Gauge symmetries of musical and visual forces

References

• Arnheim, R. (1974). Art and visual perception. A psychology of the creative eye (extended 2nd ed.). University of California Press. 1st edition from 1954.
   Google Scholar
• Arnheim, R. (1984). Perceptual dynamics in musical expression. The Musical Quarterly, 70, 295–309. https://doi.org/10.1093/mq/LXX.3.295
   Web of Science ®Google Scholar
• Baroin, G., & Calvet, A. (2019). Visualizing temperaments: Squaring the circle? In M. Montiel, F. Gomez-Martin, & O. A. Agustín-Aquino (Eds.), Mathematics and computation in music (pp. 333–337). Springer.
   Google Scholar
• beim Graben, P. (2011). Naphtas Visionen. Perspektivität in der Naturwissenschaft In M. Knaup, T. Müller, & P. Spät (Eds.), Post-Physikalismus (pp. 122–141). Alber.
   Google Scholar
• beim Graben, P. (2016). Comment on Gil's: What are the best hierarchical organizations for the success of a common endeavour. Mathematical Anthropology and Cultural Theory, 9. Article number 9.
   Google Scholar
• beim Graben, P., & Blutner, R. (2017). Toward a gauge theory of musical forces. In J. A. de Barros, B. Coecke, & E. Pothos (Eds.), Quantum interaction. 10th international conference (QI 2016), LNCS (Vol. 10106, pp. 99–111). Springer.
   Google Scholar
• beim Graben, P., & Blutner, R. (2019). Quantum approaches to music cognition. Journal of Mathematical Psychology, 91, 38–50. https://doi.org/10.1016/j.jmp.2019.03.002
   Web of Science ®Google Scholar
• beim Graben, P., & Mannone, M. (2020). Musical pitch quantization as an eigenvalue problem. Journal of Mathematics and Music, 14, 329–346. https://doi.org/10.1080/17459737.2020.1763488
   Web of Science ®Google Scholar
• Berger, H. (1929). Über das Elektroenkephalogramm des Menschen. Archiv für Psychiatrie, 87, 527–570. https://doi.org/10.1007/BF01797193
   Google Scholar
• Blutner, R. (2017). Modelling tonal attraction: Tonal hierarchies, interval cycles, and quantum probabilities. Soft Computing, 21, 1401–1419. https://doi.org/10.1007/s00500-015-1801-7
   Web of Science ®Google Scholar
• Blutner, R., & beim Graben, P. (2016). Quantum cognition and bounded rationality. Synthese, 193, 3239–3291. https://doi.org/10.1007/s11229-015-0928-5
   Web of Science ®Google Scholar
• Blutner, R., & beim Graben, P. (2021). Gauge models of musical forces. Journal of Mathematics and Music, 15, 17–36. https://doi.org/10.1080/17459737.2020.1716404
   Web of Science ®Google Scholar
• Brading, K., & Castellani, E. (2007). Symmetries and invariances in classical physics. In J. Butterfield & J. Earman (Eds.), Handbook of the philosophy of science (Vol. 2). The Philosophy of Physics, North-Holland.
   Google Scholar
• Busemeyer, J. R., & Bruza, P. D. (Eds.). (2012). Quantum models of cognition and decision. Cambridge University Press.
   Google Scholar
• Castellano, M. A., Bharucha, J. J., & Krumhansl, C. L. (1984). Tonal hierarchies in the music of North India. Journal of Experimental Psychology: General, 113, 394–412. https://doi.org/10.1037/0096-3445.113.3.394
   PubMed Web of Science ®Google Scholar
• Chew, G. (1991). Ernst Kurth, music as psychic motion and ‘Tristan und Isolde’: Towards a model for analysing musical instability. Music Analysis, 10, 171–193. https://doi.org/10.2307/854002
   Web of Science ®Google Scholar
• Costère, E. (1954). Lois et styles des harmonies musicales: Genèse et caractères de la totalité des échelles, des gammes, des accords et des rythmes. Presses universitaires de France.
   Google Scholar
• Eguchi, T., Gilkey, P. B., & Hanson, A. J. (1980). Gravitation, gauge theories and differential geometry. Physics Reports, 66, 213–393. https://doi.org/10.1016/0370-1573(80)90130-1
   Web of Science ®Google Scholar
• Einstein, A. (1920). Relativity: The special and the general theory. Methuen.
