Abstract
This is an investigation of musical creativity. Improvisation is a complex system for understanding musical creativity. Improvisation is often expressed through jazz music. This chapter focuses on the measurement of jazz improvisation in order to better understand musical creativity. The science and art of music analysis are discussed. Improvisation can be a measure for musical creativity; however, there are limitations with existing measurement methods. Instead, fractal analysis offers an approach that addresses such limitations. In a case study approach, the work of John Coltrane and his relevant biographical events are discussed along with a fractal analysis examining the sequential structure of pitches in his saxophone solos. Saxophone solos were transcribed from sheet music into a format that represents an absolute pitch numerically. The pitch sequences were examined using power spectral analysis. Results indicate that all 18 Coltrane saxophone solos display sequences of successive pitches that are consistent with anti-persistent fractional Brownian motion having 1/f α power spectra with scaling exponent α between 1.6 and 1.8. Brownian motion is a type of statistical pattern that is symptomatic of self-similar or fractal patterning across time (Mandelbrot 1998). In addition, average mutual information analyses revealed various dominant regular rhythmic patterns in several of the pieces. Eighth-note patterns were dominant in his earlier work, while greater irregularity was present in rhythmic patterns of his later work. Thus, Coltrane’s improvised solos, including his later avant-garde compositions, are comprised of Brownian fractal patterns, which others using a different pitch encoding technique have previously identified in performances of both classical and jazz music (e.g., Boon and Delcroly 1995). These fractal patterns quantify the concepts of order and complexity addressed in the Birkhoff’s Theory of Aesthetic Value. Fractal analysis offers another approach toward understanding the dynamics of improvisation and musical creativity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Abbott, E. A. (1884, 1992). Flatland: A romance of many dimensions. New York: Dover Publications.
Aitken, A. E. (1976). A self-instructional audio-imitation method designed to teach trumpet students jazz improvisation in the major mode. Dissertation Abstracts International, University of Oregon.
Aitken, P. (2005). Unity and form in Miles Davis’ “Blue in Green”. McMasterMusic Analysis Colloquium, 4, 1–11.
Aloupis, G., Fevens, T., Langerman, S., Matsui, T., Mesa, A., Nunez, Y., et al. (2006). Algorithms for computing geometric measures of melodic similarity. Computer Music Journal, 30, 67–76.
Alterhaug, B. (2004). Improvisation on a triple theme: Creativity, jazz improvisation and communication. Studia Musicologica Norvegica, 30, 97–118.
Aristotle (1882). Aristotle’s psychology (E. Wallace, Trans.). London: Cambridge University Press.
Azzara, C. D. (2002). Improvisation. In R. Colwell & C. Richardson (Eds.), The new handbook on research of music teaching and learning (pp. 171–187). New York: Oxford.
Azzara, C. D., Grunow, R. F., & Gordon, E. E. (1997). Creativity in improvisation. Chicago, IL: GIA.
Bair, J. (2003). Cyclic patterns in John Coltrane’s melodic vocabulary as influenced by Nicolas Slonimsky’s “Thesaurus of scales and melodic patterns”: An analysis of selected improvisations. University of North Texas.
Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice-Hall.
Birkhoff, G. D. (1933). Aesthetic measure. Cambridge, Massachusetts: Harvard University Press.
Boon, J. P., & Delcroly, O. (1995). Dynamical systems theory for music dynamics. Chaos, 5, 501–508.
Brown, R. (1827). A brief account of microscopical observations Made in the Months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. London: Cambridge University Press.
Burnsed, C. V., & Price, H. E. (1984). Improvisation and Evaluation. Research Proceedings of the National Association of Jazz Educators, 6, 35–42.
Cartwright, J. H. E., Gonzalez, D. L., & Piro, O. (1999). Nonlinear dynamics of the perceived pitch of complex sounds. Physical Review Letters, 82, 5389–5392.
Chacon, R., Batres, Y., & Cuadros, F. (1992). Teaching deterministic chaos through music. Physics Education, 27, 151–154.
Charyton, C., Holden, J. G., Jagacinski, R. J., & Elliott, J. O. (2012). A historical and fractal perspective on the life and saxophone solos of John Coltrane. Jazz Perspectives, 6(3), 311–335. doi:10.1080/17494060.2013.806031.
Cheshire, N. (1996). The empire of the ear: Freud’s problem with music. International Journal of Psychoanalysis, 77, 1127–1168.
Coan, C., Coltrane, R., & Schiff, R. (1995). John Coltrane’s Solos. Milwaukee, WI: Hal Leonard Publications.
Coltrane, J. (1959, 2007a). “Giant Steps,” Giant Steps, Rhino/Atlantic.
Coltrane, J. (1959, 2007b) “Countdown,” Giant Steps, Rhino/Atlantic Records.
