Nathan Torunsky

Neuroscience and Gestures

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.

Mathematical Gesture Theory

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.

Ontology and Oniontology

This short chapter introduces the global architecture of ontology of music which this book is going to discuss in detail.

General Introduction by Guerino Mazzola

This introduction gives a general orientation about the book’s topic, its philosophy, and its collaborative authors.

The Need for a Gesture Theory in Music

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.

Generalities about Signs, Neumes, Periods and Development Sentences

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.

De Saussure and Peirce: the Semiotic Architecture

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.

Recapitulation of the First Three Dimensions: Realities, Semiotics, Communication

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.

Frege’s Prison of Functions

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.

The MIDI Code

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.