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Guerino Mazzola · Jason Noer
Yan Pang · Shuhui Yao · Jay Afrisando
Christopher Rochester · William Neace
The Future
of Music
Towards a Computational Musical
Theory of Everything
The Future of Music
Guerino Mazzola • Jason Noer • Yan Pang •
Shuhui Yao • Jay Afrisando •
Christopher Rochester • William Neace
The Future of Music

Towards a Computational Musical Theory
of Everything
Guerino Mazzola Jason Noer
School of Music Department of Theatre Arts & Dance
University of Minnesota University of Minnesota
Minneapolis, USA Minneapolis, USA
Yan Pang Shuhui Yao

Department of Theatre Arts & Dance School of Music
Jay Afrisando Christopher Rochester

School of Music School of Music
William Neace
School of Music
University of Minnesota
Minneapolis, USA
ISBN 978-3-030-39708-1 ISBN 978-3-030-39709-8 (eBook)

https://doi.org/10.1007/978-3-030-39709-8
© Springer Nature Switzerland AG 2020
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt
from the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors, and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or
the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Switzerland AG.
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Dedicated to Ida Mazzola
Photo by Guerino Mazzola

Preface
The idea for this book came from a reading of the trilogy The Three-Body Problem,
The Dark Forest, Death’s End by the famous science fiction author Cixin Liu,
which was recommended to me by my student Shuhui Yao. It was less the concrete
narrative of these books—spread over the entire universe in time and space—than
the very category of “science fiction” which was troubling. Science fiction deals
with future and more or less fictitious perspectives of the world’s physical reality,
together with narratives that inhabit those fictions.
It prompted the authors to ask themselves as creators, theorists, and performers
of music and dance whether there was something like “music fiction,” a narrative in
a musical fictitious future.
While this book is inspired by a science fiction, this book’s proposed concep-
tualization of music fiction is not about fiction of a musical future. Instead, it is a
historical and theoretical investigation with the purpose of predicting the future of
music.
We started our inquiry by thinking about how music—instead of science—could
look and feel in 50 years. As Guerino Mazzola was then teaching his university
course “The Mathematical Design of Future Music,” his next step was to envisage a
project about the possible realms of future music.
In the Fall 2018, Mazzola therefore offered a graduate course on writing a book
following these ideas. The precise goal of this project was to envisage a book that
would be the first step towards what we have come to call a “Computational Music
Theory of Everything” (ComMuTE). This title was borrowed from what in physics
is now the Big Science ideal for finding a theory that explains everything. This
“Theory of Everything” (ToE) would unify the four fundamental forces: electro-
magnetic, weak, strong, and gravitational. The unification of the electromagnetic
and weak to the electro-weak being the first big step towards ToE.
We, the collaborators, who took part in this collective effort, represent diverse
experiences and contribute expertise in specialities including composition, im-
provization, and dance. This collaborative effort offers not only new directions
and perspectives that arise from their routine work with creativity that includes new
vii
viii Preface
technologies, but also new interpretations of the social and aesthetic role of music
in its multicultural global variety.
This book is the result of our collaboration that was extended to the Spring 2019
semester and offers a breathtaking spectrum of new vectors into the future of music.
In the general introduction, Chap. 1, a perspective of future developments will be
drawn on the basis of the book’s chapters.
We are pleased to acknowledge the strong support for writing such a demanding
treatise from Springer’s science editor Thomas Hempfling.
Minneapolis, USA Guerino Mazzola

Minneapolis, USA Jason Noer
Minneapolis, USA Yan Pang
Minneapolis, USA Shuhui Yao
Minneapolis, USA Jay Afrisando
Minneapolis, USA Christopher Rochester
Minneapolis, USA William Neace
May 2019
From left to right: William Neace, Jay Afrisando, Jason Noer, Yan Pang, Guerino Mazzola, Shuhui
Yao, Christopher Rochester. Image reprinted with kind permission from the Authors
Contents
Part I Introduction
1 General Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3
1.1 The Collaborative Authors .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3
1.2 Not State of the Art, but Milestones to the Future .. . . . . . . . . . . . . . . . . 4
1.3 Outdated Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4
1.3.1 A Total Reengineering of Music . . . . . . .. . . . . . . . . . . . . . . . . . . . 5
1.4 The Book’s Architecture of Future Musical Perspectives . . . . . . . . . . 5
1.4.1 Part I: Introduction . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5
1.4.2 Part II: Technological Tools . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 6
1.4.3 Part III: Mathematical Concepts . . . . . . .. . . . . . . . . . . . . . . . . . . . 8
1.4.4 Part IV: Cultural Extensions . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 9
1.4.5 Part V: Creative Strategies . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 10
1.4.6 Part VI: COMMUTE . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 11
2 Ontology and Oniontology.. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 13
2.1 Ontology: Where, Why, and How . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 13
2.2 Oniontology: Facts, Processes, and Gestures . . .. . . . . . . . . . . . . . . . . . . . 14
2.3 A Short Characterization .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 15
3 The Basic Functions of Music . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 17
3.1 Surveys of Basic Functions of Music . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 17
3.1.1 Theoretical Approaches . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 18
3.1.2 Empirical Approaches .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 18
3.1.3 The Comprehensive Empirical Investigations .. . . . . . . . . . . . 19
3.2 Music and the Hippocampal Gate Function.. . . .. . . . . . . . . . . . . . . . . . . . 20
4 Historicity in Music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 23
4.1 The System of Music and Its History . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 23
4.2 Utopia .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 24
4.3 Musical Anticipation .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 26
ix
x Contents
5 Only One Restriction: Quality . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 27

5.1 Intellectual Properties in Music . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 27
5.2 Communication of a Musical Message. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 28
5.3 Medium .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 29
5.4 Cultural Factor/Relevance . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 29
5.5 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 30
Part II Technological Tools

6 Software Tools and Hardware Options. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 35
6.1 Composition and Sound Synthesis: DAWs . . . . .. . . . . . . . . . . . . . . . . . . . 35
6.1.1 Recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 35
6.1.2 Project Managing/General Editing.. . . .. . . . . . . . . . . . . . . . . . . . 36
6.1.3 Audio Editing .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 37
6.1.4 MIDI Programming/Recording . . . . . . . .. . . . . . . . . . . . . . . . . . . . 39
6.1.5 Mixing/Mastering . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 40
6.2 Composition and Sound Synthesis: Audio Programming .. . . . . . . . . 41
6.2.1 Object-Oriented Programming and Its Advantages .. . . . . . 42
6.2.2 Graphical Programming Language . . . .. . . . . . . . . . . . . . . . . . . . 43
6.2.3 Text-Based Programming Language.. .. . . . . . . . . . . . . . . . . . . . 43
6.2.4 Which Language Is Better? . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 46
6.2.5 Audio Programming and DAW . . . . . . . .. . . . . . . . . . . . . . . . . . . . 46
6.3 Analysis and Experiment . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 47
6.3.1 Rhythm and Melody Creation via Automata .. . . . . . . . . . . . . 47
6.3.2 RUBATO Components for Analysis .. . . . . . . . . . . . . . . . . . . . 48
6.4 Software-Base Experimental Music Theory: Rubato’s
MetroRubette for Brahms’s Sonata Op. 1 . . . . . .. . . . . . . . . . . . . . . . . . . . 50
6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 50
6.4.2 Inner Metric Analysis . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 51
6.4.3 Inner Metric Analysis of Piano Sonata Op. 1,
Movement 1, Allegro .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 54
6.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 61
6.5 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 62
6.5.1 NotePerformer . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 62
6.5.2 RUBATO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 63
6.5.3 Melodyne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 64
6.6 Improvisation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 64
6.6.1 Nodal .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 65
6.6.2 Impro-Visor . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 66
6.6.3 Band in a Box .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 67
6.7 Notation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 67
6.8 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 69
6.8.1 Auralia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 69
6.8.2 Syntorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 69
6.8.3 Counterpointer .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 71
Contents xi
6.9 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 71
6.9.1 Input .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 71
6.9.2 MIDI Keyboards .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 72
6.9.3 Alternative MIDI Input Tools . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 74
6.9.4 Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 75
6.9.5 Output .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 78
7 New Concepts of Musical Instruments . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 81
7.1 The Classification of Instruments.. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 81
7.1.1 Acoustic/Mechanical . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 81
7.1.2 Electroacoustic/Electromagnetic .. . . . . .. . . . . . . . . . . . . . . . . . . . 82
7.2 Expansive Realization . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 82
7.3 Creative Realization .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 84
8 Musical Distribution Channels: New Networks . . . . .. . . . . . . . . . . . . . . . . . . . 87
8.1 A Conceptual Understanding of the Evolution of Music
Distribution in History . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 87
8.1.1 Pre-Internet Electronic Music Distribution Media:
Phonographic Disc, Cassette, and Compact Disc . . . . . . . . . 88
8.2 Present Internet-Based Channels . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 90
8.3 Ubiquity and Omnipresence: Effects on Music
Consumption Styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 92
8.4 The Global Village of Music as Reshaped by Algorithms . . . . . . . . . 93
9 Big Science in Music. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 95
9.1 Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 95
9.2 Language, Models and Theorems . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 97
9.3 Experiments and the Operationalization of the Theory.. . . . . . . . . . . . 99
9.3.1 Database Management System Research .. . . . . . . . . . . . . . . . . 99
9.3.2 High Performance Combinatorics and New
Methods in Statistics . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 100
9.3.3 Laboratories .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 101
9.4 Political Acceptance.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 102
Part III Mathematical Concepts

10 Mathematical Music Theory . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 105
10.1 The MaMuTh Components . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 105
10.1.1 The Language in MaMuTh.. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 106
10.1.2 Models and Theorems .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 109
10.1.3 Experiments .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 110
10.2 The Creative Power of MaMuTh . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 110
11 Serialism: Failure of New Concepts Without Musical Impact . . . . . . . . 111
11.1 Principles of Serialism . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 111
11.2 Boulez’s Construction and Ligeti’s Critique . . . .. . . . . . . . . . . . . . . . . . . . 112
11.3 Generalization of Boulez’s Construction to 12 Instruments.. . . . . . . 116
xii Contents
11.4 Critique of These Results . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 116

