ACADEMIA Letters Sound: mathematical and modern rationality Carlos Enrique Maldonado Martínez, Universidad Michoacana de San Nicolás de Hidalgo The objective in this text is to present sound, and music extensively, as an instance of the mathematization of nature based on the characterization made by Edmund Husserl in his 1936 text, The Crisis of European Sciences and Transcendental Phenomenology. In this text, Husserl states that, from the improvement of the measurement technique, the study of nature turned to a merely abstract instance, which characterizes modern rationality. In this way, from the mathematization of nature, sound, music, and a good part of its theoretical assumptions are rooted in the modern rationality criticized by Husserl. The emphasis placed on the measurable, abstract and reproducible aspect of music works to understand why certain sound practices prevail over others, as is the case of popular music over other sound manifestations: from everyday noise to music not aligned with the canons predominant. Sound practices will then reflect modern rationality. The mathematization of the world, or nature, responds to the implementation of a scientific rationality that is imposed through an abstract model of the sciences. Husserl’s proposal about the mathematization of the world through measurement and the improvement of said measurement has unavoidable consequences not only in the scientific field, but also in current cultural, economic, and political life. Through presenting Galileo as the main figure in the establishment of modernity as the dominant rationality from the development of geometry in its most abstract aspect. So, there is a split between the objects of the world and the geometric objects. There is no instance of a pure geometric body, geometry proposes “ideal” or abstract forms.[1] Although Husserl’s original intention is to account for a crisis in science from the qualitative distance from the world, in favor of a merely quantitative analysis. An example that seems pertinent as a sample of the apparent mathematization of nature Academia Letters, June 2022 ©2022 by the author — Open Access — Distributed under CC BY 4.0 Corresponding Author: Carlos Enrique Maldonado Martínez, [email protected] Citation: Maldonado Martínez, C.E. (2022). Sound: mathematical and modern rationality. Academia Letters, Article 5548. 1 is an experiment on the FEM (frequency elevation mapping)[2] from the auditory experience of sounds arranged in different spatial coordinates. This experiment is based on a fact that at first does not arouse suspicion: sounds are frequencies. The frequency would be defined as the “number of oscillations per second, often expressed in hertz [Hz]”.[3] If we examine the ontological implication of this assertion, we have that a phenomenon of sensory experience is being measured in two areas, on the one hand, there is the part of the frequency, where the numerical relationship determines (or seems to determine) the quality of a sound: high and low. On the other hand, it is a spatial measurement, in which sound is encased in coordinates, or an abstract representation of space. Although in language we use expressions to refer to the qualities of sounds such as high, low, sharp, flat, far, close, strong, weak, we can notice qualities that the sound shares within space. If we start from the abstraction of space as pure geometry, it is possible to extrapolate the measurement of geometric abstractions to the sound realm. Sound, when examined as a physical phenomenon,[4] has measurable and quantifiable characteristics. Taking sound as a frequency, we have that the human audible spectrum, that is, the sound range that can be heard by the human ear, is limited between 20 Hz and 16,000 Hz.[5] From this abstraction of sound in frequency operates one of the devices in which the mathematization of nature in the musical field is manifest. The configuration and division of the sounds in tones, semitones, grouped in octaves, and defining each tone by its frequency. Although the division of the sounds in the chromatic scale has 12 sounds for each octave, that is, every time the frequency doubles, the interval between the double of one frequency and another is divided into twelve to assign a musical note to each value.[6] In this way, represented graphically on a staff, the low sounds are written at the bottom and the high sounds at the top, rising or falling progressively. Another point to consider that the article mentions is that musical notation seems to represent sounds in the same way where high-pitched sounds have a high frequency (or faster vibration) and low-pitched sounds have a low frequency (slower vibration). In musical scores staves, the high sound occupies a high position and the low sound a low position. The study indicates that different sounds with measurable qualities have a spatial correlation based on their listening and it is possible to abstract the sound so that it can be located on an abstract plane. It is in this way that a correlation can be established between the abstract form of the sound (the frequency), the musical notation, the spatial representation, and the physical nature of the sound.[7] The intuitive quality of the world constantly moves between the qualitative and the quantitative, preferably in the quantitative to explain the phenomena of the world through science. In this way, even if modern rationality is present in music and it is from it that the quantificaAcademia Letters, June 2022 ©2022 by the author — Open Access — Distributed under CC BY 4.0 Corresponding Author: Carlos Enrique Maldonado Martínez, [email protected] Citation: Maldonado Martínez, C.E. (2022). Sound: mathematical and modern rationality. Academia Letters, Article 5548. 