   Google Scholar
• Einstein, A. (1922). The meaning of relativity: Four lectures delivered at Princeton university. Methuen.
   Google Scholar
• Ellard, B. (1973). Edmond Costère's Lois et Styles des Harmonies Musicales, an english translation and commentary [PhD Thesis]. University of Rochester, Eastman School of Music.
   Google Scholar
• Fermüller, C., & Aloimonos, Y. (2001). Statistics explains geometrical optical illusions. In L. S. Davis (Ed.), Foundations of image understanding (pp. 409–445). Springer.
   Google Scholar
• Fermüller, C., & Malm, H. (2004). Uncertainty in visual processes predicts geometrical optical illusions. Vision Research, 44, 727–749. https://doi.org/10.1016/j.visres.2003.09.038
   PubMed Web of Science ®Google Scholar
• Fraser, J. (1908). A new visual illusion of direction. British Journal of Psychology, 2(3), 307.
   Google Scholar
• Fugiel, B. (2022). Quantum-like melody perception. Journal of Mathematics and Music, 17(2), 319–331.
   Web of Science ®Google Scholar
• Goude, G., & Hjortzberg, I. (1967). En experimentell provning. In R. Arnheim (Ed.), Art and visual perception. A psychology of the creative eye. (p. 15) University of California Press, 1974. Stockholm University.
   Google Scholar
• Herbener, G. F., van Tubergen, G. N., & Whitlow, S. S. (1979). Dynamics of the frame in visual composition. Educational Technology Research and Development, 27(2), 83–88.
   Google Scholar
• Himpel, B. (2022). Geometry of music perception. Mathematics, 10, 4793. https://doi.org/10.3390/math10244793
   Web of Science ®Google Scholar
• Huron, D. (2006). Sweet anticipation: Music and the psychology of expectation. MIT Press.
   Google Scholar
• Jackson, J. D., & Okun, L. B. (2001). Historical roots of gauge invariance. Reviews of Modern Physics, 73, 663–680. https://doi.org/10.1103/RevModPhys.73.663
   Web of Science ®Google Scholar
• Janata, P. (2005). Brain networks that track musical structure. Annals of the New York Academy of Sciences, 1060, 111–124. https://doi.org/10.1196/annals.1360.008
   PubMed Web of Science ®Google Scholar
• Janata, P., Birk, J. L., Horn, J. D. V., Leman, M., Tillmann, B., & Bharucha, J. J. (2002). The cortical topography of tonal structures underlying western music. Science (New York, N.Y.), 298, 2167–2170. https://doi.org/10.1126/science.1076262
   PubMed Web of Science ®Google Scholar
• Kandinsky, W. (1947). Point and line to plane: Contribution to the analysis of the pictorial elements. Solomon R. Guggenheim foundation for the museum of non-objective painting (H. Dearstyne & H. Rebay, Trans.).
   Google Scholar
• Kant, I. (1999). Critique of pure reason (The Cambridge Edition of The Works Of Immanuel Kant). Cambridge University Press.
   Google Scholar
• Kessler, E. J., Hansen, C., & Shepard, R. N. (1984). Tonal schemata in the perception of music in Bali and in the West. Music Perception, 2, 131–165. https://doi.org/10.2307/40285289
   Web of Science ®Google Scholar
• Koffka, K. (1935). Principles of gestalt psychology. Harncourt, Brace & Co.
   Google Scholar
• Köhler, W. (1969). The task of gestalt psychology. Princeton University Press.
   Google Scholar
• Krebs, W. (1998). Innere Dynamik und Energetik in Ernst Kurths Musiktheorie, Frankfurter Beiträge zur Musikwissenschaft Vol. 28, Hans Schneider.
   Google Scholar
• Krumhansl, C. L. (1979). The psychological representation of musical pitch in a tonal context. Cognitive Psychology, 11, 346–374. https://doi.org/10.1016/0010-0285(79)90016-1
   Web of Science ®Google Scholar
• Krumhansl, C. L., & Cuddy, L. L. (2010). A theory of tonal hierarchies in music. In M. R. Jones, R. R. Fay, & A. N. Popper (Eds.), Music perception (pp. 51–87). Springer Handbook of Auditory Research, Springer.
