UPDATE: Here are a few more items to consider regarding the relationship of color and sound, specifically the visible spectrum of light and the audio spectrum.
Art history portrays two different art movements in the early 20th century that embrace the relationship of sound and color: Orphism and Synchromism.
In addition to this here is a contemporary composer that recently presented musical works at the FermiLab that interpret data collected from the behavior of subatomic particles into musical form. The composer, Dr. David Ibbett, uses the process of sonification to transpose the spectrum of visible light into a musical scale.
This is achieved by doubling the tone as in raise an octave but do this 40 times to reach visible light frequencies. Or go from a color's frequency and divide by the same constant and derive a tone. For example, if you raise "the note A 440 Hertz" forty octaves it's frequency is close to 483.79 THz which is in the range of the color orange.
Here is a graphic that demonstrates the conversion of light to sound.
This update suggests a standard way to convert notes into colors, but still there is some room for interpretation. For one thing the visible spectrum is just shy of an octave, 400–790 THz so trying to make a full octave means that if you start with Red, the top note won't be visible or if you start with infrared to see the highest note then the lowest note might not be visible. Additionally, the audio spectrum we can hear is about 10 octaves, so it is arbitrary which of the 10 audio octaves to convert the color. Also, visible light is both made of particles and waves, where audio is simply waves.
This update (2-28-2021) shows a more scientific way to convert music to color but still has a lot of room for arbitration. My answer below from 7 years ago should now read that there is a way to covert A 440 Hz to a color, but not necessarily every note is so secure to have a color such as E through F# appear to be on the borders.
================== Original Answer ============================================
There is no standard for converting musical notes into colors. This would be an arbitrary process as there is no way to convert say "A" 440 Hz into a specific wave length of light. It might be interesting to perhaps make up your own. Many artists have tried to correlate color with sound so it is definitely a notion that has been around for a long time.
You might want to see how scientists use pseudo-color to assist in illustrating a condition or concept. Here is a wiki on this:
NASA, NOAA, and many astronomy images use pseudo-color:
Here's some off the wall thing I found about music, this might be the sort of tool you are looking to use: