Carey, Norman, A. "Distribution Modulo 1 and Musical Scales"
AUTHOR: Carey, Norman, A
TITLE: Distribution Modulo 1 and Musical Scales
INSTITUTION: University of Rochester
BEGUN: July 1996
COMPLETED: February 1998
ABSTRACT:
This dissertation examines the relationships between the
mathematics of distribution modulo 1 and the theory of
well-formed scales. Distribution modulo 1 concerns the
distribution of real numbers between 0 and 1. In particular,
finite sets of real numbers have been studied with respect to the
Steinhaus Conjecture, proven by S�s and others. Well-formed
scales, first introduced in Carey and Clampitt 1989, are
generated by iterations of a given musical interval modulo the
octave, the standard musical interval of periodicity.
An introductory survey of ten scale theorists provides a context in which to understand the properties of the well-formed scale. A scale is well-formed if each generic interval comes in two specific sizes, or if it consists of equal step intervals. The structure of the well-formed scale is a function of the continued fraction representing the log ratio of the generator ("fifth") and the interval of periodicity ("octave"). The diatonic scale in Pythagorean tuning serves as the prototype: the generator is the overtone fifth (3:2) and the interval of periodicity is the octave (2:1). The diatonic is a member of an infinite hierarchy of well-formed scales, recursively generated by the continued fraction of Log 2 (3/2). This hierarchy also includes the pentatonic and chromatic collections. In general, the well-formed scale belongs to a hierarchy determined by the continued fraction of, Log I (G), where I is the frequency ratio of the interval of periodicity and G is the frequency ratio of the generator. Five theorems are presented that characterize well-formed scales, their hierarchies, and the patterns of step intervals they exhibit. The step patterns themselves form the basis for a secondary system of well-formed scale classification. The conditions on "coherence" for well-formed scales are fully characterized. Also discussed are applications and extensions of the theory, including tuning theory, rhythmic analysis, and composition.
KEYWORDS:
scale theory, well-formed, maximally even, Myhill's Property,
diatonic, coherence, microtonal, rhythm, distribution modulo 1,
continued fractions
TOC:
I Diatonic Theory
II Well-formed Scales
III Five Theorems Concerning Well-formed Scales
IV Applications and Extensions
CONTACT:
Eastman School of Music
nac@theory.esm.rochester.edu
AUTHOR: Djordjevic, Michael, L.
TITLE: Discrete Tone Relations Determined by the Hearing Phenomenon
within Five-Dimensional Sound-Musical Continuum
INSTITUTION: Radio Belgrade, Hilandarska 2, 11000 Belgrade, Serbia, YU
BEGUN: January, 1990
COMPLETITION: June, 1995
ABSTRACT:
I. Theory
Five-Dimensional Sound-Musical Continuum materializes itself into
objective Sound Space and subjective Musical Space defined as
MOS-Musical Organisation of Sound. Sound-Musical Space is defined as
union of the sets: A the set of parameters related to the sound signal
at its source, B the set of parameters of the sound signal with a
listener. A and B interactions with binary relations of ordered pairs
represents the new set C. MOS defined as set X implicates Y as set of
aural, final psychological perception of music.
II. Experiments
Quantum of Hearing Discrimination was elaborated in experiments MATEST
1 and 2 with values in cents ranged from 3-7, extreme 2, being
constant along the greater part of the frequency spectrum, 4
cents. Unit called Unitary Distance was defined. Phase Space Cell
signifies distribution of DTR within the Sound-Musical Space as
matrix. MATEST 2 included several different tonal systems for
comparison and DTR system justification.
III. Practice DTR-Discrete
Tone Relations: 1. Hearing discrimination 2. Temperament 3.
Intonation 4. Musical abilities 5. Compositional organization of DTR
6.Ortography and notation 7. Reproductive medium with its limits 8.