11.4.1 Mathematical Abstraction .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 117
11.4.2 Absence of Ordered Syntagm .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . 117
11.4.3 Failure of Communication . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 117
11.4.4 No Harmony, Rhythm, or Melody . . . . .. . . . . . . . . . . . . . . . . . . . 118
11.4.5 The Sociological Role of Serialism . . . .. . . . . . . . . . . . . . . . . . . . 118
12 Mazzola’s Sonata Construction: A Technical Approach
and Its Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 119
12.1 Boulez’s Creative Analysis . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 119
12.2 Applying Creative Analysis to Beethoven’s Hammerklavier
Sonata Op. 106, Allegro Movement . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 119
12.2.1 Modulation Theory . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 119
12.2.2 The Generic Motive . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 120
12.3 Transfer to a New Sonata Allegro Construction: Mazzola’s
Op. 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 121
12.3.1 Modulation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 121
12.3.2 The Generic Motive and the Main Melody .. . . . . . . . . . . . . . . 122
12.4 The Moebius Type Motivic Construction . . . . . . .. . . . . . . . . . . . . . . . . . . . 122
12.5 A Model for Future Composition or Just Uncreative Copying? . . . 126
13 Imaginary Time: Extending Musical Time Concepts
to Cognitive Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 129
13.1 Einstein’s and Hawking’s Time Concepts . . . . . . .. . . . . . . . . . . . . . . . . . . . 129
13.2 Musical Consciousness and Creativity . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 130
13.3 Descartes’ Dualism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 130
13.4 Synthesizing the Real with the Imaginary: Introducing
Complex Time in Music . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 131
13.5 Performing Symbols to Physical Gestures . . . . . .. . . . . . . . . . . . . . . . . . . . 132
13.6 Application of Imaginary Time to Composition .. . . . . . . . . . . . . . . . . . . 134
14 Mathematical Gesture Theory . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 137
14.1 Historical Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 137
14.1.1 Tommaso Campanella .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 137
14.1.2 Hugues de Saint-Victor .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 138
14.1.3 Paul Valéry .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 139
14.1.4 Jean Cavaillès . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 139
14.1.5 Maurice Merleau-Ponty . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 140
14.2 Definition of a Gesture .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 140
14.3 Hypergestures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 142
14.4 Future Technology for Gestures . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 143
15 Future Theories (Counterpoint Etc.) . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 145
15.1 Future Counterpoint Theories . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 146
15.1.1 The History of Counterpoint Until Palestrina . . . . . . . . . . . . . 147
15.1.2 The Miraculous Effect of Composition on
Consonances and Dissonances . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 148
Contents xiii
15.1.3 The Mathematical Understanding of the Miracle . . . . . . . . . 148

15.1.4 Future Contrapuntal Perspectives .. . . . .. . . . . . . . . . . . . . . . . . . . 151
15.2 Future Theories and Creativity . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 151
Part IV Cultural Extensions

16 A Critique of the Western Concept of Music . . . . . . . .. . . . . . . . . . . . . . . . . . . . 155
16.1 Disembodied Music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 155
16.2 Absent Gesture Theory.. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 155
16.3 Paper Music Fiction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 156
16.4 Time Without Now .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 156
16.5 Sub Specie Aeternitatis: The Devil of Improvisation . . . . . . . . . . . . . . 157
16.6 Expert Music Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 158
17 Improvisation and the Synthesis Project on the Presto Software . . . . . 159
17.1 The Role of Improvisation for the Future of Musical Creativity .. . 159
17.2 Software Construction and Improvisation: Mazzola’s
Synthesis Project.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 160
17.2.1 Principles of the Project . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 160
17.2.2 The presto Software . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 161
17.2.3 The Overall Architecture of the Composition .. . . . . . . . . . . . 163
17.2.4 Symmetries in Music .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 164
17.2.5 Second Movement: Morphing Melodies . . . . . . . . . . . . . . . . . 165
17.2.6 Third Movement: The Music of Poetry . . . . . . . . . . . . . . . . . . . 166
17.2.7 Improvisation with the Software Construction:
Turing’s Test, the CD, and Some Critique .. . . . . . . . . . . . . . . . 166
18 Art Making as Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 169
18.1 Choreography, Composition, and Improvisation in Music
and Dance.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 169
18.2 Practice as Research .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 171
18.3 Methodology: An Example and Extension from Dance Studies .. . 173
19 Human and Machine Music . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 177
19.1 Artificial Intelligence.. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 178
19.2 Some AI Components in Music . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 178
19.3 The No/Body Problem . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 179
20 The Role of Music in the Diversifying Cultures (Africa, East
Asia, South Asia).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 183
20.1 Africa: Ghana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 183
20.2 East Asia: China, Japan .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 184
20.3 South Asia: Indonesia .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 185
21 Cultural Theories of Gesture .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 187
21.1 The Origin of Gesture . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 187
21.2 Gestures in Relation to Culture .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 189
21.2.1 Gesture in American Hip Hop DJing . .. . . . . . . . . . . . . . . . . . . . 189
xiv Contents
21.2.2 The Sign Language Formalism of the Noh Theater .. . . . . . 189

21.2.3 Chinese Gestural Notation and Opera Performance . . . . . . 191
21.3 The Role of Gestures in Future Music . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 193
Part V Creative Strategies

22 Recapitulation of Creativity Theory .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 197
22.1 Defining Creativity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 197
23 The Specifically Musical Walls Against Creativity... . . . . . . . . . . . . . . . . . . . 199
23.1 Tradition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 199
23.2 Extramusical References .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 201
23.3 Missing Ontological Connections . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 202
24 Examples of Creative Extensions in Music . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 203
24.1 New Counterpoint .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 203
24.2 Bitches Brew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 203
24.3 Free Jazz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 204
25 Performance and Composition . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 205
25.1 Performance of Composition . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 205
25.2 Composition of Performance . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 206
26 Are Aesthetics and Business Antagonists? .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 209
26.1 Commercial Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 209
26.2 Conceptual Conflict of Money and Composition .. . . . . . . . . . . . . . . . . . 210
26.2.1 Selling Beauty . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 210
26.2.2 Artistic Integrity and the Pressure
of Commercialization . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 211
26.2.3 Conflict of Art vs. Commercial .. . . . . . .. . . . . . . . . . . . . . . . . . . . 211
26.3 Reconceptualizing to Allow for Monetary Value
and Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 212
26.3.1 Moving from High Versus Low to Inner Versus Outer . . . 212
26.3.2 Conceptualizing the ‘Value’ of Composition.. . . . . . . . . . . . . 213
26.4 Final Step: Testing Our Extension.. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 213
Part VI Commute
27 COMMUTE: Towards a Computational Musical Theory
of Everything .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 217
27.1 The Physical Theory of Everything (ToE) . . . . . .. . . . . . . . . . . . . . . . . . . . 217
27.2 Why Would We Think About a Musical ToE (COMMUTE)? . . . . . . 218
27.3 Some Directions Towards COMMUTE . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 221
27.3.1 Harmony and Rhythm .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 221
27.3.2 Gestures for Harmony and Counterpoint .. . . . . . . . . . . . . . . . . 222
27.3.3 Counterpoint Worlds for Different Musical Cultures . . . . . 223
27.3.4 Complex Time for Unification of Mental and
Physical Realities in Music . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 223
Contents xv
27.3.5 Symbolic and Real Gestures . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 224

27.3.6 Unifying Note Performance and Gestural
Performance: Lie Operators.. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 224
27.3.7 Unifying Composition and Improvisation?.. . . . . . . . . . . . . . . 224
27.4 Imagining Big Science for COMMUTE . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 225
27.5 Hegel’s Weltgeist and the Big Bang . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 226
References .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 227
Index . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 233
Part I
Introduction
Chapter 1
General Introduction
1.1 The Collaborative Authors
To write a book about the future of music, the strategies in composition and
technology, is a delicate enterprise. Beyond a display of theoretical, technological,
and practical tools, one has to sketch the cultural and sociological perspectives in a
world that changes at a very high pace.
What type of authorship should one set up to this end? There are two polar
forces here: one the one hand, the maximal experience in the development of
theoretical, technological, and practical components should be addressed. This role
could be taken by author Guerino Mazzola, who has worked as a music theorist,
music software programmer, and jazz musician for over four decades. But on the
other hand, the future of music must also be investigated by those who will have to
shape musical creativity in the near future: young composers, musicians, dancers,
or students of these fields. The perspectives of their own vital future directions
are as important as those given by long experience. For this reason, the present
authors were chosen to provide the reader with a balanced account of experience
and prospects. Jason “J-Sun” Noer is a disciplinary head of the Hip Hop dance
track at the University of Minnesota. Yan Pang is a professional composer and
dance faculty at the University of Minnesota, opening the multicultural perspective
between Western and Chinese traditions. Shuhui Yao is a smart master’s student,
Jay Afrisando, William Neace, and Christopher Rochester are very engaged PhD
students of composition.
© Springer Nature Switzerland AG 2020 3

G. Mazzola et al., The Future of Music,
https://doi.org/10.1007/978-3-030-39709-8_1
4 1 General Introduction
1.2 Not State of the Art, but Milestones to the Future
The dominant vector of this book is not a description of the state of the art, but a
set of strong directives where to go, and where not to go. This is its provocative
character, imagining and designing the unknown future.
1.3 Outdated Principles
The book’s directive vectors should comprise a critique the following outdated
principles/concepts. Let us state these principles as components of a traditional
ideal creative musician. Observe that in the traditional understanding, a musician
is always masculine because of the outdated ideology that women cannot create
music. Here is a leading general ideological statement, where the outdated
principles/concepts are included:
He is the divinely inspired genius who expresses his deep emotions of (biologi-
cal) survival for the distinguished artist in works of individual excellence.
Here are principles which would replace those outdated ones:
1. creative engineering replacing genius, i.e., the systematic investigation of
creative strategies built upon creativity theory
2. free flow of information replacing divine inspiration, i.e., not being closed, but
sensitive to all input, but also filtering out invalid alternatives
3. abolish split inside/outside replacing individualism, i.e., the “individual” was
the non-split, the box that defined inside and outside. This is outdated, we are a
kind of Moebius space
4. counterworlds replacing biological survival motivation, i.e., counterworlds
are about survival of mental states, not biological entities. This is much more
important than a biological function
5. instant mirroring of poiesis with aesthesis replacing dualism of artist vs.
audience, i.e., instant switch of roles, the linear model is replace by an
“infinitesimal” transfer poiesis <—> aesthesis, i.e., the passionate activity:
passive and active at the same time
6. gestural mediation replacing dominance of emotions, i.e., emotions are too
limited, also too disembodied
7. continuous interaction with knowledge replacing work concept, i.e., works
are static, like dead bodies, versions in time replace static works
8. basic vital function replacing artistic vs. business, i.e., breathing the world
must be free of charges.
And here is the characterization of a person/musician who would embody these
eight points:
• (What?) He/She uses the free flow of information for creative engineering to
elaborate the gestural dynamics of sounding counterworlds
1.4 The Book’s Architecture of Future Musical Perspectives 5
• (How?) in an incessant interaction with knowledge on both sides of the cognitive

Moebius space
• (What for?) to breathe his/her life in its mirror of passionate activity.
1.3.1 A Total Reengineering of Music
There is something larger that underlies all the music principles, but which we
cannot name yet. The idea of a Computational Music Theory of Everything
(COMMUTE) is pointing in the right direction, but it is quite abstract and socially
and economically vague. The applied science of engineering is a realization in the
case of physics. But do we have an analogous situation of “musical engineering”?
Such questions are paramount when talking about the future of music.
The traditional situation, which has defined the present state as described above,
looks like asking for a total reengineering of the concept and reality of music,
theoretically, technologically, socially, and financially, see also [148]. The reason
for this impression is given by the comparison to physics. It may be a strange
comparison, but it definitely opens perspectives that were hidden to this date.
1.4 The Book’s Architecture of Future Musical Perspectives
In this section we present the book’s parts and chapters in their role as vectors to
future developments.
1.4.1 Part I: Introduction
This part gives a general orientation about the music’s general ontology and role.
1.4.1.1 Chapter 1: General Introduction
This chapter!
1.4.1.2 Chapter 2: Ontology and Oniontology
This short chapter introduces the global architecture of ontology of music, which
this book is going to use extensively. It provides the reader with the generic modes
of being of music.
1.4.1.3 Chapter 3: The Basic Functions of Music
In this chapter we will focus on the basic functions of music and divide its focus into
two distinguished approaches, theoretical and empirical. In the theoretical approach
we will deduce the basic function of music based on theoretical frameworks based
on evolutionary and non-evolutionary approaches. Within the empirical functions
we will discuss the role of music in daily life, as well as discover potential
fundamental dimensions implied by the multiple functions of music. Then we
discuss how music acts on the human brain like a drug through the hippocampal
gate function. This gives us an overview of all potential functions, for past, present,
and future times.
1.4.1.4 Chapter 4: Historicity in Music
Music appears also as a function of historical determinants. How is music

determined by such factors? What could be New Music versus Old Music? We
argue against such fashionable but superficial terms. Music shares a deep connection
to its temporal coordinates.
1.4.1.5 Chapter 5: Only One Restriction: Quality
Quality is a concept that greatly varies based on the predilection we develop

throughout our lifetimes. In order for us to create a hypothesis on the trajectory of
quality in future music, we need to establish the criterion in which we can attempt
to objectively discern the value in all music. We discuss the methodology we have
created to limit the innate prejudices developed throughout our lifetimes and aim to
create an equitable means of categorization in which we value quality in conception
through a combination of multiple facets.
1.4.2 Part II: Technological Tools
This part gives an overview of the technological perspectives of the musical

development.
1.4.2.1 Chapter 6: Software Tools and Hardware Options
With the advent of recording and playback, the role of tools in the process of
composing continues to grow its importance. Modern composing tools are not
limited to the instant feedback of sound, but also have a great boost in visual
aid. As for whether the future hardware and software can go beyond the physical
level, for example, providing composers with psychological analysis etc., it is still
a remaining question. But today’s tools have been able to provide strong support
in composition, analysis, (improvisation) performance, notation, and education.
We discuss some of these tools together with their impact on musical creativity.
Hardware for music is increasingly powerful for storage and processing purposes.
We discuss this vector for its role in present musical productivity and its future.
In Sect. 6.4, an application of software for rhythm analysis (MetroRubette) to
Brahms’s Sonata op. 1 is described. This analysis is coauthored by Guerino
Mazzola, Ruhan Alpaydin, and Bill Heinze.
1.4.2.2 Chapter 7: New Concepts of Musical Instruments
As we create a means to cogitate the future of music composition, we need to

consider the relationship between composer and the medium in which music is
performed. The concept of the development of musical instruments finds its
foundation in the need for musicians to create sounds in ways that require more than
one’s own physical body. Currently we organize musical instruments in a system
based on the production modality of sound. We distinguish acoustic instruments,
which generate sounds in a mechanical way, from electroacoustic instruments which
create sounds by electromagnetic devices. With the groundwork of instruments
being steadily refined, the focus of development of musical instruments can
generally be accomplished by two strategies. The first is the expansive realization of
an instrument, i.e., the improvement of the versatility of an existing instrument. The
second is the creative realization of a new instrument, which has been the primary
focus of development for the majority of music.
1.4.2.3 Chapter 8: Musical Distribution Channels
Distribution of music is an essential component of its social relevance. It can more

and more be a core factor of the music’s socially relevant shape, in particular when
given the direction of a quasi-simultaneous network resonance. This development
will be essential for future musical productivity.
1.4.2.4 Chapter 9: Big Science in Music
In physics, Big Science is defined by a theory (models and theorems), an exper-

imental paradigm, extensive laboratories, international collaboration, and political
acceptance. In this chapter, we discuss such an option for the science of music.
1.4.3 Part III: Mathematical Concepts
This part presents some basic mathematical concept architectures for a future music.
1.4.3.1 Chapter 10: Mathematical Music Theory
Mathematical Music Theory offers a new view on musical conceptualization,

in particular the power of generalization of models and theorems for musical
phenomena. We stress the creative power of this approach, as opposed to traditional
conservative music theories, and also as a tool for the music’s future constructions.
1.4.3.2 Chapter 11: Serialism: Failure of New Concepts Without Musical

Impact
We discuss the serial approach, in particular exemplified on Boulez’s Structures

pour deux pianos. We prove the failure of this approach in terms of musical
parameters: communication, understanding, and creative power. This chapter
should act as a caveat in front of mislead conceptualizations.
1.4.3.3 Chapter 12: Mazzola’s Sonata Construction: A Technical

Approach and Its Limits
This chapter gives a prototypical example of mathematical methods that should

play a role in musical composition of the future. Mazzola’s sonata is an explicit
experiment to understand the mechanisms of sonata construction and its creative
limitations, starting from the analysis of Beethoven’s Hammerklavier Sonata Op.
106 to compose a new sonata. This is an example of Boulez’s creative analysis. We
then critically review the Boulezian idea and the new composition.
1.4.3.4 Chapter 13: Imaginary Time
Imaginary time is a creative extension of musical time concepts, including a

synthesis of Descartes’ dual theory of mind versus body and its consequences for
the understanding of consciousness and musical reality. This could provide us with
a new understanding of time that should be important for the future of musical
ontology.
1.4.3.5 Chapter 14: Mathematical Gesture Theory
The theory of gestures in music is a new approach to musical shaping forces. We

discuss its potential (pre)semiotic impact on the dynamics of future music beyond
scores and other symbolic approaches.
What is a gesture? This is a concept which everyone knows, but no one is able
to define. In that way, it is similar to its counterpart, time.
The concept of gesture is very important in art, philosophy, and communication.
Formally, a gesture is a system of continuous curves connecting points in space
and time. A curve that connects a gesture to another one is a hypergesture. We
explore the creativity of new music which uses the gesture as a starting point for
composition.
1.4.3.6 Chapter 15: Future Theories (Counterpoint etc.)
The mathematical approach to music theory is specifically enabling new theories,

theories of the future, of perspectives designing where to move.
1.4.4 Part IV: Cultural Extensions
This part discusses cultural extensions of music under the influence of new social
and industrial constraints.
1.4.4.1 Chapter 16: A Critique of the Western Concept of Music
This chapter presents a radical critique of the dominant Western concept of music.
We question the role of score-driven reproduction of music and its power of
abstraction from human reality in the making of organized sounds.
1.4.4.2 Chapter 17: Improvisation and the Synthesis Project on the Presto
Software
After a critical review of improvisation, especially in jazz, this chapter deals with
the confrontation of mathematical music theory, as implemented in the composition
software presto , with the improvisational flight of Mazzola’s piano in the piano
concerto Synthesis.
1.4.4.3 Chapter 18: Art Beyond Music Alone
Music is an art that must be viewed in deep connection to other art forms, such as
dance, poetry, or theater. This chapter investigates how art-making methodologies
from different disciplines can contribute to each other and suggests that these
approaches can be used as modes of academic inquiry.
1.4.4.4 Chapter 19: Human and Machine Music
Music is a genuinely human expression, but it also carries some machine charac-
teristics when misunderstood. They become virulent if reproduction of musical
compositions is taken over by humans who function as machines, as perfect puppets.
This topic includes a strong critique of so-called Artificial Intelligence, this concept
being abused to confuse musical creativity and semiotically flat machine learning
algorithms.
1.4.4.5 Chapter 20: Music in Diversifying Cultures
We describe the different ways of understanding traditional music in Ghana for

Africa, China and Japan for East Asia, and Indonesia for South Asia. This
view is important for a future inclusive treatment of social and cultural musical
environments.
1.4.4.6 Chapter 21: Cultural Theories of Gestures
In this chapter, we examine the role of gestures in musical performance. The focus
of this examination is on the physical, symbolic, and psychological movements
of musicians in different traditions—American Hip Hop, Free Jazz, Japanese Noh
Theater, and Chinese Folk. We locate these gestures in the bodies, scores, and
sounds of and made by performers. It is also necessary to honor and acknowledge
the cultural specificity of each musical tradition by recognizing the importance
of different geographies, power dynamics, and histories. We describe the role
of gestures as cultural expressivity, complementing the mathematical theory of
gestures.
1.4.5 Part V: Creative Strategies
This part deals with perspectives of creativity for a musical future.

1.4.5.1 Chapter 22: Recapitulation of Creativity Theory
This chapter recapitulates our theory of musical creativity to initiate a discourse on

how to proceed in musical creativity for the future.
1.4.5.2 Chapter 23: The Specifically Musical Walls Against Creativity
The theory of creativity relies on the concept of walls against creativity. We discuss
a number of important walls in the musical realm.
1.4.5.3 Chapter 24: Examples of Creative Extensions in Music
We discuss creative extensions such as new counterpoint, rock jazz, and free jazz,
which go beyond the original intention of a genre.
1.4.5.4 Chapter 25: Performance and Composition
We discuss creative extensions by performance of composition and composition of

performance for a future enrichment of creative options.
1.4.5.5 Chapter 26: Are Aesthetics and Business Antagonists?
We analyze the problematic but very powerful alliance of artistic expressivity with
its commercial framework. For a lot of artists, making money from their art can
feel repulsive because (1) selling beauty seems like a contradiction, (2) it is unclear
how monetary value can be assigned to an artistic work, and (3) the high art vs. low
art, divine versus human paradigm. However, making money from composing is
necessary. In this chapter, we will discuss what needs to change to make this more
acceptable and look at examples of it working in the past. As artists, we need to
remind ourselves that both making and selling are a part of a balanced equation of
being a successful artist.
1.4.6 Part VI: COMMUTE
This part presents a short sketch of how a Computational Musical Theory of

Everything might look like.
1.4.6.1 Chapter 27: COMMUTE: Towards a Computational Musical

Theory of Everything
This final chapter draws future perspectives of music as a comprising cultural

achievement of humans. We discuss the role of music for mathematics and physics
from Pythagoras to String Theory, its global human presence, transcending specific
fields of knowledge in its synthetical force that unifies distant fields of knowledge
and action in the concrete and abstract realms.
Chapter 2
Ontology and Oniontology
This chapter is about ontology of music, including three dimensions: realities,

semiotics, and communication. It also includes the extension of ontology to the
fourth dimension of embodiment. We call this extension “oniontology” for reasons
that will become evident soon.
2.1 Ontology: Where, Why, and How
Ontology is the science of being. We are therefore discussing the ways of being that
are shared by music. As shown in Fig. 2.1, we view musical being as spanned by
three ‘dimensions’, i.e., fundamental ways of being. The first one is the dimension
of realities. Music has a threefold articulated reality: physics, psychology, and
mentality. Mentality means that music has a symbolic reality, which it shares with
mathematics. This answers the question of “where” music exists.
The second dimension, semiotics, specifies that musical being is also one of
meaningful expression. Music is also an expressive entity. This answers the
question of “why” music is so important: it creates meaningful expressions, the
signs that point to contents.
The third dimension, communication, stresses the fact that music exists also
as a shared being between a sender (usually the composer or musician), the
message (typically the composition), and the receiver (the audience). Musical
communication answers the question of “how” music exists.

