Colors or hues are said to be harmonic if their spacing on the color wheel meets certain criteria. Harmonic colors are said to be color coordinated, and work well together in principles of design and art.
Harmonics refers to the mathematical relationship between different wavelengths, and can be found in any type of wave, from sound waves to waves in the ocean. As an analogy, in music, harmonics can be used to tune a stringed instrument. If two notes, played together, are 1/2 of the wavelength (λ/2) out of sync, the waves will fit perfectly within each other and the note will be a steady sound. These notes are exactly the same, only in different octaves, so the waves form a continuous noise. If the notes are different, the wavelength of each note will be separated by a distance of less than λ/2. When the different notes are played together, they will sometimes reinforce each other, causing constructive interference, and at other times will counteract each other, causing destructive interference. The result is a combined note that has qualities of a wavelength in between. The notes will also have rhythmic oscillations, becoming louder and softer and louder again, caused by the waves falling into phase at regular intervals. These oscillations decrease in frequency as the notes are tuned. At λ/4 the oscillations will occur every fourth wave. However, as the string is tuned toward either λ or λ/2 the oscillations will occur less frequently, until they disappear entirely. At λ/2, the strings are said to be tuned to the second-generation harmonic.
In many respects, light waves behave in a very similar fashion as sound waves. A light wave that is λ/2 shorter than an accompanying light wave will be harmonically in-sync. However, every wave in the visual spectrum is less than λ/2 out of sync with every other wave. For every wave in the visual spectrum, the second-generation harmonic exists outside of the visual range. Therefore, different lightwaves always produce rhythmic oscillations when paired together. For example, 604 nm (orange) is exactly λ/14 shorter than 650 nm (red). Therefore, the oscillations will cycle every fourteenth wave. However, these light waves are too small and occur too frequently to discern any oscillations with the naked eye, although they can be exposed with the use of an optical flat. Typically, the combined interference of the waves will produce a perceived color that is between the two wavelengths, or multiple waves can produce colors that do not exist in the rainbow, such as pink, teal, maroon, or brown.
Colors that are λ/4 out of sync are harmonically opposite from each other. These are colors that usually form blackish hues when mixed as paints, such as green and red, blue and orange, or purple and yellow. These colors are opposites on the color wheel. When mixed as light waves, however (i.e.: such as pixels in a computer monitor), they will usually form a color in between. For example, when light waves of red and green are mixed, the result is a yellowish-orange light. When all light waves interfere with each other, the result is a harmonic pattern that is nearly random and repeats only after long intervals, forming white light. If a color wheel is attached to a fast motor (or even a twisted rubber band), when spinning the colors on the wheel will appear to turn white.
Harmonics are not just found in the visual spectrum, but occur all throughout the electromagnetic spectrum. These are often utilized by lasers, turning beams of invisible radiation into visible of even ultraviolet radiation. Nd:YAG lasers emit beams of infrared radiation at 1064 nm. By using a non-linear crystal, such as potassium titanyl phosphate (KTP), the frequency of the beam can be doubled and its wavelength cut in half, changing it into the second-generation harmonic. Thus, the 1064 beam of the laser can be turned into a green beam at 532 nm. By creating a 2/3 wavelength distance between the waves, the laser can be transformed into its third-generation harmonic, emitting a purple beam at 355 nm. High harmonic generation (HH) produces beams of fourth, fifth, and sixth-generation harmonics, typically making wavelengths shorter than visible, creating high-energy harmonics in the UV to x-ray range.
- Cohen-Or, Daniel (2006). "Color Harmonization". ACM Transactions on Graphics (ACM) 25:3: 624. ISSN 0730-0301.
- Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium By Cheng Jin -- Springer 2013