网络波动
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).
在生活中，我们经常面临选择正确颜色的挑战。 当我们需要选择适合彼此的衣服，适合衣服的鞋子，为儿童房选择不同的壁纸，化妆，为我们的网站选择颜色等等时，就会发生这种情况。 选择几种相互组合的颜色的过程称为调色板(色域)的构造。
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 and, usually, having the same brightness. Harmonious perception of which is not sufficiently substantiated from the physical point of view.
在色彩学中，有几种方法用于基于色环中彼此之间的颜色排列(通常具有相同的亮度)构造调色板(伽玛)。 从物理角度来看，对其的和谐感知还不能充分证实。
基于颜色和声波之间的关系，以及音乐理论中的和声(和声)概念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. Below is a more detailed description of the method.，构建调色板的波动方法 。 下面是该方法的更详细说明。
This site allows you to choose the most harmonious combination of colors for your site, clothing, interior, etc.
该站点使您可以为站点，衣服，室内装饰等选择最和谐的颜色组合。
The corresponding article was published on the site
相应的文章已在网站arxiv.org — arxiv.org上发布— https://arxiv.org/abs/1709.04752. Results are available on https://arxiv.org/abs/1709.04752 。 结果可在our site — 我们的网站 — wavepalette.com.wavepalette.com上获得 。
建立调色板的波浪方法 (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.
在音乐理论中，有辅音间隔的概念。 谐音称为间隔，听起来更柔和和谐。 共分为三组：非常完美的(完美的一致，八度)，完美的(完美的五重奏，完美的四重奏)和不完美的(大三分，小三分，六分)。 还有一个辅音和弦的概念-一个仅包含辅音间隔的大或小三重音。
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.
听觉上，谐音和不谐音之间差异的本质是用规则重复的振动群的不同周期长度表示的。 谐音和不谐音之间区别的标准是关系的简单性或复杂性：关系越简单，声调就越高，困难越不和谐。 数值比例可以用两种方式表示：通过弦的长度之比或通过振动数之比。 换句话说，两个音符的谐和度由每单位时间声压对时间的依赖性的相应谐波函数的周期的重合次数确定。
For example, notes C and G (perfect fifth) have the lengths of sound waves differing 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.
例如，音符C和G(完美的第五个)的声波长度相差1.5倍。 当音符C的声压函数发生两次振荡时，音符的声压随时间变化的函数图在横坐标轴上相交(声压等于零)，并且音符G的函数为三个(图1)。 在图1上，此刻用垂直线标记。
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).
如果我们想象声压在固定时间(靠近声源)在空间中的传播，那么我们将得到相同的数字(图2)。
The notes С and E (the big third) have lengths of sound waves differing 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.
音符С和E(占三分之一)的声波长度相差5/4倍。 当音符C的声压函数产生4次振动，而音符C的E函数产生5次振动时，它们的图在横坐标轴上相交。这就是为什么完美的五分音要比大的三分音调更谐和的原因。
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.
颜色像声音一样，也是波(波粒二象性)。 在构造颜色的辅音间隔的情况下，我们不受一小部分音符的限制，但受可见光波长限制的限制，就像声音受可听声音的波长限制的限制一样。
Consider building of color palette for spectral and non-spectral colors.
考虑构建用于光谱和非光谱颜色的调色板。
光谱色 (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.
光谱色是具有特定波长的颜色。 要构建调色板，首先让我们采用最辅音的颜色-它是一种波长相差1.5倍但不超出可见光谱的颜色。 此外，类似地，我们将减少辅音间隔，直到我们在所需的调色板中达到所需的颜色数量为止。
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.
以波长为450 nm的蓝色为例。 波长小于1.5倍的颜色超出了可见辐射范围。 波长大于1.5倍(675纳米)的颜色是红色。 波长大3/4倍(600纳米)的颜色是橙色。 结果，我们得到了以下调色板：主要颜色是蓝色，最合适的颜色是红色，不太适合蓝色的颜色是橙色(图3)。 通过操作频率而不是波长可以获得相同的结果。
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.
