putting the math in math rock matt g-y chiu Slides: Code: https://tinyurl.com/wqztm87 introduction introduction TTNG, 2008 “Chinchilla” introduction “extensive use of asymmetrical … time signatures” Cateforis 2002, 244 introduction “cyclical repetition of ostinati” Osborn 2010, 43 introduction discrete Fourier transform (DFT) introduction outline 1. math rock(s) 2. DFT Introduction 3. methodology 4. analysis of… “Never Meant” by American Football “Pool” by Tricot “Cat Fantastic” by TTNG 1. math rock(s) 1. math rock(s) 1. math rock(s) 1. math rock(s) 1. math rock(s) “Emotional hardcore” math-emo { 1. math rock(s) math-emo { “twinkle” topic (Howie, 2019) 1. math rock(s) emo metal math math-emo math-metal https://open.spotify.com/playlist/0YMehqtnDK9X1pBsVc0ftN math rock(s)? https://open.spotify.com/playlist/0YMehqtnDK9X1pBsVc0ftN math rock(s)? https://open.spotify.com/playlist/0YMehqtnDK9X1pBsVc0ftN math rock(s)? https://open.spotify.com/playlist/0YMehqtnDK9X1pBsVc0ftN 1. math rock(s) math-emo 1 3 “emo-ness” 2 math-metal 2. DFT walkthrough 2. DFT walkthrough The Discrete Fourier Transform Input (DFT) v = (n0,…,n11) Output length/2 non-trivial Fourier Components: fn DFT Magnitude Phase | fn | ϕn 2. DFT walkthrough Lewin 1959, 2001: Interval Function Quinn 2007; Callender 2007 Yust 2015; Amiot 2016: harmonic geometries and spaces Callender, Quinn, and Tymoczko 2008; Tymoczko 2008: relating DFTs to voice leading and set-class similarities Yust 2019: describing stylistic trends between composers Chiu and Kahrs 2020: chord spacing and timbre Milne, Burger, and Herff 2017; Chiu 2018; Yust forthcoming 2. DFT walkthrough 2. DFT walkthrough Input v = (n1,…,n8) [0, 0, 0, 0, 0, 0, 0, 0] / ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ Output 4 Fourier Components: fn Magnitude Phase | fn | ϕn 2. DFT walkthrough Input v = (n1,…,n8) f1 / ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ f 2 / ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ f 3 / ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ f 4 / ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ 2. DFT walkthrough (Large 1994) (Large and Jones 1999) 2. DFT walkthrough Quinn: 2007 Yust and Tymoczko: 2019 Chiu: 2019 Callender: 2007 2. DFT walkthrough 2. DFT walkthrough ˙ ˙ / œ œ œ œ f2 ˙ ˙ / œ œ œ œ f4 œ œ œ œ / ˙ ˙ ˙ ˙ / œ œ œ œ 2. DFT walkthrough “particular attentional state” London 2004 f2 ˙ ˙ / ˙ ˙ / œ œ œ œ œ œ œ œ f4 œ / ˙ œ ˙ œ œ / ˙ œ œ œ œ ˙ 2. DFT walkthrough sinusoidal decomposition subdivisional / ˙ ˙ œ œ œ œ projection entrainment 2. DFT walkthrough Input j j j / œ ‰ ‰ œ ‰ ‰ œ ‰ [1, 0, 0, 1, 0, 0, 1, 0] DFT: Tresillo DFT Magnitude Component 2. DFT walkthrough j j j / œ ‰ ‰ œ ‰ ‰ œ ‰ [1, 0, 0, 1, 0, 0, 1, 0] DFT: Tresillo DFT Magnitude Component 2. DFT walkthrough 3. methodology 3. methodology [Array] <data encoding> Weighted Event DFT input rule- rank based Results Logx 3. methodology Accent Rules -MPR 1. parallelism + 1 to highest Rule-based accent in grouping -MPR 3. event + 1 -MPR 6. bass notes + 1 -contour change (adjacent) + 1 Lerdahl/ -Leap of P4 or more + 1 Jackendoff -PEC: second of two isolated Povel/Essens - tones + 1 -PEC: initial and final tones of a based cluster of 3 or more tones + 1 4. analysis: Never Meant 4. analysis: Never Meant [3, 1, – 1, 2, 3, 1, 1, 1, 3, 1, 1, 2, 3, 3, 1, 1, 3, 1, 1, 2, 3, 1, 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 ˙ ˙ & ˙ ˙ ˙ ˙ Accent Array: [5,[0, 2,0, 2,0, 4,0, 1,0, 1,0, 2,0, 1,0, 4,0, 1,0, 2,0, 1,0, 1,0, 1,0, 1,0, 1,0, 2,0, 1,0, 1,0, 1,0, 2,0, 2,0, 1,0, 1]0] 4. analysis: Never Meant [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 ˙ ˙ & ˙ ˙ ˙ ˙ Never Meant: Composite Rhythm 4. analysis: Never Meant E . Gtr. œ œ œ œ œ œ œ œ œ œ œ Magnitude (Lead) & œ œ œ œ œ œ œ œ œ œ œ œ œ œ f12 f6 f j Components3 ˙.. ˙. ˙ œ. œ agnitude M Component ˙ ˙ œ 4. analysis: Never Meant agnitude M Component ˙ ˙ f9 œ 4. analysis: Never Meant agnitude M Component ˙ ˙ œ 4. analysis: Never Meant [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™ ˙ 4. analysis: Never Meant [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 f ˙. œ x3.428 10 [3, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 0, 0, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1] E. Gtr œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ (Rhythm)4.& analysis:œ Never Meantœ J œ œ œ œ & ˙ œ™ ˙œ™ œ™ ˙ œ™ ˙ Division Neverinto 4Meant: parts Rhythm Guitar, Rhythmic Profle 0 4 7 Magnitude 18 f1 6 7 6 j Components ˙. œ x3.428 12 [3, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 0, 0, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1] E. Gtr œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ (Rhythm)4.& analysis:œ Never Meantœ J œ œ œ œ & ˙ œ™ ˙œ™ œ™ ˙ œ™ ˙ Division Neverinto 4Meant: parts Rhythm Guitar, Rhythmic Profle 0 4 7 Magnitude 18 f1 6 7 6 j Components ˙. œ x3.428 12 [3, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 0, 0, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1] E. Gtr œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ (Rhythm)4.& analysis:œ Never Meantœ J œ œ œ œ & ˙ œ™ ˙œ™ œ™ ˙ œ™ ˙ Division into 9 parts 24/9 = 3.428 (?) Never Meant: Rhythm Guitar, Rhythmic Profle 0 4 7 Magnitude 18 f1 6 7 6 7 j Components ˙. œ x3.428 12 [3, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 0, 0, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1] E. Gtr œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ (Rhythm)4.& analysis:œ Never Meantœ J œ œ œ œ & ˙ œ™ ˙œ™ œ™ ˙ œ™ ˙ Division into 9 parts 24/9 = 3.428 (?) Never Meant: Rhythm Guitar, Rhythmic Profle 0 4 7 f Magnitude 18 1 6 7 6 j 12 Components ˙. œ x3.428 4. analysis: Never Meant 4. analysis: Never Meant Never Meant: Rhythm Guitar, Rhythmic Profle Magnitude j f Components ˙. œ x3.428 10 Never Meant: Rhythm Guitar, Rhythmic Profle 4. analysis: Never Meant Magnitude j Components ˙. œ x3.428 4. analysis: Never Meant f2 f3 f4/5 3 f4 f6 f9 3 f8 f12 f18 3 f16 f24 f36 3 f10 4. analysis: Pool 4. analysis: Pool 4. analysis: Pool "adrenalized math rock” Rolling Stone 2015 Tricot, Pool [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 [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 4. analysis: Pool j Length = 15 œ [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 j j Components œ x5 œ x2.5 Measures of 5/8 subdivision(?) 4. analysis: Pool j Length = 30 œ [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 Consistent Quarter pulse j j j j ( Components œ x10 œ x5 (œ x3.3 œ x2.5 œ division pseudo-measure Of pseudo-measure into 2 4. analysis: Pool [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 Or a “conflict” Between projections of 2 and 3 Magnitude division of ( 10 into 4 j j j j Components œ x10 œ x5 (œ x3.3 œ x2.5 œ division of 10 into 3 4. analysis: Pool [4,3 0, +0, 31, 0,+0, 21, +0, 2,2 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 4.