   Google Scholar
• Krumhansl, C. L., & Kessler, E. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review, 89, 334–368. https://doi.org/10.1037/0033-295X.89.4.334
   PubMed Web of Science ®Google Scholar
• Krumhansl, C. L., & Shepard, R. N. (1979). Quantification of the hierarchy of tonal functions within a diatonic context. Journal of Experimental Psychology: Human Perception and Performance, 5, 579.
   PubMed Web of Science ®Google Scholar
• Krumhansl, C. L., Toivanen, P., Eerola, T., Toiviainen, P., Järvinen, T., & Louhivuori, J. (2000). Cross-cultural music cognition: Cognitive methodology applied to north sami yoiks. Cognition, 76, 13–58. https://doi.org/10.1016/S0010-0277(00)00068-8
   PubMed Web of Science ®Google Scholar
• Larson, S. (1993). On Rudolf Arnheim's contribution to music theory. Journal of Aesthetic Education, 27, 97–104. https://doi.org/10.2307/3333503
   Web of Science ®Google Scholar
• Larson, S. (2012). Musical forces: Motion, metaphor, and meaning in music. Indiana University Press.
   Google Scholar
• Larson, S., & van Handel, L. (2005). Measuring musical forces. Music Perception, 23, 119–136. https://doi.org/10.1525/mp.2005.23.2.119
   Web of Science ®Google Scholar
• Leeuwenberg, E. L. J. (1971). A perceptual coding language for visual and auditory patterns. American Journal of Psychology, 84, 307–349. https://doi.org/10.2307/1420464
   PubMed Web of Science ®Google Scholar
• Lerdahl, F. (1996). Calculating tonal tension. Music Perception, 13, 319–363. https://doi.org/10.2307/40286174
   Web of Science ®Google Scholar
• Leyssen, M. H. R., Linsen, S., Sammartino, J., & Palmer, S. E. (2012). Aesthetic preference for spatial composition in multiobject pictures. i-Perception, 3, 25–49. https://doi.org/10.1068/i0458aap
   PubMed Web of Science ®Google Scholar
• Mack, G. (1995). Gauge theory of things alive. Nuclear Physics B, 42, 923–925. https://doi.org/10.1016/0920-5632(95)00423-7
   Google Scholar
• Mack, G. (1998). Allgemeine Relativitäts und Eichtheorie, Lecture Notes University of Hamburg.
   Google Scholar
• Mack, G. (2001). Universal dynamics, a unified theory of complex systems. emergence, life and death. Communications of Mathematical Physics, 219, 141–178. https://doi.org/10.1007/s002200100397
   Web of Science ®Google Scholar
• Matsunaga, R., Yasuda, T., Johnson-Motoyama, M., Hartono, P., Yokosawa, K., & J. I. Abe (2018). A cross-cultural comparison of tonality perception in Japanese, Chinese, Vietnamese, Indonesian, and American listeners. Psychomusicology: Music, Mind, and Brain, 28, 178–188. https://doi.org/10.1037/pmu0000219
   Google Scholar
• Mazzola, G. (1990). Geometrie der Töne. Birkhäuser.
   Google Scholar
• Mazzola, G. (2002). The topos of music: Geometric logic of concepts, theory, and performance, Vol. I: Theory. Springer.
   Google Scholar
• McManus, I. C., Stöver, K., & Kim, D. (2011). Arnheim's gestalt theory of visual balance: Examining the compositional structure of art photographs and abstract images. i-Perception, 2, 615–647. https://doi.org/10.1068/i0445aap
   PubMed Web of Science ®Google Scholar
• Meyer, L. B. (1956). Emotion and meaning in music (paperback 1961 ed.). University of Chicago Press.
   Google Scholar
• Milne, A. J., & Holland, S. (2016). Empirically testing Tonnetz, voice-leading, and spectral models of perceived triadic distance. Journal of Mathematics and Music, 10, 59–85. https://doi.org/10.1080/17459737.2016.1152517
   Web of Science ®Google Scholar
• Noll, T., & beim Graben, P. (2022). Quantum-musical explorations on Zn. In M. Montiel, O. A. Agustín-Aquino, F. Gómez, J. Kastine, E. Lluis-Puebla, & B. Milam (Eds.), Mathematics and computation in music (pp. 369–375) Springer.
