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Articles

Rethinking the Role of the Golden Section in Music and Music Scholarship

REFERENCES

  • Abel, A. B. (2003). The effects of a baby boom on stock prices and capital accumulation in the presence of social security. Econometrica, 71, 551–578. doi:10.1111/ecta.2003.71.issue-2
  • Adams, C. S. (1996). Erik Satie and golden section analysis. Music & Letters, 77, 242–252. doi:10.1093/ml/77.2.242
  • Adams-Webber, J. (1992). Construct asymmetry and the range of relevance of personal anticipations. European Journal of Social Psychology, 22, 465–481. doi:10.1002/(ISSN)1099-0992
  • Adler, G., & Strunk, W. O. (1932). Haydn and the Viennese classical school. The Musical Quarterly, 18, 191–207. doi:10.1093/mq/XVIII.2.191
  • Adler, I., Barabé, D., & Jean, R. V. (1997). A history of the study of phyllotaxis. Annals of Botany, 80, 231–244. doi:10.1006/anbo.1997.0422
  • Allen, B. D. (2004). Spiral growth in plants: Models and simulations”. Teaching Mathematics and Its Applications, 23, 41–47. doi:10.1093/teamat/23.1.41
  • Allison, S. T., & Beggan, J. K. (1994). Estimating popular support for group decision outcomes - an anchoring and adjustment model. Journal of Social Behavior and Personality, 9, 617–638.
  • Atlas, A. W. (2003). Stealing a kiss at the golden section: Pacing and proportion in the act i love duet of La Bohème. Acta Musicologica, 75, 269–291.
  • Bailey, N., & Areni, C. S. (2006). When a few minutes sound like a lifetime: Does atmospheric music expand or contract perceived time? Journal of Retailing, 82, 189–202. doi:10.1016/j.jretai.2006.05.003
  • Bellos, A. (2010). Alex’s adventures in numberland. London, UK: Bloomsbury.
  • Bellos, A. (2014). Introduction. In L. Roberts,R. Wright, & A. Bellos (Eds.), Golden meaning: Fiftyfivegraphic experiments. 12–19. London, UK:Graphic Design &.
  • Benjafield, J. G. (2010). The golden section and American psychology, 1892-1938. Journal of the History of the Behavioral Sciences, 46, 52–71. doi:10.1002/jhbs.20409
  • Bent, M. (1991). Deception, exegesis and sounding number in Machaut’s Motet 15. Early Music History, 10, 15–27. doi:10.1017/S026112790000108X
  • Bigand, E. (2002, October 25–27). More about the musical expertise of musically untrained listeners. Paper presented at the Conference on Neurosciences and Music: Mutual interactions and implications on developmental functions, Venice, Italy.
  • Boogaart, J. (2001). Encompassing past and present: Quotations and their function in Machaut’s Motets. Early Music History, 20, 1–86. doi:10.1017/S0261127901001012
  • Boselie, F. (1984). The aesthetic attractivity of the golden section. Psychological Research-Psychologische Forschung, 45, 367–375. doi:10.1007/BF00309712
  • Clarke, E. F., & Krumhansl, C. L. (1990). Perceiving musical time. Music Perception, 7, 213–252. doi:10.2307/40285462
  • Cook, N. (1987). The perception of large-scale tonal closure. Music Perception, 5, 197–206. doi:10.2307/40285392
  • Cooke, T. J. (2006). Do Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis? Botanical Journal of the Linnean Society, 150, 3–24. doi:10.1111/j.1095-8339.2006.00490.x
  • Deliège, I., Mélen, M., Stammers, D., & Cross, I. (1996). Musical schemata in real-time listening to a piece of music. Music Perception, 14, 117–159. doi:10.2307/40285715
  • Ernest, G. (1902). Some aspects of Beethoven’s instrumental forms. Proceedings of the Royal Music Association, 29, 73–98. doi:10.1093/jrma/29.1.73
  • Evans, B. (1992). Number as form and content: A composer’s path of inquiry. Leonardo, 25, 303–311. doi:10.2307/1575855
  • Fechner, G. T. (1876). Vorschule der aesthetik, Chapter XIV. Leipzig, Germany: Breitkopf & Härtel.
