Kant’s Theory of Musical Sound: an Early Exercise in Cognitive Science

  • Graham Solomon
Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 65)


Kant is well known as the philosopher who spent his life hunting for a prioris, philosophically identifiable characteristics of the make-up of human beings. These characteristics are species-universal, and are necessary presuppositions of the possibility of the success of various kinds of cognitive and cultural strategies. Kant bagged some big game. Space, time and the categories are a priori conditions of the possibility of human cognition. God, freedom and immortality are a priori conditions of the possibility of morality. The sensus communis is the a priori condition of the possibility of the universalization ofjudgments of taste. The hardwon trophies are presuppositions of possibilities. Once they were thought to be properties of a universe well ordered by a substantive god. No longer. Now we must look upon them as entrenched contributions of what it is to be human, as preconditions of human potentialities.


Aesthetic Experience Simple Arithmetic Animal Spirit Aesthetic Appreciation Tonal Structure 
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  1. 2.
    I use James Meredith’s translation, Immanuel Kant: Critique of Judgment (Oxford University Press 1964). I will refer to this work as KU, and will refer to section and page numbers of the Academy Edition, Kants gesammelte Schriften. I will refer to the Critique of Pure Reason as KVR, and will follow the custom of giving page numbers of the fiirst and second editions.Google Scholar
  2. 3.
    “Eindrücke”, literally “impressions”, but meaning, of course, impressions of sense. Google Scholar
  3. 4.
    See also Immanuel Kant, Anthropologyfrom a Pragmatic Point of View, translated by Mary J. Gregor (The Hague: Neihoff 1974).CrossRefGoogle Scholar
  4. 5.
    Kant’s word for “play” is “Spiel”, a word having as many and varied uses as its English counterpart. The choice of words is not, I think, intended to minimize the importance of ordered impressions of sense. Quite the contrary, since the aesthetic reaction is directed to an object taken to be freely created (which is part of what Kant means by his expression “purposiveness without purpose”), we are invited to think of the ordered sensations to which we react aesthetically as playful only in the sense of being taken to be freely created. One is not playing a game if one is compelled to do so. I do not react with pleasure to music in the same way in which I react to felt pains. I will return to Kant’s important distinction between single sensations and plays of sensation in the discussion of point 3 of his theory, below.Google Scholar
  5. 6.
    Kant argues that subjective taste can be universalized by appeal to the sensus communis, a public sense, where reflection takes into account the collective reason of mankind (KU, sect. 40, pp. 293ff). In the Anthropology he refers to the appreciation of music as a “social pleasure” (sect. 18, p. 155).Google Scholar
  6. 7.
    I am deliberately ignoring tempered or atonal scales, which violate the Pythagorean scale but are nevertheless heard as beautiful. Kant’s theory can probably accommodate tempered scales. I had thought that the fact that we aesthetically appreciate atonic music falsified Kant’s theory of musical sound. After conversations with my colleague Thomas Lennon, I am now not so sure. More of this below, section 5.Google Scholar
  7. 8.
    I realize that ‘detemporalize ’and ‘despatialize ’are mongrel expressions at best. But Kant is dealing here with the aesthetic object, and that object is not the biological flower, not the painted surface, not the heard sounds. These objects can be given straightforward physical explanations, which depend crucially upon determination of geometrical angles and distances, and often also upon measures of time. It is well known that such physical explanations of the beautiful object are unavailing for the purpose ofaccounting for aesthetic appreciation. apprehensions ofbeauty are affective states, feelings. This changes the status of the predicates we employ. it seems uncontroversial to say ‘this flower has three petals ’or ‘this sound is intense enough to break glass of a certain strength’. Such predication seems idle when we are describing aesthetically appreciated objects. A statement like `I appreciate this beautiful porcelain vase because it is delicate (has a fine form, difficult to produce) ’seems to me largely meaningless as an aesthetic judgment unless translated to say `I appreciate this vase delicately’. Strange as that locution may seem, it catches the affective character of the aesthetic experience in a way that is completely lacking in the other, normal statement ofpredication. aesthetic objects do not have or lack properties. Some tampering with ordinary ways of speech therefore seem innocuous.Google Scholar
  8. 9.
