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About this book

This book explains music’s comprehensive ontology, its way of existence and processing, as specified in its compact characterization: music embodies meaningful communication and mediates physically between its emotional and mental layers. The book unfolds in a basic discourse in everyday language that is accessible to everybody who wants to understand what this topic is about. Musical ontology is delayed in its fundamental dimensions: its realities, its meaningful communication, and its embodied utterance from musical creators to an interested audience.

The authors' approach is applicable to every musical genre and is scientific, the book is suitable for non-musicians and non-scientists alike.

Table of Contents

Frontmatter

Introduction

Frontmatter

Chapter 1. General Introduction by Guerino Mazzola

Abstract
This introduction gives a general orientation about the book’s topic, its philosophy, and its collaborative authors.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 2. Ontology and Oniontology

Abstract
This short chapter introduces the global architecture of ontology of music which this book is going to discuss in detail.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Realities

Frontmatter

Chapter 3. Physical Reality

Abstract
To begin our discussion of the realities of music, we start with the most basic: the physical reality. It consists of the features of the world that we see in action every day. This includes the variety of ways in which music occurs and can be described, such as through sound waves, instruments, and human motion. There are different ways in which we can create and analyze music. We discuss Fourier analysis, frequency modulation, wavelets, and physical modeling as well as the hearing with the ear and brain.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 4. Psychological Reality

Abstract
The psychological reality of music is involved with the way that humans perceive and react to music. In this section we discuss the prominent theories regarding the relationship between music and emotions, the ways in which music interacts with psychopathology, and how human reactions to music can be measured.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 5. Mental Reality

Abstract
We have seen how music lives in the physical reality and in the mechanisms of human perception and emotion. In this chapter, we will discuss how music lives in the symbolic dimension of score notation, the tuning spaces, and their mathematical symmetries for harmony and counterpoint.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Semiotics

Frontmatter

Chapter 6. Generalities about Signs, Neumes, Periods and Development Sentences

Abstract
Semiotics is the dimension of meaning. It studies the structure of symbols and signs and their associated meanings. We will start by introducing the basic principles of semiotics: the different levels of symbols and the structure of musical symbolism. We will then discuss philosophers and linguists that studied semiotics, and explain their theories as they relate to music. We will apply the theories of Ferdinand de Saussure, who is perhaps the most influential scholar of semiotics, to analyze and exemplify music as a symbolic system. In an overview of more contemporary analyses of symbolism in music, we will discuss the HarmoRubette software and Riemann harmony. Additionally, we will discuss the Babushka Principle of semiotics, which leads into such topics as connotation, motivation, and metatheory.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 7. De Saussure and Peirce: the Semiotic Architecture

Abstract
Semiotics has been studied by linguists and philosophers for many years. The first attempts to define the components of a sign system were made in 1865 by the United States philosopher, Charles Sanders Peirce. After Peirce came Ferdinand de Saussure, Louis Hjelmslev, and Roland Barthes, each with differing views on the components of a sign system. In this chapter we will explore contributions made by the four aforementioned semiotic theorists and discuss the semiotic architecture that their theories illustrate.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 8. Riemannian Harmony and The HarmoRubette Software

Abstract
In music, the production of meaning is prominently described in harmony. This means that musical objects such as chords are given a signification as harmonic signs. The classical approach to this enterprise was proposed by Hugo Riemann (Figure 8.1).
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 9. De Saussure’s Six Dichotomies

Abstract
As mentioned in Chapter 2, Ferdinand de Saussure was a Swiss linguist known as one of the founding fathers of the field of semiotics. In one of his most important theories, de Saussure presented six dichotomies that describe the characteristics of signs and symbols. In this section we will discuss and provide examples for each of these six dichotomies.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 10. The Babushka Principle in Semiotics: Connotation, Motivation, and Metatheory

Abstract
In this chapter, we introduce the idea of what we call the semiotic Babushka Principle (sign systems within sign systems) presented by Louis Hjelmslev. We discuss the implications of applying this principle to the analysis of music and musical scores. We argue that, through the conceivably infinite mapping of connotational systems, music is capable of accomplishing significant symbolic depth.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Communication

Frontmatter

Chapter 11. What Is Art?

