How Many Dimensions has Music?

Thinking about dimensions in relation to art forms. A sculpture is unquestionably three dimensional

Painting is a little less easy to pin down, in that paint has varying degrees of thickness. That aside it would be classed by most people as a two dimensional art form. The illusion of three dimensions can be achieved by clever use of perspective, light and shade, but the paint is laid out on a flat two dimensional surface.

Music is the really interesting art form, in that time is the only dimension involved. The written down form of music involves representing pitch and various parameters of the score in the form of dot patterns on a series of horizontal lines called a staff or stave. Before Einstein introduced the concept of space-time in which time is the forth dimension most people would not have recognised time as a dimension at all.

Musical Staff

The vertical position of a note on the staff represents it’s pitch (frequency) and the characteristic shape of the note represents the duration for which the note is held. Time flowing left to right across the staff. The pitch of the note is its frequency, this being the number of repetitions of the sound wave pattern each second. For example a pitch of middle C designates a sound pressure wave having 261.6 repetitions every second referred to as 261.6 Hertz. Musical note D, one tone above C, has a frequency of 293.7 Hertz and so on.

Sound pressure variation

The frequency has units of ‘per second’, again time being the only dimension involved. So on the face of it music is a one dimensional art form, or is it?

Looking at the staff, it is in the form of a graph, time in seconds measured along the horizontal axis and the reciprocal of time (one divided by time) along the vertical axis. Can a meaning be attached to the area of the graph, it’s length times its breadth? The area of the graph is seconds horizontally multiplied by per seconds vertically, that is seconds divided by seconds. In other words the area of the staff is dimensionless, it is zero dimensional. It is as though the music itself is floating above the staff, an ethereal presence outside the physical structure of its written format. After all the staff is not the music, an artist singing or playing an instrument from memory makes no direct reference to it at all. Perhaps this partly explains how so much pleasure can be derived from listening to or playing music, it is a pure construct of the human mind being outside the normal definitions of dimensionality. Music exists only in time.

How is music represented in our brain, is it mapped onto a two dimensional sheet of neurones or deeper three dimensional structures. How can we reconcile the idea of a zero dimensional entity being stored within the three spacial dimensions of the human brain. Do other species make and appreciate music, certainly birds appear to sing for the sheer pleasure of it.

What do you think. Please share and invite comments, we need to explore this concept further, or do we? Perhaps we should just sit back and enjoy the music.

Brian Kershaw