Constructing new musical instruments 9. Aesthetics and axiology
KEYWORDS: discrete, tone, relations, DTR, UD, unitary, distance, STTR, PSC, phase, space, cells, QHd, quantum, hearing, discrimination, phenomenon, sound, musical, continuum, fivedimensional, matest, system
TOC:
Introduction
I. Theoretical aspects:
II. Experimental aspects:
III. Practical aspects:
CONTACT:
P. Lekovica 44/4
11000 Belgrade
Serbia, YU
phone: 381-11-3546262
e-mail: mihajlod@EUnet.yu
URL: http://SOLAIR.EUnet.yu/~mihajlod
AUTHOR: Lemieux, Glenn C.
TITLE: "Music in Twelve Parts" by Philip Glass:
Reconstruction, Construction and Deconstruction
INSTITUTION: University of Iowa
BEGUN: January 1998
COMPLETED: June 1999, projected completion
ABSTRACT:
"Music in Twelve Parts" is a major work by Philip Glass written
between 1971 and 1974. In essense, it summarizes the
compositional techniques Glass was using which have come under
the rubric of minimalism. Glass says:
"All of my works which predate 1976 fall within the highly reductive style known as minimalism. I feel that minimalism can be traced to a fairly specific timeframe, from 1965 through 1975, and nearly all my compositions during this period may be placed in this general category. All such categories are arbitrary, however, and can be misleading. For example, although "Music in 12 Parts" would most likely be classified as a minimal work, it was a breakthrough for me and contains many of the structural and harmonic ideas that would be fleshed out in my later works. It is a modular work, one of the first such compositions, with twelve distinct parts which can be performed separately in one long sequence, or in any combination or variation. Each part concentrated on several of these techniques (cyclic, additive and repetitive structure), and by the completion of Part 10, the cataloguing was fairly intact. Thus Part 11 concentrated on the joining places of the other parts, which, to the listener, appeared as modulations. Part 12 turned to cadence--the formal closing phrases we are accustomed to hearing in western music--as a fitting end to such an extended piece.”
The major problem in examing the music is that a full score of "Music in Twelve Parts" does not exist. In fact, it is only available as a partially-orchestrated sketch and a set of hand-written instrumental parts. To solve this problem, Dunvagen Music Publishers, Glass’s own company, has approved the engraving of this piece in FINALE as part of this project. In addition, an in-depth analysis of whole piece does not exist, although various general descriptions and single movement analyses can be found. To date, three recordings of the piece have been made: in 1974, parts one and two were recorded on the Caroline label; in 1989, a recording of the entire piece was made by Virgin Records; and in 1996, Nonesuch released another recording of the entire piece.
KEYWORDS: minimalism, cyclicism, additive, repetitive, rhythm, modular
TOC:
I. Introduction
II. Reconstruction: background to the music
III. Construction: making the score
IV. Deconstruction: Analysis of the piece
V. Conclusion
CONTACT:
Glenn Lemieux
P.O. Box 2771
Iowa City, IA 52244
319-339-1651 (h)
319-335-5877 (w)
glenn-lemieux@uiowa.edu
AUTHOR: Quaglia, Bruce, W.
TITLE: Compositional Practice and Analytic Technique;
Schoenberg’s Atonal Works: Reconciling Approaches to
Sets, Lines and Developing Variation.
INSTITUTION: University of Utah
BEGUN: 9/97
COMPLETED: 10/98
ABSTRACT:
This thesis examines the application of linear reductive analytic
techniques as applied to pieces from Arnold Schoenberg’s atonal
period. Basic nomenclature and concepts from pitch-class set
theory are invoked as well. Analyses of Schoenberg’s Op. 11 no.
1 and Op. 15 song X are presented within the context of
Schoenberg’s own compositional theories as suggested by his
pedagogical and critical writings. A brief discussion of the
relevant theoretical and analytical literature is also presented
in order to place the present analyses within the relevant
context.
