I make musical instruments and would like to correlate musical notes
to colors. By looking at the frequency of a note, ie. middle C and
transposing that up by octaves into the light spectrum can the color
be determined?  For example,  C = Red  D = Orange, etc.  I'd like to
match these up by science as apposed to art.  Also, to better
understand what I'm trying to do, see my website at www.joiatubes.com

Joia1

Hi   joia     

Interesting question: Mapping sound to color

Comment below has some merit, but I am going to offer
different mapping, mapping based on human perception
of color and sound. It is still scientific, but it takes the
properties of sensors into account. 

1) perception of color:
  
 Somewhat technical explanation of chromatic coefficients   is given here
    http://www.math.ubc.ca/~cass/courses/m309-03a/m309-projects/vaxenga/part5.html

  We can clarify it as much as needed, on request.
 For starters: each perceived color can be described by three number
 The numbers (coordinates or coefficients) differ vsry slightly from
person to person, once we exclude colorblind subjects).

 There are different transformations of those three;

 A simple set is this:  hue  saturation and luminance .    

Luminance describes to intensity of light  (volume of the sound)
 Hue would match the dominant tone  (pitch) of sound (low or base)
 Saturation,which increase as we are  going from white to pastels to 
pure (rainbow) color  has no obvious analog. You have to choose.
 you may choose duration of a note, or something like timbre.

  Since duration of the tone may mapped on the duration of flash, it
may be better to reserve saturation for another property of sound.
  
 

Visually, all this is explained here:
  
http://images.google.com/imgres?imgurl=psychology.uww.edu/305WWW/COLOR/ColorSolid.JPG&imgrefurl=http://psychology.uww.edu/305WWW/COLOR/COLOR.htm&h=531&w=288&sz=160&tbnid=CXvztRxwjQcJ:&tbnh=127&tbnw=69&prev=/images%3Fq%3Dcolor%2Bsolid%26hl%3Den%26lr%3Dlang_cs%7Clang_en%26ie%3DUTF-8%26inlang%3Dpl%26c2coff%3D1%26safe%3Doff

 This picture is taken from the site 
  http://psychology.uww.edu/305WWW/COLOR/ColorVis.html    

 which has additional explanation on human perception of color.
Look at the pages there. 

2) Perception of sound:

Physics represents sound and light in a similar way, by a spectrum
(a graph which how much energy is in each frequency band).
              http://www.phys.unsw.edu.au/music/sound.spectrum.html   

A sound spectrum is explained here:
    http://www.phys.unsw.edu.au/music/sound.spectrum.html

However, they eye and inner ear differ. Light is filtered through 3
types of cones and so has three dimensions.
 Inner ear has many more sensors, and sound perception has more dimension.

 Since intensity naturally corresponds to volume, you must select two  
characteristics of the sound spectrum to map on the other two dimensions of light.

Dominant tone (main peal in the spectrum) would be a good match to HUE.

Purity (spectral with)  would be a good  match for SATURATION.

Pure tone (single line a spectrum) would then correspond to a pure color,
and 'white noise' would map on white color.(zero saturation)

 
      If you are happy with the answer, please do rate it . It helps me 
     to improve my skills if I know how well,or how badly, I did answer.
     If you are not happy, please do ask for clarification.
      

Hedgie

---

Clarification of Answer by hedgie-ga on 22 Mar 2004 05:10 PST

Hi  joia1-ga

I have read your comment. In general, it is better for you to use
'request for clarification' button. That way I am notifiedd about your RFC.
I usually come back to read the comments, but it is not required or
guaranteed. As GA researcher I cannot communicate with you directly
(using e-mail). Commenters (racecar,  ofer)  do not have this
restriction.
 However, I will answer your CRFs as needed.

I see no conflict between the answers. The mapping between frequencies
(color and pitch), which racecar  sketched can be, and should be, described
by a mathematical function. Unless you provide additional requirements,
such function is not unique. Linear function (roughly, racecar's choice)
is simplest. You also may choose if you want to map whole visible range
to whole audible range as I suggested, or use just part of the range,
as racecar does.

Audible range changes a bit with age. For younger people it is
20Hz to 20kHz, which is more then the segment which racecar picked.

Th eother difference between Racecar's answer and mine is in this:

Racecar considers only pure (spectral) colors and tones. 

I considered more general mapping: Mapping of all sounds we can hear to
all colour shich we can differentiate.  There are colors which are not pure,
but which we do see as different from pure colors (e.g. brown, grey etc).

If you are satisfied with a subset of colors and  subset of  tones and
simple function, then racecar's mapping  is without a fault.

hedgie

To racecar.ga your thoughts and complete breakdown of the notes and
colors is an exceptional resource for me in my field. Also, thank you
for your follow up.  Outstanding!
Hedgie-ga, Thanks for the clarification and your brain on this.  I got
it!  racecar provided the foundation and you provided the map to
expand on this issue.  I have no idea what researchers would charge
for this information but here's at least another $25.00 for your work.
 You guys (or girls?) are great!

