Escalas no octavantes como forma de organización tonal

Autores/as

DOI:

https://doi.org/10.35699/2317-6377.2025.57172

Palabras clave:

Escalas sin repetición de octava, Teoría de la música, Análisis musical, Teoría de las escalas, Composición, Improvisación

Resumen

Aunque la mayoría de las escalas del mundo repiten a la octava, lo cierto es que también se han empleado escalas no octavantes para organizar el contenido tonal en diferentes culturas musicales desde la Edad Media hasta nuestros días. Sin embargo, son escasos los estudios académicos que abordan el tema en profundidad, más allá de la aplicación de determinadas escalas no octavantes en contextos musicales concretos. Por lo tanto, no ha existido hasta la fecha un estudio de referencia, al que puedan recurrir investigadores y músicos potencialmente interesados en la cuestión, que recoja la medida en la cual estas estructuras han servido para determinar el contenido tonal de la música. El presente trabajo se basa en una variedad de fuentes diferentes para presentar una visión detallada y estructurada del uso de escalas no octavantes en una amplia gama de contextos musicales, confirmando así la hipótesis de que estas estructuras han demostrado ser una forma útil y consolidad de organizar el contenido tonal en la música.

Biografía del autor/a

  • Emmet Crowley, Universidad Internacional de la Rioja

    Doctor en Música por la Universidad Politécnica de Madrid. Con amplia experiencia como guitarrista, compositor y profesor, es actualmente Jefe de Estudios del Grado de Música en la Universidad Internacional de la Rioja. Sus áreas de especialización incluyen la interpretación de la guitarra eléctrica, técnicas de improvisación, estudios de conjunto, armonía y composición.

  • Francisco Gómez-Martín, Universidad Politécnica de Madrid

    Profesor de Matemáticas en la Universidad Politécnica de Madrid. Investiga sobre teoría matemática y computacional de la música y es miembro activo de esa comunidad. Es miembro de un grupo de investigación sobre musicología sistemática. Sus intereses de investigación incluyen música y emociones, análisis automático de la música, escalas multioctavas, entre otros. También es músico y su especialidad es la flauta dulce.

Referencias

Ayari, Mondher, and Stephen McAdams. 2003. “Aural Analysis of Arabic Improvised Instrumental Music (Taqsīm).” Music Perception 21 (2). doi:10.1525/mp.2003.21.2.159. DOI: https://doi.org/10.1525/mp.2003.21.2.159

Baker, D. 1990. Modern Concepts in Jazz Improvisation. Van Nuys, California: Alfred Music Publishing Co., Inc.

Belianski, Eugene. 2015. “Russian Folk Tradition in Contemporary Musical Literature for Winds.” Toronto, Ontario: York University.

Brown, Douglas Wayne. 2019. Hyperscales: Analysis, Historical Uses, and Possible Applications in Contemporary Music Composition. West Virginia University.

Brown, Steven, and Joseph Jordania. 2013. “Universals in the World’s Musics.” Psychology of Music 41 (2). doi:10.1177/0305735611425896. DOI: https://doi.org/10.1177/0305735611425896

Buelow, G J. 2016. The Late Baroque Era: Vol 4. From The 1680s To 1740. Man & Music. Hampshire, United Kingdom: Palgrave Macmillan UK. https://books.google.es/books?id=1uuuCwAAQBAJ.

Burns, Edward M. 1999. “Intervals, Scales, and Tuning.” In The Psychology of Music. doi:10.1016/b978-012213564-4/50008-1. DOI: https://doi.org/10.1016/B978-012213564-4/50008-1

Carey, Norman. 1998. “Distribution modulo 1 and Musical Scales.” Eastman (University of Rochester).

Cohen, David E. 2008. “Notes, Scales, and Modes in the Earlier Middle Ages.” In The Cambridge History of Western Music Theory. doi:10.1017/chol9780521623711.013. DOI: https://doi.org/10.1017/CHOL9780521623711.013

Corcelli, John. 2016. Frank Zappa FAQ: All That’s Left to Know About the Father of Invention. Lanham, Maryland: Rowman & Littlefield.

Crowley, Emmet, and Francisco Gómez-Mart’in. 2023. “Structural Properties of Multi-Octave Scales.” Journal of Mathematics and Music 17 (2). Taylor & Francis: 291–318. DOI: https://doi.org/10.1080/17459737.2022.2128450

Demsy, David. 1991. “Chromatic Third Relations in the Music of John Coltrane.” Annual Review of Jazz Studies 5 (5): 145–180.

Derby, Richard. 1981. “Carter’s ‘Duo for Violin and Piano.’” Perspectives of New Music 20 (1/2). doi:10.2307/942410. DOI: https://doi.org/10.2307/942410

Dixon, Gavin Thomas. 2007. “Polystylism as Dialogue: A Bakhtinian Interpretation of Schnittke’s Symphonies 3, 4, and His Concerto Grosso No.4/Symphony No.5.” Goldsmiths College.

Dubinets, Elena. 2015. “Non-Conformism or Nationalism? Yuriy Butsko and His Russian Dodecaphony” Studia Musicologica 56 (4). Akadémiai Kiadó: 317–325. DOI: https://doi.org/10.1556/6.2015.56.4.2

Erickson, Raymond. 2001. “Musica Enchiriadis, Scolica Enchiriadis.” Oxford University Press. doi:10.1093/gmo/9781561592630.article.19405. DOI: https://doi.org/10.1093/gmo/9781561592630.article.19405

Exarchos, Dimitris, and Daniel Jones. 2011. “Sieve Analysis and Construction: Theory and Implementation.” In Xenakis International Symposium.

Farraj, J, and S A Shumays. 2019. Inside Arabic Music: Arabic Maqam Performance and Theory in the 20th Century. New York, New York: Oxford University Press. https://books.google.es/books?id=etShDwAAQBAJ.

Gogotishvili, Vladimer. 2010. “On Authentic and Plagal Types of Monotonic (Non-Octave) Scales in Georgian Traditional Vocal Polyphony.” Echoes from Georgia: Seventeen Arguments on Georgian Polyphony (Focus on Civilizations and Cultures), Eds R. Tsurtsumia and J. Jordania (New York, NY: Nova Science Publishers). Citeseer, 147–156.

Grønseth, Anders Lønne. 2015. “The Bitonal Scale System - a Draft for a Modal-Harmonic System.”

Hoffman, Joel. 2005. “String Quartet 3 - Program Note.”

Hoffman, Joel. 2008. “Piano Concerto 2008 - Program Note.”

Ismael-Simental, Emilia. 2016. “Alfred Schnittke and the Znamennyi Rospev.” In Schnittke Studies, edited by Gavin Dixon, 30–58. Philadelphia: Routledge. DOI: https://doi.org/10.4324/9781315607702-3

Kirkman, A, and A Ivashkin. 2016. Contemplating Shostakovich: Life, Music and Film. Philadelphia: Routledge. DOI: https://doi.org/10.4324/9781315573779

Kostenko, A. 1985. Nardodnie Pesni Nechernozemia. Edited by N Savintseva. Moscow, Russia: Sovetsky Compozitor.

Lehmann, Zhanna A. 2018. “Alfred Schnittke’s Quest for a Universal Musical Language in the Penitential Psalms (1987–88).” University of Illinois at Urbana-Champaign.

Liebman, D. 1991. A Chromatic Approach to Jazz Harmony and Melody. Van Nuys, California: Advance Music.

Maloy, Rebecca. 2009. “Scolica Enchiriadis and the `Non-Diatonic’ Plainsong Tradition.” Early Music History 28. Cambridge University Press: 61–96. http://www.jstor.org/stable/40800897. DOI: https://doi.org/10.1017/S0261127909000369

McGill, Thomas Scott. 2013. “Dennis Sandole’s Unique Jazz Pedagogy.” Current Research in Jazz 5 (5): 1–45.

Messiaen, O. 1944. Technique de Mon Langage Musical. Bibliothèque-Leduc. Paris, France: Alphonse Leduc. https://books.google.es/books?id=pWAJAQAAMAAJ.

Nettl, Bruno. 2007. Maqam. Encyclopedia Britannica. https://www.britannica.com/art/maqam-music.

Nikolsky, Aleksey. 2016. “Evolution of Tonal Organization in Music Optimizes Neural Mechanisms in Symbolic Encoding of Perceptual Reality. Part-2: Ancient to Seventeenth Century.” Frontiers in Psychology 7: 1–32. doi:10.3389/fpsyg.2016.00211. DOI: https://doi.org/10.3389/fpsyg.2016.00211

Pace, Ian. 2001. “The Harpsichord Works of Iannis Xenakis.” Contemporary Music Review 20 (1). Routledge: 125–140. doi:10.1080/07494460100640121. DOI: https://doi.org/10.1080/07494460100640121

Pahlevanian, Alina, Aram Kerovpyan, and Svetlana Sarkisyan. 2001. “Armenia, Republic Of.” Oxford University Press. doi:10.1093/gmo/9781561592630.article.42078. DOI: https://doi.org/10.1093/gmo/9781561592630.article.42078

Persichetti, Vincent. 1961. Twentieth Century Harmony: Creative Aspects and Practice. New York, New York: W. W. Norton & Company, Inc.

