener. Dismissed from the laboratory, aesthetics lost its claim to science, to an empirical foundation. At the same time, psychology ceded its claims to kinship with physics, to the mathematical expressions of physics, and became a statistical science. Of psychophysics, only the Fechner-Weber law would survive, and that because of its practical application—most notably (today) to audio file-compression.

If the vessel holding together an aestheticized science and a scientific aesthetics did shatter into any number of brittle and professionalized disciplinary shards—comparative musicology, modern music theory, experimental psychology—this was not the end of the narrative. Both Hui and Steege close on an almost elegiac note. While Helmholtz's concern with sensation is abandoned in favor of a return to idealization on the part of theorists such as Riemann and Kurth, it infects composers such as Debussy and Schoenberg. A concern with sensation becomes a hallmark with modernity (and a point of criticism). Music came to flicker between Empfindung and Vorstellung, sensation and representation—as did Helmholtz's ear.

The notion of a systematic musical aesthetics itself moved into the twilight. It has not vanished. But the end of the psychoacoustic episode marked a loss of authority—an authority that we today would somehow sense as authoritarian. Steege closes with a reading of Max Weber's unpublished sociology of music, dating to the second decade of the new century, wherein Helmholtz's ideation of sensation gives leverage to a profound reversal. For Weber, “primitive” music, attentive to sensation, is superior to the denatured, pallid, institutionalized sound of modern Western music. Musical aesthetics transforms into critique. It survives also in other guises—technological fantasies being but one. It becomes a negative space into which all manner of things can be written. But it can only do so in so much as our own sense of musical aesthetics takes shape as an afterimage of the aesthetic sciences of Fechner, Helmholtz, Mach—an aesthetics we might dismiss as quaint or curious, but one whose power is so elegantly and convincingly detailed in these two books.

1.
Gustav Fechner, Elemente der Psychophysik, 2 vols. in 1 (Leipzig: Breitkopf & Härtel, 1860).
2.
Idem, Vorschule der Aesthetik, 2 vols. in 1 (Leipzig: Breitkopf & Härtel, 1876).
3.
Hermann von Helmholst, Die Lehre von dem Tonempfindungen als physiologische Grundlage für die Theorie der Musik (Braunschweig: Friedrich Vieweg und Sohn, 1863).
4.
Carl Stumpf, Tonpsychologie, 2 vols. (Leipzig: S. Hirzel, 1883–90).
5.
Ernst Mach, Einleitung in die Helmholtz'sche Musiktheorie (Graz: Leuschner und Lubensky, 1866).
6.
Idem, Die Analyse der Empfindungen und das Verhältnis des Physischen zum Psychischen (Jena: Fischer, 1886).