The remaining dissertation requirement is an original composition: "In A Mirror Dimly" for Soprano, Violin, Picc./Alto Flute, Percussion and Computer Synthesized Tape.
KEYWORDS: Schoenberg, Forte, Developing Variation, 20th C. Analysis, Linear Analysis, Set Theory.
CONTACT:
Bruce Quaglia
c/o Dept. of Music
204 Gardner Hall
University of Utah
SLC, UT 84
bruce.quaglia@m.cc.utah.edu
AUTHOR: Van Colle, Sue, J
TITLE: "Music therapy process with cerebral palsied
children: connections with psychoanalytic models,
particularly that of Winnicott"
INSTITUTION: University of Reading, Department of Music
BEGUN: 4, 1988
COMPLETION: 10, 1999
ABSTRACT:
This research aims to make a detailed description of processes that occur
in interactive music therapy with cerebral palsied children.
The writer has made a video-tape collection of her clinical work which she undertook, over one academic year, with two groups each of four severely and multiply handicapped cerebral palsied children. Data analysis involves both manual and computerised systems, and draws on ethological methods. There are two major aims: (1) to generate the hypothesis that the role of the music therapist is like that of the good-enough mother as described by Donald W Winnicott, and (2) to generate some broad rules of music therapy.
KEYWORDS:
music therapy, child, handicap, cerebral palsy, piano, process,
interaction, psycoanalytic, Winnicott, ethological
TOC:
1. Music Therapy: Introduction and Broad Historical Overview
2. Music Therapy Research in Great Britain
3. The Use and Significance of the Piano in Music Therapy
4. The Writer's Clinical Work
5. Research Method
6. Measures of Behaviour: Description of Observables
7. Descriptive Analysis
8. Results of Teacher's Ratings
9. Examining the Process of Music Therapy
10. Conclusion
CONTACT:
University of Reading
35 Upper Redlands Road
Reading, Berkshire
RG1 5JE, UK
svc@clive.jenkins.clara.net
AUTHOR: Vives, Thomas E.
TITLE: The Effect of Timbre on the Chord Identification
Accuracy of Sophomore-Level College Music Theory Students
INSTITUTION: University of Florida
BEGUN: September, 1997
COMPLETED: August, 1998
ABSTRACT:
This study examined electronic keyboards in use at college and
university music departments, the available sounds these
keyboards have in common, and the effects of these sounds on
students’ identification accuracy in harmonic aural skills
exercises. Correlations were made between the different timbres
and the students’ levels of accuracy. The primary question that
this study attempted to address was as follows: Does any one
specific timbre facilitate greater student accuracy? This study
comprised a single experimental trial--a prepared treatment that
contained forty-five random examples of triads and seventh
chords--that tested several timbral conditions under a single
test condition--specifically, the identification of triad or
seventh chord quality. The dependent variable for this trial was
the subjects’ accuracy in identifying both triads and seventh
chords. The independent variables were (1) the nine different
types of triads and seventh chords (5 seventh chord types and 4
triads) and (2) the five different timbres. The five timbres
(electric piano, harpsichord, organ, acoustic piano, and
vibraphone) were selected for this study based on communication
with keyboard manufacturers. All timbres were generated via
digital synthesizers. Two intact first-semester sophomore-level
music theory classes served as the sample for this study.
Multiple analysis of variance showed that timbre by itself had no
significant overall effect on the accuracy of subjects’
responses, although the electric piano and acoustic piano timbres
produced slightly, but not significantly, more accurate
responses. Closer analysis of the data, including the interaction
of gender and principle performance instrument, indicated that
neither gender nor principle performance instrument significantly
affected subjects’ response accuracy, although due to the small
size of the subject pool, the results for principle performance
instrument were considered unreliable. Suggestions for further
research and future studies are included.
KEYWORDS: Timbre, Perception, Pedagogy, Aural Skills, CAI, CBI.