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14 2 Ontology and Oniontology
Fig. 2.1 The three-dimensional cube of musical ontology. © Guerino Mazzola
2.2 Oniontology: Facts, Processes, and Gestures
Beyond the three dimensions of ontology, we have to be aware that music is not
only a being that is built from facts and finished results. Music is strongly also
processual, creative, and living in the very making of sounds. Musical performance
is a typical essence of music that lives, especially in the realm of improvisation,
while being created. The fourth dimension, embodiment, deals with this aspect; it
answers the question “how to come into being?” It is articulated in three values:
facts, processes, and gestures. This fourth dimension of embodiment gives the
cube of the three ontological dimensions a threefold aspect: ontology of facts, of
processes, and of gestures. This four-dimensional display can be visualized as a
threefold imbrication of the ontological cube, and this, as shown in Fig. 2.2, turns
out to be a threefold layering, similar to an onion. This is the reason why we coined
this structure “oniontology”—it sounds funny, but it is an adequate terminology.
2.3 A Short Characterization 15
Fig. 2.2 The hypercube of musical oniontology. © Guerino Mazzola
2.3 A Short Characterization
The four dimensions of musical oniontology can be put together to present a short
characterization of music:
Music embodies
meaningful communication
and
mediates physically
between its
emotional and symbolic layers.
Chapter 3
The Basic Functions of Music
Music is ubiquitous and it’s pull irresistible. Uniquely, the need of music is
unlike the need of food; we will not die without it, but we keep being driven to
listen to music, or at least, to be exposed to it. There are many ways to access
music. For example; attending a performance, going to a club or a restaurant,
buying physical recordings (such as CDs, cassettes, and vinyls), accessing a music
streaming services, and playing a musical instrument. One might need to listen
to music while commuting or driving, to use music as an accompaniment while
studying, to watch a performance of already-known or newly-recognized musicians,
to get into a certain community where a specific genre of music becomes an identity,
or to listen to it in one’s leisure time. With several numbers of necessity to access
music, we pose a question here: what is the basic functions of music to the human
being?
3.1 Surveys of Basic Functions of Music
Scholars have proposed potential functions of music over decades through theo-
retical point of views and empirical studies. A comprehensive list of theoretical
approaches and empirical investigations was surveyed by Thomas Schäfer, Peter
Sedlmeier, Christine Städtler, and David Huron [143]. They scrutinized discussions,
speculations, and investigations regarding the functions of music listening, and
provided a summary as follows.

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18 3 The Basic Functions of Music
3.1.1 Theoretical Approaches
In theoretical approaches, functions of music were theorized and deduced from prior
theoretical frameworks, but none was the result of empirical testing and exploratory
data-collection. These approaches consist of evolutionary and non-evolutionary
approaches.
1. Evolutionary Approaches These approaches focus on single function of music,
comprising as follows:
• Music projects a social signal of psychological fitness as anyone who can
afford the biological luxury of making music exudes vitality (see [124])
• Music serves a means of social and emotional communication, such as coordi-
nating group activities and reinforcing social bonds, through communicating
shades of emotional meaning by the melodic character of emitted sounds as
found in work and war songs, lullabies, and national anthems (see [136])
• Music is intended to maintain infant-mother attachment through humming and
singing (see [31, 32])
2. Non-evolutionary Approaches These approaches focuses on the needs and
concerns of the listeners and attempts to explain how people select and use media
in everyday lives to serve these needs, comprising as follow:
• Music provides ways for entertainment, identity formation, sensation seeking,
or culture identification (see [10])
• Music can be used to activate associations, memories, experiences, moods,
and emotions (see [18])
3.1.2 Empirical Approaches
In empirical approaches, functions of music were analyzed through gathering

respondent’s data. Two goals are intended from the empirical approaches: (1) to
observe or identify one or more ways in which music is used in daily life, and (2)
to discover potential fundamental dimensions implied by the multiple functions of
music. In the latter goal, large numbers of respondent’s data are reduced into a few
basic dimensions. This will be further discussed within Sect. 3.2. The following is
some lists of dimensions of functions of music:
• emotional use, rational use, and background use (see [22])
• ten dimensions according to Boer: emotion, friends, family, venting, back-
ground, dancing, focus, values, politics, and culture (see [13])
• eight dimensions according to Lonsdale and North: identity, positive and
negative mood management, reminiscing, diversion, arousal, surveillance, and
social interaction (see [103])
3.1 Surveys of Basic Functions of Music 19
• six dimensions according to Hays: linking, life events, sharing and connecting,
wellbeing, therapeutic benefits, escapism, and spirituality (see [45])
3.1.3 The Comprehensive Empirical Investigations
Schäfer, Sedlmeier, Städtler, and Huron argued that both theoretical and available
empirical approaches have some deficiencies. One the one hand, theoretical
approaches only focus on single-account function of music, most often because this
facet was observed that did not focus on music but focused on other psychological
phenomena (e.g. the use of music in managing psychological arousal, the use
of music for possible therapeutic functions in clinical settings, etc.). Also, many
publications suggest functions of music without providing a clear connection to
any theory; some collections remains obscure how the author(s) came up with the
functions proposed.
On the other hand, the available empirical investigations, because of using an
open approach (i.e. trying to capture the variety of musical functions through
surveys and questionnaire studies) or using pre established collections of functions
(resulting from specific theoretical approaches or literature research), have yielded
quite heterogeneous collections of possible musical functions. Moreover, the overall
picture of distilled dimensions of musical functions remains obscure, although at
some points they have come to some agreements.
Therefore, Schäfer, Sedlmeier, Städtler, and Huron led an empirical investi-
gations of musical functions, aiming to pursue their analysis without biasing the
materials to any particular theory and to use a broad range of all potential musical
functions all at once. They identified more than 500 items concerned with the
musical use of function, assembled an aggregate list of all of the questions and
statements that were theoretically derived or used in previous empirical studies,
posing the questions “I listen to music because. . .”, then eliminated and combined
redundant items to settle on (eventually) 129 distinct items. After that they
categorized the items into three fundamental dimensions. These dimensions are:
1. Self-awareness that includes statements about self-related thoughts, emotions
and sentiments, absorption, escapism, coping, solace, and meaning. This
dimension expresses private relationship with music listening; music assists
people to think about who they are, who they would like to be, and how they
manage their own path.
2. Social-relatedness that includes statements about social bonding and affiliation.
This dimension articulates the use of music for feeling close to friends, for
expressing one’s identity and values to others, and to gather information related
to one’s social environment.
3. Arousal and mood regulation that includes statements about the use of music
as background pastime and deviation and as a means to get into a positive mood
and regulate one’s psychological arousal.
20 3 The Basic Functions of Music
3.2 Music and the Hippocampal Gate Function
It is common knowledge that music and emotions are intimately related. The
results of the depth EEG conducted by Heinz-Gregor Wieser, Guerino Mazzola,
and their collaborators from 1984 to 1988 suggest a mechanism that could explain
this relation on the neurophysiological and cognitive level. Through the test, it can
be seen that the emotional brain in its hippocampal structures has a pronounced
response to elementary structures of harmony and counterpoints: the intervals in
their consonance-dissonance dichotomy in the western classical harmony. Now,
the classical thesis of Papez and MacLean [104] states that the limbic system, a
prominent part of the archicortex, is responsible for emotional human behavior,
this is why it is also called the emotional brain. So the hippocampal sensitivity to
consonances vs. dissonances could relate to the emotional function of music, i.e., of
musical intervals in our case. The question is, how musical signs which are by no
means emotions by themselves can evoke and signify emotions in humans, and why
this is done in such a way that the same music may evoke a great variety of such
reactions and significations. Evidently these outputs are the result of a determined
sample of music plus an individual human ingredient.
The point is that the hippocampal formation has been recognized as a key
structure for memory [151]. The neuroscientist Jonathan Winson has proposed a
more specific theory of the hippocampal memory function [158], in that he argues
that the hippocampus performs a gate function to the subconscious, i.e. to memory
contents of emotional character. This means that the hippocampus is a structure that
plays the role of a gateway to hidden memory contents. It is well known that humans
do not have a free or controlled access to their memory contents, in particular not
on the level of long-term and emotional memory, concerning early childhood, for
example.
This suggests that special mechanisms must be activated in order to open the
hippocampal gate to unveil locked memory contents. It is straightforward from
our neurophysiological findings and the gate function of the hippocampus that its
musical stimulation could yield such a “key” to open the gate to hidden memory
contents. If this were the case, two specifics of the relation of music and emotion
would be explained at once:
1. The emotional contents are not generated by music, they are merely retrieved
and evoked from a memory database, whence the individual emotional response
to one and the same music would receive a logical explanation.
2. It is highly unlikely that the musical stimulation of the hippocampus is indepen-
dent of the human individual who undergoes this process. In other words, if the
music is a key, each individual is likely to have his/her individual key to unlock
the “subconscious”. This would explain why there are so many different musical
tastes—beyond musical education and culture. This would also explain why it is
often a specific tune or musical mood that is the personal preference: If this tune
played a role in the encoding of a specific emotional memory content, the same
key-tune could play a role in the decoding process.
3.2 Music and the Hippocampal Gate Function 21
Summarizing, we may conclude that consonant and dissonant intervals and

associated harmonic or contrapuntal structures evoke a hippocampus state process
which activates a gateway to mainly subconscious memory contents. In other words,
Winson’s gate hypothesis of the hippocampal formation must also be stated in the
sense of the existence of a musicogenic key to the gate.
This thesis does not mean that music produces emotions. We state that it only
retrieves and reactivates them from a memory database; it acts on the brain like a
drug and produces psychic effects. In this metaphor, the ‘chemical formula’ of the
music drug corresponds to the involved musical structure.
Chapter 4
Historicity in Music
4.1 The System of Music and Its History
In all fields of knowledge, there is a historical and a systematic perspective. The

former describes the evolution of the field in time, whereas the latter describes the
field’s determinants which could persist along the temporal evolution and define its
fundamental, systematic objectives. However, these two aspects mostly interact:
the systematic part may change along time, while the historical development may
be driven by strong systematic vectors.
In physics, for example, the systematic shape which was defined by the
Aristotelian writings until the beginning seventeenth century, changed dramatically
with Galileo’s introduction of the experimental and mathematical paradigm. And
nowadays, the theoretical physics more and more dominates the experimental setup.
The search for a ToE (Theory of Everything, see Chap. 27) is a purely theoretical
axiom, no experimental evidence thereof has been given. But the history of physics
is still a purely historiographic fact: physics is mainly the evolution of a big system,
not the anecdotal sequence of isolated events. Its history is the trace of abstract ideas
of conceptual nature, Newtonian time and gravitation, Einstein’s time relativity and
curved space-time of gravitation, etc.
Philosophy, to mention a very different case, is not the history of big systems,
but can be identified with its history of continuously deepened question complexes.
Philosophical systems are a sidetrack of this field, where questioning everything
testifies the unfolding of a radical critique of one’s own reflection. Philosopher
Georg Wilhelm Friedrich Hegel argued that this world is the history of an ever
waking up “Weltgeist” (world-spirit), Friedrich Nietzsche taught us to “learn to
swim”, and postmodern philosophy of Jacques Derrida argued for what is termed
“deconstruction”.

