A Model of Metric Coherence

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1 A Model of Metric Coherece Ier Metric Aalysis u Metric weight, Metric Coherece Aja Volk Uiversity of Souther Califoria Itegrated Media Systems Ceter Ier Metric Aalysis Ier Metric Aalysis u Metric weight, Metric Coherece u Metric weight, Metric Coherece Further developmets Further developmets u JMetro,Spectral weight u JMetro,Spectral weight Listeig Tests ISE 599: 2004Title goes here 1

2 I defie the meter of a work as the uio of all layers of motio (i.e., series of regularly recurrig pulses) active withi it. Harald Krebs Model of Ier Metric Aalysis Metric ad Spectral weight RUBATO, JMetro the importace of pitch structure, specifically of chage i the harmoic or melodic domai, i the formatio of layers; ew-evet accets are amog the most frequet producers of layers of motio Dyamic accet, placemet of log duratios amog short oes (agogic or duratioal accets), thickly textured evets amog more thily textured oes (desity accets),, by registral high ad low poits (registral accets), by the affixig of a oramet to a ote start period legth ISE 599: 2004Title goes here 2

3 Ier metric structure Outer metric structure ISE 599: 2004Title goes here 3

4 Ier metric structure Outer metric structure Symphoy C Major K Movemet (4/4) Wolfgag A. Mozart Excerpt from Metric weight W 2,2 of the expositio (bars 1-55) Adieu sweet Amarillis (4/4) Joh Wilbye Taze ud Sprige (3/4) Has Leo Haßler W 2,2 W 2,2 ISE 599: 2004Title goes here 4

5 3. Symphoy, 1. movemet (6/4) Johaes Brahms Excerpt from Metric weight W 2,2 of the expositio (bars 1-36) 2. Symphoy, 1. movemet Johaes Brahms B Mior Mass Plei sut coeli (3/8) Joha Sebastia Bach W 2,2 ISE 599: 2004Title goes here 5

6 Metric Coherece correspodece betwee ier ad outer metric structure presuppositio:occurrece of regularity (weight layers correspodig to specific periods) a metric subscale of outer metric hierarchy sigificat i the ier metric weight phase-coicidece, phase-displacemet Guillaume Dufay Mass: Se la face ay pale Kyrie II, Soprao Welltempered Clavier Joha Sebastia Bach ISE 599: 2004Title goes here 6

7 Welltempered Clavier Joha Sebastia Bach Welltempered Clavier Joha Sebastia Bach All voices Bass Coherece Preludes 11 Fuges 12 Welltempered Clavier Joha Sebastia Bach Welltempered Clavier Joha Sebastia Bach Spectral Weight of the all 3 Voices(Excerpt) Spectral Weight of the Bass (Excerpt) ISE 599: 2004Title goes here 7

8 3rd Symphoy (Rheish Symphoy) Robert Schuma 3rd Symphoy (Rheish Symphoy) Robert Schuma where subsurface melodic progressio occurs at a regular rate; a risig arpeggiatio of the toic triad is succeeded by a descedig stepwise lie, each pitch of both the risig ad the fallig gesture occupyig twelve eighth-ote pulses Harald Krebs (Fatasy Pieces) 3rd Symphoy (Rheish Symphoy) Robert Schuma 3rd Symphoy (Rheish Symphoy) Robert Schuma First Violis: Aalysis of the Expositio: (3/4) First Violis: Aalysis of the Expositio: (3/2) Excerpt Excerpt Aalysis of bars 1-20 Excerpt Aalysis of bars 1-20 (4/4) ISE 599: 2004Title goes here 8

9 Sarabade Suite d-mior Georg Friedrich Hädel ISE 599: 2004Title goes here 9

10 Ier Metric Aalysis u Metric weight, Metric Coherece Further developmets u JMetro,Spectral weight l=2, p=4 3rd Symphoy (Rheish Symphoy) Robert Schuma Aalysis of bars 1-20 Spectral weight of the theme: Bars 1-20 ISE 599: 2004Title goes here 10

