I. H. Godlove, "Improved Color-Difference Formula, with Applications to the Perceptibility and Acceptability of Fadings," J. Opt. Soc. Am. 41, 760-772 (1951)
A simple formula for computing fadings or other color differences from Munsell notations has been derived from one simple assumption. Experimental data for the relative visual magnitudes of the Munsell “value” and chroma steps have been incorporated into the formula. It has been tested with several sets of experimental data and found valid even for some large differences. A table of constants facilitates quick application. The formula has been applied to the computation of the color differences of a great many dyes changing in concentration only, for example, from 2 percent to 0.5 percent. This change is known in the textile industry as “on-tone” fading. The user of dyed fabrics dislikes changes of hue more than equally perceptible changes in saturation or lightness, so that acceptability and perceptibility are not identical; hence, the importance of on-tone fading. For the 2–0.5 percent case, hue change as a function of hue of the stronger dyeing gave a well-defined curve. Maximum hue changes occur at 2R and 8YR, with zero change between. The total change is lowest for yellows (explaining why dyers find it most difficult to judge their fastnesses) and highest in the blues. Other published formulas yield the reverse of this fact. The question whether fastness is in large part a matter of perceptibility of changes was examined. The graphs of perceptibility and of average light-fastness ratings, both as a function of hue, show little resemblance, indicating that the fastness ratings are not primarily due to mere concentration change.
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* “On-tone fading” (concentration change only) 2 to 0.5 percent. In each pair, the upper figures refer to the 0.5 percent dyeing, the lower figures to the 2 percent dyeing or to the pair together. In column 1, C refers to cotton, W refers to wool, and M to a mixture.
Ser. No.
H
C
V
ΔH
ΔC
ΔV
0.1C2ΔH
∂H
5∂H
I4
J4
In
C1022
2.0GY
8.1
9.3
C1023
1.0GY
8.7
9.2
+1.0
0.6
0.1
+0.87
0.28
1.40
0.89
1.39
5.9
W587
7.5 Y
10.2
8.3
W588
6.0Y
12.7
8.1
+1.5
2.5
0.2
+1.91
1.14
5.70
2.83
3.55
16.3
C1020
9.0Y
9.5
8.7
C1021
5.8Y
10.4
8.0
+3.2
0.9
0.7
+3.33
3.97
19.85
3.55
5.34
20.2
C1024
7.0Y
9.3
8.5
C1025
4.8Y
10.7
7.9
+2.2
1.4
0.6
+2.35
1.28
6.40
3.00
3.76
17.2
W553
5.0Y
8.3
7.9
W554
3.6Y
11.0
7.3
+1.4
2.7
0.6
+1.54
2.25
0.45
3.68
3.91
17.9
W591
5.0Y
12.6
8.1
W592
3.0Y
14.9
7.7
+2.0
2.3
0.4
+2.98
0.99
4.95
2.97
3.58
19.2
W40
4.5Y
8.5
5.6
W41
2.8Y
10.6
6.7
+1.7
2.1
0.9
+1.80
0.43
2.15
4.22