2 tion or improvement of measurements in the sound field produces technologies that improve the reproduction or recording of sounds under the abstract premise of sound, understanding sound quality as an increase in sampling or bit depth, only quantitative aspects. The mathematical assimilation of music, and even of sound, can be traced, as well as enlightened or modern rationality, to classical Greece, as shown by the work of compiling and editing ancient musical theories, with examples of musical notation. updated graphics, by Carolus Janus (Karl von Jan)[8] which is an example of the way in which the qualities of sounds and their properties, such as consonance, dissonance, harmonization, among others, were studied and written. But not for that reason the pre-modern musical experience, or the one that is outside the canons or beyond the musical experience as we know it, since mathematical rigor has been present since this Western antiquity. Although throughout the development of music in different cultures and parts of the world there are proposals that move away from this type of musical notation,[9] Western canon and modern rationality are fixed in mathematical terms that only vary in the way of dividing or quantifying the frequencies to assign them the name of a sound. It is in this way that the sound experience, including sound perception, is subject to modern scientific rationality that abstracts the experience to measure it (or mathematize it). This type of mathematization as a model of modern rationality is consistent with what Adorno and Horkheimer tell us at the beginning of Concept of Enlightenment: “Enlightenment has always regarded anthropomorphism, the projection of subjective properties onto nature”.[10] Although they attribute to Bacon the enlightened movement in the sciences (Husserl does the same with Galileo), they trace from ancient Greek thought indices that only develop as a set of ideological characteristics operating in capitalist modernity. While the correlation between sound and its abstraction is functional, some sound experiences such as noise are not compatible with modern rationality since they do not fit into the mode of modern production. In the words of Salomé Voegelin: “noise is a social signifier: determining unknown boundaries and waging invisible wars.”[11] While for Husserl “all this pure mathematics has to do with bodies and the bodily world only through an abstraction, i.e., it has to do only with abstract shapes within space-time, and with these, furthermore, as purely “ideal” limit-shapes.”[12] Outside of modern rationality there would seem to be a plethora of experiences that overflow it due to their little predisposition to being mathematized or measurable. In this brief text, some aspects of modern rationality as understood by Edmund Husserl were explored and the relationship between the mathematization of nature with the abstract aspect of sound that functions as the warp in music was traced. It remains to examine in depth the historical, technical, and practical repercussions that the mathematical abstraction Academia Letters, June 2022 ©2022 by the author — Open Access — Distributed under CC BY 4.0 Corresponding Author: Carlos Enrique Maldonado Martínez, [email protected] Citation: Maldonado Martínez, C.E. (2022). Sound: mathematical and modern rationality. Academia Letters, Article 5548. 3 of sound has in musical aspects such as the division of frequencies into tones, and in other instances such as digital sound. In the same way, it will be necessary to examine instances of the world such as noise or silence that would seem to escape modern rationality. Academia Letters, June 2022 ©2022 by the author — Open Access — Distributed under CC BY 4.0 Corresponding Author: Carlos Enrique Maldonado Martínez, [email protected] Citation: Maldonado Martínez, C.E. (2022). Sound: mathematical and modern rationality. Academia Letters, Article 5548. 4 References [1] Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology , trans. David Carr (Evanston: Northwestern University Press, 1970). §9-a. [2] Cesare V Parise, Katharina Knorre, and Marc O Ernst, “Natural auditory scene statistics shapes human spatial hearing,” Proceedings of the National Academy of Sciences of the United States of America 111, no. 16 (Aug. 3, 2014): 6104–8, http://www.jstor.org/stable/ 23771509. [3] Michel Chion, Sound: An Acoulogical Treatise , trans. James A. Steintrager (Durham and London: Duke University Press, 2016), p. 17. [4] Cf. Mark Grimshaw and Tom Garner, Sonic Virtuality: Sound as emerging perception (New York: Oxford University Press, 2015). They propose a definition of sound as “perception embodied in the world”, synthesizing both the physical process and the perceptual and memory processes, being able to have sounds without a physical correlate as the source of the sound. [5] Chion, Sound: An Acoulogical Treatise, p. 22. [6] Cf. ibid. p. 55. “In school and in musical theory handbooks we learn—and it is true—that A above middle C in the current, official tuning has a frequency of 440 Hz, whereas an A an octave higher has a frequency twice that, at 880 Hz. Likewise, the interval heard as a perfect fifth, to use the Western terminology, has a mathematical ratio with regard to frequency of two to three. More concretely, a string divided in half vibrates an octave higher—and the sound from one octave to the next is, as far as our ear is concerned, the “same” sound, all the while situated in another register (without thinking about it, we all sing in our own register and transpose to the octave that suits our voice if we want to be in unison).”. [7] Husserl points out that: “The shapes in it that are sensibly experienceable and sensiblyintuitively conceivable, and the types [of shapes] that are conceivable at any level of generality, fade into each other as a continuum. In this continuity they fill out (sensibly intuited) space-time, which is their form.” Edmund Husserl, The Crisis of European Sciences and Transcendental Phenomenology, §9-a p. 27. [8] Karl von Jan, Musici scriptores graeci: Aristotle, Euclid, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat (in aedibus BG Teubneri, 1895). Academia Letters, June 2022 ©2022 by the author — Open Access — Distributed under CC BY 4.0 Corresponding Author: Carlos Enrique Maldonado Martínez, [email protected] Citation: Maldonado Martínez, C.E. (2022). Sound: mathematical and modern rationality. Academia Letters, Article 5548. 5 [9] Cf. The French translation of two Arabic music treatises Rodolphe Erlanger, La Musique Arabe , vol. 2 (P. Geuthner, 1930); as well as the text translated by Lorena Díaz Núñez on Luca Conti’s doctoral thesis: Luca Conti, “Sperimentalismo e Microtonalismo Nell’opera Di Julián Carrillo” (University of Bologna-DAMS, 1997). [10] Max Horkheimer and Theodor W Adorno, Dialectics of the Enlightenment: Philosophical Fragments (Standford University Press, 2002), p. 4. [11] Salomé Voegelin, Listening to noise and silence: Towards a philosophy of sound art (New York: Continuum, 2010), p. 45. [12] Husserl, The Crisis of European Sciences and Transcendental Phenomenology. §9-b p. 29. Academia Letters, June 2022 ©2022 by the author — Open Access — Distributed under CC BY 4.0 Corresponding Author: Carlos Enrique Maldonado Martínez, [email protected] Citation: Maldonado Martínez, C.E. (2022). Sound: mathematical and modern rationality. Academia Letters, Article 5548. 6