# Course:PHYS 341/Relation between music and colour

The relationship between music and colour, both consisting of wavelengths, has been a contentious topic and saw serious interest in the 20th century. However, interest in the topic surfaced in antiquity with Plato. With the advent of digital analysis and the recent interest in audio/visual art, this debate intensified. While [1] does demonstrate that a relationship between sound and colour exists, and brain scans show that distinct areas of the brain are activated, this is a purely subjective experience and is very difficult to measure. The focus of this article is on mathematical, observable theories of the issue that can be considered and experienced by everyone.

Fig. 1 Chart by Joseph Schillinger graphing Johann Sebastian Bach's Invention no. 8 in F Major, BWV 779. A graph making use of colour to plot musical notes.

## Characteristics of Sound

Sound consists of mechanically created vibrations that take the form of wavelengths. These wavelengths disturb the surrounding air, and eventually the cochlea in our ears, in order for us to perceive sound. However, sound does not have the electrical and magnetic fields that visible light doest. The audible sound spectrum consists of sounds between frequencies of 20 Hz and 20,000 Hz that are much slower and larger than light wavelengths. Sound wavelengths are approximately a billion times larger than light wavelengths. [1]

Fig. 2 spectogram of Bach's chorales for organ showing time, frequency, and amplitude

## Sources of Colour and Sound

Sound and colour have different origins. Sound emanates from an object mechanically acted upon that disturbs the air around it, and in turn causes the cochlea in our ears to vibrate. On the other hand, an object appears to be coloured because of the interaction of white light with the object. White light strikes an object, the object absorbs certain parts of the light, and the light leaving the object then contains whatever colour is left, or blue for the example. This is not accurate because the object itself is not coloured. Colour is perceived as the reaction of light with an object. [2]

## Theories of Music and Colour

One of the most serious theories of the relation of music and colour was Sir Isaac Newton, seen in Figure. 3

Fig. 3 Newton's colour circle with musical notes

According to Van Nostrand's Encyclopedia, results on tests with a spectrometer gave the correlations seen in figure 4.

Fig. 4 A diagram by Van Nostrand's Encyclopedia showing their relation between pitch and colour

This is a fairly basic theory that provides quite wide connections based on the colours of the rainbow:

"Audible frequencies are from 20 Hz. to 25,000 Hz. The basis of the logic for pitch/colour connection is as follows: Assume the speed of light in a vacuum is a constant i.e. 299,792,458 metres per second. The wave length of a particular colour may be expressed in metres (nanometres or Angstroms). We assume that 299,792,458 metres is equivalent to a number of wavelengths, which may be determined by dividing 299,792,458 by the distance in metres of one wavelength." [3]

In 1978 MIT Press published a brief paper by W. Garner expanding on Leonardo's theory of music and colour. He notes that an octave on a piano consists of 12 semitones: C, sharp, D, D sharp, E, F, F sharp, G, G sharp, A, A sharp, B, and C. Making mathematical relations between a simplified artificial scale starting at middle C with vibrations per second of - 25.0; 135.4; 145.8; 156.2; 166.6; 177.8; 187.5; 197.9; 208.3; 218.7; 229.1; 239.5; and 250.0. The spectrum of visible light ranges from approximately from wavelength 0.4000 x 10-3 to 0.8000 x 10-3 mm.

He argues that multiplying by 100 gives the same range of frequencies as the particular octave on the piano which is played. Therefore, we can speculate that "the eye may 'think' in octaves, like the ear, and that it might be possible to 'translate' an octave of sound precisely into an octave of light" This is because the eye divides the spectrum into 12 distinguishable colours: red, red-orange, orange, orange-yellow, yellow yellow-green, green, green-blue, blue, blue-indigo, indigo, indigo-violet, and violet. By this logic, it should be possible to match on a graph a colour that corresponds to any given note [4]