Uniform color scales*

David L. MacAdam

doi:10.1364/JOSA.64.001691

Journal of the Optical Society of America
Vol. 64,
Issue 12,
pp. 1691-1702
(1974)
•https://doi.org/10.1364/JOSA.64.001691

Uniform color scales

David L. MacAdam

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David L. MacAdam, "Uniform color scales*," J. Opt. Soc. Am. 64, 1691-1702 (1974)

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Abstract

Judgments of relative magnitudes of color differences exhibited by 128 selected nearest-neighbor pairs of 59 colored tiles were recorded by 49 to 76 observers, all of whom had normal color vision. Scale values that represent the perceived magnitudes of the color differences were obtained by statistical analysis of their reports. From colorimetric specifications of the tiles, formulas have been devised that define a three-dimensional euclidean space in which the distances between the points that represent the colors correlate reasonably well with the reported magnitudes of the perceived color differences. Lattice points of a regular rhombohedral crystal in that space have been used to specify about 500 colors that are being made for distribution by the Optical Society. Because of the manner of selection of those colors, each except the most saturated of the chosen colors will exhibit equal magnitudes of color difference from 12 others. About 2500 equally noticeable color differences can be exhibited by suitable arrangements of those colors. Each except the most saturated of the colors can be arranged in six different series. Each of those series exhibits from three to ten color differences, all of equal magnitude. Such a series of colors, which exhibits equal color differences is known as a uniform color scale. Provision of a set of colors with which the maximum possible number and variety of uniform color scales can be constructed was the goal of the Optical Society Committee on Uniform Color Scales, of which this is a report.