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24 4 Historicity in Music
So where can we locate music in its historic and systematic coordinates? Is it

like physics the evolution of one big system of abstract ideas or is it identical with
its historic sequence of never-ending variations of the same like philosophy? And
what is its role with respect to other fields of knowledge?
To begin with, music is the characteristic art of time, more even than dance
since its embodiment is not strictly dependent upon physical bodies. Music not
only describes an objectively given time dimension like physics, it also creates time:
making (composing/improvising/performing) music establishes a time structure and
therefore—following its very logic—time must play a different role also in the
music’s historical unfolding. Let us have a look at a number of consequences of
this musical principle.
4.2 Utopia
A first consequence of the creative relation to time in music is that it relativizes

its own history: musical creators often imagine an utopian world: the world of
a far future. Composer Karlheinz Stockhausen (1928–2007) viewed himself as
being sent from a far star: “I was educated at Sirius and want to return to there,
although I am still living in Kü near Cologne.” And he added his understanding
of the universe: “Why should these large celestial bodies exist if they do not
stand for something? I cannot imagine that there is anything senseless in the
universe. There is much we do not understand.” Stockhausen’s creativity was
always utopian, the present time was for him a small spot within a big plan. And
jazz genius John Coltrane was transcending the present time through Buddhist and
similar universalist weltanschauungen (world views), also interpreting compositions
such as “Out of this World”, or transcending present musical limits in collective
improvisations such as “Om”. Jazz composer Sun Ra (1914–1993) insisted on his
origin from Saturn, he viewed his earthly presence as a small event within an eternal
thread of cosmic art. The titles of his art are typical for this attitude, e.g., “The
Futuristic Sounds of Sun Ra” is an album recorded October 10, 1961 for the Savoy
label.
It is interesting to notice that a famous utopist, the French sociologist and
economist Charles Fourier (1772–1837, not to be confused with Joseph Fourier,
the physicist) wrote an utopian view of humanity [34] where humans are freed from
normal work and can enjoy food and make love and are also emancipated from
the inequalities of gender and race.1 The remarkable characteristic of this utopian
perspective is that Fourier classifies his societal structures according to musical
principles. On page 341 of the second volume, he describes cosmic principles in
these words2 : “Mercure, 5e satellite de la terre, lune favorite ou rectrice e l’octave
1 Fourier seems to be the creator of the idea of women’s emancipation, more than 180 years ago!
2 Mercury, fifth Earth satellite, favorite moon or rector and major octave.
4.2 Utopia 25
majeure (. . .)” All of Fourier’s principles are musically driven. His harmony is a
musical utopia.
The musical utopia was also stressed by Richard Wagner’s idea of a music of the
future in his essay “The Artwork of the Future”, published 1849. In this work, he
proposes an artwork of the future, which would comprise music, dance, and poetry,
and would converge in what he called “Gesamtkunstwerk” (total work of art), a
concept which anticipated the idea multimedia art.
The futuristic ideas in music also became virulent in the first decades of the
twentieth century and was coined “Neue Musik” (new music) by the German
conductor and music critic Paul Bekker in 1919. New music includes the search
for new sounds, new forms or combinations of old styles, either through the
continuation of existing traditions, or through the break with tradition. Journal titles
such as “Perspectives of New Music” are symptomatic for this spirit.
These attitudes prove that the future has often been a standard topic in music’s
history. The musical characteristic is also a historical feature. But what about the
past music? How does the past of musical creativity relate to the present and future?
Looking at the recent history of musical developments, one observes that the past
has also been revitalized. For example, orchestras with original eighteenth century
instruments,3 such as propagated by Nikolaus Harnoncourt, were introduced, and
the oxymoron of “New Tonality”, “New Simplicity” were introduced by composers
such as Arvo Pärt or Krzysztof Penderecki, who, after serial experiments returned
to tonal composition. And the famous “Switched-On Bach” studio album by the
American composer Wendy Carlos, released in October 1968 by Columbia Records,
testifies that new perspectives (this time electronic sounds) of old music are always
a creative contribution to deepen what was thought to be completely understood.
But going back is also an essential tool in composition! The recapitulation in the
sonata form means looking back and expressing the changes which occurred in the
development when playing the exposition a second time: Time is recycled in this
very classical method. In other words, the historical dimension in music is different
from the case of physics or philosophy. Music has, by its very internal logic, a
creative relationship to past and future.
Does this mean that there is no systematic layer in the history of music, i.e., that
music is always recycling the past and anticipating the future like philosophy, and
there is no deeper systematic level of the “science and art of music”? No, this is
too simple. Music has always had a strong theory, from Pythagorean intervals to
contrapuntal theories of Johann Joseph Fux or Hugo Riemann’s harmony, but those
theories developed more in the spirit of mathematics than in the physical paradigm.
Let us make this clear. Mathematics also develops, and sometimes with a giant steps.
But mathematical theorems are never replaced by new theorems because they turn
out to be wrong. They are only replaced by theorems which cover deeper structural
insights.
3 Observe that playing classical early nineteenth century composers on twentieth century instru-
ments is also a synthesis of different musical times.

26 4 Historicity in Music
Music evolves more in this style: deepening insights, not replacing results
because they are wrong. This is a clear difference to astronomy, where some
experimental results may enforce a radical revision of an outdated theory. For
example, the principle of circular orbits of planets had to be replaced by elliptic
orbits in Kepler’s theory. But musical historicity is also different from mathematics,
where the shaping of time is not a relevant category, neither historically nor within
the mathematical processuality.
4.3 Musical Anticipation
The history of music has a remarkable interaction with the development of other
sciences. It is interesting, for example, to list all the points where music and its
theory were in advance of physics:
1. Pythagorean world formula of tetractys was a musical paradigm that could be
reified only much later, in the theoretical physics of the twentieth century.
2. Gesture theory in music was developed much earlier than physical string theory.
Gestures are essential theoretical concepts in performance theory as described by
Graeser, Adorno, Sessions, and Lewin.
3. Kepler’s laws describing the movement of the planets were musically motivated,
he was in search of musical interval fractions (3/2 for the fifth, etc.) to understand
astronomy.
4. In music theory, the three basic harmonic intervals, octave, third, and fifth,
were conceived as independent harmonic directions, an interpretation which
could later be confirmed mathematically when mathematicians had introduced
the concept of linear independence in linear algebra.
5. Grothendieck’s mathematical topos theory was applied by Mazzola to music
theory before the physical application of topos theory took place, essentially by
the work of mathematical physicist John Carlos Baez, a cousin of singer Joan
Baez.
6. Symmetries as fundamental tools for music theory were applied by music theorist
and mathematician Wolfgang Graeser 4 years earlier than in physics by Emmy
Noether.
7. And a sad anticipation: Music business was destroyed earlier than the open
source catastrophe in the sciences.
8. Contrapuntal experiments in musical composition were executed since the early
polyphony around 900 AD, before Galilei’s approaches took place in physics in
the seventeenth century.
Chapter 5
Only One Restriction: Quality
5.1 Intellectual Properties in Music
The concept behind our first step in objectively determining the quality in music
is created from our ability to discern how much intellectual effort is needed to
recreate the same work. Through analysis, we can determine that the composer
uses different theoretical concepts from the traditional Western harmony canon to
create their work.
It is imperative to acknowledge our first caveat in the realization of intellectual
property in music. There will oftentimes be situations in which the audience
member cannot truly determine the extent of intellectual property in the quality. In
Fig. 5.1 a collection of notes that, to a trained musician, would assume were selected
by an excitable child at random. Only through an in-depth analysis, one realizes a
great deal of time was afforded to the selection of these notes by composer Pierre
Boulez. For a more in depth analysis of Pierre Boulez, see Chap. 11.
Though it is relevant to recognize the structural complexity in creation, it is more
important to acknowledge the application of theoretical knowledge. We, as listeners,
need to realize there is a language-like quality to music. In certain cases, our age
may determine how accurately we are able to perceive the intellectual properties
presented in music.
Neuroscience has shown that there is a critical window in the development of
humans, in which as time progresses through maturation, a definitive correlation is
apparent between age and the ability to learn language. Scientists do not dispute the
correlation, but are still attempting to discern the reasoning as to why it works in
this fashion.
This relationship is relevant because spoken language, to an extent, is a collection
of sounds. As we mature, our ability to recognize sound begins to deteriorate
unless we are constantly exposed to sounds that are not usually around us. The
speakers of tonal languages, such as Chinese, are more likely to possess perfect pitch
which stems from semantic differences by varying the intonation given to words or