    It is too simple, but nonetheless true, to say that Kant thought that because we are all in principle capable of doing sums, we are all in principle capable of apprehending beauty in the arithmetical structures of music.Google Scholar
  9. 10.
    For a wonderful survey of the problems of theorizing about the consonances, see H. F. Cohen, Quantifying Music: The Science ofMusic at the First Stage ofthe Scientific Revolution, 15801650 (Dordrecht: Kluwer 1984).Google Scholar
  10. 11.
    Some tensions in Kant’s thought about music must be mentioned here. Normally, Kant distinguishes charm from beauty. The object taken to be beautiful is contemplated, reflected upon; both a sensuous and an intellectual act are involved in the aesthetic response, which is uniquely active, combining as it does both the free play of the imagination and the constraints of understanding. That which is charming, on the other hand, repeatedly arouses our attention, but the mind is a passive recipient of the experience of charm. This would seem to entail that music is not beautiful but only charming. I do not think Kant has a consistent view of the difference between charm and beauty. His discussion of pleasure in music appears to depend only on a distinction between passive and active reception of that which is taken to be beautiful. The seeming inconsistency emerges frrom the fact that he takes music to arise directly firom sensation, and not frrom that kind of mnental culture that expands our cognitive capacities. Because music is nonconceptual, it must rank below those arts that are directly expressive of concepts or aesthetic ideas. However, because he thinks music has form to which we respond, and form or design is the hallmark ofbeauty, he does seem to hold that music can be beautiful, although passively received, whereas other arts — poetry, for example — also require attention to conceptual content. He claims quite explicitly in KU sect. 53 that consonant music gives expression to an aesthetic idea. Surely he holds that charm is compatible with beauty, and writes in ways suggestive of the point that aesthetic experiences of what is charming can be had. I will return to this question below in section 4 in my discussion of the crucial passage at KU sect. 51.Google Scholar
  11. 12.
    In the Anthropology, Kant writes as follows (sect. 18, p. 155): “As for vital sense, music, which is a regular play of aural sensations, not only moves it in a way that is indescribably vivacious and varied, but also strengthens it; so music is, as it were, a language of mere sensations (without concepts). Its sounds are tones, which are to hearing what colours are to sight — a way of communicating feelings at a distance to all those present anywhere within a certain space, and a social pleasure that is not diminished by the fact that many people participate in it.”Google Scholar
  12. 13.
    A phrase can have grammatical integrity without being grammatically correct. To have grammatical integrity, a phrase must only be recognizable by speakers of the language as an allowable group of sounds or of inscriptions. Much grammatically incorrect intoned spoken language has integrity. Consider the dialects of North American teenagers, who communicate with one another in grammatically incorrect ways, although in ways which for them have integrity.Google Scholar
  13. 14.
    A view that might well be disputed by the lover of fabrics, the gourmet and the blender of perfumes. I cannot pause to investigate the matter here, but it may be that one can make out a difference between the “languages” of touch, taste and smell, on the one hand, and sight and sound on the other, by pointing out that the first three languages are intrinsically metaphorical, whereas the second two are literal. This would seem to be a distinction Kant could accept, given that, in the case of colour, specifiic affective states are the “language” ofparticular colours. Those who classify wines on the basis ofmodes of taste and odour, and those who distinguish between textures by refined forms of touching will dispute my suggested distinction between the kinds oflanguages of sensation. The experienced oenophile or the blender ofperfumes will point out that the sense of smell can detect 5,000 aromas and flavours. The University of California-Davis Aroma Wheel presents a staggering array of nasally detectable sensations. See Ann Noble, et al., “The U. C. Davis Aroma Wheel”, American Journal ofEnology and Viticulture 35 (1984), pp. 107–109. Whether these modes of the sense of smell have an associated language of sensations is a moot point.Google Scholar
  14. 15.