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Pair	Tiles		Observed scale difference	Computed color difference	Error	Ratio of computed lightness difference to total difference
1	1	2	2.311	2.388	0.077	0.14
2	1	3	2.608	2.909	0.301	0.24
3	2	3	2.176	2.210	0.034	0.17
4	2	5	2.160	2.251	0.091	0.02
5	2	6	1.818	2.189	0.371	0.27
8	3	4	2.569	2.059	−0.510	0.27
9	3	6	2.788	2.582	−0.206	0.09
10	3	7	2.038	2.188	0.150	0.23
11	4	7	1.877	2.136	0.259	0.02
13	4	8	2.127	1.981	−0.146	0.23
15	5	6	2.268	2.114	−0.154	0.31
16	5	10	2.602	2.560	−0.042	0.11
17	5	11	1.746	2.521	0.775	0.12
18	6	7	2.039	2.220	0.181	0.13
20	6	11	2.054	2.455	0.401	0.14
21	6	12	1.240	2.276	0.104	0.00
22	7	8	2.234	1.637	−0.597	0.30
23	7	12	1.560	2.539	0.979	0.11
25	7	13	1.957	2.068	0.111	0.23
26	8	9	2.944	2.359	−0.585	0.24
27	8	13	1.706	2.085	0.379	0.47
29	8	14	2.525	1.969	−0.556	0.38
31	9	14	2.133	2.481	0.348	0.08
32	9	15	2.727	2.061	−0.666	0.15
33	10	11	1.705	2.203	0.498	0.27
34	10	17	2.537	2.209	−0.328	0.33
35	10	18	2.177	2.320	0.143	0.07
36	11	12	2.122	2.053	−0.069	0.16
38	11	18	2.728	2.364	−0.364	0.32
39	11	19	1.655	2.287	0.632	0.08
40	12	13	1.943	2.097	0.154	0.09
42	12	19	2.279	2.489	0.210	0.21
44	12	20	1.972	2.115	0.143	0.23
45	13	14	2.122	1.766	−0.356	0.13
47	13	20	1.860	2.533	0.673	0.11
49	13	21	1.994	2.122	0.128	0.11
50	14	15	2.462	1.942	−0.520	0.06
51	14	21	1.689	2.486	0.797	0.18
53	14	22	2.391	2.004	−0.387	0.19
54	15	16	1.739	1.566	−0.173	0.04
56	15	22	2.312	2.326	0.014	0.11
57	15	23	2.436	2.154	−0.282	0.22
58	16	23	2.315	2.196	−0.119	0.19
60	16	24	2.538	1.818	−0.720	0.12
61	17	18	1.709	1.670	−0.039	0.34
62	17	25	3.399	2.472	−0.927	0.05
63	18	19	2.247	2.081	−0.166	0.28
64	18	25	3.345	2.628	−0.717	0.26
66	18	26	3.223	2.471	−0.752	0.21
67	19	20	2.342	1.967	−0.375	0.01
68	19	26	3.019	2.542	−0.477	0.44
70	19	27	2.588	2.241	−0.347	0.45
72	20	21	2.257	1.834	−0.423	0.03
73	20	27	2.459	2.394	−0.065	0.44
74	20	28	2.387	1.850	−0.537	0.02
76	21	22	1.599	1.986	0.387	0.04
77	21	28	1.792	2.037	0.245	0.01
79	21	29	2.358	2.007	−0.351	0.12
81	22	23	1.409	1.849	0.440	0.11
83.	22	29	1.643	2.261	0.618	0.14
84	22	30	2.160	1.895	−0.265	0.17
85	23	24	1.846	1.870	0.024	0.10
86	23	30	1.872	2.097	0.225	0.05
87	23	31	2.507	2.147	−0.360	0.10
88	24	31	2.907	2.295	−0.612	0.17
90	24	32	2.974	2.787	−0.187	0.42
91	25	26	2.232	1.992	−0.240	0.07
93	25	33	3.389	2.642	−0.747	0.18
95	26	27	2.126	2.093	−0.033	0.05
96	26	33	3.001	2.588	−0.413	0.24
97	26	34	2.740	2.173	−0.567	0.18
99	27	28	2.000	2.088	0.088	0.52
100	27	34	2.734	2.395	−0.339	0.21
102	27	35	2.513	1.885	−0.628	0.06
103	28	29	2.014	2.018	0.004	0.11
104	28	35	2.730	2.504	0.226	0.39
105	28	36	1.957	1.859	−0.098	0.34
107	29	30	1.369	1.645	0.276	0.01
109	29	36	2.071	2.090	0.019	0.20
110	29	37	1.496	1.479	−0.017	0.02
111	30	31	2.052	2.366	0.314	0.04
113	30	37	2.483	1.914	−0.569	0.02
115	30	38	2.039	2.246	0.207	0.18
117	31	32	1.218	1.905	0.687	0.41
118	31	38	2.519	2.181	−0.338	0.14
119	31	39	2.487	2.233	−0.254	0:32
120	32	39	2.564	2.094	−0.470	0.03
122	33	34	2.709	1.979	−0.730	0.11
124	34	35	1.805	1.792	−0.013	0.34
125	34	40	2.435	2.563	0.128	0.00
127	35	36	1.889	1.916	0.027	0.18
128	35	40	2.150	2.643	0.493	0.23
129	35	41	2.372	2.694	0.322	0.07
131	36	37	1.915	1.916	0.001	0.20
133	36	41	2.853	2.775	−0.078	0.20
134	36	42	2.024	3.296	1.272	0.15
135	37	38	1.489	2.253	0.764	0.17
137	37	42	2.436	3.057	0.621	0.29
138	37	43	2.525	3.294	0.769	0.21
139	38	39	1.457	2.002	0.545	0.20
141	38	43	2.945	2.795	−0.150	0.11
143	40	41	2.242	1.840	−0.402	0.22
144	41	42	2.093	2.236	0.143	0.02
147	42	43	1.275	1.386	0.111	0.14
151	R1	R2	1.611	1.431	−0.180	0.25
152	R1	R3	3.497	2.952	−0.545	0.82
153	R1	R4	3.150	2.732	−0.418	0.75
154	R2	R3	3.538	3.422	−0.116	0.82
155	R2	R4	2.590	2.728	0.138	0.89
156	R3	R4	3.253	3.090	−0.163	0.12
157	Y1	Y2	2.498	2.263	−0.235	0.04
158	Y1	Y3	3.365	3.262	−0.103	0.83
159	Y1	Y4	3.701	3.302	−0.399	0.82
160	Y2	Y3	2.773	2.808	0.035	0.93
161	Y2	Y4	2.610	2.700	0.090	0.97
162	Y3	Y4	2.253	1.395	−0.858	0.00
163	G1	G2	1.733	2.155	0.422	0.31
164	G1	G3	3.375	3.262	−0.113	0.88
165	G1	G4	2.804	2.975	0.171	0.85
166	G2	G3	3.803	3.814	0.011	0.93
167	G2	G4	3.375	3.429	0.054	0.93
168	G3	G4	2.508	2.088	−0.420	0.17
169	B1	B2	1.835	2.686	0.851	0.22
170	B1	B3	2.467	2.981	0.514	0.74
171	B1	B4	3.151	3.026	−0.125	0.65
172	B2	B3	2.641	3.203	0.562	0.88
173	B2	B4	2.936	3.057	0.121	0.84
174	B3	B4	3.008	2.654	−0.354	0.09
Weighted means			2.483	2.453
rms error					0.421

