**NCS-Farbmodell (Natural Color System, 1979)**

The Natural Color System (NCS) is a color system that originated from the Hering-Johansson theory and was realized in the form of a color atlas by Hesselgren in 1953. Subsequently, in 1972, Hård, Sivik, and Tonnquist further developed the NCS, which became a Swedish standard in 1979.

The foundational concept of the NCS revolves around Hering’s idea of six elementary color perceptions: white (W), black (S), yellow (Y), red (R), blue (B), and green (G), with all other color perceptions having varying degrees of relation to these six. In the NCS, each color is defined by its similarity to these six elementary colors [4].

Notably, a color cannot be similar to more than two hues simultaneously. For instance, yellow and blue, as well as red and green, are mutually exclusive. The NCS chromaticness (c) is determined by the sum of color variables, while its hue (F) is determined by their ratio.

Colors in the NCS are denoted as sc-F, where s represents blackness, c represents chromaticness (linked to saturation), and F represents the hue of the color. The s and c values, both comprising two digits, are written without space and are separated from F by a hyphen. For example, in the notation 2040-G40Y, the hue is intermediary between green (G) and yellow (Y) in a ratio of 40 to 60.

The geometric representation of the NCS is a symmetric double cone with white and black at the vertices. The other four primary hues are positioned on the circle of full colors, forming corners of a square that touches this circle (refer to Figs. 4, 5, and 6). This geometric configuration mirrors that of the Ostwald system.

## Coloroid System

The Coloroid System, developed at Budapest Polytechnical University by Nemcsics and first published in 1975, is a color system that focuses on surface colors illuminated by daylight and perceived by individuals with normal color vision. It is built upon harmonic color differences that aim to approximate aesthetic uniformity. Recognized as a Hungarian standard since 2002, Coloroid has semipolar coordinates representing color points in a linear circular cylinder. These coordinates include the angular coordinate denoting hue (A), radial coordinate representing saturation (T), and vertical axial coordinate indicating luminosity (V).

In the Coloroid system, absolute white (W) and absolute black (S) are positioned at the upper and lower limits of the color space, respectively. White corresponds to the color of a surface illuminated by CIE D65 beam distribution, while black represents a surface perfectly absorbing light. Coloroid limit colors, forming a closed curve within the color space, are the most saturated colors on the Coloroid cylinder. The system also includes 48 Coloroid basic colors, characterized by integer numbers and evenly distributed on the CIE 1931 diagram.

Coloroid color planes are defined by the achromatic axis, with each plane having the same hue and dominant wavelength. Delimited by the neutral axis and Coloroid delimiting curves, these planes determine the shape of surfaces for each hue. Coloroid basic hues, corresponding to basic colors, are organized into 48 sections. Saturation (T), lightness (V), and hue (A) values define the color in the Coloroid system, with notation expressed as hue–saturation–lightness (A–T–V), such as 13-22-56.

Notably, Coloroid saturation quantifies a surface color’s saturation, measured on a scale close to aesthetic uniformity. Lightness denotes the distance from absolute black on a graduated scale, while hue indicates the color’s position within 48 sections based on dominant wavelength. The system’s geometric representation is a regular symmetric double cone, providing a comprehensive framework for defining and categorizing surface colors.

## Küppers’ Atlas and Rhombohedric Color System

The German engineer Harald Küppers has introduced an atlas designed specifically for the graphic arts and printing industry, encompassing more than 5,500 nuances. The color samples in this atlas are generated through the four-color printing technique, blending transparent dyes—yellow, magenta, cyan, and black—alongside the white background of the paper.

The gradations of these mixtures are quantified in percentages, directly corresponding to the proportion of surface covered by each dye. This notation serves not only to distinguish different nuances but also functions as a formula for color reproduction. The variations are denoted by 10% differences between individual samples and between consecutive color charts.

The published color charts are categorized into five series, with three being characterized as achromatic mixtures due to the inclusion of black, and the remaining two designated as chromatic mixtures with exclusive interventions of yellow, magenta, and cyan. In the initial three series, black is incrementally added to a mixture of two chromatic dyes, maintained at a consistent 10% variation throughout the entire series and from one chart to another. In the fourth series, yellow is successively introduced to a fixed mixture of two chromatic dyes (magenta and cyan). Series 1–4 consist of 11 charts, representing 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 99% of the dye added to the fixed binary mixture. The fifth series includes two additional charts: one featuring yellow-cyan mixtures and 99% magenta, and the other with yellow-magenta mixtures and 99% cyan.

Küppers also represents his system in a three-dimensional space, visualized either as a cube or with a rhombohedric shape, comprising an upper tetrahedron, a central octahedron, and a lower tetrahedron. In the rhombohedric model, white is positioned at the upper vertex of the upper tetrahedron, housing the three subtractive primaries—yellow, magenta, and cyan—in its base. This base also serves as one of the faces of the central octahedron. The lower triangular face of the octahedron features the three colors resulting from the mixture of subtractive primaries in pairs: green (yellow with cyan), red (yellow with magenta), and blue (cyan with magenta). This face is, in turn, shared with the lower tetrahedron, where black is situated at the lower vertex.

Sources: Nemcsics, A. & Caivano, J. L. (2015). Color order systems. In *Springer eBooks* (S. 1–16). https://doi.org/10.1007/978-3-642-27851-8_232-7