Thanks,
Rick

The frequencies of light of various colors can indeed be expressed in
terms of musical notes, but there is not a visible color for every
note, because an octave represents a doubling in frequency, and the
highest frequency of light our eyes can see is not quite twice the
lowest frequency.  We can see light from about 4.3 E14 to 7.5 E14 Hz. 
(7.5 E14 means 750000000000000).  The frequency of middle C is 262 Hz,
so the frequency of the C 41 octaves above middle C is 262 * 2^41 =
5.8 E14, which is the frequency of green light.  So if we could hear
green, it would be a C.  The highest frequency we can see (7.5 E14 Hz)
is between E and F 41 octaves above the E and F above middle C.  The
lowest frequency we can see (4.3 E14 Hz) is the G 40 octaves above the
G above middle C.  So the colors would go like this:

G (196): deep crimson (4.31 E14)
G#(208): red-orange   (4.57 E14)
A (220): orange       (4.84 E14)
A#(233): yellow       (5.12 E14)
B (247): yellow-green (5.43 E14)
C (262): green        (5.75 E14)
C#(277): turquois     (6.10 E14)
D (294): blue         (6.46 E14)
D#(311): blue-purple  (6.84 E14)
E (329): violet       (7.25 E14)

And F and F# are not visible.

After each not is its frequency (for the G below middle C up to the E
above it), and after each color the corresponding frequency 41 octaves
higher.  I just kind of guessed when naming the colors, but they're
approximately right.

after each *note*...

Hi Rick,

Hedgie and Ofer are correct that there are an infinite number of
possible arbitrary ways to define a function which links colors and
sounds, and that would be about all that could be said on the subject
if you wanted to assign each color to an animal, say, or each musical
note to a continent.  But as you know, the musical scale is a
frequency scale: it would be cumbersome to refer to each note by its
frequency in hertz, so instead we give each note a letter name, kind
of a shorthand.  In western music, the octave is broken up into twelve
increments (notes), and in the tuning system known as just intonation,
all steps are the same size.  The frequency of each note is a factor
of 1.05946... times that of the previous note.  Anyway, the point is
that the musical scale is just a way of measuring frequency, nothing
more.  And each pure spectral color has a frequency, which can be
measured using any frequency scale, including the musical one.  As
Hedgie has pointed out, most sounds that you hear and most light that
you see are made up of a mixture of various frequencies.  This mixture
is what makes a note played on one instrument distinguishable from the
same note played on a different instrument, and it accounts for the
property of visible light known as saturation. In fact, even if you
paint your instruments with the colors I have suggested, each color of
paint will reflect not just a single frequency, but a range of them. 
The color perceived by the eye, however, can be the same as if the
light were monochromatic.  All these details aside, in my view, the
answer to the original question is simple and unambiguous.  The
question was:

"By looking at the frequency of a note, ie. middle C and
transposing that up by octaves into the light spectrum can the color
be determined?"

And the answer is, unequivocally, yes.

This answer is based on basic principles of optics and music theory,
so a reference shouldn't be necessary.  If you would like assurance
that the answer is correct, one thing you could do is post a question
asking other GA researchers.  If you like, you can direct your
question at specific researchers whose answers you would trust.  In my
opinion, mathtalk-ga would be a good choice in this case.

Last thing: I repeat that while the frequencies I listed are accurate,
the color names are only approximate, and you should check them.

Here is just an idea to dig into ;-)

Nobody has yet mentioned the musical harmony. The chords can be
consonance and dissonance and color prception, althoug extremely
subjective, also has some rules about combining the colors. For
instance 'red is no good to combine with green' or 'some blue shades
match light-yellow' - there is lots of literature on how to and how
not to combine colors. I have not heared about a formal study about
color harmony and consonance. If such would exist it will be extremely
beneficial to the mapping of the music to color. I realise of course
that it has nothing to do with analog music playback - applicable only
to the rendition of notes (MIDI, MOD or live play)

Out of curiosity - and I know I didn't pay for this question - I heard
that George Gershwin may have had a brain "disorder" that allowed him
to see sound.  Hence, Rhapsody in Blue actually sounded like the color
blue.  Is there any truth to this rumor, and if so, do the techniques
outlined here to match color with sound equate with Gershwin's match
of colors and sound?

the "disorder" that jeffbridges comments on is a true gift called
synaesthesia. those of us who have this gift see colors for letters,
numbers, and musical notes. for more information on synaesthesia, and
some brilliant famous people who are synaesthetes, you may want to
check out this link:

http://www.psychiatry.cam.ac.uk/isa/frames.html

synaesthetes can be very possessive of the colors they associate with
certain letters, numbers, or notes, and will argue to the death why A
flat should be lavender (or whatever) - emotion and perception are the
key factors in determining these colors for most, not science. a
scientific correlation such as joia1 is trying to create is a
completely different scenario and seems much less likely to rile up
any vehement synaesthete. hope that's clear!

Regarding mapping sound to color, as well as color harmony and
consonance and their application to musical performance, I have been
toying around with the idea of using pure color, and it's direct
variations (hue, tone, etc) to represent frequency range cutting and
boosting, also known as an equalizer, or EQ. EQ's are used most
frequently with DJ audio-mixing, elctronically generated music, and
audio recording and mastering. For simplicity, I have been focusing on
the Disc-jockey EQ, which traditionally uses three frequency ranges
(bass, mid, treble) with a -26Db cut and a +12Db boost associated to
each. I would like to hear some comments on how a 3-band EQ might use
color to reresent changes. Any ideas?