Coltrane, J., (1959, 2008). “Some Other Blues,” Coltrane Jazz, Rhino/Atlantic.
Coltrane, J. (1960, 1999). “26-2,” Coltrane’s Sound, Atlantic Records.
Coltrane, J. (1960, 1990). “My Favorite Things,” My Favorite Things, Atlantic Records.
Coltrane, J. (1960, 1999). “Equinox,” Coltrane’s Sound. Atlantic Records.
Coltrane, J. (1961, 2008). “Africa,” Africa/Brass. New York, NY: Impulse! Verve/Impulse!
Coltrane, J. (1961, 1962). “Olé,” Olé. Warner Jazz/Atlantic Records.
Coltrane, J. (1961, 1963, 2008). “Impressions,” Impressions. New York, NY: Impulse!/Universal Distribution.
Coltrane, J. (1961, 1998). “Spiritual,” Live at the Village Vanguard. New York, NY: Impulse! Records.
Coltrane, J. (1962, 2002). “Tunji,” Coltrane. New York, NY: Impulse! Records.
Coltrane, J. (1962, 2008). “Nancy (with the Laughing Face)” Ballads. New York, NY: Impulse! Records.
Coltrane, J. (1963, 2008). “Alabama,” Live at Birdland. New York, NY: Impulse! MCAD.
Coltrane, J. (1963, 1995). “Lush Life,” John Coltrane and Johnny Hartman. GRP/Impulse!
Coltrane, J. (1964, 2002). “A Love Supreme,” A Love Supreme: Deluxe Edition. New York, NY: Impulse! Records.
Coltrane, J. (1964, 2003). A Love Supreme. New York, NY: Impulse! Records.
Coltrane, J. (1964, 2008). Crescent, New York, NY: Impulse! Records.
Coltrane, J. (1965, 1967). “Welcome,” Kulu Sé Mama. New York, NY: Impulse! Records.
Coltrane, J. (1966, 2011). “Naima,” Live at the Village Vanguard Again!. New York, NY: Impulse! Records/Universal Distribution.
Coltrane, J. (1966, 1991). “Crescent,” Live in Japan. New York, NY: Impulse! Records.
Coltrane, J. (1967, 1993). “Expression,” Expression. New York, NY: Impulse! Records.
Coltrane, J. (1967, 2000). “Jupiter,” Interstellar Space. New York, NY: Impulse! Records.
Csikszentmihalyi, M. (1990). Flow: The psychology of optimal experience. New York, NY: Harper Collins.
Davidson, P. D. (2010). The role of self-efficacy and modeling in improvisation among intermediate instrumental music students. Journal of Band Research, 45(2), 42–58.
Diaz de Chumaceiro, C. L. (1993). Richard Wagner’s Life and Music: What Freud knew. In S. Feder, R. L. Karmel, & G. H. Pollock (Eds.), Psychoanalytic explorations in music: Second series. Madison, CT: International Universities Press Inc.
Einstein, A. & Infeld, L. (1938). The evolution of physics: From early concepts to relativity and quanta. New York, NY: A Touchstone Book.
Eke, A., Herman, P., Bassingthwaighte, J. B., Raymond, G. M., Percival, D. B., Cannon, M., et al. (2010). Physiological time series: Distinguishing fractal noises from motions. European Journal of Physiology, 439, 403–415. doi:10.1007/s004249900135.
Euclid. (1803). By Robert Simson, M. D. The elements of Euclid, the first six books together with the eleventh and twelfth, the errors, by which heon or others, have long ago vitiated these books, are corrected, and some of Euclid’s demonstrations are restored. Also, the book of Euclid’s data in the like manner corrected. Philadelphia: Homas and George Palmer for Conrad and Co.
Fourier, J. (1878). The analytical theory of heat. Cambridge: At the University Press.
Fraim, J. (1996). Spirit catcher: The life and art of John Coltrane. West Liberty, OH: Great House Co.
Fujioka, Y., Porter, L., & Hamada, Y. (Eds.). (1995). John Coltrane: A discography and musical biography. Newark, N.J.: Scarecrow Press.
Gabrielsson, A. (2003). Music performance research at the millennium. Psychology of Music, 31(3), 221–272.
Gardner, H. (1993). Creating minds: An anatomy of creativity as seen through the lives of Freud, Einstein, Picasso, Stravinsky, Eliot, Graham and Gandhi. New York: NY: Harper Collins Publisher.
Gordon, E. (1984). A longitudinal predictive validity study of the Intermediate Measures of Music Audiation. Bulletin of the Council for Research in Music Education, 1–23.
Gordon, E. E. (1997). Learning sequences in music: Skill, content, and patterns: A music learning theory. Chicago, IL: GIA Publications Inc.