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28 5 Only One Restriction: Quality
Fig. 5.1 A collection of notes. © Christopher Rochester
syllables of a similar sound. The reason lies in the concept of the degree to which
they have been exposed to the intellectual properties in speech which translates to
an understanding of tonal nuances in music.
As research continues into child development in neuroscience, we will eventually
have a greater ability to perceive the intellectual properties of music.
5.2 Communication of a Musical Message
We cannot focus solely on the application of theory as a criterion in determining the

worth of music. The communication of the musical message, or the relationship
between the poesis and aesthesis is instrumental in the evaluation of quality
in music. Oftentimes, a perceived lack of the application of music theoretical
knowledge can be eclipsed by the success brought forth in the communication of
a thought-provoking idea.
African American work songs used by the Underground Railroad during slavery
are a powerful example of vital musical messages. Many of these compositions
contained coded directions or warnings for escaping slaves. “Wade in the Water”
let people know to get in the water to avoid being seen and “Sweet Chariot”
alerted individuals to prepare to escape. Musical composition was considered in the
creation but the primary importance of these work songs is the message conveyed
to listeners and the history that accompanies them.
Coded messages have been a part of African American music since work songs
and emerged in jazz, blues, soul, funk, and Hip Hop. Most famously, Chuck D of
Public Enemy has said, “Rap is the CNN of young Black America” which refers
to how information is spread through Hip Hop music and calls attention to racist
framings of news reports about African Americans. Although Hip Hop music in
5.4 Cultural Factor/Relevance 29
particular is derided as lacking complex musicality, many groups like Digable Plan-
ets, Ice-T, and RUN-DMC crossed genres to create rap rock, rap metal, and jazz rap.
5.3 Medium
Instrumentation factors in heavily in the execution of a work. . . A work song per-

formed by a group of MIDI instruments would result in a completely different reac-
tion from the viewpoint of the aesthesis. The use of this example is not to denounce
the relevance of MIDI instruments. . . Rather, it is an acknowledgement of the idea
that there is an important relationship between the artist’s medium and audience.
We must acknowledge that our criteria of quality cannot devalue fundamental
aesthetics and definitions in non-classical forms of music. Hip Hop DJs innovated
the scratch as a foundational technique in the art of turntablism but are considered
arrangers and not composers through the lens of classical music. For example, Q-
Bert suggests the existence of at least twenty-five different scratches such as the
Bubble Scratch, Crab Scratch, and the Hydroplane (“A Taxonomy of Scratching”
[91]). How do we translate the compositions of scratches which have been validated
by musicologists and musicians as legitimate in academic settings (“A Scratch
Composition” [92])? Sampling is another technique from this musical form that
is derided because of the use of pre-recorded tracks. Can we consider this prejudice
as lock-stepped in an acoustic mind-set of Tradition? It is well-known that even
Mozart sampled popular songs of the time and incorporated these harmonies into
his most famous compositions. What is the difference between concepts and
approaches of non-traditional techniques in varying musical forms? Ideas about
instrumentation must, for the sake of continued relevance beyond the ivory tower,
regard ways of composing that differ from the entrenched classical tradition as
important and valuable to the field of music study. While this distinction is
important, we do recognize that Hip Hop turntablism is a different medium than
acoustic instrumentation and requires a different skill set.
5.4 Cultural Factor/Relevance
Our quality is primarily determined by the combination of these factors. We have

attempted to separate the cultural relevance as a means of determining quality in
this situation. The contributions of people of color have been largely disregarded
in popular music pedagogy. Consider the concept that there is music that does not
necessarily perform well within our set criterion, but this same music has the ability
to enhance its own quality when we acknowledge its cultural importance.
Beethoven’s influence on the classical genre has spanned generations of musi-
cians and his music is regarded as a pinnacle of excellence in the field. Compar-
atively, Tupac Shakur, a highly influential Hip Hop artist, whose enormous global
impact on society can only be measured in orders of magnitudes in issues of social
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present the bust of Simon Bolivar. Among the West Indies are many
samples of “cut money.” The law permitting money to be quartered
had to be repealed, because the traders of the West Indies made the
wonderful mathematical discovery that five quarters make a whole!
Leaving both the eastern and the western world and their coins,
there is a single piece, of small commercial value, which is yet a
light-house in mid-ocean. This is the one cent of the Sandwich
Islands, the only venture of that kind made by the enterprising little
kingdom. The inscription is “Kamehameha III., one hundredth,
Hawaii.” The name of the king being interpreted signifies “the solitary
one,” which is singularly well adapted to the coin.
Colonial Coins.
In 1684, the charter of the Massachusetts Bay Company was
revoked, and the governor recalled; one of the alleged grievances by
the crown was a colonial law concerning the Mint. The currency used
by the colonies was chiefly from England, Spain, and Portugal, but
the supply was limited from these sources, and the mother-country
was jealous of any infringement of her prerogative of coinage. There
are various specimens of the “pine-tree” money of Massachusetts in
the Cabinet. Some doubt has arisen as to the species of tree
intended, but it is generally accepted as the emblematic pine. This is
claimed to be about the second colonial issue, a kind of semi-official
coin. The first was from the Bermudas.[13] It is a shilling piece,
stamped by one John Hall, silversmith, of the city of Boston, 1652,
who made a very good speculation of the privilege. There has lately
been added to the Cabinet a sixpence of this rare money. The work
on this species of coins is so exceedingly simple as to present little
save a planchet. On the obverse, a double ring around a pine-tree;
legend, “Massachusetts in;” and on the reverse, a double ring also,
containing the legend, “New England An Dom.[14]”
Charles II., it appears, was easily deceived in regard to the
significance of the “pine-tree shilling.” Sir Thomas Temple, a friend of
the colonies, adroitly presented one of these obnoxious coins to the
irate monarch, explaining that the tree was the “royal oak” which had
saved his majesty’s life. Whereupon the king, laughing, denominated
his trans-Atlantic subjects “honest dogs,” and allowed the coinage to
proceed.
During the reign of George I. a new species of coin was issued
from the English Mint, denomination half penny, and it is asserted
upon good authority that this was the only issue ever authorized by
the home government for general circulation in the colonies. It was a
coin of mixed metal, resembling brass. The head of the king was on
the obverse; inscription, “Georgius Rex.” The reverse, a large double
rose under a crown; legend, “Rosa Americana.” Upon a scroll, “Utile
Dulci.[15]”
“Peltry,” we learn, was one of the principal articles of currency, and
was known as “pelt,” or Massachusetts currency, and was
extensively used in trading between Indians and whites, sometimes
called “Beaver Money,” “Corne, Wheate, Barley, and Rye;” and a still
more quaint currency was established, as will be found in an old
Massachusetts court order, as follows: “It is likewise ordered that
muskett balletts of a full boare shall passe current for a farthing a
peece, provided that noe man be compelled to take above 12d. att a
tyme of them.”
In Maryland, not only cattle, tobacco, and other produce was
accepted as currency, but powder and shot were also included. Lord
Baltimore, in 1660, sent over to Maryland the “Baltimore” shilling. In
the colonial case there is a series of these exceedingly rare coins.
They were a shilling, sixpence, groats, and are all of the same
design, differing only in denomination. They were coined in London,
and compare favorably with any minting of that age. The bust of Lord
Baltimore on the obverse is very well cut; his name “Cecil,” is the
legend. On the reverse, the coat of arms of Cecil, Lord Baltimore, is
given; this device has been re-adopted by the State of Maryland.
The substitution of any legal tender seems to be fraught with danger,
and at best is jealously scanned by the people; and there was
trouble to put this coin into circulation. The people, though
demanding coin, did not yield their old currency of “wheat, corn,
tobacco, powder, and shot,” without a demonstration. The Carolinas,
Virginia, and New Hampshire all followed Maryland in the
introduction of a colonial coinage.
In the interval of the Revolution, known as the Confederacy, the
growth of the spirit of independence in the people is plainly written
on their coins, especially upon their tokens or individual coins. We
notice one inscription attributed to Franklin, “Mind your business;”
and others, such as “Good copper,” “Cut your way through,” and like
characteristic expressions. The “New York Doubloon” was coined in
1787, value sixteen dollars. This coin is highly esteemed by reason
of its rarity, and its market value to-day is about five hundred dollars,
as only three or four are known to be in existence.
The Washington cent of 1791 (so-called) was not a coin of the
United States, but was struck at a private mint in Birmingham,
England, (Boulton’s), partly, no doubt, to bespeak the “job,” and
partly to please Americans generally.
It has been said that Washington objected to putting his head on
the coins, and it may be true; but it was also objected that no man’s
head should appear on the coin of a republic, which, whether good
doctrine or not, is still the prevailing idea. The “cent of 1791” is of two
types, one very rare and costly, with a small eagle. The other, with a
large eagle, is more common, and perhaps sells for about five
dollars at a public coin sale.
United States Coins.

The first copper coins made by the United States Mint were one
cent and one-half cent issues, of which there were four designs: 1st,
the “chain cent;” 2d, the “wreath cent;” 3d, the “flowing hair;” and 4th,
the “liberty cap,” which was used for a number of years. The “chain”
device was not acceptable to the sensitive American mind, and of
consequence the accidental breaking of the die was not a subject of
regret, but “quite the contrary.” The pattern sections of United States
coins are very beautiful and varied, especially those in gold.
The Trade Dollar.
This coin bears on the obverse a female figure seated on bales of

merchandise, holding in her left hand a scroll on which is the word
“liberty.” At her back is a sheaf of wheat; this and the bales of goods
indicate the commercial character of the coin. Her right hand,
extended, offers the olive branch. On a scroll beneath the figure are
the words “In God we trust,” and the date below, “1873.” The reverse
has a circling inscription, “United States of America, Trade Dollar.” In
the centre is an eagle, in his claws three arrows and a sprig of olive.
On a label above are the words “E Pluribus Unum.” Below, “420
grains fine,” very beautiful in design.
History of the Trade Dollar.
The coinage of the Trade Dollar was authorized by act of February

12, 1873, and was not intended for circulation in the United States,
but for export to China.
It was designed to compete with the Spanish and Mexican dollar.
That empire, having no mint for the coinage of gold or silver,
depended upon foreign coin for its domestic circulation, and until the
institution of the Trade Dollar the principal shipments of coin to China
were in the form of Mexican dollars.
The Trade Dollar was made a trifle more valuable than the
American and Mexican dollar, thus not only affording a market for the
surplus silver of the mines of the Pacific Coast, but furnishing
merchants and importers from China with silver in a convenient form
for payment for commodities, instead of their being obliged to
purchase Mexican dollars for that purpose.
When its coinage was authorized it was inadvertently made a legal
tender to amount of five dollars, but this was repealed by section 2,
Act of July 22, 1876.
Brief History of the Standard Silver Dollar.
Authorized to be coined, Act of April 2, 1792. Weight, 416 grains,

standard silver; fineness, 892.4; equivalent to 371¼ grains of fine
silver, with 44¾ grains alloy of pure copper.
Weight changed, Act of January 18, 1837, to 412½ grains, and
fineness changed to 900, preserving the same amount of pure silver
= 371¼ grains, with ⅒ alloy.
Coinage discontinued, Act of February 12, 1873.
Total amount coined, from 1792 to 1873, $8,045,838.
Coinage revived, two million dollars per month required to be
coined, and issue made legal tender for all debts, public and private,
Act of February 28, 1878.
Total amount coined, February 28, 1878, to November 1, 1884,
$184,730,829.
Pacific Coast.
The semi-official coins of the Pacific coast present quite a glittering

array of monetary enterprise, and signify the great wealth and daring
spirit of that part of the world. The fifty-dollar octagon gold piece,
issued in 1851, is a very beautiful coin. “Gold slugs” are novelties;
are oblong gold pieces, and are valued at sixteen dollars. The Utah
coins also attract attention. They are of gold, fine. The device is an
“all-seeing eye” and two clasped hands; reverse, “a bee-hive,” with
inscription, “Holiness to the Lord.” Some have for legend, “G. S. L. C.
P. G.,” which the initiated receive as “Great Salt Lake City, Pure
Gold.”
The series of the United States coins is complete, and can be
readily examined. The changes have been very gradual. The motto,
“In God we trust,” was introduced in 1866.
There is one specimen which illustrates how a coin may become
famous without the least premonition, and also is a witness of the
positive law which protects and governs coinage. A law passed
Congress in 1849 ordering twenty-dollar gold pieces to be issued.
One piece was struck. Something intervened to delay the work, and
the year closed; then, of course, the dies had to be destroyed, as no
more could be lawfully issued of 1849. The coin just beside this,
marked 1850, of same value, is not worth the collector’s
consideration, while “1849” cannot to be purchased. It is marked
“unique,” and is really the only one in gold. One specimen exists in
brass.
Coins of the Southern Confederacy.
It has been said and repeated as a historical fact that the Southern
Confederacy had no metallic currency. After a lapse of eighteen
years the following official document from the Confederate archives
explains itself, and substantiates the fact that silver to a limited
extent was coined at the New Orleans Mint by order of the
Confederate Government, in the early days of the rebellion, and only
suspended operations on account of the difficulty in obtaining bullion
for coinage.
War Department, Adjutant General’s Office,

