MTO Dissertation Listings

Volume 3.5 1997

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  1. Longo, Lauren, M. Pietro Gianotti's Le Guide du compositeur
  2. Noll, Thomas. Morphological Foundations of Occidental Harmony
  3. Vlagopoulos, Panos. Le noble rhetorique: Mental Models in the Song Production of Guillaume de Machaut


Longo, Lauren M. Pietro Gianotti's Le Guide du compositeur

AUTHOR: Longo, Lauren, M.
TITLE: Pietro Gianotti's Le Guide du compositeur: A Reworking of
   Rameau's "L'Art de la basse fondamentale"--An Annotated
   Translation and Critical Edition of Part I
INSTITUTION: City University of New York
BEGUN: 
COMPLETED: July 1997

ABSTRACT:
"L'Art de la basse fondamentale" (MS 2474, Institut de France) is a
relatively unknown treatise by Rameau that served as the textbook
draft for a six-month long composition course offered between 1737 and
1744.  Pietro Gianotti later issued his own printed version of "L'Art"
as Le Guide du compositeur in 1759.  This dissertation provides an
English translation of Part I of Gianotti's Guide and a critical
edition that cites the corresponding passages of Rameau's two drafts
of "L'Art" in English translation alongside Gianotti's in a
three-column format.  Critical assessment of the presentation of ideas
from each author's point of view follows each of Gianotti's 15
chapters in editorial commentaries.  Volume II of the critical edition
also furnishes a full transcription of each manuscript draft of
Rameau's first section of "L'Art."

KEYWORDS:
Rameau, Gianotti, Fundamental bass, Pedagogy, Harmony text

CONTACT:
798 Franklin Lake Road
Franklin Lakes, NJ 07417
e-mail: longol@saturn.montclair.edu

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Noll, Thomas. Morphological Foundations of Occidental Harmony

AUTHOR: Noll, Thomas
TITLE: Morphologische Grundlagen der abendlaendischen Harmonik
   (Morphological Foundations of Occidental Harmony)
INSTITUTION: Technical University of Berlin
BEGUN: October, 1992
COMPLETED: July, 1995
ABSTRACT:
The dissertation has been published in German as volume 7 of
the series "Musikometrika," edited by Moisei Boroda, Universitaets
Verlag Brockmeyer, Bochum 1997

I. Musikalischer Teil:

I.1 Tone und Intervalle
I.1.1 Vorbereitung
I.1.2 Der Torus der abstrakten Toene
I.1.3 Basistoene und das Intervallbuendel
I.1.4 Fraktale Toene
I.1.5 Die Konsonanz / Dissonanz - Dichotomie fuer Intervalle

I.2 Akkorde
I.2.1 Chorde und Chordklassen
I.2.2 Fraktale Akkorde
I.2.3 Endomorphismen

I.3 Funktionsharmonik: Versuch einer Rekonstruktion
I.3.1 Die Funktionmorpheme
I.3.2 Hauptdreiklaenge, Nebendreiklaenge und Medianten
I.3.3 Die Konsonanz / Dissonanz - Dichotomie fuer fraktale Toene
I.3.4 Repraesentanten der Dominante

I.4 Enharmonizitaet
I.4.1 Eine Autokomplementaritaetsfunktion im Eulermodul
I.4.2 Die Mutation
I.4.3 Enharmonizitaet als Unschaerferelation der Symmetriegruppe


II. Semiotischer Teil:

II.1 Syntaktik der Musik
II.1.1 Das Morrissche Programm
II.1.2 Syntaktik1: Formale Aspekte musikalischer Zeichen
II.1.3 Syntaktik2: Relationen zwischen musikalischen Zeichen
II.1.4 Syntaktik3: Komplexe musikalische Zeichen

II.2 Das harmonische Vokabular
II.2.1 Methodologische Ueberlegungen
II.2.2 Akkorde und Zusammenklaenge der traditionellen Harmonielehre
II.2.3 Zusammenklaenge bei Skrjabin
II.2.4 Zusammenklaenge bei anderen Komponisten

II.3 Morphologie der Funktionsharmonik
II.3.1 Der metamusikalische Status der Funktionstheorie
II.3.2 Das Riemannsche Programm und das Dahlhaussche Problem
II.3.3 Anwendung: Funktionsharmonik und Auffuehrungssimulation