音乐中也有音调的概念。 音符的组合不仅可以和谐地听起来，而且还可以带有阴影-音调(爱奥尼亚语，多利安语，phrygian，lydian等)。 在构建调色板时，可以通过使用相应的比例将类似的感觉转移到调色板上。
非光谱色 (Non-spectral colors)
Nonspectral colors include colors that are not contained in the spectrum and consist of several spectral colors. Proceeding from the Grassmann additivity law it follows that in the case of selecting a color palette for non-spectral colors the same operations should be performed on its constituent colors preserving the proportions and considering the wavelength boundaries of the visible spectrum.
非光谱颜色包括光谱中不包含的颜色，并且由几种光谱颜色组成。 从格拉斯曼加和定律出发，可以得出以下结论：在为非光谱色选择调色板的情况下，应对其组成色执行相同的操作，以保留比例并考虑可见光谱的波长边界。
Let us consider a more recent phenomenon of consonance between two non-spectral colors. The musical sound consists of elementary tones, since along with the oscillation of the sound source itself as a whole, its parts also oscillate. Vibrations of the parts of the vibrating body give rise to weak prisms — overtones absorbed in the basic tone. The scale of simple tones of the corresponding amplitudes forming a complex sound is called the frequency spectrum. All elementary tones that enter into a complex sound are called harmonics. The degree of consonance of the interval is determined by the number of coinciding harmonics of the spectra of both notes: the greater number of coinciding harmonics — the more consonant interval.
让我们考虑一下两种非光谱颜色之间的更和谐的现象。 音乐声由基本音组成，因为随着声源本身整体的振荡，其各部分也会振荡。 振动体各部分的振动会导致棱镜变弱，即基音中吸收的泛音。 形成复杂声音的相应振幅的简单音调的标度称为频谱。 进入复杂声音的所有基本音调都称为谐波。 间隔的谐音程度由两个音符频谱的重合谐波数确定：重合谐波数越大—辅音间隔越大。
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 (fig. 4). 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. This concept of degree of consonance extends also to non-spectral colors, since they are also wave functions.
从这一点出发，我们认为和谐(和声)现象的本质在于两个波的静止同步状态(能量等于零)。 在图表上，这种静止状态显示在横坐标(时间)轴上的两个波动函数的交点上(图4)。 两个波函数的谐音程度由每单位时间(或在相同传播速度条件下的长度)这种交点的数量确定：越大—声调越高。 共鸣度的概念也扩展到非光谱色，因为它们也是波函数。
在计算机图形学中的应用 (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.
人类能够看到波长在380至780 nm范围内的颜色。 任何四种颜色都是线性相关的，但是线性独立的三种颜色的组合是无限的(格拉斯曼第一定律)。 根据格拉斯曼的说法，颜色的独立性在于，无法通过以任意比例混合其他两种颜色来获得由这三种颜色中的一种引起的颜色感觉。 注意到用红色，绿色和蓝色进行操作是最方便的。 几乎所有现代显示器都遵循此原则。
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.
1931年，国际照明大会(CIE)根据Wright和Guild在1926年至1930年获得的结果，采用了平均(标准)观察者的色彩特性。 该比色标准的基础是以下颜色：700 nm。 (红色)，546.1 nm(绿色)和435.8 nm。 (蓝色)(RGB系统)。 所接收的特性包含混合物的所得波长与给定混合物中红色，绿色和蓝色的数量之间的关系。
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.
后来，为了进行舒适度计算，国际照明大会引入了基于虚幻色彩的抽象系统CIE XYZ。 该坐标系非常适合从一个系统过渡到另一个系统。 而且，基于从RGB系统获得的结果，计算可见光的波长和CIE XYZ混合物的相应坐标。
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.
为了在不同的输出设备(显示器或打印机)上再现相同的色彩感觉，每个此类设备都有其自己的颜色配置文件，其中包含与抽象CIE XYZ系统的关系。 换句话说，颜色配置文件用于在不同颜色系统(sRGB，AdobeRGB等)之间进行切换的可能性。 最常见的色彩空间是sRGB系统。
On the site the construction of the following consonant intervals is done:
在站点上，完成以下辅音间隔的构建：
- quint (3/2) symbolized 3/2↑ and 3/2↓ 五位(3/2)代表3/2↑和3/2↓
- quart (4/3) symbolized 4/3↑ and 4/3↓ 夸脱(4/3)表示4/3↑和4/3↓
- small third (6/5) symbolized 6/5↑ and 6/5↓ 小三(6/5)代表6/5↑和6/5↓
Three systems are used for construction — sRGB (white point D65), CIE XYZ and xyY, as well as tables containing wavelengths of visible light — CIE 1931 2-deg (XYZ CMFs).
sRGB(白点D65)，CIE XYZ和xyY以及包含可见光波长的表格(CIE 1931 2度(XYZ CMF))用于构建三个系统。
For
对于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 of the color using the xyY system is also performed.光谱颜色 (在站点的主页上)，我们建立辅音间隔，该间隔不会超出可见光谱。 还使用xyY系统按比例增加或减少了颜色的相对亮度。
For
对于sRGB colors (on the sRGB page) we construct consonant intervals that do not go beyond the visible spectrum for each (red, green, and blue) color separately. If the interval goes beyond the visible spectrum, we leave the color as is. Further, all three colors obtained are summed separately by each RGB component (red, green and blue) according to relative brightness using the xyY system.sRGB颜色 (在sRGB页面上)，我们构造的辅音间隔不会超出每种(红色，绿色和蓝色)颜色的可见光谱。 如果间隔超出可见光谱，我们将颜色保持不变。 此外，使用xyY系统，根据相对亮度，将每个RGB分量(红色，绿色和蓝色)分别对获得的所有三种颜色求和。
网站 (The site)
The site presents two different implementations of the wave method — spectral (on the main page) and sRGB (on the RGB page).
该站点介绍了wave方法的两种不同实现方式-光谱(在主页上)和sRGB(在RGB页上)。 Spectral implementation reflects the essence of the wave method. Here you can choose the most harmonious palette for spectral colors. The colors coming first are the most suitable. Next to each color are its wavelength, rgb and hex codes.频谱实现反映了波动法的本质。 在这里，您可以为光谱颜色选择最和谐的调色板。 首先出现的颜色是最合适的。 每种颜色的旁边是其波长，rgb和十六进制代码。 sRGB implementation allows you to build a palette for all SRGB colors (more than 16 million colors), and not just spectral ones. But, since the wave method is applied in this case to each of the three colors (red, green, blue) individually, not all colors are harmonious and you will have to make a choice manually. This method allows you to get more interesting combinations of colors, but requires a self-dependent choice. Next to each color are its rgb and hex codes.sRGB实现使您可以为所有SRGB颜色(超过1600万种颜色)构建调色板，而不仅仅是光谱颜色。 但是，由于在这种情况下波动方法分别应用于三种颜色(红色，绿色，蓝色)中的每一种，因此并非所有颜色都是和谐的，因此您必须手动进行选择。 这种方法可以使您获得更多有趣的颜色组合，但是需要一种独立的选择。 每种颜色的旁边是其rgb和十六进制代码。
The Refresh button builds a color scheme for a random color.刷新按钮可为随机颜色建立配色方案。 Share button opens a link to the resulting palette, which you can share with friends.“共享”按钮将打开指向结果调色板的链接，您可以将其与朋友共享。
The
光谱实现中的RGB button in the spectral implementation switches to the sRGB implementation with the same base color. The color palette in the sRGB implementation will differ from the spectral one due to the application of the wave method to each of the colors separately.RGB按钮切换到具有相同基色的sRGB实现。 由于将wave方法分别应用于每种颜色，因此sRGB实现中的调色板将不同于光谱的调色板。
The
付费版本和免费版本的Mobile Application in the paid and free versions differs only in the presence of advertising.移动应用程序仅在存在广告的情况下有所不同。
结论 (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.
上面我们从物理角度描述并证明了由我们开发的构造调色板的波动方法。 被描述了我们对和谐现象本质的理解。 该方法可广泛用于各种设计行业。
网络波动