  • Firmino, E. A., Bueno, J. L. O., & Bigand, E. (2009). Travelling through pitch space speeds up musical time. Music Perception, 26, 205–209. doi:10.1525/mp.2009.26.3.205
  • Fischer, R. (1969). Out on a (phantom) limb. Variations on the theme: Stability of body image and the golden section. Perspectives in Biology and Medicine, 12, 259–271.
  • Fischler, R. (1981). On the application of the golden ratio in the visual arts. Leonardo, 14, 31–32. doi:10.2307/1574475
  • Ghyka, M. (1977). The geometry of art and life. New York, NY: Dover Publications Inc.
  • Granot, R. Y., & Jacoby, N. (2011). Musically puzzling I: Sensitivity to overall structure in the sonata form? Musicae Scientiae, 15(3), 365–386. doi:10.1177/1029864911409508
  • Granot, R. Y., & Jacoby, N. (2012). Musically puzzling II: Sensitivity to overall structure in a Haydn E-minor sonata. Musicae Scientiae, 16(1), 67–80. doi:10.1177/1029864911423146
  • Green, C. D. (1995). All that glitters - a Review of psychological-research on the aesthetics of the golden section. Perception, 24, 937–968. doi:10.1068/p240937
  • Gross, S. R., & Miller, N. (1997). The “golden section” and bias in perceptions of social consensus. Personality and Social Psychology Review, 1, 241–271. doi:10.1207/s15327957pspr0103_4
  • Haylock, D. W. (1988). The golden section and Beethoven’s Fifth. In J. B. Condat (Ed.), Nombre D’or Et Musique, Goldener Schnitt Und Musik, golden section and music (pp. 121–124). Frankfurt am Main, Germany: Verlag Peter Lang.
  • Herz-Fischler, R. (1983). An examination of claims concerning Seurat and “the golden number”. Gazette des beaux-arts, 101, 109–112.
  • Höge, H. (1992). The golden section has no special aesthetic attractivity! Empirical Studies of the Arts, 10, 1–18. doi:10.2190/QB14-NK7B-ARYT-W5QT
  • Höge, H. (1997). The golden section hypothesis - its last funeral. Empirical Studies of the Arts, 15, 233–255. doi:10.2190/2PNH-8TT0-EMC5-FTW5
  • Hohmaier, S. (2002). Mutual roots of musical thinking: György Kurtág, Péter Eötvös and their relation to Ernö Lendvai’s theories. Studia Musicologica Academiae Scientiarum Hungaricae, 43, 223–234.
  • Howat, R. (1983a). Bartók, Lendvai and the principles of proportional analysis. Music Analysis, 2(1), 69–95. doi:10.2307/853953
  • Howat, R. (1983b). Debussy in proportion. Cambridge, UK: Cambridge University Press.
  • Jalas, J. (1988). Sibelius symphonies and the golden section. In  J. B. Condat (Ed.), Nombre d’or et musique, goldener schnitt und musik, golden section and music (pp. 117–120). Frankfurt am Main, Germany: Verlag Peter Lang.
  • Johnson, T. (2002, April). Lendvai comes to Cologne: György Ligeti in the 1950s and ‘60s. Paper presented at the European Music Analysis Conference, Bristol University, UK.
  • Jones, M. R., & Boltz, M. (1989). Dynamic attending and responses to time. Psychological Review, 96(3), 459–491.
  • Kellaris, J. J., & Altsech, M. B. (1992). The experience of time as a function of musical loudness and gender of listener. In J. F. Sherry Jr. & B. Sternthal. (Eds.), Advances in Consumer Research (Vol. 19, pp. 725–729). Provo, UT: Association for Consumer Research.
  • Kellaris, J. J., Powell Mantel, S., & Altsech, M. B. (1996). Decibels, disposition, and duration: The impact of musical loudness and internal states on time perceptions. In K. P. Corfman & J. Lynch Jr. (Eds.), Advances in consumer research (Vol. 23, pp. 498–503). Provo, UT: Association for Consumer Research.
