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### Figures (11)

Fig. 1

I.C.I. chromaticity diagram showing change in position of the point ω1=ω3=0 for I.C.I. Illuminant C adaptation as a function of α=Y/Y0.

Fig. 2

Simplified nomographs for making the transformation from X, Y, Z, to ω1, ω2, ω3, and vice versa. Find X on scale A, Y on scale D, and with a straightedge read ω1 on scale E. Find Z on scale A, Y on scale C, and read ω3 on scale F. Find Y on scale A and read ω2 on scale B.

Fig. 3

Comparison of Eqs. (10) [solid line] and (13) [dotted line], showing deviations from the recommended Munsell value in units of one value step when the recommended Y for Munsell values from 1 to 10 is used in the two equations.

Fig. 4

Transformation of constant hue lines in the ω1ω3 plane to the I.C.I. chromaticity diagram. Points were calculated for Y=10.

Fig. 5

The Munsell 100 hue circle plotted in the ω1ω3 plane.

Fig. 6

Colors of the Munsell 100 hue circle, showing the correlation between the Munsell hue number and the hue angle θ from Fig. 5.

Fig. 7

The Munsell colors of value 5.

Fig. 8

The recommended positions of the Munsell colors of value 5.

Fig. 9

Munsell colors of hue 5R and the recommended positions plotted in a constant hue plane.

Fig. 10

Munsell colors of hue 5B and the recommended positions.

Fig. 11

Munsell colors of hue 5GY and the recommended positions.

### Equations (20)

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$ω 1 = 2 ( p 1 - 0.95 p 2 ) 0.168 ( 1.63 + p 2 ) 1 2 - 0.119 , ω 3 = 2.27 ( p 3 - 1.10 p 2 ) 1.2 0.628 ( 1.80 + p 2 ) 1 2 - 0.521 .$
$p 1 = X - X 0 Y 0 = Y ( x / y ) - Y 0 ( x 0 / y 0 ) Y 0 , p 2 = Y - Y 0 Y 0 , p 3 = Z - Z 0 Z 0 = Y ( z / y ) - Y 0 ( z 0 / y 0 ) Y 0 .$
$p 1 - 0.95 p 2 = 0 p 2 - 1.10 p 2 = 0.$
$x y = [ x 0 y 0 + 0.95 ( α - 1 ) ] 1 α , z y = [ z 0 y 0 + 1.10 ( α - 1 ) ] 1 α .$
$x = x 0 + 0.95 y 0 ( α - 1 ) 1 + 3.05 y 0 ( α - 1 ) , y = α y 0 1 + 3.05 y 0 ( α - 1 ) , z = z 0 + 1.1 y 0 ( α - 1 ) 1 + 3.05 y 0 ( α - 1 ) ,$
$x 0 = 0.95 y 0 and z 0 = 1.1 y 0 .$
$x 0 = 0.3115 , y 0 = 0.3279 , z 0 = 0.3606.$
$ω 1 = X - 0.95 Y 0.084 Y 0 ( 0.63 + Y / Y 0 ) 1 2 - 0.0595 Y 0 , ω 3 = ( Z - 1.1 Y ) 1.2 0.2768 Y 0 1.2 ( 0.8 + Y / Y 0 ) 1 2 - 0.2296 Y 0 1.2 .$
$ω 1 = X - 0.95 Y 0.3757 ( 12.6 + Y ) 1 2 - 1.19 , ω 3 = ( Z - 1.1 Y ) 1.2 2.253 ( 16 + Y ) 1 2 - 8.36 .$
$Value = 5.0 ( p 2 + 1 ) 0.426 ,$
$ω 2 = 41.7 ( p 2 + 1 ) 0.426 ,$
$ω 2 = 11.64 Y 0.426$
$Value = 6.58 ( p 2 + 1 ) 0.343 - 1.52 ,$
$Value = 2.357 Y 0.343 - 1.52 ,$
$ω 2 = 19.62 Y 0.343 - 12.5.$
$( 1 - x - 2.1 y ) 1.2 x - 0.95 y = β F ( Y ) ( y Y ) 0.2 ,$
$F ( Y ) = 2.253 ( 16 + Y ) 1 2 - 8.36 0.3757 ( 12.6 + Y ) 1 2 - 1.19 .$
$1 - x - 2.1 y = 0 ,$
$x - 0.95 y = 0 ,$
$ω 3 / ω 1 = tan - 1 θ , ω 1 2 + ω 3 2 = ρ 2 .$