    The colours of the spectrum. See Newton, Opticks, Book 1, Part 2. Kant seems to presuppose, but does not discuss, Newton’s confidence that each of the colour bands (from red to violet) can, by analogy, be linked to similar vibration bands, the breadth of the seven colour bands in the spectrum being viewed as analogous to the seven string lengths needed to produce the scale. Newton’s analogy is somewhat arbitrary. The colours of the spectrum actually blend imperceptibly into one another, and there is no reason to choose indigo as a colour between blue and violet. It has been pointed out that he might just as well have chosen a colour between blue and green, or between orange and yellow, or between yellow and green. Reliance upon the seven notes in the musical scale no doubt prejudiced Newton’s identification. Kant’s insistence that the privileged scale is that used for sightsinging (see note 20) must have made it easy for him to accept the Newtonian analogy. (See Percy A. Scholes, The Oxford Companion to Music, 10th ed. Oxford: Oxford University Press, 1970, pp. 205206.) I have not been able to locate the source of Kant’s identification of each spectral colour with a particular affective state. He leaves the impression that these identifications are as familiar as the identifications of various objects with the different wedding anniversaries.Google Scholar
  15. 16.
    In Anthropology section 71, p. 247, Kant asks why, among the fine (linguistic) arts, poetry is more prized than rhetoric. His answer: “Because it is also music (it can be sung) and tone: a sound that is pleasant in itself, which mere speech is not. Even rhetoric borrows from poetry a sound that approximates tone: accent, without which the oration lacks the alternating moments of rest and animation it needs.” I call this passage to mind only to reinforce the centrality of the close connection between sound and language that underwrites much of Kant’s theory of music.Google Scholar
  16. 17.
    Kant knew about the ocular harpsichord invented by Louis-Bertrand Castel, employing Descartes’s theory oflight, as modified by Constantijn Huygens. The harpsichord matched the sounding of pitches with displays of analogous colours. Interest in his instrument and in the theories relating sound and colour continued in Germany for some time after Castel’s death in 1757. In a letter to Kant of December 13, 1790, Christoph Friedrich hellwag provides an elaborate description of what Castel hoped to achieve with his instrument. I am grateful to my colleague Patrick Maynard for calling Castel’s invention to my attention.Google Scholar
  17. 18.
    In a letter (January 3, 1791) in reply to one from Hellwag referred to in note 16, Kant writes that when he wrote this section of KU, he had in mind his best friend, the English merchant Joseph Green, who was tone-deaf. Green had learned to play the clavier by note, but could not tell one tune from another when played by someone else. Kant takes this to mean that Green could not distinguish pitches from mere noise. Poor Green also could not tell the difference between poetry and prose, and could not read Pope’s Essay on Man with pleasure because of its forced and unnatural arrangement of syllables (gezwungese und geschrobene Sylbenstellung). Kant also writes that he had read somewhere of a family in England whose members could not distinguish between light and shade, and, although they apparently had healthy eyes, saw all objects as if they were the colour of copperplate engravings (Kants gesammelte Schriften, Berlin: Königlich-Preussische Akademie der Wissenschaften, 1902, pp. 11, 245).Google Scholar
  18. 19.
    Kant does not carefully distinguish the modalities of tone: pitch, force and tone colour (Helmholtz’s Klangfarbe). When he writes about tone, he seems to have principally in mind pitch, where the pitch of a tone is the number of vibrations completed in a given time. What he means by the “intensity” of a sensation (sound) is ambiguous. He can mean either pitch (frequencies of vibrations) or force or amplitude (intensity of oscillations). Technically, following Helmholtz (On the Sensations of Tone, 2nd ed., translated by Alexander Ellis, New York: Dover, 1954, Part 1, chapter 1) the quality of a tone is exemplifiied by notes of the same force and pitch sounded successively on different instruments. Although Kant does not introduce these technical distinctions, what he means by the quality of a tone, as distinct from its intensity (as either force or pitch) seems to be very much what Helmholtz comes to define more precisely in his concept ofKlangfarbe. Helmholtz comes to agree with Kant that tonal qualities are most richly represented by the human voice, and writes that “human speech employs these very qualitative varieties of tone, in order to distinguish different letters. The different vowels, namely, belong to the class of sustained tones which can be used in music, while the character of consonants mainly depends upon brief and transient noises” (p. 19).Google Scholar
  19. 20.
