MTSE: 2020 Chiu Appalachian State University Putting the Math in Math Rock Matt Chiu
Fig. 1 Math Rock Timeline
Math Rock Playlist: https://open.spotify.com/playlist/0YMehqtnDK9X1pBsVc0ftN
Fig. 2 DFT Mathematics Explained
Tresillo Timeline: [1, 0, 0, 1, 0, 0, 1, 0]
Fig. 3 DFT Calculation on the Tresillo MTSE: 2020 Chiu Appalachian State University
ACCENT PROFILE RULES MPR 3: Event +1 wherever there is a note MPR 6: Bass Note +1 to lowest note of any 5 contiguous units PEC: Second of Two +1 to second to two adjacent notes PEC: Initial and Final Tones +1 to both ends of an adjacent string of notes Large Leaps +1 to any leap of 5 semitones or more +1 to all changes in the contour: contour is established after Continuous/Contour 2 moves in the same direction MPR 1: Parallelism +1 to parallelism projects PEC = Povel/Essens Clock (Rules) MPR = Metric Preference Rules (Lerdahl and Jackendoff) Fig. 4 Accent Profile Rule
[5, 2, – 2, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1] E . Gtr. œ œ œ œ œ œ œ œ œ œ œ (Lead) & œ œ œ œ œ œ œ œ œ œ œ œ œ œ
˙ œ j œ œ ˙ œ™ œ & ™ œ ˙ ™ J J
˙ ˙ ˙ ˙ ˙ ˙ & agnitude M
Component ˙ ˙ œ Fig. 5 Never Meant: Guitar 1 (top); Rhythmic Profile (bottom) MTSE: 2020 Chiu Appalachian State University [4, 2, 2, 3, 1, 2, 1, 3, 2, 3, 3, 0, 0, 5, 2, 3, 1, 2, 1, 1, 4, 2, 2, 1] E. Gtr œ œ œ œ œ œ œ œ œ œ (Gtr 2) & œ œ œ œ J œ œ œ œ œ œ œ œ œ
& ˙ œ ˙œ™ œ™ ˙ œ™ ˙ ™ Never Meant: Rhythm Guitar, Rhythmic Profle Magnitude
Components j x3.428 ˙. œ Fig. 6 Never Meant: Guitar 2 (top); Rhythmic Profile (bottom)
f2 f3 f4/5 3
f4 f6 f9 3
f8 f12 f18 3
f16 f24 f36 3
Fig. 7 DFT Components (left); Metric Ski-Hill Graph (right)
MTSE: 2020 Chiu Appalachian State University [5, 2, 2, 2, 0, 5, 1, 2, 2, 0, 5, 1, 2, 3, 0,
œ & œ œ ‰ j œ œ ‰ œ ‰ œ J œ #œ #œ œ #œ
Pool: Guitar, Rhythmic Profle Magnitude
Components j x5 j x2.5 œ œ Fig. 8 Pool: Guitar (top); Rhythmic Profile (bottom)
[4, 0, 0, 1, 0, 0, 1, 0, 2, 0, 4, 0, 0, 1, 0, 0, 2, 0, 1, 0, 3, 0, 0, 0, 0, 0, 1, 0, 2, 0]
& œ™ bœ™ bœ œ œ™ bœ™ œ œ #œ™ ‰ Œ nœ œ
Pool: Voice, Rhythmic Profle
Magnitude j j j ( Components x10 j x5 x3.3 x2.5 œ œ (œ œ œ Fig. 9 Pool: Voice (top); Rhythmic Profile (bottom)
MTSE: 2020 Chiu Appalachian State University
Electric Guitar/Voice ° 7 œ œ #œ œ #œ j j 3 œ #œ 7 &8 Œ Œ J J ‰ J Ó Œ ‰ œ œ œ 8 J ‰ J 8 1) j Bass Guitar ? 7 œ œ œ œ #œ œ œ œ j 3 j #œ 7 ¢ 8 J œ œ œ œ 8#œ 8
° 7 œ #œ œ j œ j 4 7 &8 ‰ ‰ #œ œ ‰ Œ Œ œ œ œ ‰ #œ ‰ œ 8 j ‰ j ‰ 8 2) J J #œ œ j j j ? 7 œ œ œ œ #œ œ œ œ 4 j #œ œ 7 ¢ 8 J œ œ œ œ 8#œ 8