Washington, March 27, 1879.
Dr. B. F. Taylor, New Orleans, La.
Dear Sir:—The enclosed circular will explain to you the
nature of the duties upon which I am now engaged; I would
like to have from you, from file with confederate archives, a
letter stating when you were appointed Chief Coiner of the
Confederate States Mint, instructions received copies of the
originals of any official papers, sketches, descriptions, etc., of
all the coins made, etc. This will make a valuable addition to
Confederate history, and I know no one but you can give it.
Very truly yours,
MARCUS J. WRIGHT.
New Orleans, La., April 7, 1879.
To Hon. Marcus J. Wright.
Dear Sir:—Your favor requesting a statement of the history
of the New Orleans Mint, in reference to the coinage under
the Confederate Government, is received. That institution was
turned over by the State of Louisiana, the last of February,
1861, to the Confederate States of America, the old officers
being retained and confirmed by the government, viz.: Wm. A.
Elmore, Superintendent; A. J. Guyrot, Treasurer; M. F.
Bonzano, M. D., Melter and Refiner; and Howard Millspaugh,
Assayer. In the month of April, orders were issued by Mr.
Memminger, Secretary of the Treasury, to the effect that
designs for half-dollars should be submitted to him for
approval. Among several sent, the one approved bore on the
obverse of the coin a representation of the Goddess of
Liberty, surrounded by thirteen stars, denoting the thirteen
States from whence the Confederacy sprung, and on the
lower rim the figures, 1861. On the reverse there is a shield
with seven stars, representing the seceding States; above the
shield is a liberty-cap, and entwined around it stalks of sugar
cane and cotton, “Confederate States of America.” The dies
were engraved by A. H. M. Peterson, Engraver and Die
Sinker, who is now living in Commercial Place. They were
prepared for the coining press by Conrad Schmidt, foreman of
the coining room (who is still living), from which four pieces
only were struck. About this period an order came from the
secretary suspending operations on account of the difficulty of
obtaining bullion, and the Mint was closed April 30, 1861.
Of the four pieces mentioned, one was sent to the
Government, one presented to Prof. Biddle, of the University
of Louisiana, one sent to Dr. E. Ames of New Orleans, the
remaining one being retained by myself. Upon diligent inquiry
I am unable to find but one piece besides my own, that being
in the possession of a Confederate officer of this city, who
transmitted it to his son as a souvenir of his father’s in the
Confederate cause.
So soon as copies are made I will take pleasure in sending
you a specimen for the archives you represent.
Very respectfully, your obedient servant,
B. F. TAYLOR, M. D.
Formerly Chief Coiner C. S. A.
The most notable and valuable silver coin is the dollar of 1804. It is
said that the scarcity of this dollar was owing to the sinking of a
China-bound vessel having on board almost the entire mintage of
the 1804 dollars in lieu of the Spanish milled dollars. It is believed
that there are not more than seven, possibly eight, genuine 1804
dollars extant. The rarity of the piece and the almost fabulous prices
offered for it are patent facts.
Sketch of the 1804 Dollar.[16]
This coin among collectors is known as the “king of American

rarities.” But seven or eight pieces are known to exist. The 1804
dollars are of two classes, to wit: first, originals, which are from but
one obverse and one reverse die,—draped bust of Liberty facing
right; the head bound with a fillet; hair flowing; 6 stars before and 7
behind the bust above LIBERTY, upper right hand star almost
touching letter y; reverse heraldic eagle bearing on his breast a
broad shield, in his beak a scroll, inscribed E Pluribus Unum; 12
arrows in right talon, a branch of olive in left; above, an arc of clouds
from wing to wing of eagle; in field beneath 13 stars; UNITED
STATES OF AMERICA; edge lettered ONE HUNDRED CENTS,
ONE DOLLAR OR UNIT, which are lightly struck in some parts. The
first specimen in the Mint Cabinet weighs 415.2 grs.; second, Mr. M.
A. Stickney procured from the Mint in 1843 in exchange for other
coins; third, W. S. Appleton bought, at an advance of $750, in 1868,
from E. Cogan, who purchased it from W. A. Lilliendahl, who bought
it at a sale of collection of J. J. Mickley, 1867, for $750; fourth, L. G.
Parmelee bought, at sale of E. H. Sandford’s collection, 1874, for
$700, who obtained it in 1868 from an aged lady, who got it at the
Mint many years before; fifth, W. B. Wetmore bought of Mr.
Parmelee, 1868, for $600, from sale of H. S. Adams’ collection,
1876, at $500, from sale of M. J. Cohen’s collection, 1875, at $325
(in fair condition); sixth, present owner unknown to us, formerly in
possession of collection of Mr. Robert C. Davis, of Philadelphia, and
recently sold for $1200; seventh, S. H. and H. Chapman purchased
October, 1884, at a sale in Berlin, and resold to a Mr. Scott, a dealer
in coins, for $1000 at their Philadelphia sale, in May, 1885.
Restrikes. There were struck at the Mint in 1858 restrikes with
plain edges, of which three were recovered after diligent search; two
of these were destroyed in the Mint, and the other placed in the
Cabinet, where it remains. The difference between these and the
originals are as follows: obverse, the original die was re-cut in the
word Liberty, the stars and date, which made them larger and
deeper, especially noticeable in the stars, which are broadened; also
in the date, it making the outline sharp and square, whereas in the
originals they are somewhat rounded; reverse, not having the
original die, they used another, which differs in many respects, most
easily noticeable in that the A touches the eagle’s claw, the OF much
nearer of the end of eagle’s wing than S in States (in the original it is
equally spaced); edge, plain; weight, 381.5 grains. One specimen is
in the Mint and another in England,—struck between 1860 and 1869,
as in the latter year all dies remaining were destroyed, same as the
above, but endeavors were made to letter the edges in the absence
of a complete collar by using pieces of collars which did not contain
all the letters, but repeated some of them several times. There was
one of these pieces sold in the Berg collection in 1883 for $740, and
showed all the peculiarities mentioned, and its weight was said to be
inaccurate. The dies were destroyed in the winter of 1868-69. No
counterfeit dies of the 1804 dollar were ever made. After the close of
each year all dies are now destroyed.
Double Eagle.
Among the rare coins in the Cabinet at the Mint is a Double Eagle.
The dies for this piece were made in 1849, and only one was struck.
“Unique” and beyond price. There is also a Quarter Eagle of 1842,
and the only one known extant at the Mint.
SELECTIONS.
Having referred many times to this case, it may be as well to
append the entire list of its contents, as they, almost without
exception, are rare, spanning the world from remotest antiquity to the
present day, beginning with the gold Daric of Darius, and ending with
the twenty-mark piece of Kaiser William.
Greece.
1. Four drachma, Athens, b. c. 500; 2. Oboloi of Athens; 3. One-
half obolos, 1⅓ of a cent; 4. Daric, Darius, of Persia, b. c. 520,
value, five dollars and fifty cents; 5. Silver Daric; 6. Brass Ob.
Berenice, b. c. 284; 7. Ptolemy and Berenice, copy; 8. Maneh of
Ptolemy Philadelphus, b. c. 284, value, $17.70; 9. Drachma, Cyrene,
b. c. 322; 10. Coin of Syracuse, copy, about b. c. 300; 11. Silver
coin, Bactria, b. c. 126; 12. Brass of Bactria, b. c. 180; 13.
Cleopatra, b. c. 30; 13a. Denarius of Cleopatra and Mark Antony;
14. Alexander the Great, b. c. 36; 15. Philip, b. c. 323; 16. Stater of
Seleucus; 17. Alexander Balas, b. c. 150; 18. Antiochus VI; 19.
Philip, King of Syria, b. c. 93.
Rome.
20. Roman aes, b. c. 500; 21. Denarius of Augustus, b. c. 31; 22.
Tiberius, a. d. 14; 23. Simon, Bar Cochab, false Christ, a. d. 133; 24.
Vespasian, a. d. 49; 25. Gold bezants, a. d. 610; 26. Justinian, a. d.
527; 26a. Kingdom of Cyprus and Jerusalem, Peter 1, 1361 to 1372,
testoon, Kingdom of Jerusalem; 26b. Amaury II., 1194 to 1205.
English.
27. Gold of Britain; 28. Carausius, Roman Emperor of Britain, a. d.
287; 29. Penny of Ethelbert, King of Kent, 858 a. d.; 30. Harold the
Dane, a. d. 1036; 31. William the Conqueror, 1066, a. d.; 32. Edward
the Confessor, a. d. 1041; 33. Robert the Bruce, a. d. 1306; 34.
Elizabeth, Double Ryal, a. d. 1558; 35. James I, 1603, Ryal (30
shillings) and sovereign; 36. Charles I, sovereign; 37. Siege pound of
Charles I, 1642; 37a. Gold sovereign of Oliver Cromwell; 38. Crown,
and half crown and shilling, Oliver Cromwell, 1658; 38a. Farthing,
Queen Anne; 39. George IV; 40. Coins of Australia.
France.
41. Deniers of Charlemagne, 806; 42. Medalet, Marie Antoinette;
43. Five francs, Napoleon I; 44. Gold, Napoleon I, 1851; 45. Five
francs, Paris Commune.
Germany.
46. Bracteats; 47. German Crown, Ob. St. Stephen; 48. Ducat,
Ob. Luther and Melanchthon, 1730; 49. Crown, Maximilian, a. d.
1615; 50. Ducat, Nuremburg; 51. Ducat Hamburg; 52. Monument,
Bavaria; 53. King’s family, Bavaria; 54. Coins of Prussia; 55. Silver
piece, Frederick William and Augusta.
Spain.
56. Ferdinand and Isabella; 57. Charles II., Spain; 58. Alphonso,
Spain.
Italy.
59. Silver of Venice under the Doges, twelfth century; 60. Ducat of
Venice; 61. Copper of San Marino; 62. Silver piece of Lombardy; 63.
Gold twenty lira piece; 64. Swiss crown, ob. St. Vincent; 65. African
shell money; 66. African ring money.
Oriental.
67. Siamese coins; 68. Chinese tael; 69. Widow’s mite; 70. Jewish
shekel; 70a. Herod the Great, 37 b c.; 70b. Herod Archelaus, 4 b. c.;
71. Glass coin, Egypt; 72. Gold of Alnaser, a. d. 1222; 73. Dirhem of
Mahomet V., a. d. 854; 74. Dirhem of Walid, Caliph of Damascus, a.
d. 713; 75. Haroun Alraschid, Koran text, 806; 76. Fire Worshippers,
a. d. 300; 77. Gold of Japan, 1634; 78. Gravel stone of Burmah; 79.
Late coin of Turkey; 80. Mexican dollar used in China; 81. Coin of
Cochin China.
The most notable coin in this case, and perhaps the most
celebrated coin in the world, is the “Widow’s Mite.” Its name
bespeaks its commercial insignificance. Yet visitors every day, upon
entering the Cabinet of the Mint, ask first to see the “Widow’s Mite.”
The following letter from Wm. E. Du Bois, will be found of interest
to the reader.
THE WIDOW’S MITE.
Sir: The curators of the mint cabinet do not consent to the