Tile	x	y	Y	g	j	L
1	0.3120	0.5412	30.50	6.859	7.125	−0.24
2	0.2952	0.4786	29.96	5.934	4.948	−0.47
3	0.3466	0.4899	29.28	4.177	6.237	−0.73
4	0.3949	0.4897	27.15	2.385	7.089	−1.12
5	0.2627	0.4254	29.58	6.027	2.700	−0.43
6	0.3039	0.4358	27.84	4.261	3.666	−0.89
7	0.3550	0.4477	27.16	2.477	4.955	−1.09
8	0.3933	0.4506	25.06	1.085	5.662	−1.44
9	0.4469	0.4595	26.79	−0.423	7.389	−1.04
10	0.2376	0.3652	29.51	5.810	0.164	−0.32
11	0.2747	0.3785	28.26	3.989	1.249	−0.65
12	0.3159	0.3928	27.56	2.346	2.436	−0.89
13	0.3616	0.4073	28.68	0.803	3.842	−0.75
14	0.4025	0.4161	27.55	−0.577	4.920	−0.91
15	0.4475	0.4224	27.30	−2.058	6.172	−0.83
16	0.4833	0.4221	26.54	−3.358	7.043	−0.79
17	0.2305	0.3215	30.03	5.136	−1.809	0.29
18	0.2531	0.3311	29.53	3.801	−0.980	−0.11
19	0.2863	0.3418	28.39	2.070	0.016	−0.52
20	0.3247	0.3584	28.84	0.608	1.333	−0.54
21	0.3627	0.3704	28.75	−0.815	2.488	−0.59
22	0.4068	0.3840	28.21	−2.241	3.868	−0.64
23	0.4459	0.3884	28.23	−3.747	4.921	−0.50
24	0.4916	0.3973	26.38	−5.000	6.294	−0.64
25	0.2368	0.2855	29.58	3.309	−3.470	0.37
26	0.2661	0.3005	29.83	1.745	−2.245	0.26
27	0.3007	0.3189	30.26	0.244	−0.790	0.20
28	0.3342	0.3340	27.95	−1.024	0.462	−0.57
29	0.3738	0.3455	28.77	−2.629	1.664	−0.41
30	0.4090	0.3570	28.49	−3.793	2.827	−0.42
31	0.4588	0.3637	27.72	−5.744	4.161	−0.35
32	0.4869	0.3649	28.29	−7.218	5.085	0.20
33	0.2519	0.2619	30.72	0.987	−4.642	0.70
34	0.2797	0.2814	30.73	−0.218	−3.087	0.55
35	0.3064	0.2960	29.14	−1.331	−1.820	0.12
36	0.3406	0.3133	29.18	−2.552	−0.384	−0.12
37	0.3787	0.3272	28.12	−3.905	0.917	−0.40
38	0.4199	0.3336	28.50	−5.843	2.004	−0.13
39	0.4555	0.3383	28.14	−7.523	3.015	0.15
40	0.2938	0.2605	29.86	−2.586	−4.066	0.55
41	0.3225	0.2740	28.77	−3.839	−2.781	0.26
42	0.3609	0.2870	28.65	−5.633	−1.447	0.23
43	0.3866	0.2940	27.92	−6.733	−0.627	0.09
R1	0.5150	0.3380	10.60	−7.078	2.959	−3.78
R2	0.4916	0.3477	10.30	−5.697	2.854	−4.03
R3	0.4424	0.3160	18.10	−6.914	1.289	−2.06
R4	0.4874	0.3661	17.27	−5.702	4.107	−2.32
Y1	0.3708	0.4040	79.95	0.396	5.877	5.22
Y2	0.3896	0.4340	80.15	1.001	8.055	5.15
Y3	0.4054	0.4334	58.27	0.023	7.667	3.31
Y4	0.3868	0.4409	58.85	1.406	7.480	3.30
G1	0.2674	0.3504	28.85	3.515	0.064	−0.44
G2	0.2434	0.3636	30.07	5.561	0.202	−0.03
G3	0.2560	0.3926	18.37	4.549	1.218	−2.47
G4	0.2265	0.3406	18.70	4.819	−0.823	−2.22
B1	0.1930	0.1766	6.48	1.404	−6.289	−5.10
B2	0.2248	0.2276	6.04	0.865	−3.726	−5.52
B3	0.2136	0.2379	11.74	2.226	−4.461	−3.54
B4	0.2432	0.2212	10.98	−0.389	−4.838	−3.72

