• Miroslaw Sienkiewicz

Honours Project Development: Optical sensation of colour vs pitch of the sound


Source: https://www.mathpages.com/home/kmath578/kmath578.htm

TECHNICALITY:

Sound (human hearing range): 20 Hz to 20,000 Hz (about 10 octaves)

Visible spectrum (optical sensation): 380 trillion Hz to 760 trillion Hz (1 octave)

Spectrum of visible light:

By Gringer - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=4639774

Spectral colours https://en.wikipedia.org/wiki/Visible_spectrum

Dominant wavelengths with Red: 670 nm, Green: 530 nm, Blue: 430 nm:

Vanessaezekowitz at en.wikipedia [CC BY 3.0-2.5-2.0-1.0 (https://creativecommons.org/licenses/by/3.0-2.5-2.0-1.0)]

COLOURS:

Most perceived colours represent a continuous spectral density profile with non-zero energy over the entire range of visible frequencies so it’s not accurate to say that colours correspond to frequencies.

Linear combination (additive mixing) of red, green and blue colours constitute an effective basis for many (but not all) of other colours.

Combinations of red, green and blue can give different colours (theory by Thomas Young in early 1800’s) like on image below:

By SharkD at English WikipediaLater versions were uploaded by Jacobolus at en.wikipedia. - Transferred from en.wikipedia to Commons., Public Domain, https://commons.wikimedia.org/w/index.php?curid=2529435

Our eyes have discrete receptors: cones and rodes and cones are responsible for perception of colour. Three types of cones in the retina are sensitive to

  • short (S sensitivity at 440 nm) wavelength (blue)

  • medium (M sensitivity at 545 nm) wavelength (green)

  • long (L sensitivity at 565 nm) wavelength (red)

The signal that is send to brain contain information of to which degree each of the three types of cones have been simulated. Information about amplitude or frequency is not included.

Our sense of colour is three-dimensional: ’every color we perceive corresponds to some combination of three scalars, representing the degree to which each of the three types of cones is being excited.’

Humans are able to distinguish wavelength differences as small as 0.2 nm.

DIFFERENCES BETWEEN EYE AND EAR (HEARING AND SIGHT):

To recognize the absolute ‘colour’ of audible tones the same way we can recognize absolute red our ears would need to have only a few individual sensing elements, each tuned to one particular absolute frequency. But ear needs to respond to much larger range of frequencies (about 10 octaves) than eye (1 octave) and the space dimensionality is also much greater. We can distinguish much greater variety of spectral characteristics of sound than we can of light. Coiled cochlea of the human ear performs detailed spectral analysis of incoming waves: about a 3000-point spectral profile. So, it’s at least 3000 dimensions for ear over only three dimensions for eye (optical stimuli).

To get sensation of eg. Purple colour, blue (S) and red (L) must be combined in equal measures, in other words purple colour sensation results from the superposition of two frequencies at opposite ends of visible spectrum. Single frequency will not excite both S and L cones in eye as absorption spectra of those cones do not overlap very much.

Because of that a ‘colour wheel’ can exist even though the underlying phenomenon is a linear sequence of frequencies.

J. Arthur H. Hatt [Public domain]

The existence of colour wheel would be paradoxical if colours would be mapped directly to frequencies. Example:

Purple colour effectively wraps around from the high to low frequency end of the optical spectrum enabling us to conceive of the colour spectrum as a closed loop.

Cycles exist also for acoustical pitch but the basis for the former is completely different than for the latter. Fictional pitch sensation (like in case of purple colour) that would wrap around from the high back to low end of audible spectrum, doesn’t exist.

Acoustic pitch cycles are based on harmonic relations (octaves) where we associate a tone with its equivalent in other octaves. Each octave contains logarithmically divided twelve tones (for traditional musical scale).

Soundwaves propagate only in material medium, electromagnetic waves propagate through vacuum.

Pitch of sound and colour of a light wave are related to the frequency of the wave.

Perfect absolute pitch when someone can identify frequency (corresponding musical note) of isolated tone is extremely rare but nearly everyone has perfect ‘absolute pitch’ for optical frequencies: by seeing red we can recognize it as red without comparison with any reference colour.

‘we experience each color as an absolutely identifiable sensation, with no direction sensation of higher or lower light frequencies. If people are asked whether red has a higher or a lower frequency than blue, they probably don’t know (indeed they might guess red, because red seems like a “hotter” color), and yet they can very accurately recognize red and blue as absolute sensations.’

Our perception of colour is influenced by context. Our optical processing compensates for variations in the illumination applied to familiar scenes. Example:

Red apple lay next to green leaf when seen in full daylight. Different daylight affects absolute spectra: during sunset will add orange glow. Visual processing infers shift in illumination and compensate for it so we can still perceive apple as red and leaf as green.

Expected analogy would be recognition of melody played in different key. But in this case, we are shifting the whole frequencies. In case of sight common spectral component is filtered out from all the elements of a scene. This process of compensation relies also on memories of the past perception.

‘sound waves consist of pressure fluctuations parallel to the direction of propagation (so they are called longitudinal waves), whereas light waves consist of electric and magnetic fluctuations perpendicular to the direction of propagation (so they are called transverse waves). The transverse nature of electromagnetic waves accounts for the phenomenon of polarization, which has no counterpart in purely longitudinal waves.’

Both ears and eyes exhibit Doppler shifts: frequency rise when the source of the wave is approaching us, for both kind of waves (colour, sound) sensed intensity is dependant on amplitude of the wave.

SUMMARY:

Optical sense cover almost one octave (380 trillion hz for lowest red to 760 trillion Hz for the highest violet). If hypothetically cones in eye were analogous to strings where tension and length would be turned into frequencies, we could speculate that red sensors (L) would be able to absorb energy in the violet range just as string has a second energy mode at twice the base of frequency. Beside this even in terms of the excitation levels of atoms, an arithmetic sequences of preferred energy level (Balmer and Lymen: absorption and emission frequencies of hydrogen atoms) do not favour frequencies rations of 2 to 1 so musical octave analogy is not valid for our sense of colour.

It happens that L cones (red) have a secondary response characteristic in the extreme blue end of the spectrum which is why violet is perceived to have a reddish tint and this is why L cones contribute to our sense of a cycle rather than linear sequence of colours.


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