Degree Of Freedom

An attempt of a mathematical concept to determine individual freedom of musical expression in an improvising music group.

“The freedom of the individual ends where the freedom of others begins.” (Immanuel Kant)

Degree of Freedom is the attempt to examine and describe improvisational musical ensembles by using the concepts of mechanics. This attempt is still not more than a first idea and a small collection of thoughts about the topic.

In physics, the mechanical movement possibilities of material systems are displayed by independent, generalized coordinates. With the degree of freedom ƒ the number of possible movements of these systems are described.

For example, complex molecules have many degrees of freedom, while a car only has three. The change in position on the x and y coordinates and the direction of travel.

When it comes to improvised music, I am interested in the following questions: How do musicians influence each other when improvising together and how does the number of musicians in an ensemble impact their personal musical freedom of expression?

A single improvising musician, for example, can express himself unreservedly on his instrument at will. He alone determines the tempo, rhythm and key.

With a duo the situation already looks different. Now both musicians have to agree on a common tempo, a common rhythmic and harmonic framework.
With each additional musician in an ensemble, the space for personal musical expression is reduced for the one. His musical freedom of movement is virtually restricted, while for the listener the musical diversity of the group is increased, due to the increment in instrumental voices and ideas.

What effect do instruments such as drum machines, sequencers or loopers have on the improvisational band structure, is another interesting question.

By acting like additional automated band members, these tools provide a static harmonious and/or rhythmic framework for the musical performance, which at the same time limits the freedom of all musicians involved.

If you try again to create a maximum of musical freedom for the musicians by eliminating the harmonic tonality, by free rhythm and expansion of the concept of music, such as in free jazz or free improvisation, this band structure would be similar to an easily deformable substance such as gas or water, equipped with an infinite number of degrees of freedom.

The exact opposite applies for notated music. Here all the grades are already given and the musical work is static. The personal freedom of the performing musician is almost zero. Accordingly the degree of freedom would be ƒ = 0 from the start.

The following table is a first, rather rudimentary attempt at calculating the degree of freedom.

ƒ = 65

*) simplified