    Kants gesammelte Schriften, Vol. 11, p. 245. The reference is obviously to Guido d’Arezzo’s method of solmization, singing the notes of the scale to the monosyllables ut, re, mi,fa, sol, la, si, with do eventually replacing ut. Thomas Lennon has pointed out to me that Kant’s theory is supported by the fact that our musical notation derives from the neumes of mnedieval music. The neumes evolved from the diacritical marks on Greek characters that directed how plainsong was to be sung. An acute accent marked a rising pitch, grave a falling, circumflex a rising followed by a falling.Google Scholar
  20. 21.
    There are other ways of expressing the notes within the octave, but Kant was probably impressed by the similarity between Guido’s scale, and that of Newton, a scale of the pattern: C, D, E flat, F, G, A, B flat. if one assumes, as Kant did (following Euler) that both sound and light appear as the result of vibrations of the air, then the vibration times for the intermediate colours of the spectrum discussed above roughly correspond to the periods of vibration of the notes in Newton’s scale. Both Castel, and, I think, Kant, were inclined to take this correspondence literally. For Kant, any method of objectifying (mathematizing) intensive quantities was a step forward. For more on Kant and the intensive quantities, see Gordon G. Brittan, “Kant’s Two Grand Hypotheses”, in Robert E. Butts, ed., Kant ‘s Philosophy of Physical Science (Dordrecht: Reidel, 1986), pp. 61–94.Google Scholar
  21. 22.
    A contemporary cognitive scientist puts it this way: “It is quite difficult to design a reliable voicing decision procedure, or to formulate a reliable algorithm for computing the larynx frequency, which of course determines the subjectively perceived pitch of the voice; but for the moment we will disregard these difficulties and adopt the convenient fiction that each syllable contains a voiced section (usually a vowel, though not always) of a well-defined if varying pitch. One can in fact produce quite a realistic pitch contour for a natural utterance by assigning musical notes to the syllables” (H. Christopher Longuet-Higgins, Mental Processes: Studies in Cognitive Science, Cambridge: MIT Press, 1987, p. 282).Google Scholar
  22. 23.
    This is not the same as saying that we cannot illustrate the octave. That can be done by sounding it in any of a variety of ways, by using stretched strings, vibrating forks, or by playing a bit of music on a well-tuned instrument. Nevertheless, the octave is not a concept with a referent, there is nothing in the world that is picked out by the word `octave’. Being an octave is mathematically describable, and is from time to time a sensation. I suppose Galileo would say that independently of being heard, ‘octave ’is a mere name. It is surprising how much of Kant’s account of the sensory reception of tones agrees with Galileo’s nominalism of sense qualities. See Robert E. Butts, “Tickles, Titillations, and the Wonderful Accidents of Sounds. Galileo and the Consonances”, in Victor Coehlo, ed., Music and Science in the Age of Galileo (Dordrecht: Kluwer, 1992).Google Scholar
  23. 24.
    There is a difficult point here that needs further development in another context. To say that I have enjoyed a performance of Mozart’s 35th Symphony certainly is not equivalent to saying that I enjoyed the single and simultaneous tones which add up to that performance, from beginning to end. The aesthetic object in music is not the sum of the inscriptions which present it. That object is a complex affective state in the listener or reader.Google Scholar
  24. 25.
    In Anthropology (sect. 31) Kant discusses three capacities of the faculty of sensibility employed in the construction of ideas: imagination (either involuntary [fantasy], or voluntary [composition or fabrication]), association and affinity. The artist engages in all three cognitive tasks; the beholder in the second two. Kant writes: “The law of association is this: empirical ideas that have often followed each other produce in us a mental habit such that, when one is produced, this causes the other to arise as well”. Kant thinks that this law is at work in matching various structures: a sound felt now that recalls a previous affective state; hearing consonant sounds and recalling previously experienced patterns of modulation.Google Scholar
  25. 26.