TOC:
ABSTRACT
CHAPTERS
1 INTRODUCTION
2 REVIEW OF LITERATURE
3 REVIEWING THE PRODUCTS
4 METHODOLOGY
5 RESULTS
6 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH
APPENDICES
A TABLES
B FIGURES
C TEST INSTRUMENT MATERIALS AND CORRESPONDENCE
D SUBJECTS’ WRITTEN RESPONSES TO TEST INSTRUMENT
BIBLIOGRAPHY
CONTACT:
Ted Vives
4158-C Sycamore St.
Los Alamos, NM 87544
(505) 661-8547
tedandgwyn@uswest.net
AUTHOR: Weisser, Benedict J.
TITLE: Notational Practice in Contemporary Music: A Critique of Three Compositional Models
(Luciano Berio, John Cage, and Brian Ferneyhough)
INSTITUTION: The City University of New York
BEGUN: July, 1995
COMPLETED: July, 1998
ABSTRACT:
The purpose of this dissertation is to to examine the
integration of notation and content in contemporary music. In
particular, it is to show that for the three composers I have
chosen, Luciano Berio, John Cage, and Brian Ferneyhough, the
notation of a work is not just a traditional “encoding” but is
inextricably linked to its form and content. Their compositional
agendas are in many respects defined by their notation.
Following an introductory chapter, in which the breadth of twentieth-century notational innovation and experimentation is presented, chapter two deals with the music of Luciano Berio. I compare the 1958 version of his Sequenza I with the 1992 version in metered notation. The title of chapter two, “notation-as-play within a predefined system,” is the basis of what I see as the success of Berio’s works both from a compositional as well as a performance standpoint.
In chapter three I study notational aspects of the late music of John Cage, the works known as the “time-bracket” or “number” pieces. In these late works, Cage uses notation to reconcile and accommodate himself to certain elements of musical expression, most notably harmony and the very notion of vertical relationships. Purely notational considerations produce harmonic situations that Cage could accept, a flexible, “anarchic harmony” which is also highly determinate and “coherent.”
In the case of Brian Ferneyhough, the subject of chapter four, notation is approached as a kind of “inventory of processes,” where various pre-compositional generations of multi-metric structures and compositional transformations of material are presented in an ostensibly unfiltered manner. One now encounters a situation where the composer has no discernible interest in compromising his material to the predispositions of the performer. Instead, Ferneyhough is interested in using notation as a “behavior-altering agent,” a new notion of “communication” radically different from both Berio and Cage.
Finally, in a concluding chapter I put Berio, Cage, and Ferneyhough in a deeper context, comparing them to each other and reflecting on their importance. I also venture my own opinions as to the future influence of the kind of notational thought they each embody.
KEYWORDS: graphic notation, proportional notation, Eco, time-brackets, number pieces, experimental music, McLuhan, new complexity
TOC:
Abstract
Preface
Acknowledgements
List of Examples
Chapter 1 - An Introduction to Notational Practice since 1945
Chapter 2 - Luciano Berio: Notation-as-play within a predefined system
Chapter 3 - John Cage: “...the whole paper would potentially be sound”: Time-Brackets and the Number Pieces (1981-92)
Chapter 4 - Brian Ferneyhough: Notation-as-Inventory
Chapter 5 - Conclusions
Appendix A - Interview with Luciano Berio
Appendix B - Berio, Sequenza I (1958 version)
Appendix C - Berio, Sequenza I (revised version, 1992; marked up by B.W.)
Bibliography
CONTACT:
Benedict Weisser
Visiting Assistant Professor of Composition, Oberlin Conservatory of Music
77 West College Street
Oberlin, OH 44074
phone: 440 775 8254
e-mail: BenWeisser@aol.com
Ben_Weisser@qmgate.cc.oberlin.edu
home address:
140 Elm Street apt. 2
Oberlin, OH 44074
phone: 440 775 0248
FAX: 440 775 8942
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