Melodic Variations: Toward Cross-Cultural Transformation

Melodic Variations:Toward Cross-Cultural TransformationbyCheng-Zhi Anna HuangB.M. & B.S., University of Southern California (2006)Submitted to the Program in Media Arts and Sciences,School of Architecture and Planning,in partial fulfillment of the requirements for the degree ofMaster of Media Arts and Sciencesat theMASSCHUSETTS INSTITUTE OF TECHNOLOGYSeptember, 2008 Massachusetts Institute of Technology 2008. All rights reserved.Author .Program in Media Arts and SciencesSeptember 5, 2008Certified by .Barry L. VercoeProfessor of Media Arts and SciencesThesis SupervisorAccepted by .Deb RoyChair, Academic Program in Media Arts and Sciences

2

Melodic Variations:Toward Cross-Cultural Transformationby Cheng-Zhi Anna HuangSubmitted to the Program in Media Arts and Sciences,School of Architecture and Planning, on September 5, 2008,in partial fulfillment of the requirementsfor the degree of Master of Media Arts and SciencesAbstractWe all share similar innate emotions, but our cultural experiences nurtureus to express them differently. The musical form “theme and variations” offerus a unique lens to uncover in each culture the relationships between themusical surface that touches us most directly, and the underlying structuresthat are more abstract. Variations are musical surfaces composed to explorethe expressive potentials of the theme by transforming it along certainmusical dimensions, while the theme itself can be seen as an intermediatepathway to the more abstract structures of a style.I approach cross-cultural transformation in music as a kind of crosscultural variation, as the theme and variations tradition offers us a frameworkto explicitly consider which musical elements to stay fixed and which to vary.I propose to treat cross-cultural variation as a four-step process. First, theprocess of “melodic reduction” reduces the melodic surface of a theme to ross-culturaltransformation” maps the uncovered progressions to those idiomatic in thecultural style that carries the variation. These cross-cultural mappings areapproached by considering which of the melodic properties in the underlyingprogressions to preserve and which to transform. These properties includecontour, scale-degree function, melodic formulae and tension.Third,“melodic elaboration” retrieves the melodic surfaces that possess the mappedmelodic progressions.Fourth, “backward cross-cultural transformation”adjusts the melodic surface of the variation to strengthen its resemblance tothe theme.My experimentation begins with the melodic variations on two historicallyrelated instruments, the Chinese zither, gu-zheng, and the Japanese zither,koto.Even though their repertoires evolved culturally to render verydifferent melodic surfaces, it has been pointed out by ethnomusicologist AlanThrasher that there is a high degree of similarity between their underlyingstructures. This enables a cross-cultural mapping at the structural level thatties together stylistically different melodic surfaces to exhibit a kind of crosscultural variation. I will conclude by briefly discussing the effectiveness ofvariation as an approach to cross-cultural transformation.Thesis supervisor: Barry L. Vercoe, D.M.A.Title: Professor of Media Arts and Sciences3

4

Thesis CommitteeThesis supervisor Barry L. VercoeProfessor of Media Arts and SciencesMassachusetts Institute of TechnologyThesis reader . Rosalind PicardProfessor of Media Arts and SciencesMassachusetts Institute of TechnologyThesis reader . Elaine ChewAssociate Professor / FellowUniversity of Southern California / Radcliffe for Advanced Study at HarvardThesis reader . Peter RowFacultyNew England Conservatory5

6

Melodic Variations:Toward Cross-Cultural Transformationby Cheng-Zhi Anna HuangThesis supervisor Barry L. VercoeProfessor of Media Arts and SciencesMassachusetts Institute of Technology7

8

Melodic Variations:Toward Cross-Cultural Transformationby Cheng-Zhi Anna HuangThesis reader . Rosalind PicardProfessor of Media Arts and SciencesMassachusetts Institute of Technology9

10

Melodic Variations:Toward Cross-Cultural Transformationby Cheng-Zhi Anna HuangThesis reader . Elaine ChewAssociate Professor / FellowUniversity of Southern California / Radcliffe for Advanced Study at Harvard11

12

Melodic Variations:Toward Cross-Cultural Transformationby Cheng-Zhi Anna HuangThesis reader . Peter RowFacultyNew England Conservatory13

14

AcknowledgementsI must first thank my advisor, Barry Vercoe, most ardently for connecting meto such heritage. I want to thank my readers Professors Rosalind Picard,Elaine Chew, Peter Row and again Barry Veroce for their teaching.I want to thank the Music, Mind and Machine group, Judy Brown, Mihir Sarkar,Owen Meyers, and our alums Paris Samaragdis, Brian Whitman, YoungmooKim, Michael Casey and John Harrison, and all of our UROPS, particularlyAdrianna Tam. I want to thank Wu-Hsi Li most heartily for being the bestofficemate and friend throughout my media lab experience.I want to thank the Nightmarket Team, Jackie Lee, Daniel Chao, Francis Lam,Edward Shen, Chaochi Chang, James Teng, Michael Lin, Dori Lin, Nan-weiGong, Sheng-Ying Pao, Peggy Chi, Elisa Lin and Wu-Hsi Li, for sharingpassionate conversations and making me feel at home at the Media Lab.I want to thank my fellow classmates, Annina Rust, Anita Lillie, PolychronisYpodimatopoulos, Dawei Shen, Alyssa wright, Taemie Kim and Sanghoon Lee,and also Jaewoo Chung, Noah Vawter and Mark Feldmeier.Most of all, I want to thank my family for always being there for me.15

