Abstract
Microtonality appears in a wide range of historical and ethnomusicological contexts, particularly in theoretical aspects of tuning systems and as intonation in performance. Theoretical concepts of microtonality can be inaccessible due to difficulties arising in the reconciliation of mathematical and musical approaches. The development of sophisticated geometrical representations of pitch cognition has largely been focused on the Western tonal tradition with limited incorporation of microtonality. This paper presents a spatial model of microtonal intervals and their relational structures. The model enhances accessibility of microtonal-theoretic concepts through a visually intuitive representation. It also acts as a unifying framework with respect to the comparative assessment of microtonal schemes and the integration of the different dimensions of pitch cognition. The integrative characteristics of the model demonstrate the psychological emergence of cognitive structures and their potential isomorphism with algorithmic approaches. The comparative features of the model may provide the basis for computational applications of broader scope than a culturally specific model can provide, while the intuitive spatial aspects may inspire improvements in the human-computer interaction of such applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Griffiths, P., Lindley, M., Zannos, I.: Microtone. In: Sadie, S., Tyrrell, J. (eds.) The New Grove Dictionary of Music and Musicians, vol. 16, pp. 624–625. Macmillan, London (2001)
Lindley, M.: Tuning. In: Sadie, S., Tyrrell, J. (eds.) The New Grove Dictionary of Music and Musicians, vol. 25, pp. 884–885. Macmillan, London (2001)
Leedy, D., Haynes, B.: Intonation (ii). In: Sadie, S., Tyrrell, J. (eds.) The New Grove Dictionary of Music and Musicians, vol. 12, pp. 503–504. Macmillan, London (2001)
Lindley, M.: Temperaments. In: Sadie, S., Tyrrell, J. (eds.) The New Grove Dictionary of Music and Musicians, vol. 25, pp. 248–268. Macmillan, London (2001)
Nolan, C.: Music Theory and Mathematics. In: Christensen (ed.) The Cambridge History of Western Music Theory, pp. 272–304. Cambridge University Press, Cambridge (2002)
Adkins, C.: Monochord. In: Sadie, S., Tyrrell, J. (eds.) The New Grove Dictionary of Music and Musicians, vol. 17, pp. 2–4. Macmillan, London (2001)
Mathiesen, T.J.: Greek Music Theory. In: Christensen (ed.) The Cambridge History of Western Music Theory, pp. 109–135. Cambridge University Press, Cambridge (2002)
Klumpenhouwer, H.: The Cartesian Choir. Music Theory Spectrum 14(1), 15–37 (1992)
Gouk, P.: Music, Science and Natural Magic in Seventeenth-Century England. Yale University Press, New Haven (1999)
Mooney, M.K.: The ‘Table of Relations’ and Music Psychology in Hugo Riemann’s Harmonic Theory. Ph.D. diss., Columbia University (1996)
Shepard, R.N.: Geometrical Approximations to the Structure of Musical Pitch. Psychological Review 89(4), 305–333 (1981)
Krumhansl, C.L.: Cognitive Foundations of Musical Pitch. Oxford University Press, New York (1990)
Chew, E.: Modeling Tonality: Applications to Music Cognition. In: Proceedings of the 23rd Annual Meeting of the Cognitive Science Society (2001)
Chew, E.: The Spiral Array: An Algorithm for Determining Key Boundaries. In: Anagnostopoulou, C., Ferrand, M., Smaill, A. (eds.) ICMAI 2002. LNCS (LNAI), vol. 2445, pp. 18–31. Springer, Heidelberg (2002)
Chew, E., Chen, Y.C.: Real-Time Pitch Spelling Using the Spiral Array. Computer Music Journal 29(2), 61–76 (2005)
Gollin, E.: Some Aspects of Three-Dimensional “Tonnetze”. Journal of Music Theory 42(2), 195–206 (1998)
Polansky, L.: Paratactical Tuning: An Agenda for the Use of Computers in Experimental Intonation. Computer Music Journal 11(1), 61–68 (1987)
Lindley, M.: Well-Tempered Clavier. In: Sadie, S., Tyrrell, J. (eds.) The New Grove Dictionary of Music and Musicians, vol. 27, pp. 274–277. Macmillan, London (2001)
Wolf, A.: Graphic Representation and Functional Systematics of Historic Musical Temperaments. ISO Information 21, 41–70 (1980)
Kellner, H.A.: A Visualization of Organ Tunings for Perception of their Structure. Das Musikinstrument 44(10), 76 (1995)
Sandoz, R.: Les problèmes posés par les tempéraments. Revue Musicale de Suisse Romande 35(3), 140–145 (1982)
Sundberg, J., Friberg, A., Frydn, L.: Rules for Automated Performance of Ensemble Music. Contemporary Music Review 8, 89–109 (1989)
Haruko, K., Mihoko, N.: Theory and Notation in Japan. In: Nettl, B., Stone, R. (eds.) The Garland Encyclopedia of World Music, vol. 7, pp. 565–584. Routledge, New York (2002)
Haluška, J.: Equal Temperament and Pythagorean Tuning: A Geometrical Interpretation in the Plane. Fuzzy Sets and Systems 1148, 261–269 (2000)
Sethares, W.A.: Tuning, Timbre, Spectrum, Scale, 2nd edn. Springer, London (2005)
Wright, O.: Safi al-Din. In: Sadie, S., Tyrrell, J. (eds.) The New Grove Dictionary of Music and Musicians, vol. 22, pp. 86–87. Macmillan, London (2001)
Yarman, O.: A Comparative Evaluation of Pitch Notations in Turkish Makam Music. Journal of Interdisciplinary Music Studies 1(2), 43–61 (2007)
Stadler, M., Kruse, P.: Gestalt Theory and Synergetics: From Psychophysical Isomorphism to Holistic Emergentism. Philosophical Psychology 7(2), 211–226 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stylianou, N. (2011). Exploding the Monochord: An Intuitive Spatial Representation of Microtonal Relational Structures. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds) Mathematics and Computation in Music. MCM 2011. Lecture Notes in Computer Science(), vol 6726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21590-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-21590-2_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21589-6
Online ISBN: 978-3-642-21590-2
eBook Packages: Computer ScienceComputer Science (R0)