Schillinger, Joseph. 1946. The Schillinger System of Musical Composition. New York, New York: Carl Fisher, Inc.

Schnittke, Alfred. 2002. A Schnittke Reader. Bloomington, Indiana, USA: Indiana University Press. DOI: https://doi.org/10.2979/2893.0

Seroussi, Edwin, Joachim Braun, Eliyahu Schleifer, Uri Sharvit, Sara Manasseh, Theodore Levin, Tang Yating, et al. 2001. “Jewish Music.” Oxford University Press. doi:10.1093/gmo/9781561592630.article.41322. DOI: https://doi.org/10.1093/gmo/9781561592630.article.41322

Sethares, William. 2005. Tuning, Timbre, Spectrum, Scale. Berlin, Germany: Springer.

Slonimsky, Nicolas. 1947. Thesaurus of Scales and Melodic Patterns. New York, New York: Shirmer Books.

Squibbs, Ronald. 1996. “An Analytical Approach to the Music of Iannis Xenakis: Studies of Recent Works.” Connecticut: Yale University.

Squibbs, Ronald. 2002. “Some Observations on Pitch, Texture, and from in Xenakis’ Mists.” Contemporary Music Review 21 (December): 91–108. doi:10.1080/07494460216653. DOI: https://doi.org/10.1080/07494460216653

Swan, Alfred J. 1940a. “The Znamenny Chant of the Russian Church–Part II.” The Musical Quarterly 26 (3). Oxford University Press: 365–380. http://www.jstor.org/stable/738771. DOI: https://doi.org/10.1093/mq/XXVI.3.365

Swan, Alfred J. 1940b. “The Znamenny Chant of the Russian Church–Part I.” The Musical Quarterly 26 (2). Oxford University Press: 232–243. http://www.jstor.org/stable/738849. DOI: https://doi.org/10.1093/mq/XXVI.2.232

Taruskin, R. 2008. On Russian Music. Berkeley, California, USA: University of California Press.

Trehub, Sandra, Judith Becker, and Iain Morley. 2015. “Cross-Cultural Perspectives on Music and Musicality.” Philisophical Transactions of the Royal Society B 370 (December). doi:10.1098/rstb.2014.0096. DOI: https://doi.org/10.1098/rstb.2014.0096

Tymoczko, Dmitri. 2004. “Scale Networks and Debussy.” Journal of Music Theory 48 (2). Duke University Press: 219–294. doi:10.1215/00222909-48-2-219. DOI: https://doi.org/10.1215/00222909-48-2-219

Velimirovic, Milos, Irene� Lozovaya, Gregory Myers, and Leonora DeCarlo. 2001. “Russian and Slavonic Church Music.” Oxford University Press. doi:10.1093/gmo/9781561592630.article.43458. DOI: https://doi.org/10.1093/gmo/9781561592630.article.43458

Wall, Jeffery B. 2009. “The Influence of Znamenny Liturgical Chant on the Nineteenth-Century Russian Choral School: A Guide for Performance.” The Choral Journal 50 (3). American Choral Directors Association: 20–32. http://www.jstor.org/stable/23559804.

Weitzman, Ronald. 1996. “Schnittke: Symphony No. 4 / Three Sacred Hymns.” Chandos. https://www.chandos.net/chanimages/Booklets/CH9463.pdf.

Weston, Craig. 2020. “Some Properties of Non-Octave-Repeating Scales, and Why Composers Might Care.” In Proceedings of SCI Region VI Conference. Washington DC.

Wilcox, A Gordon. 1967. “Perfect Fourths as a Scalar Option.” Perspectives of New Music 5 (2). Perspectives of New Music: 141–145. http://www.jstor.org/stable/832164. DOI: https://doi.org/10.2307/832164

Wilkox, Derek. 2001. “Kakhuri Nanina.” Chela: Cambridge Georgian Choir. https://www.scoreexchange.com/scores/63606.html.

Xenakis, Iannis. 1992. Formalized Music: Thought and Mathematics in Composition. Stuyvesant, New York: Pendragon Press.

Yöre, Seyit. 2012. “Maqam in Music as a Concept, Scale and Phenomenon.” Zeitschrift Für Die Welt Der Türken/Journal of World of Turks 4 (3): 267–286.

Zheng, Yan. 2017. “Analysing the Semiotic Contribution of Traditional Aesthetics to Contemporary Chinese Music.” In Proceedings of the 9th European Music Analysis Conference. Strasbourg, France.

Publicado

2025-05-30

Número

Sección

Artículos

Cómo citar

“Escalas No Octavantes Como Forma De organización Tonal”. 2025. Per Musi 26 (May): 1-38. https://doi.org/10.35699/2317-6377.2025.57172.