II.4 Das geometrische Paradigma
II.4.1 Die Yoneda-Philosophie
II.4.2 Perspektiven in der Logik
II.4.3 Perspektiven im Kontrapunkt
II.4.4 Form und Prozessualitaet


III. Mathematischer Teil:

III.1 Affine Endomorphismen von Z12
III.1.1 Restklassen modulo 12
III.1.2 Die Idempotenzzerlegung

III.2 Akkordklassifikation
III.2.1 Konjugationsklassen musikalischer Halbgruppen
III.2.2 Konjugationsklassen von Chord-Endomorphismen

III.3 Bigenerische Halbgruppen
III.2.1 Systematik
III.2.2 Bigenerische (�)-Akkorde
III.2.3 Die Klassifikation musikalischer bigenerischer (�)-Akkorde

III.4 Strukturtheorie der Euleralgebra
III.4.1 Affine Endomorphismen des Eulermoduls
III.4.2 Euleralgebra und Exponentialfunktion
III.4.3 Kommutatoren und Kommutatorklassen von SL2(Z)

Anhang:

Tabellen: Die Klassenliste der H�llakkorde
Literaturverzeichnis

(ISBN 3-8196-0493-6) 

The monograph presents a semiotic theory of occidental harmony. In
contrast to the accoustical, resp. psychoacoustical approaches it
consideres tones, chords, intervals and interval dichotomies as
morphological objects. Following Guerino Mazzolas Mathematical Theory
od Music the 12-tone system is interpreted as a torus whose internal
symmetries - the 144 fractal tones - make it possible to define the
morphological features of chords, as well as to characterize the
prototypical representatives of tonal functions intesionally, resp. to
reconstruct the full variety of possible representatives
extensionally. It is demonstrated that the chords preferably used in
the European music for a long period are especially rich in fractal
tones. Further, the Fuxian and the Riemannian dichotomies of
consonance and dissonance are algebraically and geomtrically
reconstructed and related one to each other. A theory of the
enharmonicity is suggested, making it possible to explain the
interrelations between the three-dimensional tone system of "just
tuned" octaves, fifths and thirds and the 12-tone system as its
commutative deep structure.  Moisei Boroda

KEYWORDS:
Mathematical Music Theory, Musical Semiotics, Functional Harmony,
Consonance/Dissonance-Dichotomy, Enharmonicity, Fractal Tones, Fractal
Chords, Tone Persectives, Harmonic Topology, Chord Neighborhood

TOC:
Einleitung

I. Musikalischer Teil:

I.1 Toene und Intervalle
I.1.1 Vorbereitung
I.1.2 Der Torus der abstrakten Toene
I.1.3 Basistoene und das Intervallbuendel
I.1.4 Fraktale Toene
I.1.5 Die Konsonanz / Dissonanz - Dichotomie fuer Intervalle

I.2 Akkorde
I.2.1 Chorde und Chordklassen
I.2.2 Fraktale Akkorde
I.2.3 Endomorphismen
I.2.4 Fraktale Intervalle ubd Intervallakkorde

I.3 Funktionsharmonik: Versuch einer Rekonstruktion
I.3.1 Die Funktionmorpheme
I.3.2 Hauptdreiklaenge, Nebendreiklaenge und Medianten
I.3.3 Die Konsonanz / Dissonanz - Dichotomie fuer fraktale Toene
I.3.4 Repraesentanten der Dominante

I.4 Enharmonizitaet
I.4.1 Eine Autokomplementaritaetsfunktion im Eulermodul
I.4.2 Die Mutation
I.4.3 Enharmonizitaet als Unschaerferelation der Symmetriegruppe


II. Semiotischer Teil:

II.1 Syntaktik der Musik
II.1.1 Das Morrissche Programm
II.1.2 Syntaktik1: Formale Aspekte musikalischer Zeichen
II.1.3 Syntaktik2: Relationen zwischen musikalischen Zeichen
II.1.4 Syntaktik3: Komplexe musikalische Zeichen

II.2 Das harmonische Vokabular
II.2.1 Methodologische Ueberlegungen
II.2.2 Akkorde und Zusammenklaenge der traditionellen Harmonielehre
II.2.3 Zusammenklaenge bei Skrjabin
II.2.4 Zusammenklaenge bei anderen Komponisten