  • Kellaris, J. J., & Kent, R. J. (1992). The influence of music on consumers’ temporal perceptions: Does time fly when you’re having fun? Journal of Consumer Psychology, 1, 365–376. doi:10.1016/S1057-7408(08)80060-5
  • King, S., Beck, F., & Lüttge, U. (2004). On the mystery of the golden angle in phyllotaxis. Plant, Cell & Environment, 27, 685–695. doi:10.1111/j.1365-3040.2004.01185.x
  • Kinsella, S. (2005). Can you keep a secret? New York, NY: Dell Publishing Company.
  • Kleerekoper, H., Anderson, V. M., & Timms, A. M. (1973). Logarithmic spiral components in locomotor patterns of fish. Canadian Journal of Zoology, 51, 397–400. doi:10.1139/z73-057
  • Kokich, V. G. (2004). Evaluation of “golden proportion” in individuals with an esthetic smile. Journal of Esthetic and Restorative Dentistry, 16, 193. doi:10.1111/jerd.2004.16.issue-3
  • Konečni, V. J. (2003). The golden section: Elusive, but detectable. Creativity Research Journal, 15(2–3), 267–275.
  • Kramer, J. D. (1988). The time of music. New York, NY: Schirmer Books.
  • Lendvai, E. (1971). Béla Bartók: An analysis of his music. London, UK: Kahn and Averill.
  • Lendvai, E. (1984). Remarks on Roy Howat’s ‘Principles of proportional analysis’. Music Analysis, 3, 255–264. doi:10.2307/854140
  • Levinson, J. (2006). Concatenationism, architectonicism, and the appreciation of music. Revue Internationale De Philosophie, 60, 505–514.
  • Lewis, C. (1981). Tonal focus in atonal music: Berg’s Op. 5/3. Music Theory Spectrum, 3, 84–97. doi:10.2307/746136
  • Locke, D. (1987). Numerical aspects of Bartók’s string quartets. The Musical Times, 128, 322–325. doi:10.2307/1193733
  • Maor, E. (2003). Review: Symbol of perfect proportions. Science, 299, 1016. doi:10.1126/science.1081616
  • Markowsky, G. (1992). Misconceptions about the golden ratio. The College Mathematics Journal, 23, 2–19. doi:10.1080/07468342.1992.11973428
  • Meyer, L. B. (1991). A pride of prejudices; or, delight in diversity. Music Theory Spectrum, 13, 241–251. doi:10.2307/745900
  • Noseworthy, T. J., & Finlay, K. (2009). A comparison of ambient casino sound and music: Effects on dissociation and on perceptions of elapsed time while playing slot machines. Journal of Gambling Studies, 25, 331–342. doi:10.1007/s10899-009-9136-x
  • Olsen, S. (2006). The golden section, nature’s greatest secret. Glastonbury, UK: Wooden Books Ltd.
  • Perry-Camp, J. (1979). Time and temporal proportion: The golden section metaphor in Mozart, music, and history. Journal of Musicological Research, 8, 133–176. doi:10.1080/01411897908574509
  • Phillips, M. E., & Cross, I. (2011). About musical time - effect of age, enjoyment, and practical musical experience on retrospective estimate of elapsed duration during music listening. Lecture Notes in Computer Science, 6789, 125–136.
  • Porter, L. (1985). John Coltrane’s a love supreme: Jazz improvisation as composition. Journal of the American Musicological Society, 38(3), 593–621. doi:10.2307/831480
  • Putz, J. F. (1995). The golden section and the Piano Sonatas of Mozart. Mathematics Magazine, 68, 275–282. doi:10.1080/0025570X.1995.11996333
  • Raghubir, P., & Greenleaf, E. A. (2006). Ratios in proportion: What should the shape of the package be? Journal of Marketing, 70, 95–107. doi:10.1509/jmkg.70.2.095
  • Roesner, E. H. (2003). Labouring in the midst of wolves: Reading a group of ‘Fauvel’ Motets. Early Music History, 22, 169–245. doi:10.1017/S0261127903003048
  • Rosenstiel, S. F., Ward, D. H., & Rashid, R. G. (2000). Dentists’ preferences of anterior tooth proportion: A web-based study. Journal of Prosthodontics, 9, 123–136.
  • Rothwell, J. A. (1977). The phi factor: Mathematical proportions in musical forms. PhD diss., University of Missouri.
  • Ryschawy, H., & Stoll, R. W. (1988). Die bedeutung der zahl in Dufays kompositionsart: Nuper Rosarum Flores. Musik Konzepte, 60, 3–73.
  • Samuels, R. (2011). Unit 22 ‘Sonata Form’. In T. Bray (Ed.), A224: ‘Inside Music’, Block 3. Milton Keynes, UK: The Open University, 270-312.
  • Science. (1998). Math or mat. Science, 279, 487. doi:10.1126/science.279.5350.487b
  • Segall, M. H., Campbell, D. T., & Herskovits, M. J. (1963). Cultural differences in the perception of geometric illusions. Science, 139, 769–771. doi:10.1126/science.139.3556.769
  • Sibelius. (2014, February 20). Plugins for Sibelius. Retrieved from http://www.sibelius.com/download/plugins/index.html?versionname=&category=6
  • Siegele, U., & Clayton, A. (1992). Bach’s theological concept of form and the F Major duet. Music Analysis, 11, 245–278. doi:10.2307/854028
  • Sims, E. (1994). Long enough to reach the ground or how long should a man’s legs be? Perspectives of New Music, 32, 208–213. doi:10.2307/833165
  • Smyth, D. (1999). Schenker’s octave lines reconsidered. Journal of Music Theory, 43, 101–133. doi:10.2307/3090691
  • Snow, S. R. (1999). Esthetic smile analysis of maxillary anterior tooth width: The golden percentage. Journal of Esthetic and Restorative Dentistry, 11, 177–184. doi:10.1111/jerd.1999.11.issue-4
  • Somfai, L. (1981). Manuscript Versus Urtext: The primary sources of Bartók’s works. Studia Musicologica Academiae Scientiarum Hungaricae, 23, 17–66.
  • Stannard, I. (2007). ‘Arrest and Movement’: Tippett’s second piano sonata and the genesis of a method. Twentieth-Century Music, 4, 133–161. doi:10.1017/S1478572208000455
  • Tatlow, R. (2001), “Golden Section”, in The New Grove Dictionary of Music and Musicians, Ed. Sadie, S., London, UK: Macmillan, 10-95.
  • Tatlow, R. (2006). The use and abuse of Fibonacci numbers and the golden section in musicology today. Understanding Bach, 1, 69–85.
  • Thomas, R. G. (1978). Principles of search techniques for hydrogeology. Ground Water, 16, 264–272. doi:10.1111/gwat.1978.16.issue-4
  • Tillmann, B., & Bigand, E. (2004). The relative importance of local and global structures in music perception. The Journal of Aesthetics and Art Criticism, 62, 211–222. doi:10.1111/jaac.2004.62.issue-2
  • Tovey, D. F. (1935). Essays in musical analysis, Volume I-II, symphonies. London, UK: Oxford University Press.
  • Ward, D. H. (2007). A study of dentists’ preferred maxillary anterior tooth width proportions: Comparing the recurring esthetic dental proportion to other mathematical and naturally occurring proportions. Journal of Esthetic and Restorative Dentistry, 19, 324–339. doi:10.1111/j.1708-8240.2007.00114.x
  • Warner, T. J. (2006, June 13- 15). Quantitative listening: Temporal proportion in recordings of Mozart’s piano sonatas. Paper presented at the 7th WSEAS International Conference on Acoustics & Music: Theory & Applications, Cavtat, Croatia.
  • Webster, J. H. D. (1950). Golden-mean form in music. Music & Letters, 31, 238–248. doi:10.1093/ml/XXXI.3.238
  • WOW inc. (2014, June 18). “addlib”. Retrieved from. https://itunes.apple.com/gb/app/addlib/id352892127?mt=8
  • Yost, C. S. (2013). Numbers. ICU Director, 4, 52. doi:10.1177/1944451613477947
  • Zeising, A. (1854). Neue lehre von den proportionen des menschlichen körpers. Leipzig, Germany: Weigel.
  • Zhu, X., Jing, X., & Cheng, L. (2012). Magnetorheological fluid dampers: A review on structure design and analysis. Journal of Intelligent Material Systems and Structures, 23, 839–873. doi:10.1177/1045389X12436735
  • Ziv, N., & Omer, E. (2010). Music and time: The effect of experimental paradigm, musical structure and subjective evaluations on time estimation. Psychology of Music, 39, 182–195. doi:10.1177/0305735610372612

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