16

Table of Contents1 Introduction and Background .231.1 “Theme and variations” as analytical framework .241.2 Form as a teaching machine .251.3 Theme as pathway to deeper structure.251.4 Variations as perspectives .261.5 The tradition of variation .271.6 Melodic variations on the Chinese gu-zheng and Japanese koto.291.7 Personal motivations.321.8 Roadmap .332 The Concept of Cross-Cultural Transformation .342.1 The term “transformation” .352.2 Fixed and varied elements as deep and surface structures.352.3 Cross-cultural analogy as variation on deep structures.362.4 Forward and backward cross-cultural transformation .372.5 Possible interpretations on a “variation”.372.6 Fusion versus cross-cultural variation .382.7 The process of cross-cultural transformation .392.8 Cross-cultural transformation stretches the limit of variation .402.9 Levels of structure.413 Melodic Reduction.433.1 The concept of melodic reduction.433.1.1 The process of melodic reduction .443.2 Modal system .453.2.1 The concept of a musical scale .463.2.2 Learning pitch-stability hierarchy from a Japanese score .473.2.3 Learning pitch-stability hierarchy from a Chinese score .553.3 Meter and grouping .613.3.1 Meter induction .613.3.2 Grouping.643.4 Time-span reduction .663.4.1 Time-span reduction on the koto .663.4.2 Time-span reduction approximation for the gu-zheng .673.5 The overall process of a informed melodic reduction .6917

4 Cross-Cultural Mapping .704.1 Melodic formulae and scale degrees .724.1.1 Analysis on melodic formulae and scale degrees in Danmono .724.1.2 Analysis on melodic formulae and scale degrees in Baban .744.2 Cross-cultural time warp .784.3 A short example.794.3.1 Melodic reduction (from surface to deep structure).804.3.2 Forward cross-cultural transformation (between deep andhyper-deep structure) .814.3.3 Melodic elaboration (from deep to surface structure) .824.3.4 Backward cross-cultural transformation (adaptation of surfacestructure).835 Contribution and Future Work .865.1 Contribution .865.1.1 Implementation of proposed transformation processes.865.1.2 Computer-assisted composition (CAC) tool .875.2 Future work.915.2.1 Listening tests .935.2.2 Grammar induction.955.3 The effectiveness of melodic variation as an approach to cross-culturaltransformation .986 Bibliography .9918

List of Figures1-1: The existence of a deeper structure beneath the musical surface of the theme and variations. 261-2: Bach, some bass lines from “Goldberg Variations” (score excerpt from Green, 1965) . 281-3: Paganini, Twenty-fourth caprice, theme with implied harmony (score excerpt from Ahn,2000). .291-4: The cantus firmus reveals yet a deeper layer of structure than the themes of the individualpieces. . 301-5: Two phrases from the Japanese Rokudan (top stave, transposed up a minor 6th) juxtaposedagainst the Chinese Chu Shu Lian and its cantus firmus (bottom three staves, transposedup an octave). . 301-6: Bach, Wenn wir in höchsten Nöthen sen, Vol. V, No. 51 (score excerpt from Kennan, 1999). 311-7: Brahms, Es ist ein Ros’ entsprungen, No.8 of Eleven Chroale Preludes, Op.122 (scoreexcerpt from Kennan, 1999). . 312-1: Deep and surface structure illustrated as the fixed and varied elements in a theme andvariation . 362-2: Cross-cultural analogy as variation at the level of deep structure. 372-3: The flowchart for the processes involved in a cross-cultural transformation. 392-4: The structural components of a variation after the process of CCT. . 403-1: This schematic illustrates the overall process of structure induction, extracted from (Lerdahl& Jackendoff, 2001). . 443-2: A flowchart of the processes and hierarchies that take part in the process of structureinduction, extracted from (Lerdahl & Jackendoff, 2001). . 453-3: The pitch distribution of Japanese Rokudan transposed down a major third. 483-4: The in scales, the raw Rokudan scale and the “koto scales”. 503-5: This figure, extracted from Lerdahl’s Tonal pitch space, shows “the basic pitch spaceoriented to I/C”, “with anchoring strength indicated by level” and neighboring attractionsshown by arrows (Lerdahl, 2001, p.162).523-6: Pitch-class transition distribution matrix of transposed Japanese Rokudan. . 533-7: The pitch-class distribution of Chinese Chu Shui Lian transposed down a perfect fifth (left)and the pitch-class distribution of its cantus firmus Baban in the hard mode (right). . 563-8: The Chinese modes, the two modal interpretations of Chu Shui Lian and the “gu-zhengscales”. . 583-9: Pitch-class transition distribution matrix of transposed Chinese Chu Shui Lian. . 593-10: Pitch-class transition distribution matrix of transposed Chinese Chu Shui Lian. . 603-11: “Stability conditions” are informed by the modal system of a culture which is approximatedby the pitch-class stability hierarchy learned from its repertoire. . 613-12: A 4/4 metrical grid for the first phrase of the Bach chorale “Christus, der ist mein Leben”,extracted from (Lerdahl, 2001). . 623-13: The first two phrases of Japanese Rokudan notated in 4/4, with numbers below showingdifferent kinds of accents. 6219