œ œ œ j j œ œ ° 7 Œ Œ #œ ‰ #œ Ó Œ ‰ œ œ œ 5 ‰ #œ ‰ 7 3) &8 J J J 8 J J J 8 j j ? 7 œ œ œ œ #œ œ œ œ 5 j #œ œ 7 ¢ 8 J œ œ œ œ 8#œ 8 #œ #œ j j œ #œ ° 7 œ œ ‰ #œ Œ Œ ‰ œ œ œ ‰ ‰ œ #œ ‰ 6 œ œ J 4) &8 J #œ œ J J 8 7 j j 6 #œ œ #œ ? 8 œ œ œ œ #œ œ œ œ œ œ œ œ 8#œ œ œ ¢ J Fig. 10 Cat Fantastic: Milankovitch Cycle
C = 24 Cat Fantastic: First Iteration, Rhythmic Profle C = 25 Cat Fantastic: Second Iteration, Rhythmic Profle Magnitude Magnitude
j j j j j Components œ x7/12 œ x3.428 œ x2.5 œ Components œ x7 œ x3.428
C = 26 Cat Fantastic: Tird Iteration, Rhythmic Profle Magnitude
j j Components œ x7 œ x3.71 Fig. 11 Cat Fantastic: Rhythmic Profiles for Milankovitch Cycle MTSE: 2020 Chiu Appalachian State University References
Amiot, Emmanuel. 2016. Music Through Fourier Space: Discrete Fourier Transform in Music Theory. Springer. Callender, Clifton. 2006. “Continuous Harmonic Spaces” JMT 51(2): 277–332. Callender, Clifton, Ian Quinn, and Dmitri Tymoczko. 2008. “Generalized Voice-Leading Spaces.” Science 320. Cateforis, Theo. 2002. “How Alternative Turned Progressive: The Strange Case of Math Rock” in Progressive Rock Reconsidered, ed. by Kevin Holm-Hudson, 243–260. New York, NY: Routledge. ———. 2018. “Total Trash: Analysis and Post Punk Music.” JPS 30(4): 95–112. Chiu, Matt. 2018. “Metric Forms through Fourier Space.” Boston University Masters Thesis. Covach, John. 1997. “Progressive Rock ‘Close to the Edge,’ and the Boundaries of Style” in Understanding Rock: Essays in Musical Analysis, ed. John Covach and Graeme M. Boone, 3–31. New York, NY: Oxford University Press. Large, Edward W., and Mari Riess Jones. 1999. “The Dynamics of Attending: How People Track Time-Varying Events.” PR 106(1). London, Justin. 2004. Hearing in Time: A Psychological Aspects of Musical Meter. OUP. Milne, Andrew J., David Bugler, Steffen A. Herff. “Exploring the space of perfectly balanced rhythms and scales.” JMM 11(2). Osborn, Brad. 2010. “Beats that Commute: Algebraic and Kinesthetic Models for Math Rock Grooves.” Gamut 3, no. 1 ———. 2011. “Understanding Through-Composition, in Post-Rock, Math-Metal, and other Post-Millennial Rock Genres.” Music Theory Online vol 17, no. 3 (October). Temperley, David. 2018. The Musical Language of Rock. New York, NY: Oxford University Press. Quinn, Ian. 2006. “General Equal-Tempered Harmony: Introduction and Part I.” Perspectives of New Music vol. 44, no. 2: 114–158. Yust, Jason. 2015. “Schubert’s Harmonic Language and Fourier Phase Space.” Journal of Music Theory vol. 59, no. 1. ———. 2019. “Stylistic Information in Pitch-Class Distributions.” Journal of New Music Research vol. 48, no. 3. ———. Forthcoming. “Steve Reich's Signature Rhythm, and an Introduction to Rhythmic Qualities.” Music Theory Spectrum.