Gordon, E. E. (1998). Harmonic improvisation readiness record and rhythm improvisation readiness record. Chicago, IL: GIA Publications Inc.
Gordon, E. E. (2000). Studies in harmonic and rhythm improvisation readiness. Chicago, IL: GIA Publications Inc.
Gordon, E. E. (2012). Learning sequences in music: A contemporary music learning theory. Chicago, IL: GIA Publications Inc.
Gottlieb, G. (1998). Normally occurring environmental and behavioral influences on gene activity: From central dogma to probabilistic epigenesis. Psychological Review, 105, 792–802.
Guilbault, D. M. (2009). The effects of harmonic accompaniment on the tonal improvisations of students in first through sixth grade. Journal of Research in Music Education, 57(2), 81–91.
Honerkamp, J. (1994). Stochastic dynamical systems: Concepts, numerical methods, data analysis (K. Linderberg, Trans.). New York: VCH Publishers.
Hsu, K. J., & Hsu, A. (1990). Fractal geometry of music (physics of melody). Proceedings of the National Academy of the Sciences, 87, 938–941.
Hsu, K. J., & Hsu, A. (1991). Self-similarity of the “1/f noise” called music. Proceedings of the National Academy of the Sciences, 88, 3507–3509.
Hughes, J. R., Daaboul, Y., Fino, J. J., & Shaw, G. L. (1998). The “Mozart Effect” on epileptiform activity. Clinical Electroencephalography, 29, 109–119.
Jeong, J., Joung, M. K., & Kim, S. Y. (1998). Quantification of emotion by nonlinear analysis of the chaotic dynamics of electroencephalograms during perception of 1/f music. Biological Cybernetics, 78, 217–225.
Johnson-Laird, P. (2002). How jazz musicians improvise. Music Perception, 19(3), 415.
Kofsky, F. (1998). John Coltrane and the Jazz Revolution of the 1960’s. Atlanta, GA: Pathfinder.
Langer, S. (1951). Philosophy in a new key. London: O.U.P.
Little, L. (1976). Improvisation readiness test (pp. 22–23). Dec/Jan: NAJE Education.
Lyuu, Y. D. (2002). Financial engineering and computation: Principles, mathematics, algorithms. New York: Cambridge University Press.
Mandelbrot, B. B. (1998). Multifractals and 1/f noise. New York: Springer.
Mandlebrot, B. B. (1975). Stochastic models for the Earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proceedings of the National Academy of the Sciences, 72 (10), 3825–3828.
May, R. (1975). The courage to create. New York: W.W. Norton & Company.
May, L. F. (2003). Factors and abilities influencing achievement in instrumental jazz improvisation. Journal of Research in Music Education, 51(3), 245–258.
McDaniel, W. T. (1974). Differences in musical achievement, musical experience, and background between jazz-improvising musicians and non improvising musicians at the freshman and sophomore college levels (Doctoral dissertation, University of Iowa, 1974). Dissertation Abstracts International, 35 (12), 7948A.
McGlashan, A. R. (1987). Music as a symbolic process. Journal of Analytic Psychology, 32, 327–344.
Miller, A. I. (1992). Scientific creativity: A comparative study of Henri Poincare and Albert Einstein. Creativity Research Journal, 5, 385–418.
Newton, I. (1720). Universal arithmetick: or, a treatise of arithmetical composition and resolution. To which is added, Dr. Halley’s method of finding the roots of equations arithmetically (Latin by the late Mr. Raphson (Trans.), and Mr. Cunn (revised and corrected)). London: J. Senex, W. Taylor, T. Warner, and J. Osborn.
Nisenson, E. (1995). Ascension: John Coltrane and his quest (1st Da Capo Press ed.). New York: Da Capo Press.
Peterschmitt, G., Gomez, E. & Herra, P. (2001) Pitch-based solo location. Proceedings of MOSART Workshop on Current Research Directions in Computer Music, Barcelona, Spain, 239–243.
Pfenninger, R. C. (1990). The development and validation of three rating scales for the objective measurement of jazz improvisation achievement. Dissertation Abstracts International (Temple University, UMI No. 9100327).
Porter, L. (1998). John Coltrane: His life and music. Ann Arbor: University of Michigan Press.
Pressing, J. (1994). Novelty, progress and research method in computer music composition. Proceedings of the 1994 International Computer Music Conference-Aarhus, San Francisco, CA: ICMA, 27–30.
Ratliff, B. (2007). Coltrane: The story of sound. New York, NY: Farrar, Straus and Giroux.
Running, D. J. (2010). Creativity research in music education: A review. Applications of Research in Music Education, 27(1), 41–47.
Santa, M. (2003). Nonatonic progressions in the music of John Coltrane. Annual Review of Jazz Studies, 13, 13–25.