4.42
18.9
W561
3.0Y
9.2
8.0
W562
1.1Y
12.5
7.5
+1.9
3.3
0.5
+2.37
1.63
8.15
4.06
4.80
22.4
C1038
2.5Y
11.5
8.3
C1039
9.7YR
13.5
7.8
+2.8
2.0
0.5
+3.78
4.78
23.90
3.58
5.65
24.1
C415
7.9YR
10.1
7.5
C416
5.1YR
12.5
6.5
+2.8
2.4
1.0
+3.50
3.89
19.45
5.06
6.42
30.2
W517
2.5YR
14.9
6.4
W518
0.3YR
16.2
5.6
+2.2
1.3
0.8
+3.57
4.59
22.95
4.06
5.91
23.0
W593
7.1R
13.9
5.6
W594
7.6R
15.0
4.5
−0.5
1.1
1.1
−0.75
0.21
1.05
4.56
4.65
12.9
C701
7.5R
14.2
4.9
C702
7.2R
14.5
3.9
+0.3
0.3
1.0
+0.44
0.41
0.082
4.02
4.06
8.6
W565
1.0R
11.0
3.2
W566
5.1R
8.6
2.3
−4.1
2.4
0.9
−3.52
6.24
31.20
5.00
7.07
26.7
C1086
3.5R
12.7
5.3
C1087
5.0R
11.0
4.4
−1.5
1.7
0.9
−1.65
1.23
6.15
4.13
4.69
17.8
W595
9.5RP
11.7
5.8
W596
1.6R
12.7
4.5
−2.1
1.0
1.3
−2.56
2.58
12.90
5.54
6.40
21.5
W575
5.2RP
11.9
4.6
W576
8.3RP
11.8
3.3
−3.1
0.1
1.3
−3.66
5.31
26.55
5.69
7.32
22.7
M464
1.6RP
5.1
3.2
M449
2.6RP
2.8
1.8
−1.0
2.3
1.4
−0.28
0.057
0.28
6.06
6.07
16.4
W32
6.5P
5.0
4.0
W33
8.0P
5.3
2.3
−1.5
0.3
1.7
−0.80
0.23
1.15
6.82
6.89
14.3
W630
8.3P
8.1
5.4
W631
7.6P
10.5
3.9
+0.7
2.4
1.5
+0.74
0.16
0.80
6.48
6.53
19.1
W709
2.5P
6.3
3.2
W710
2.5P
4.5
1.8
0.0
1.8
1.4
0.00
0.00
0.00
5.88
5.88
13.8
W606
9.4PB
11.3
3.3
W607
9.7PB
11.7
2.1
−0.3
0.4
1.2
−0.35
0.05
0.25
4.82
4.84
9.8
W699
7.0PB
8.9
3.5
W700
7.7PB
8.0
2.0
−0.7
0.9
1.5
−0.56
0.14
0.70
6.08
6.13
13.9
W608
5.3PB
9.6
4.3
W609
7.2PB
11.4
2.7
−1.9
1.8
1.6
−2.16
1.55
7.75
6.77
7.21
23.7
W531
5.0PB
8.3
4.2
W532
6.3PB
8.9
2.5
−1.3
0.6
1.7
−1.16
0.49
2.45
6.86
7.00
16.6
W505
4.0PB
8.7
4.3
W506
5.9PB
9.5
2.6
−1.9
0.8
1.7
−1.80
1.17
5.85
6.93
7.26
19.8
W507
2.7PB
7.1
4.8
W508
5.3PB
8.5
3.1
−2.6
1.4
1.7
−2.21
1.60
8.00
7.06
7.50
23.2
W711
9.2B
6.7
4.5
W712
2.0PB
6.0
2.7
−2.8
0.7
1.8
−1.68
1.24
6.20
7.32
7.65
19.6
W346
5.0B
8.1
4.7
W112
7.9B
8.9
3.3
−2.9
0.8
1.4
−2.58
2.38
11.90
5.86
6.63
21.1
W567
1.5B
5.9
4.3
W568
1.5B
4.6
2.5
0.0
1.3
1.8
0.00
0.00
0.00
7.32
7.32
14.7
W569
7.9BG
8.7
4.7
W570
8.0BG
8.0
3.2
−0.1
0.7
1.5
−0.08
0.00
0.00
6.04
6.04
11.4
M778
7.8BG
6.4
4.5
M648
6.8BG
5.8
2.9
+1.0
0.6
1.6
+0.58
0.75
0.15
6.44
6.48
13.7
W571
3.3BG
8.2
4.8
W572
2.5BG
8.1
3.2
+0.8
0.1
1.6
+0.65
0.17
0.85
6.42
6.47
12.5
W675
6.5G
8.0
6.0
W676
5.8G
9.0
4.5
+0.7
1.0
1.5
+0.63
0.14
0.70
6.10
6.14
14.5
Table I is a condensation, merely giving examples taken from a very much longer Table I scheduled to appear almost simultaneously in the American Dyestuff Reporter. Index of Dyestuffs in Table I.—All of 2 and 0.5 percent concentration (relative to weight of fiber), except in the case of mixtures, where the percentages making up the total of 2 percent in the heavier dyeing, are given.
Table II
Values of ϕ(H)=1−cos3.6°ΔH.