   Google Scholar
• Palmer, S. E., Gardner, J. S., & Wickens, T. D. (2008). Aesthetic issues in spatial composition: Effects of position and direction on framing single objects. Spatial Vision, 21, 421–449. https://doi.org/10.1163/156856808784532662
   PubMedGoogle Scholar
• Palmer, S. E., & Guidi, S. (2011). Mapping the perceptual structure of rectangles through goodness-of-fit ratings. Perception, 40, 1428–1446. https://doi.org/10.1068/p7021
   PubMed Web of Science ®Google Scholar
• Parncutt, R. (2011). The tonic as triad: Key profiles as pitch salience profiles of tonic triads. Music Perception, 28, 333–366. https://doi.org/10.1525/mp.2011.28.4.333
   Web of Science ®Google Scholar
• Pauli, W. (1927). Zur Quantenmechanik des magnetischen Elektrons. Zeitschrift für Physik, 43, 601–623. https://doi.org/10.1007/BF01397326
   Google Scholar
• Pearce, M. T. (2018). Statistical learning and probabilistic prediction in music cognition: Mechanisms of stylistic enculturation. Annals of the New York Academy of Sciences, 1423, 378–395. https://doi.org/10.1111/nyas.2018.1423.issue-1
   PubMed Web of Science ®Google Scholar
• Pothos, E. M., & Busemeyer, J. R. (2013). Can quantum probability provide a new direction for cognitive modeling? Behavioral and Brain Sciences, 36, 255–274. https://doi.org/10.1017/S0140525X12001525
   PubMed Web of Science ®Google Scholar
• Putz, V., & Svozil, K. (2017). Quantum music. Soft Computing, 21, 1467–1471. https://doi.org/10.1007/s00500-015-1835-x
   Web of Science ®Google Scholar
• Rehding, A., & Floud, R. (2003). Hugo Riemann and the birth of modern musical thought. Cambridge University Press.
   Google Scholar
• Riemann, B. (1998). On the hypotheses which lie at the bases of geometry (W. K. Clifford, Trans.). Nature, 8, 14, 183–184.
   Google Scholar
• Sewell, G. L. (2002). Quantum mechanics and its emergent macrophysics. Princeton University Press.
   Google Scholar
• Temperley, D. (2008). A probabilistic model of melody perception. Cognitive Science, 32, 418–444. https://doi.org/10.1080/03640210701864089
   PubMed Web of Science ®Google Scholar
• von Helmholtz, H. (1912). On the sensations of tone as a physiological basis for the theory of music (A. J. Ellis, Trans.). (4th ed.). Longmans Green.
   Google Scholar
• Wade, N. (2016). Art and illusionists, Vision, Illusion and Perception Vol. 1, Springer.
   Google Scholar
• Wade, N. J., & Swanston, M. T. (2001). Visual perception: An introduction (2nd ed.). Psychology Press.
   Google Scholar
• Wang, X. (2007). Laplacian operator-based edge detectors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29, 886–890. https://doi.org/10.1109/TPAMI.2007.1027
   PubMed Web of Science ®Google Scholar
• Weisstein, E. W. (n.d.). Squircle. from MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/Squircle.html.
   Google Scholar
• Wertheimer, M. (1938). Laws of organization in perceptual forms. In A source book of gestalt psychology (Vol. 4, pp. 71–88). Kegan Paul, Trench, Trubner & Company.
   Google Scholar
• Weyl, H. (1952). Space-time-matter. Dover.
   Google Scholar
• Weyl, H. (1980). Symmetry (1st edition 1952). Princeton University Press.
   Google Scholar
• Wilson, K. G. (1974). Confinement of quarks. Physical Reviews D, 10, 2445–2459. https://doi.org/10.1103/PhysRevD.10.2445
   Web of Science ®Google Scholar
• Woolhouse, M. (2009). Modelling tonal attraction between adjacent musical elements. Journal of New Music Research, 38, 357–379. https://doi.org/10.1080/09298210903180252
   Web of Science ®Google Scholar