Schilling, R. (1987). The feasibility of objective diagnostic measurement of jazz improvisation. Research Proceedings of the National, Association of Jazz Educators, 7, 101–170.
Schroeder, M. (1990). Fractals, chaos, power-laws: Minutes from an infinite universe. New York: W. H. Freeman and Company.
Schuster, P. (Ed). Stochastic phenomena and chaotic behaviour in complex systems: Proceedings of the fourth meeting of the UNESCSO working group on systems analysis Flarrnitz, Karnten, Australia, June 6–10, 1983. Berlin, Germany: Springer.
Sherry, J. L. (2004). Flow and media enjoyment. Communication Theory, 14, 328–347.
Shi, Y. (1995). Scalings of pitches in music. Eprint arXiv:adap-org/9509001. Retrieved April 20, 2008, from http://arxiv.org/PS_cache/adap-org/pdf/9509/9509001v1.pdf.
Shi, Y. (1996). Correlations of pitches in music. Fractals, 4, 547–553.
Simonton, D. (1984). Genius, creativity, and leadership: Historiometric inquiries. Cambridge, MA: Harvard University Press.
Smith, D. T. (2009). Development and validation of a rating scale for wind jazz improvisation performance. Journal of Research in Music Education, 57(3), 217–235.
Sternberg, R. J. (1999). Handbook of creativity. New York, NY: Cambridge University Press.
Sternberg, R. J. (2001). What is the common thread of creativity: Its dialectical relation to intelligence and wisdom. American Psychologist, 56, 360–362.
Voss, R. F., & Clarke, J. (1975). 1/f noise in music and speech. Nature, 258, 317–318.
Voss, R. F., & Clarke, J. (1978). 1/f noise in music: Music from 1/f noise. Journal of Acoustical Society of America, 63, 258–263.
Wagenmakers, E. J., Farrell, S., & Ratcliff, R. (2004). Estimation and interpretation of 1/f noise in human cognition. Psychonomic Bulletin & Review, 11, 579–615.
Webster, P. R. (1990a). Creativity as creative thinking. Music Educators Journal, 76(9), 22.
Webster, P. R. (1990b). Creativity as creative thinking: Introduction. Music Educators Journal, 76(9), 21.
Webster, P. R. (1994). Time, technology, and the creative process. Arts Education Policy Review, 96(1), 32–36.
Webster, P., & Hickey, M. (2001). Creative thinking in music. Music Educators Journal, 88(1), 19–23.
Weiskopf, W., & Ricker, R. (1991). Coltrane: A player’s guide to his harmony. New Albany, IN: J. Aebersold.
Wesolowski, B. C. (2013). Cognition and the assessment of interaction episodes in Jazz improvisation. Psychomusicology: Music, Mind, and Brain, 23(4), 236–242.
Westervelt, T. G. (2001). An investigation of harmonic and improvisation readiness among upper elementary age children. Dissertation Abstracts International (Temple University, UMI No. 3031569).
White, A. N. (1981). Trane n’ me (A semi-autobiography): A treatise on the music of John Coltrane. Washington, D.C.: Andrew Musical Enterprises Inc.
White, A. N. (2006). The Andrew white comprehensive catalogue of over 2000 self produced products. September 23, 2005–2006 Edition. Andrew’s Music 4830 South Dakota Ave NE Washington DC 20017 USA.
Yamaguchi, M., & Sweet, J. (2002). A creative approach to multi-tonic changes: Beyond Coltrane’s harmonic formula. Annual Review of Jazz Studies, 12, 147–167.
Acknowledgments
Sincere gratitude to Jay Holden, Richard Jagacinski, and John Elliott for their collaboration and contributions for our article in Jazz Perspectives. Gratitude to Andrew White, Lewis Porter, Shane Ruland, Sean Ferguson, Ted McDaniel, David Huron, and Glenn Elliott for tools, assistance, and advice in this analysis of John Coltrane’s music and thanks to Paul Jones for technical consultation, Alex Charyton for his constructive feedback, Steven Pond for his attention to detail, Robert Weisberg for suggesting the concept of a case study, and the John Taggart for introducing me to the work of John Coltrane. Additional gratitude to Heeyeon Chung for contributions on improvisation along with Joseph Benson and Charles Hall. Special gratitude to Sean Ferguson for assisting in library assistance with library science expertise that is genuinely beneficial.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag London
About this chapter
Cite this chapter
Charyton, C. (2015). The Impact of Improvisation on Creativity: A Fractal Approach. In: Charyton, C. (eds) Creativity and Innovation Among Science and Art. Springer, London. https://doi.org/10.1007/978-1-4471-6624-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4471-6624-5_8
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-6623-8
Online ISBN: 978-1-4471-6624-5
eBook Packages: EngineeringEngineering (R0)