intimation in a statement recently made that their widow’s
mite is not the real coin.
The expression of a doubt as to any received fact is thought
to be a sign of superior insight. Hence we have so much
“destructive criticism,” a good deal of it being fatal to the critic
himself.
The widow’s mite in our showcase of specialties, always
attracting much attention, is precisely what the Scriptures
speak of—a lepton, the smallest of Greek and Syriac coins.
The name comes from leptos, very small. The word “mite” is
English, and was formerly a weight representing the twentieth
part of a grain, but has long fallen into disuse. It was
employed in the translation of the New Testament to
represent the word lepton, simply because it was so very
small.
It is pretty certain that there was no Jewish or Hebrew coin
so small as the lepton; that people depended very much upon
outside coins for their circulation. Even their money terms had
changed to those of the Syrian-Greek Empire and of Rome,
as we see from all the instances in the New Testament. What
few copper or bronze pieces they had, struck by local princes
for a limited time, and now very rare, were large enough to
bear a show of devices and inscriptions, for which the lepton
was too minute. The one in our cabinet has a diameter of only
three-tenths of an inch, and weighs but ten grains. On one
side nothing is discernible, on the other a mint monogram,
such as were common in that era, occupies the space. It is
much like the letter x, with a line crossing it near the top.
Whether it is Samaritan, or Syriac, or Greek, we cannot be
sure; nor is it of any consequence. It is enough to show that it
is a coin, and belongs to the age shortly before and after the
advent of Christ, and its size proves it to be a lepton.
It is an interesting and confirmatory fact, that this piece was
found among the rubbish of the Temple grounds, by Dr.
Barclay, long resident in Jerusalem, and author of “The City of
the Great King.” By him it was presented to the mint cabinet.
The objector may soberly doubt whether this was one of the
identical mites offered by the widow; for the rest of his doubts
they are of no value.
We are often asked how much this famous offering
amounted to? There is some obscurity and confusion about
their coin-tables, and, therefore, some variety in the
estimation. We may say, however, that the current value of
the lepton, or mite, was about one-fifth of a cent in our money;
being eighty to the drachma or denarius, which was 16 or 15
cents.
But as the purchasing or paying power of a drachma was
probably as great in that day and country as a dollar is in
ours, we may say that the value of a lepton, judged by our
ideas, was about one cent. As the treasurer would not take a
less gift than two lepta, it follows that the poor but very liberal
woman contributed fully two cents, which is more than some
persons—neither poor nor in widowhood—throw into the
church basket.
It is worth while to add that a visitor at the mint saw a
similar piece in Jerusalem, and tried to obtain one, but on
account of its rarity did not succeed.
W. E. D.
DONATIONS OF OLD COINS.

Extract from the American Journal of Numismatics, April, 1884.
Under the head of donations, we have from Quartermaster
General Meigs, a half-dollar and pistareen of Carolus and Johana of
Spain. These pieces were presented to General Meigs at Corpus
Christi, Texas, in 1870. The special interest attached to them, is their
having been found on the beach of Padre Island, off the southerly
coast of Texas. The supposition is that they were washed up from a
sunken treasure ship wrecked on the coast, while carrying funds to
the Army of Cortez, who entered the City of Mexico in 1519. Their
good condition may warrant our accepting this briny romance Cum
grano salis. Antiquarian stories must expect to stand the test of the
chemist, as well as of the historian. This reminds me, however, of
some specimens of the Mint Cabinet, from the wreck of the San
Pedro, some account of which may not be uninteresting here.[17]
“Early in 1815, a naval armament was fitted out in Spain, by
Ferdinand VII., for the purpose of reducing the Rebellious Colonies
in South America. The military force of this expedition amounted to
ten thousand men, of whom two thousand were on board the flag
ship “San Pedro.” The vessel was also freighted to a large amount
with gunpowder, cannon balls and specie.”
The account then goes on to state that the fleet touched at the
Island of Marguerita near the coast of Venezuela. After leaving the
island, the vessel took fire, burnt four hours until the magazine
caught and exploded, and the wreck went down with four hundred
men. The right of working the wreck, was granted about thirty years
after, to a Baltimore Company, known as the “San Pedro Company.”
Divers were set to work, and the wreck found in sixty feet of water on
a hard bed of coral. Over this there was a deposit of mud, and again
over this a layer of coral, which had to be pierced to arrive at the
treasure.
The Spanish dollars recovered were sent to Philadelphia, and (up
to September, 1848) about seventy-five thousand dollars had been
recovered and re-coined. The dollars were much corroded and
encrusted, the coating having first to be removed, to bring the pieces
into fit condition for minting; the loss from corrosion was
considerable; one dollar with the impression still visible, being
reduced to thirty-four cents in value. In the light of these and other
facts, it is difficult to conceive how the pieces found in Texas, could
have come so clean from their reputed berth, of over three hundred
years, but they are worth keeping for all that, and General Meigs has
the thanks of the Republic for them.
COLONIAL COINAGES.
PLATE I.
Nova Constellatio “Quint.” 1783. Nova Constellatio “Mark.” 1783. Nova
Constellatio, Immune Columbia.
Sommer Island Shilling. “Hoggie.” New Jersey Immunis. Confederatio
Inimica, etc.
See description.
PLATE II.
Connecticut Cent, 1787. New England Elephant Token. Very Rare. 1694.
Good Samaritan Shilling, Mass.
Massachusetts Half Cent. 1787. Massachusetts Cent. New York.
See description.
Nova Constellatio.
Obverse: An eye, the center of a glory, thirteen points cross,
equidistant; a circle of as many stars. Legend: “nova constellatio.”
Reverse: “U. S. 500” inscribed in two lines, a wreath surrounding.
Legend: “libertas justitia 1783.” Border, beaded; edge, leaf work.
Known as the “Quint.”
No. 2.—Obverse: An eye, around which a narrow, plain, circular
field; outside a glory, thirteen points cross, equidistant; a circle of as
many stars. Legend: “nova constellatio.”
Reverse: “U. S. 1000” inscribed in two lines, a wreath surrounding.
Legend: “libertas justitia 1783.” Border, a wreath of leaves; edge,
leaf work; silver; size, 21; weight, 270 grains. Known as the “Mark.”
The Immune Columbia.
Obverse: An eye, on a small, plain, circular field; from the outside
of the field radiates a glory of thirteen blunt points, crossing,
equidistant, the spaces between as many stars in a circular
constellation. Legend: “nova constellatio.” Border, serrated.
Reverse: The Goddess of Liberty, seated upon a paneled cubic
pedestal, facing right; her left hand is well extended and balances
the scales of justice. A short liberty staff, crowned with a cap and
bearing a flag, rests against her right shoulder, and is supported by
the right hand. Legend: “immune columbia.” Exergue: the date
1785. Border, serrated; edge, plain or milled; size, 17; weight, gold,
128.8 grains; silver, 92 grains; copper 148 grains.
Bermuda Shilling—(“Hogge-Penny”).
Obverse: Device—A hog, standing, facing left, above which are
displayed the Roman numerals “XII.,” the whole surrounded by a
beaded circle. Legend: “sommer islands” around which is a beaded
circle like that enclosing the device.
Reverse: Device—A full-rigged ship under sail to the left, a flag
flying from each of her four masts—enclosed in a beaded circle, the
beads larger than on the obverse. Copper; size, 19; weight, 177
grains.
New Jersey Immunis.

Obverse: Goddess of Liberty, seated upon a globe, facing right; in
her extended left hand the scales of justice; right hand staff of liberty
bearing a flag and crowned with a cap. Legend: “immunis
columbia.” Exergue: “1786.” Border, serrated; edge, plain; size, 18;
weight, 160 grains.
Reverse: A shield argent, six pales gules, a chief azure. Legend:
“e pluribus unum.” Border, serrated; edge, plain; size, 18; weight,

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5 Only One Restriction: Quality . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 27

Part II Technological Tools

Part III Mathematical Concepts

11.4 Critique of These Results . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 116

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Part IV Cultural Extensions

21.2.2 The Sign Language Formalism of the Noh Theater .. . . . . . 189

Part V Creative Strategies

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1.1 The Collaborative Authors

© Springer Nature Switzerland AG 2020 3

1.2 Not State of the Art, but Milestones to the Future

1.3 Outdated Principles

• (How?) in an incessant interaction with knowledge on both sides of the cognitive

1.3.1 A Total Reengineering of Music

1.4 The Book’s Architecture of Future Musical Perspectives

1.4.1 Part I: Introduction

1.4.1.1 Chapter 1: General Introduction

1.4.1.2 Chapter 2: Ontology and Oniontology

1.4.1.3 Chapter 3: The Basic Functions of Music

1.4.1.4 Chapter 4: Historicity in Music

Music appears also as a function of historical determinants. How is music

1.4.1.5 Chapter 5: Only One Restriction: Quality

Quality is a concept that greatly varies based on the predilection we develop

1.4.2 Part II: Technological Tools

This part gives an overview of the technological perspectives of the musical

1.4.2.1 Chapter 6: Software Tools and Hardware Options

1.4.2.2 Chapter 7: New Concepts of Musical Instruments

As we create a means to cogitate the future of music composition, we need to

1.4.2.3 Chapter 8: Musical Distribution Channels

Distribution of music is an essential component of its social relevance. It can more

1.4.2.4 Chapter 9: Big Science in Music

In physics, Big Science is defined by a theory (models and theorems), an exper-

1.4.3 Part III: Mathematical Concepts

1.4.3.1 Chapter 10: Mathematical Music Theory

Mathematical Music Theory offers a new view on musical conceptualization,

1.4.3.2 Chapter 11: Serialism: Failure of New Concepts Without Musical

We discuss the serial approach, in particular exemplified on Boulez’s Structures

1.4.3.3 Chapter 12: Mazzola’s Sonata Construction: A Technical

This chapter gives a prototypical example of mathematical methods that should

1.4.3.4 Chapter 13: Imaginary Time

Imaginary time is a creative extension of musical time concepts, including a