Abstract
In this chapter, we will begin to define art. In particular, we will focus on defining music as a form of art. To do this, we will first consider the contributions of artists, thinkers, and poets such as John Cage, Karlheinz Stockhausen, Jean Molino, and François Villon. We will then provide examples from many musical genres, including classical music, opera and movie soundtracks, and pop music. We will end this chapter with contributions from jazz, discussing the works of Miles Davis and Guerino Mazzola’s Tetrade Group.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 12. The MIDI Code

Abstract
MIDI is a language for digital communication between electronic instruments and computers. It is modeled to imitate the movement of the fingers, staying down, going up and so on. It is a low level language which tells you what to do without any deeper understanding. It is very important for electronic and pop music.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 13. Global Music

Abstract
As a map of the world can be covered by a superposition of smaller maps of the different continents, music also has a global aspect. Each musical work can be seen as a whole (global) and its superposition of parts (local). The same can happen to tempo, where we can define hierarchies. Music is global in the sense that pieces and recordings can be shared through all the time and space in the world. However, a global level in the Renaissance or Baroque periods would have a much different meaning than today. If you asked Bach about globality, his answer would be totally different than from one of today’s composers. Bach would be ecstatic if his piece reached a different continent. Today, many musicians celebrate being world stars via YouTube.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Embodiment

Frontmatter

Chapter 14. Recapitulation of the First Three Dimensions: Realities, Semiotics, Communication

Abstract
Performers communicate content from various levels. In regards to music, this content is surmised of the score, its analysis, and its expressive meaning. The medium between a performer and their audience is through some sort of physical interface, such as a musical instrument. To produce the desired sounds, performers must execute precise gestures, using their training, knowledge of the score, and overall sensibility. This brings us to the peak of our discussion. All of the theoretical topics we’ve covered thus far can be summarily combined through gestures. There are many ways of making; thinking is a way of making. Listening is a very creative way of making, too. Gestures are another tool of creation. We say that they have a double ontology, existing inside the mental reality and also the physical reality. There is also a brain connection to the psychological reality. In this chapter we will explain how to contextualize gestures in the frame of realities, semiotics and communication.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 15. The Need for a Gesture Theory in Music

Abstract
Thinking is essentially a practice of making. We can also make in different ways, such as through actions which we call gestures. Western modern notation has its origin in Gregorian neumes, but music does not see such significant gestural advancements until more recent times. Through modernity, creators have come to rediscover gestures as fundamental components of artistic, and in particular musical, creation. We will analyze theories and thoughts, from Adorno to Hatten, passing through Chopin’s performances and ending with Mazzola’s contribution both as performer as well as theorist and research director.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 16. Frege’s Prison of Functions

Abstract
Masterful piano players captivate audiences not only with sound, but with the spectacle of their movements, which also influence the quality of the sound. Many interesting gestures involve rotations in space. We can use a formula to describe a rotation, but the formula denies us the understanding of its essence. Mathematical abstraction neglects the gestural aspect; it takes away from the preceding gestural essence, hiding its nature of movement that connects points in spaces. The whole movement is hidden at the very least, or destroyed at the worst. We should be able to understand a formula via its unfolding in gestures, as in the case of rotation. Several important mathematical topics can be re-thought under the light of gestures. Complex numbers can also be seen as the result of the gestural action of rotation. We will use the imagery of mirrors and vampires to help us understand. We end the chapter with the distinction between imaginary time and real time, the two components of the complex time.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 17. Music Without Scores

Abstract
A score is to a symphony as a formula is to a rotation; it has all of the instructions, but it does not contain any gestures within itself. If the formula is essential to a rotation, then one may also conclude that the score is critical to a symphony. This leads us to ask, can music exist without the score? The answer is yes. Given that real music is derived from gestures, then we must study the gestures that inherently exist. If we can understand gestures without a score, we can only better understand gestures that are accompanied by a score. However, in the score’s existence, there is no action or progression of time. Such is the belief of many musicians trained both classically and in jazz. In this chapter, we will examine the works of free-jazz pianist Cecil Taylor and the works of robots.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 18. Neuroscience and Gestures

Abstract
When we discuss the human aspects of gestures, we return to the most unique object in nature: the human brain. As with all parts of our experience, the brain is involved with producing gestures. They represent a combination of higher-order thinking and motor function (i.e. movement). While the entire brain can be studied with reference to gestures, there is a particular type of neurons that we will address here. Mirror neurons are neurons that are active both when we perform a behavior and when we see the behavior performed by others. The existence of mirror neurons suggests that gestures represent a fundamental way of learning. We end the chapter with an experiment quantifying the gestures of dancers using motion-sensitive devices to generate music.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 19. Mathematical Gesture Theory

Abstract
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.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Chapter 20. Creativity Theory

Abstract
We have seen some examples of both analytical and creative applications of musical gesture theory. Here, we will more systematically describe an approach to musical creativity based on this concept, including an application to improvisation from variations of the Beatles’ “Yesterday”.
Guerino Mazzola, Maria Mannone, Yan Pang, Margaret O’Brien, Nathan Torunsky

Backmatter

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