11 3rd Symphoy (Rheish Symphoy) Robert Schuma Aalysis of bars 1-20 (4/4) Spectral weight of the theme, iterpreted as 4/4 Spectral weight of the theme WITHOUT local meters of period 1/2 Aalysis of the Expositio Bach, WTK I Fugue 4 Spectral weight of First Violis of the expositio (excerpt) Spectral weight of First Violis of the expositio (3/2) Metric Weight of the Bass Voice (Excerpt) Spectral weight WITHOUT local meters of period of 1/2 Spectral Weight of the Bass Voice (Excerpt) ISE 599: 2004Title goes here 11

12 Hayd Presto from Soata Hoboke XVI: 24 ISE 599: 2004Title goes here 12

13 Metric weight of measures 1-40 Spectral weight of measures 1-40 Spectral weight WITHOUT local meters of period 4 ad multiples Spectral weight of the left had Spectral weight WITHOUT local meters of period 3 ad multiples Spectral weight of the right had (iterpreted as 4/4) ISE 599: 2004Title goes here 13

14 Paul Desai/Hekja Hoig: Computatioal Models of Beat Iductio: The Rule-Based Approach 105 Natioal Athems: Rhythm of the Melody Spectral weights: 63% 4/4 Argetia Suda Idia l=2, p=2 For the set of atioal athems, a correct beat ca be defied as a beat that is compatible with the meter otated i the score. For short patters that form the begiig of more tha oe athem we couted a beat as correct wheever it fitted the meter of oe of those athems. Result: Loguet-Higgis/Lee: 60% correct l=2, p=4 How about pitch? 4/4 Spectral weights: 19 % Spectral weights distiguish eve/odd: 82% Oe aspect of this problem is that at ay give timepoit, accets may arise i may simultaeously varyig musical dimesios, ad it is uclear how to sum the cotributios from all these dimesios. Roeder 1995 Spectral weights: 17 % 4/4 ISE 599: 2004Title goes here 14

15 David Lewi O Harmoy ad Meter i Brahms s Op.76, No.8 J. Syder & C. Krumhasl: Tappig to Ragtime - Cues to Pulse Fidig J. Syder & C. Krumhasl: Tappig to Ragtime - Cues to Pulse Fidig Chrysathemum Lily Pieapple Computatioal ad experimetal models are timebased! S: Both Hads S: Both Hads S: Both Hads S: Right Had S: Right Had S: Right Had S: Left Had S: Left Had S: Left Had ISE 599: 2004Title goes here 15

16 Blue Goose America Beauty Sesatios Glad Cat S: Both Hads S: Both Hads S: Both Hads S: Both Hads S: Right Had S: Right Had S: Right Had S: Right Had S: Left Had S: Left Had S: Left Had S: Left Had Joseph P. Swai: Harmoic Rhythm Joseph P. Swai: Harmoic Rhythm ISE 599: 2004Title goes here 16

17 Il Pompeo O cessate di piagarmi Alessadro Scarlatti 2. Symphoy, 3. movemet Johaes Brahms Bars : 2/4 Ier Metric Aalysis u Metric weight, Metric Coherece RUBATO Further developmets u JMetro,Spectral weight score performace Listeig Tests aalysis ISE 599: 2004Title goes here 17

18 Empirical Experimet Metric weights of differet degree of coherece of the same piece Metric weights Performace u Do metric weights with a high degree of coherece produce performaces where the iterpretatio is more clearly structured? Last measures of the altus of Gratias: Aalysis of the whole piece <---> Aalysis of the part Begiig of Credo, all voices: Aalysis of the whole piece for all voices<---> Aalysis of the whole piece for separate voices Credo: sigle voices Credo: all voices ISE 599: 2004Title goes here 18

19 ISE 599: 2004Title goes here 19

20 Mystic Circles of the Youg Girls The Rite of Sprig Igor Stravisky ISE 599: 2004Title goes here 20

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