The wave method of building color scheme
About
In life we often face the challenge of choosing the right colors. This happens when we need to choose clothes suitable for each other, shoes suitable for clothes, choose different wallpapers for the children's room, makeup, choose colors for our site and much more. The process of selecting several colors that combine with each other is called the construction of a color palette (gamut).
In colouristics there are several methods for constructing a color palette (color gamma) based on the arrangement of colors relative to each other in the color circle. Harmonious combination of which is not justified from a physical point of view.
The wave method of building color palette based on the relationship of color and acoustic waves, and also the concept of consonance (harmony) in music theory. Just as chords sound harmonious in music, colors in a picture look harmonious as well. Perfect consonances are taken as a basis: a pure fourth (a chord of notes Do and Sol), a pure fifth (a chord of notes Do and Fa). This picker uses a wave method and allows you to match the most harmonious colors to the base color, which you choose by setting wavelength, saturation and lightness.
This site allows you to choose the most harmonious combination of colors for your site, clothing, interior, etc.
The corresponding article was published on the site arxiv.org - https://arxiv.org/abs/1709.04752.
Also we have our limited nft collections on the OpenSea site - https://opensea.io/collection/wavepicker and https://opensea.io/collection/wavepalette/drop.
Below is a more detailed description of the method.
The wave method of building color palette
In music theory there is the concept of consonant intervals. Consonances are called intervals, sounding more softly and harmoniously. There are three groups of consonances: very perfect (perfect unison, octave), perfect (perfect quint, perfect quartet) and imperfect (big third, small third, sixth). There is also the concept of a consonant chord - a major or minor triad which consists only consonant intervals.
Acoustically, the essence of the difference between consonance and dissonance is expressed in different lengths of periods of regularly repeated groups of oscillations. The criterion of the difference between consonance and dissonance is the simplicity or complexity of the relationship: simpler relationship is more consonant, more difficult is more dissonant. Numerical proportions can be expressed in two ways: through the ratios of the lengths of the strings or through the ratios of the vibration numbers. In other words, the degree of consonance of two notes is determined by the number of coincidences of the periods of the corresponding harmonic functions of the dependence of sound pressure on time per unit time.
Figure 1: Graph of sound pressure versus time in fixed distance from sound source.
For example, notes C and G (perfect fifth) have the lengths of sound waves differs by 1.5 times. The graphs of the functions of the dependence of the sound pressure of the notes on time intersect on the abscissa axis (sound pressure equal to zero) when the sound pressure function of the note C makes two oscillations, and the function of the note G is three (fig. 1). On figure 1 this moment is marked with a vertical line.
Figure 2: Graph of sound pressure versus distance from sound source in fixed time.
If we imagine the propagation of sound pressure in space at a fixed time (near the sound source), then we get the same figure (fig. 2).
The notes С and E (the big third) have lengths of sound waves differs by 5/4 times. Their graphs intersect on the abscissa axis when the sound pressure function of the note C makes 4 vibrations, and the E note function - 5. That is why the perfect fifth is more consonant than the big third.
Color, like sound, is also a wave (wave-particle duality). In the case of constructing a consonant interval for a color, we are not limited by a small set of notes, but are limited by the wavelength limits of the visible light, just as the sound is limited by the wavelength limits of the audible sound.
Consider building of color palette for spectral colors.
Spectral colors
The spectral color is a color having a certain wavelength. To build a color palette, let's take, first, the most consonant color to it - it's a color with a wavelength that differs in 1.5 times, but does not go beyond the visible spectrum. Further, similarly, we will take less consonant intervals until we reach the desired number of colors in the desired palette.
Figure 3: Graph of electric field intensity (E) versus distance from source in fixed time.
Take, for example, a blue color with a wavelength of 450 nm. The color whose wavelength is less than 1.5 times exceeds the scope of visible radiation. The color with a wavelength greater than 1.5 times (675 nm.) is a red color. The color with a wavelength larger by 3/4 times (600 nm.) is an orange color. As a result, we got the following color palette: the main color is blue, the most suitable color is red, a little less suitable for the blue color is orange (fig. 3). The same results can be obtained by operating frequencies instead of the wavelengths.
Also in music there is the concept of tune. The combination of notes can sound not only harmoniously, but also have a shade - a tune (ionian, dorian, phrygian, lydian, ...). Similar feelings can be transferred to the color palette by using the corresponding proportions when constructing it.
Proceeding from this, we believe that the essence of the phenomenon of harmony (consonance) is in the synchronous state of rest (energy is equal to zero) of both waves. On the graphs, this state of rest is displayed in the intersection of two wave functions on the abscissa (time) axis. And the degree of consonance of two wave functions is determined by the number of such intersections per unit of time (or length, under the condition of the same propagation speed): the more - the more consonant.
Application in computer graphics
A human is able to see colors with wavelengths in the range of 380 - 780 nm. Any four colors are linearly dependent, but there are an infinite number of combinations of three colors that are linearly independent (Grassmann's first law). The independence of colors, according to Grassmann, is that the color feeling caused by one of these three colors can not be obtained by mixing the other two colors in any proportions. It was noticed that it is most convenient to operate with red, green and blue color. Almost all modern monitors work on this principle.
In 1931 the International Lighting Congress (CIE) adopted a characteristic of the color properties of the average (standard) observer, based on the results obtained in 1926 — 1930 by Wright and Guild. The basis of this colorimetric standard is the following colors: 700 nm. (red), 546.1 nm (green) and 435.8 nm. (blue) (RGB system). The received characteristic contains the relationship between the resulting wavelength of the mixture and the amount of red, green, and blue colors in a given mixture.
Later, for comfort calculations, the International Lighting Congress introduced the abstract system CIE XYZ, based on unreal colors. This coordinate system is very comfort for the transition from one system to another. Also, the wavelengths of visible light and the corresponding coordinates of the CIE XYZ mixture were calculated, based on the results obtained for the RGB system.
To reproduce the same color feelings on different output devices (monitor or printer), each such device has its own color profile, which contains its relationship with the abstract CIE XYZ system. In other words, the color profile is used for the possibility of switching between different color systems (sRGB, AdobeRGB, ...). The most common color space is the sRGB system.
On the site the construction of the following consonant intervals is done:
- quint (3/2) symbolized 3/2↑ and 3/2↓- quart (4/3) symbolized 4/3↑ and 4/3↓
Three systems are used for construction - sRGB (white point D65), CIE XYZ and HSL, as well as tables containing wavelengths of visible light - CIE 1931 2-deg (XYZ CMFs).
For spectral colors (on the main page of the site) we build consonant intervals that do not go beyond the visible spectrum. A proportional increase or decrease of the relative brightness and saturation of the color using the HSL system is also performed.
Conclusions
Above we described and justified from a physical point of view the wave method of constructing the color palette, developed by us. Was described our understanding of the essence of the phenomenon of harmony. This method can be widely used in various design industries.