ΔH
ϕ(H)
0.0
0.0000
0.1
0.0000
0.2
0.0001
0.3
0.0002
0.4
0.0003
0.5
0.0005
0.6
0.0007
0.7
0.0010
0.8
0.0013
0.9
0.0016
1.0
0.0020
1.1
0.0024
1.2
0.0028
1.3
0.0033
1.4
0.0039
1.5
0.0044
1.6
0.0050
1.7
0.0057
1.8
0.0064
1.9
0.0071
2.0
0.0079
2.1
0.0087
2.2
0.0095
2.3
0.0104
2.4
0.0113
2.5
0.0123
2.6
0.0133
2.7
0.0144
2.8
0.0154
2.9
0.0165
3.0
0.0177
3.1
0.0189
3.2
0.0201
3.3
0.0214
3.4
0.0227
3.5
0.0241
3.6
0.0255
3.7
0.0269
3.8
0.0284
3.9
0.0299
4.0
0.0314
4.1
0.0330
4.2
0.0346
4.3
0.0363
4.4
0.0380
4.5
0.0397
4.6
0.0415
4.7
0.0433
4.8
0.0451
4.9
0.0470
5.0
0.0489
5.1
0.0509
5.2
0.0529
5.3
0.0549
5.4
0.0570
5.5
0.0591
5.6
0.0613
5.7
0.0634
5.8
0.0657
5.9
0.0679
6.0
0.0702
6.1
0.0726
6.2
0.0749
6.3
0.0773
6.4
0.0798
6.5
0.0822
6.6
0.0849
6.7
0.0873
6.8
0.0899
6.9
0.0925
7.0
0.0952
7.1
0.0979
7.2
0.1006
7.3
0.1034
7.4
0.1062
7.5
0.1090
7.6
0.1119
7.7
0.1148
7.8
0.1177
7.9
0.1207
8.0
0.1237
8.1
0.1267
8.2
0.1298
8.3
0.1329
8.4
0.1361
8.5
0.1393
8.6
0.1425
8.7
0.1457
8.8
0.1490
8.9
0.1523
9.0
0.1557
9.1
0.1591
9.2
0.1625
9.3
0.1659
9.4
0.1694
9.5
0.1729
9.6
0.1765
9.7
0.1801
9.8
0.1837
9.9
0.1873
10.0
0.1910
10.1
0.1947
10.2
0.1984
10.3
0.2022
10.4
0.2060
10.5
0.2098
10.6
0.2137
10.7
0.2176
10.8
0.2216
10.9
0.2255
11.0
0.2295
11.1
0.2335
11.2
0.2376
11.3
0.2416
11.4
0.2457
11.5
0.2499
11.6
0.2541
11.7
0.2583
11.8
0.2625
11.9
0.2667
12.0
0.2710
12.1
0.2753
12.2
0.2797
12.3
0.2841
12.4
0.2885
12.5
0.2929
12.6
0.2974
12.7
0.3018
12.8
0.3064
12.9
0.3109
13.0
0.3155
13.1
0.3201
13.2
0.3247
13.3
0.3293
13.4
0.3340
13.5
0.3387
13.6
0.3434
13.7
0.3482
13.8
0.3529
13.9
0.3577
14.0
0.3626
14.1
0.3674
14.2
0.3723
14.3
0.3772
14.4
0.3821
14.5
0.3871
14.6
0.3921
14.7
0.3971
14.8
0.4021
14.9
0.4071
15.0
0.4122
15.1
0.4173
15.2
0.4224
15.3
0.4276
15.4
0.4327
15.5
0.4379
15.6
0.4431
15.7
0.4484
15.8
0.4536
15.9
0.4589
16.0
0.4642
Table III(a)
Munsell “5/5” colors.
1905–10 set adjusted to Y=0.1977
1926–29 set from Munsell book of color renotations
Average
x
y
x
y
x
y
5 R 5/5
0.41004
0.32766
0.3909
0.3229
0.4405
0.3253
5Y5/5
0.41409
0.42315
0.41085
0.4246
0.4125
0.4239
5 G 5/5
0.2899
0.39283
0.27655
0.3744
0.2832
0.3836
5 B 5/5
0.24344
0.28127
0.2354
0.2790
0.2394
0.2801
5 P 5/5
0.29475
0.26021
0.2959
0.2593
0.2953
0.2598
N (average)
0.3262
0.3345
Nominal notation
Munsell renotations
Hue number
5 Y 5/5
5.7 R 5/5.4
5.7
5 Y 5/5
4.7 Y 5/5.1
24.7
5 G 5/5
3.7 G 5/5.0
43.7
5 B 5/5
5.4 B 5/4.7
65.4
5 P 5/5
4.9 P 5/4.9
84.9
Neutral (center)
5.0 Y 5/0.7
25.0
Table III(b)
Color-differences between Munsell “5/5” colors and neutral gray and between successive “5/5” colors.
5/5 color to neutral gray
5/5 color to next succeeding 5/5 color in the color circle
Visual estimates determining magnitude of “n” in Eq. (13). Here the total perceptual difference, made up chiefly of chroma difference (columns “b” in Table VI(b), was taken as the unit color difference; then the relative magnitude of the other total difference, consisting largely of “value” difference (columns “a”), was estimated. Hue differences are small or nil.
Set of colors Observers
Visual estimates of ratios of differences a/b by following observers
IHG
WW
EN
STG
JB
DEM
FNH
TFG
EMW
RW
Average
1
4
2
1.5
3
3
2
4
2
3
3
2.75
2
3
1
2
1
2
1.5
1.5
2
2
2
1.80
3
2
1
1
2
1.5
2
2
1
1.5
1
1.50
4
2.5
1.5
2.5
3
2
3
2
2
2.5
2
2.30
5
1.5
1
1
1
3
1
0.5
1.5
1.5
2
1.40
6
1.5
1
1.5
1.5
3
2
2
2
2
1.5
1.80
7
2
2.5
2.5
4
6
5
3
3
2
2.5
3.25
8
6
4
4
10
10
6
10
5
6
7
6.80
9
1.5
1.5
2
2
3
2
3
1
1
1.5
1.85
10
2.5
3
3
7
6
3
5
3
4
3
3.95
11
4
3.5
3
8
6
5
5
4
3
4
4.55
12
8
5
5
6
6
10
10
6
5
5
6.60
13
5
5
3
3
4
8
3
3
4
3
4.10
14
3
3
5
2.5
3.5
6
3
3
3
2.5
3.45
15
1.5
4
1.75
2.5
2
3
1
1
1.5
1.5
1.98
16
1.5
3
2
1.5
2.5
4
2
2.5
2
3
2.40
17
5
5
6
6
4
6
7
5
6
6
5.60
18
7
5.5
7
4
6
5
7
4
5
5
5.55
Table VI(b)
Ratio of magnitudes of “value” step and chroma step calculations of total difference in each pair by formula (Eqs. (12) and (13)).
Set No.
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
17
18
18
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
a
b
H1
15.5
15.5
25.0
26.0
35.0
35.0
46.0
45.0
55.0
55.0
65.0
65.0
75.0
75.0
73.5
73.5
85.0
85.0
94.5
95.0
94.5
94.5
0.0
0.0
10.5
10.0
30.0
30.0
52.0
51.0
61.0
60.0
69.5
69.5
89.5
89.5
V1
6.9
6.9
6.2
5.0
6.2
6.2
6.0
4.9
5.1
5.1
7.1
6.1
3.2
3.2
5.2
5.3
4.1
3.3
4.2
4.3
7.4
6.3
5.2
5.2
6.3
4.3
7.1
7.1
6.4
5.0
5.2
4.2
5.2
5.2
7.3
5.3
C1
10.1
10.1
7.2
6.0
6.7
6.7
7.4
8.2
6.4
6.4
4.7
6.4
5.6
5.6
8.6
8.6
10.1
11.2
9.4
10.7
4.9
8.5
8.6
10.3
6.5
7.3
9.3
9.3
4.5
7.0
6.5
5.7
6.3
6.3
6.0
10.5
H2
15.5
14.5
26.0
25.0
35.0
35.0
45.0
45.0
55.5
55.5
65.5
66.5
74.0
75.0
74.5
74.0
85.0
85.0
95.0
94.5
95.0
95.0
99.5
0.0
10.5
10.5
30.0
30.5
50.5
50.5
60.0
59.5
69.0
70.0
91.0
91.0
V2
5.1
7.0
5.0
5.0
5.1
6.2
4.9
4.9
4.2
5.2
6.1
6.2
2.3
3.1
3.4
5.4
3.3
3.2
3.2
4.2
6.3
6.3
3.1
5.2
4.2
4.2
5.3
7.0
5.1
5.1
4.2
4.1
3.3
5.2
5.2
5.2
C2
9.0
8.2
6.0
3.9
5.4
4.0
6.6
6.6
6.0
4.4
6.4
4.5
5.9
3.9
8.5
7.9
11.2
8.4
8.4
9.4
7.3
7.3
7.0
8.6
4.7
4.7
5.8
6.9
4.6
4.6
5.7
4.0
7.1
4.6
8.6
8.6
ΔH
0.0
1.0
1.0
1.0
0.0
0.0
1.0
0.0
0.5
0.5
0.5
1.0
1.0
0.0
1.0
0.5
0.0
0.0
0.5
0.5
0.5
0.5
0.5
0.0
0.0
0.5
0.0
0.5
1.5
0.5
1.0
0.5
0.5
0.5
1.5
0.5
ΔV
1.8
0.1
1.2
0.0
1.1
0.0
1.1
0.0
0.9
0.1
1.0
0.1
0.9
0.1
1.9
0.1
0.8
0.1
1.0
0.1
1.1
0.0
1.8
0.0
2.1
0.1
1.8
0.1
1.3
0.1
1.0
0.1
1.9
0.0
2.1
0.1
ΔC
1.1
1.9
1.2
2.1
1.3
2.7
0.8
1.6
0.4
2.0
1.7
1.9
0.3
1.7
0.1
0.7
1.1
2.8
1.0
1.3
2.4
1.2
1.6
1.7
1.8
2.6
3.5
2.4
0.1
2.4
0.8
1.7
0.8
1.7
2.6
1.9
I1
2.11
1.99
1.75
2.12
1.70
2.70
1.43
1.60
1.01
2.01
2.08
1.93
1.02
1.70
1.98
0.76
1.36
2.80
1.44
1.34
2.65
1.22
2.42
1.70
2.77
2.61
3.94
2.42
1.37
2.41
1.34
1.71
2.07
1.71
3.41
1.93
a/b
1.06
0.83
0.63
0.89
0.50
1.08
0.60
2.60
0.49
1.07
2.16
1.42
1.06
1.63
0.57
0.78
1.21
1.77
I2
3.77
2.00
2.72
2.12
2.56
2.70
2.39
1.60
1.86
2.02
2.71
1.94
3.84
0.78
a/b
1.88
1.28
0.95
1.49
0.92
1.40
4.96
I3
5.51
2.01
3.82
2.12
3.55
2.70
3.43
1.60
2.74
2.03
3.52
1.95
5.73
0.81
6.44
2.43
3.93
2.42
a/b
2.74
1.80
1.31
2.14
1.35
1.81
7.07
2.65
1.62
I4
4.59
2.70
4.50
1.60
3.63
2.05
4.40
1.97
5.02
1.22
8.59
2.64
8.01
2.45
5.13
2.44
4.10
1.75
7.65
1.71
a/b
1.70
2.81
1.77
2.23
4.10
3.26
3.27
2.10
2.34
4.47
I5
4.53
1.77
4.15
2.85
5.11
1.43
6.01
1.22
9.15
1.70
10.66
2.66
9.66
2.47
5.08
1.78
9.54
1.71
10.84
1.99
a/b
2.56
1.46
3.57
4.90
5.39
4.02
3.91
2.85
5.58
5.45
I6
5.42
1.80
4.93
2.87
6.09
1.47
10.92
1.70
12.74
2.68
12.88
2.02
a/b
3.01
1.72
4.14
6.43
4.76
6.39
I7
6.32
1.84
5.71
2.89
12.71
1.70
a/b
3.43
1.98
7.48
n
3.0
3.0
3.45
3.2
3.1
3.0
6.6
2.85
6.5
5.65
4.6
6.15
5.1
4.3
3.75
4.1
5.0
5.1
Av. n......4.36
Tables (8)
Table I
* “On-tone fading” (concentration change only) 2 to 0.5 percent. In each pair, the upper figures refer to the 0.5 percent dyeing, the lower figures to the 2 percent dyeing or to the pair together. In column 1, C refers to cotton, W refers to wool, and M to a mixture.
Ser. No.
H
C
V
ΔH
ΔC
ΔV
0.1C2ΔH
∂H
5∂H
I4
J4
In
C1022
2.0GY
8.1
9.3
C1023
1.0GY
8.7
9.2
+1.0
0.6
0.1
+0.87
0.28
1.40
0.89
1.39
5.9
W587
7.5 Y
10.2
8.3
W588
6.0Y
12.7
8.1
+1.5
2.5
0.2
+1.91
1.14
5.70
2.83
3.55
16.3
C1020
9.0Y
9.5
8.7
C1021
5.8Y
10.4
8.0
+3.2
0.9
0.7
+3.33
3.97
19.85
3.55
5.34
20.2
C1024
7.0Y
9.3
8.5
C1025
4.8Y
10.7
7.9
+2.2
1.4
0.6
+2.35
1.28
6.40
3.00
3.76
17.2
W553
5.0Y
8.3
7.9
W554
3.6Y
11.0
7.3
+1.4
2.7
0.6
+1.54
2.25
0.45
3.68
3.91
17.9
W591
5.0Y
12.6
8.1
W592
3.0Y
14.9
7.7
+2.0
2.3
0.4
+2.98
0.99
4.95
2.97
3.58
19.2
W40
4.5Y
8.5
5.6
W41
2.8Y
10.6
6.7
+1.7
2.1
0.9
+1.80
0.43
2.15
4.22
4.42
18.9
W561
3.0Y
9.2
8.0
W562
1.1Y
12.5
7.5
+1.9
3.3
0.5
+2.37
1.63
8.15
4.06
4.80
22.4
C1038
2.5Y
11.5
8.3
C1039
9.7YR
13.5
7.8
+2.8
2.0
0.5
+3.78
4.78
23.90
3.58
5.65
24.1
C415
7.9YR
10.1
7.5
C416
5.1YR
12.5
6.5
+2.8
2.4
1.0
+3.50
3.89
19.45
5.06
6.42
30.2
W517
2.5YR
14.9
6.4
W518
0.3YR
16.2
5.6
+2.2
1.3
0.8
+3.57
4.59
22.95
4.06
5.91
23.0
W593
7.1R
13.9
5.6
W594
7.6R
15.0
4.5
−0.5
1.1
1.1
−0.75
0.21
1.05
4.56
4.65
12.9
C701
7.5R
14.2
4.9
C702
7.2R
14.5
3.9
+0.3
0.3
1.0
+0.44
0.41
0.082
4.02
4.06
8.6
W565
1.0R
11.0
3.2
W566
5.1R
8.6
2.3
−4.1
2.4
0.9
−3.52
6.24
31.20
5.00
7.07
26.7
C1086
3.5R
12.7
5.3
C1087
5.0R
11.0
4.4
−1.5
1.7
0.9
−1.65
1.23
6.15
4.13
4.69
17.8
W595
9.5RP
11.7
5.8
W596
1.6R
12.7
4.5
−2.1
1.0
1.3
−2.56
2.58
12.90
5.54
6.40
21.5
W575
5.2RP
11.9
4.6
W576
8.3RP
11.8
3.3
−3.1
0.1
1.3
−3.66
5.31
26.55
5.69
7.32
22.7
M464
1.6RP
5.1
3.2
M449
2.6RP
2.8
1.8
−1.0
2.3
1.4
−0.28
0.057
0.28
6.06
6.07
16.4
W32
6.5P
5.0
4.0
W33
8.0P
5.3
2.3
−1.5
0.3
1.7
−0.80
0.23
1.15
6.82
6.89
14.3
W630
8.3P
8.1
5.4
W631
7.6P
10.5
3.9
+0.7
2.4
1.5
+0.74
0.16
0.80
6.48
6.53
19.1
W709
2.5P
6.3
3.2
W710
2.5P
4.5
1.8
0.0
1.8
1.4
0.00
0.00
0.00
5.88
5.88
13.8
W606
9.4PB
11.3
3.3
W607
9.7PB
11.7
2.1
−0.3
0.4
1.2
−0.35
0.05
0.25
4.82
4.84
9.8
W699
7.0PB
8.9
3.5
W700
7.7PB
8.0
2.0
−0.7
0.9
1.5
−0.56
0.14
0.70
6.08
6.13
13.9
W608
5.3PB
9.6
4.3
W609
7.2PB
11.4
2.7
−1.9
1.8
1.6
−2.16
1.55
7.75
6.77
7.21
23.7
W531
5.0PB
8.3
4.2
W532
6.3PB
8.9
2.5
−1.3
0.6
1.7
−1.16
0.49
2.45
6.86
7.00
16.6
W505
4.0PB
8.7
4.3
W506
5.9PB
9.5
2.6
−1.9
0.8
1.7
−1.80
1.17
5.85
6.93
7.26
19.8
W507
2.7PB
7.1
4.8
W508
5.3PB
8.5
3.1
−2.6
1.4
1.7
−2.21
1.60
8.00
7.06
7.50
23.2
W711
9.2B
6.7
4.5
W712
2.0PB
6.0
2.7
−2.8
0.7
1.8
−1.68
1.24
6.20
7.32
7.65
19.6
W346
5.0B
8.1
4.7
W112
7.9B
8.9
3.3
−2.9
0.8
1.4
−2.58
2.38
11.90
5.86
6.63
21.1
W567
1.5B
5.9
4.3
W568
1.5B
4.6
2.5
0.0
1.3
1.8
0.00
0.00
0.00
7.32
7.32
14.7
W569
7.9BG
8.7
4.7
W570
8.0BG
8.0
3.2
−0.1
0.7
1.5
−0.08
0.00
0.00
6.04
6.04
11.4
M778
7.8BG
6.4
4.5
M648
6.8BG
5.8
2.9
+1.0
0.6
1.6
+0.58
0.75
0.15
6.44
6.48
13.7
W571
3.3BG
8.2
4.8
W572
2.5BG
8.1
3.2
+0.8
0.1
1.6
+0.65
0.17
0.85
6.42
6.47
12.5
W675
6.5G
8.0
6.0
W676
5.8G
9.0
4.5
+0.7
1.0
1.5
+0.63
0.14
0.70
6.10
6.14
14.5
Table I is a condensation, merely giving examples taken from a very much longer Table I scheduled to appear almost simultaneously in the American Dyestuff Reporter. Index of Dyestuffs in Table I.—All of 2 and 0.5 percent concentration (relative to weight of fiber), except in the case of mixtures, where the percentages making up the total of 2 percent in the heavier dyeing, are given.
Table II
Values of ϕ(H)=1−cos3.6°ΔH.
ΔH
ϕ(H)
0.0
0.0000
0.1
0.0000
0.2
0.0001
0.3
0.0002
0.4
0.0003
0.5
0.0005
0.6
0.0007
0.7
0.0010
0.8
0.0013
0.9
0.0016
1.0
0.0020
1.1
0.0024
1.2
0.0028
1.3
0.0033
1.4
0.0039
1.5
0.0044
1.6
0.0050
1.7
0.0057
1.8
0.0064
1.9
0.0071
2.0
0.0079
2.1
0.0087
2.2
0.0095
2.3
0.0104
2.4
0.0113
2.5
0.0123
2.6
0.0133
2.7
0.0144
2.8
0.0154
2.9
0.0165
3.0
0.0177
3.1
0.0189
3.2
0.0201
3.3
0.0214
3.4
0.0227
3.5
0.0241
3.6
0.0255
3.7
0.0269
3.8
0.0284
3.9
0.0299
4.0
0.0314
4.1
0.0330
4.2
0.0346
4.3
0.0363
4.4
0.0380
4.5
0.0397
4.6
0.0415
4.7
0.0433
4.8
0.0451
4.9
0.0470
5.0
0.0489
5.1
0.0509
5.2
0.0529
5.3
0.0549
5.4
0.0570
5.5
0.0591
5.6
0.0613
5.7
0.0634
5.8
0.0657
5.9
0.0679
6.0
0.0702
6.1
0.0726
6.2
0.0749
6.3
0.0773
6.4
0.0798
6.5
0.0822
6.6
0.0849
6.7
0.0873
6.8
0.0899
6.9
0.0925
7.0
0.0952
7.1
0.0979
7.2
0.1006
7.3
0.1034
7.4
0.1062
7.5
0.1090
7.6
0.1119
7.7
0.1148
7.8
0.1177
7.9
0.1207
8.0
0.1237
8.1
0.1267
8.2
0.1298
8.3
0.1329
8.4
0.1361
8.5
0.1393
8.6
0.1425
8.7
0.1457
8.8
0.1490
8.9
0.1523
9.0
0.1557
9.1
0.1591
9.2
0.1625
9.3
0.1659
9.4
0.1694
9.5
0.1729
9.6
0.1765
9.7
0.1801
9.8
0.1837
9.9
0.1873
10.0
0.1910
10.1
0.1947
10.2
0.1984
10.3
0.2022
10.4
0.2060
10.5
0.2098
10.6
0.2137
10.7
0.2176
10.8
0.2216
10.9
0.2255
11.0
0.2295
11.1
0.2335
11.2
0.2376
11.3
0.2416
11.4
0.2457
11.5
0.2499
11.6
0.2541
11.7
0.2583
11.8
0.2625
11.9
0.2667
12.0
0.2710
12.1
0.2753
12.2
0.2797
12.3
0.2841
12.4
0.2885
12.5
0.2929
12.6
0.2974
12.7
0.3018
12.8
0.3064
12.9
0.3109
13.0
0.3155
13.1
0.3201
13.2
0.3247
13.3
0.3293
13.4
0.3340
13.5
0.3387
13.6
0.3434
13.7
0.3482
13.8
0.3529
13.9
0.3577
14.0
0.3626
14.1
0.3674
14.2
0.3723
14.3
0.3772
14.4
0.3821
14.5
0.3871
14.6
0.3921
14.7
0.3971
14.8
0.4021
14.9
0.4071
15.0
0.4122
15.1
0.4173
15.2
0.4224
15.3
0.4276
15.4
0.4327
15.5
0.4379
15.6
0.4431
15.7
0.4484
15.8
0.4536
15.9
0.4589
16.0
0.4642
Table III(a)
Munsell “5/5” colors.