    As are the steps of a marching cadre of soldiers, the even more expressive steps of a company of dancers, the beats of a drum leading mourners to the side of a grave, and many more such regularities and their associated affective states. When Kant refers to music as giving expression to an aesthetic idea of an integral whole of an unutterable wealth of thought (KUsect. 53, p. 329), he surely has in mind the fact that musical structures call to mind many and various resembling structures. In this respect, music is unequalled as an expression of various matching structures that bear definite and remembered affective relationships to one another. He tells us in the letter to Hellwag referred to above that one cannot think of a bit of music without at the same time singing it, even if only awkwardly.Google Scholar
  26. 27.
    I have not dealt with the fact that the distinction between consonances and dissonances is itself diffiicult to apply, even to tonal music, because the discussion would take us into details of musicology that are inappropriate here. I do not think that Kant’s theory of musical sound needs to depend on this technical distinction.Google Scholar
  27. 28.
    I do not know if Kant was familiar with the operatic recitatives of the eighteenth century, vocal compositions that disregard melody and rhythm and seek to imitate intonations of speech. In all probability he was familiar with the popular eighteenth century Singspiel, the forerunner of operetta, a genre combining spoken dialogue, songs and instrumental accompaniments.Google Scholar
  28. 29.
    Galileo Galilei, “The Assayer”, in Discoveries and Opinions of Galileo, translated with an introduction and notes by Stillman Drake (New York: Doubleday, 1957). For a thorough discussion of Galileo’s general theory of sensation as applied to the case of the consonances, see Robert E. Butts, “Tickles, Titillations, and the Wonderful Accidents of Sounds” (note 23 above).Google Scholar
  29. 30.
    Galileo’s discussion of music is limited to roughly a dozen pages of the first day of the Discoursi. See Galileo’s Dialogues concerning Two New Sciences, translated by Henry Crew and Alfonso deSalvio (New York: Dover, 1954), pp. 95–108.Google Scholar
  30. 31.
    Dialogues concerning Two New Sciences, translated by Crew and deSalvio (New York: Dover, 1954), p. 104.Google Scholar
  31. 32.
    Gottfried Wilhelm Leibniz: Philosophical Papers and Letters, 2nd ed. Edited, translated and with an Introduction by Leroy Loemker (Dordrecht: Reidel, 1969), p. 641.Google Scholar
  32. 33.
    Leibniz: Philosophical Papers and Letters, 2nd ed., pp. 425–26.Google Scholar
  33. 34.
    As we have seen in the discussion of Kant, such regular and ordered variations in contexts other than essentially musical ones have an important bearing on how we account for the causes of the experience of beauty. What all early attempts to account for the consonances simply miss is the point that the causal nexus linking sounds to experiences of sounds is complex and is supplied by other kinds of experiences, such as the ones Leibniz lists. Leibniz was within an ace of anticipating Kant’s more mature theory. Unfortunately his thought was still burdened by ghosts of the past.Google Scholar
  34. 35.
    Kant’s expressive theory of art requires us to accept that artists create what he calls “aesthetic ideas” (KU sect. 49, pp. 313–14). An idea, for Kant, has no empirical exemplification or instantiation. In the case of artfully crafted objects, including musical themes, the idea, if you will, delineates the features of the composed design that renders the object beautiful. In the contemplation of such an idea one finds aesthetic feelings ofpleasure. What consonant sound, when artfully composed, designedly expresses as idea (or meaning) is affection.Google Scholar
  35. 36.
    Again, Longuet-Higgins, Mental Processes: Studies in Cognitive Science, p. 35, with appropriate variations: “We could never hope to understand [aesthetically appreciate] what is said to us [sung for us] unless we were able to use contextual, intonational, syntactic, and semantic clues for decoding the actual sounds themselves”. Joseph Green and the members of that English family presumably lacked the capacity to sort out the clues.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Graham Solomon
    • 1
  1. 1.Wilfrid Laurier UniversityWaterlooCanada

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