II.3 Morphologie der Funktionsharmonik
II.3.1 Der metamusikalische Status der Funktionstheorie
II.3.2 Das Riemannsche Programm und das Dahlhaussche Problem
II.3.3 Anwendung: Funktionsharmonik und Auffuehrungssimulation

II.4 Das geometrische Paradigma
II.4.1 Die Yoneda-Philosophie
II.4.2 Perspektiven in der Logik
II.4.3 Perspektiven im Kontrapunkt
II.4.4 Form und Prozessualitaet


III. Mathematischer Teil:

III.1 Affine Endomorphismen von Z12
III.1.1 Restklassen modulo 12
III.1.2 Die Idempotenzzerlegung

III.2 Akkordklassifikation
III.2.1 Konjugationsklassen musikalischer Halbgruppen
III.2.2 Konjugationsklassen von Chord-Endomorphismen

III.3 Bigenerische Halbgruppen
III.2.1 Systematik
III.2.2 Bigenerische-Akkorde
III.2.3 Die Klassifikation musikalischer bigenerischer-Akkorde

III.4 Strukturtheorie der Euleralgebra
III.4.1 Affine Endomorphismen des Eulermoduls
III.4.2 Euleralgebra und Exponentialfunktion
III.4.3 Kommutatoren und Kommutatorklassen von SL2(Z)

Anhang:

Tabelle 1: Die Klassenliste der Huellakkorde
Tabelle 2: Die Liste der konsonanten fraktalen Intervalle
Literaturverzeichnis

CONTACT:
Dr.phil.Thomas Noll
Technische Universitaet Berlin        Fax: (+4930) 314 21 116                        
Arbeitsstelle fuer Semiotik        Telefon: (+4930) 314 25 403           
Ernst-Reuter-Platz 7 
Sekretariat TEL 16-1                      
D-10587 Berlin                e-mail: noll@cs.tu-berlin.de

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Vlagopoulos, Panos. Le noble rhetorique: Mental Models in the Song Production of Guillaume de Machaut

AUTHOR: Vlagopoulos Panos Ph.
TITLE: Le noble rhetorique: Mental Models in the Song Production of
   Guillaume de Machaut
INSTITUTION: Ionion State University
BEGUN: September, 1995
COMPLETED: June, 1998

ABSTRACT:
The introduction contains a critique of current reductionist
interpretation models and argues for the use of - a variant of -
radical constructivism in the attempt to gain historic-musicological
knowledge. Some of the key-notions put in use are mental models,
metaphors, observer and reflexivity. On this basis the goal of the
research is set as: to first distinguish fourteenth-century mental
models in a number of different areas, from education to literature
and everyday life, then find relevant - not merely similar - models of
musical thinking in the song production of Guillaume de Machaut.
Machaut's opus is considered as the result of a highly ecletic,
complicated, past- as well as future-orientated artistic attitude,
which I try to illuminate using the notion of reflexivity and
self-reflexivity: this is brought about by an analytical examination
of concrete compositional techniques and an investigation of an
-implicit- Machaudian theory of genres, which is shown to be a
prerequisite for self-reflexivity and, at the same time, to be
regulated by it.

KEYWORDS:
Guillaume de Machaut, Ars nova, formes fixes, radical constructivism,
metaphor, mental model

TOC:
A.  Fourteenth-Century Mental Models
 
 Introduction
 Sciences
 Aristotelian Metaphysics, Sign Theory of Occam and Oresmian Physics
 Time and Measurement
 
 Ars Nova Ideology 
 Antiquus/modernus/novus
 Classification Models and Genres
 Time and Measurement
 
B.  Machaut's Musical Mind
 
 Compositional Techniques: Floskeln and Tenor Types
 Genre and the Fourteenth-Century Ordenance Concept
 Reflexivity and Self-Reflexivity As Keys to Machaut’s Concept of
   Composition
 Conclusions


CONTACT:
Panos Vlagopoulos
Ag. Sofias street 24
17123 Nea Smyrni
Athens/Greece
OR
Vas. Sofias & Kokkali
11521 Athens/Greece
tel +301 7282772 / 9343959
fax +301 7259196
panovlag@otenet.gr

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prepared by Lee A. Rothfarb, General Editor
9/16/97