1905–10 set adjusted to Y=0.1977
1926–29 set from Munsell book of color renotations
Average
x
y
x
y
x
y
5 R 5/5
0.41004
0.32766
0.3909
0.3229
0.4405
0.3253
5Y5/5
0.41409
0.42315
0.41085
0.4246
0.4125
0.4239
5 G 5/5
0.2899
0.39283
0.27655
0.3744
0.2832
0.3836
5 B 5/5
0.24344
0.28127
0.2354
0.2790
0.2394
0.2801
5 P 5/5
0.29475
0.26021
0.2959
0.2593
0.2953
0.2598
N (average)
0.3262
0.3345
Nominal notation
Munsell renotations
Hue number
5 Y 5/5
5.7 R 5/5.4
5.7
5 Y 5/5
4.7 Y 5/5.1
24.7
5 G 5/5
3.7 G 5/5.0
43.7
5 B 5/5
5.4 B 5/4.7
65.4
5 P 5/5
4.9 P 5/4.9
84.9
Neutral (center)
5.0 Y 5/0.7
25.0
Table III(b)
Color-differences between Munsell “5/5” colors and neutral gray and between successive “5/5” colors.
5/5 color to neutral gray
5/5 color to next succeeding 5/5 color in the color circle
Visual estimates determining magnitude of “n” in Eq. (13). Here the total perceptual difference, made up chiefly of chroma difference (columns “b” in Table VI(b), was taken as the unit color difference; then the relative magnitude of the other total difference, consisting largely of “value” difference (columns “a”), was estimated. Hue differences are small or nil.
Set of colors Observers
Visual estimates of ratios of differences a/b by following observers
IHG
WW
EN
STG
JB
DEM
FNH
TFG
EMW
RW
Average
1
4
2
1.5
3
3
2
4
2
3
3
2.75
2
3
1
2
1
2
1.5
1.5
2
2
2
1.80
3
2
1
1
2
1.5
2
2
1
1.5
1
1.50
4
2.5
1.5
2.5
3
2
3
2
2
2.5
2
2.30
5
1.5
1
1
1
3
1
0.5
1.5
1.5
2
1.40
6
1.5
1
1.5
1.5
3
2
2
2
2
1.5
1.80
7
2
2.5
2.5
4
6
5
3
3
2
2.5
3.25
8
6
4
4
10
10
6
10
5
6
7
6.80
9
1.5
1.5
2
2
3
2
3
1
1
1.5
1.85
10
2.5
3
3
7
6
3
5
3
4
3
3.95
11
4
3.5
3
8
6
5
5
4
3
4
4.55
12
8
5
5
6
6
10
10
6
5
5
6.60
13
5
5
3
3
4
8
3
3
4
3
4.10
14
3
3
5
2.5
3.5
6
3
3
3
2.5
3.45
15
1.5
4
1.75
2.5
2
3
1
1
1.5
1.5
1.98
16
1.5
3
2
1.5
2.5
4
2
2.5
2
3
2.40
17
5
5
6
6
4
6
7
5
6
6
5.60
18
7
5.5
7
4
6
5
7
4
5
5
5.55
Table VI(b)
Ratio of magnitudes of “value” step and chroma step calculations of total difference in each pair by formula (Eqs. (12) and (13)).