The Euclidean Groove - ein Crashkurs durch die Welt des Rhythmus

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Subject according curriculum

Analysis, music theory

Teachers

Prof. Sebastian Sprenger

Scope

Thursday, 10.30 - 12.00 Start: 10. 10. 2024

Room

BP 201

Duration

1.5 Semesterwochenstunden

Description

As is well known, Gottfried Wilhelm Leibniz interpreted music - in a letter from 1712 - as "a hidden arithmetical exercise of the mind, which does not know that it is counting". The philosopher, who according to recent research (see bibliography) was no cookie, referred to the numerical relationships underlying musical intervals and at the same time stated: "In music, we only count to five". But how far should musicians be able to consciously count in the field of rhythm?
Two extremes: in his typology of asymmetrical rhythms, ethnomusicologist Simha Arom sees all uneven, "limping" rhythmic structures as being made up of groups of 2 and 3. On the other hand, the Armenian jazz pianist Tigran Hamasyan claims to have composed a work in 256/16 time with "Entertain me"; whereby the question of the correct internal accentuation of this time signature can certainly be answered differently depending on the theoretical basis.
In this seminar, fascinating rhythmic phenomena from the music of different times, regions of the world and styles will be analyzed, compared and experienced in practice. There are always astonishing parallels to be discovered - for example between Brahms' hemiola technique and the drum music of certain Afro-Cuban cults - which cannot always be explained by "cultural appropriation", but rather seem to be based on the specific divisibility of certain numbers.
Last but not least: Even though numbers play a not insignificant role in this seminar, the mathematical knowledge acquired in elementary school and lower school is completely sufficient for understanding it. The lecturer freely admits his great difficulty in dealing with anything that cannot be counted on his own ten fingers. But according to Leibniz, even the fingers of a single hand should suffice in the musical field - as Dave Brubeck successfully proved.

Literature

Apel, Willi: The notation of polyphonic music 900 - 1600. Wiesbaden 1989

Arom, Simha: African Polyphony and Polyrhythm. Cambridge University Press 1991

Ders.: L'aksak: Principes et typologie. Cahiers de musiques traditionnelles, Vol. 17 (2004), p. 11 - 48

Butler, Mark J.: Unlocking the Groove. Rhythm, Meter, and Musical Design in Electronic Dance Music. Indiana University Press 2006

Clayton, Martin: Time in Indian Music. Rhythm, Metre, and Form in North Indian Rāg Performance. Oxford University Press 2000

Enzensberger, Hans Magnus: The number devil. A pillow book for all those who are afraid of mathematics. Munich 1997

Hartenberger, Russell/McClelland, Ryan: The Cambridge Companion to Rhythm. Cambridge University Press 2020

Krebs, Harald: Fantasy Pieces. Metrical Dissonance in the Music of Robert Schumann. Oxford University Press 1999

Osborn, Brad: Kid Algebra. Radiohead's Euclidean and Maximally Even Rhythms. Perspectives of New Music 52.1 (2014), p. 81 - 105
http://dx.doi.org/10.7757/persnewmusi.52.1.0081

Schmidt-Salomon, Michael & Salomon, Lea: Leibniz was no cookie. On the trail of the big and small questions of philosophy. Zurich/Munich 2011

Schumann, Scott C.: Asymmetrical Meters, Ostinati, and Cycles in the Music of Tigran Hamasyan. Music Theory Online 2021
https://mtosmt.org/issues/mto.21.27.2/mto.21.27.2.schumann.html

Taylor, Stephen Andrew: Hemiola, Maximal Evenness, and Metric Ambiguity in Late Ligeti, Contemporary Music Review, 31:2-3 (2012), p. 203-220

Toussaint, Godfried T.: The Geometry of Musical Rhythm. What Makes a "Good" Rhythm Good? London/New York 2020

Credits

3 Creditpoints

Comments

Course for BA and MA students of all disciplines.
Please register by stating your degree program at sebastian.sprenger[at]hfmt-hamburg.de by 8. 10. 2023.
Proof of performance: Participation in 85% of the courses; presentation or written term paper.

Modules

Musiktheoretisches Modul 1 Instrumentalisten Master, Musiktheoretisches Modul 2 Kirchenmusik A (Master), Wahlmodul freie Wahl (alle Studiengänge)