Pair	Computed lightness difference	Number of observers who picked the lightness in accord with computation
27	1.0	8
67	0.04	4
68	1.0	8
70	1.0	6
73	1.0	8
88	0.4	5
90	1.1	8
95	0.1	8
99	1.1	10
117	0.8	6

n	ΔL	Δg	Δj	ΔN	$\sum_{n}^{n} Δ N$	$\sum_{1}^{n} Δ N$	$\sqrt{2 S}$
1	±1	±1	±1	8			2.000
	0	±2	0	4	12	12
2	±2	0	0	2			2.38
	0	±2	±2	4	6	18
3	±2	±2	0	8			2.63
	±1	±3	±1	16	24	42
4	±2	±2	±2	8			2.83
	0	±4	0	4	12	54
5	±3	±1	±1	8			2.99
	±1	±3	±3	8
	0	±4	±2	8	24	78
6	±2	±4	0	8	8	86	3.13
7	±3	±3	±1	16			3.25
	±2	±4	±2	16
	±1	±5	±1	16	48	134
8	±4	0	0	2			3.36
	0	±4	±4	4	6	140
9	±4	±2	0	8			3.46
	±3	±3	±3	8
	±1	±5	±3	16
	0	±6	0	4	36	176
10	±4	±2	±2	8			3.56
	±2	±4	±4	8
	0	±6	±2	8	24	200
11	±3	±5	±1	16			3.64
	±2	±6	0	8	24	224
12	±4	±4	0	8			3.72
	±2	±6	±2	16	24	248
13	±5	±1	±1	8			3.80
	±4	±4	±2	16
	±3	±5	±3	16
	±1	±5	±5	8
	±1	±7	±1	16
	0	±6	±4	8	72	320
14				0	0	320	3.87
15	±5	±3	±1	16			3.94
	±2	±6	±4	16
	±1	±7	±3	16	48	368
16	±4	±4	±4	8			4.000
	0	±8	0	4	12	380
17	±5	±3	±3	8			4.06
	±4	±6	0	8
	±3	±5	±5	8
	±3	±7	±1	16
	0	±8	±2	8	48	428
18	±6	0	0	2			4.12
	±4	±6	±2	16
	±2	±8	0	8
	0	±6	±6	4	30	458
19	±6	±2	0	8			4.18
	±5	±5	±1	16
	±3	±7	±3	16
	±2	±8	±2	16
	±1	±7	±5	16	72	530
20	±6	±2	±2	8			4.23
	±2	±6	±6	8
	0	±8	±4	8	24	554
21	±5	±5	±3	16			4.28
	±4	±6	±4	16
	±1	±9	±1	16	48	602
22	±6	±4	0	8			4.33
	±2	±8	±4	16	24	626
23	±6	±4	±2	16			4.38
	±3	±7	±5	16
	±1	±9	±3	16	48	674
24	±4	±8	0	8	8	682	4.43
25	±7	±1	±1	8			4.47
	±5	±7	±1	16
	±5	±5	±5	8
	±4	±8	±2	16
	±3	±9	±1	16
	±1	±7	±7	8
	0	±8	±6	8
	0	+10	0	4	84	766

Pair	Tiles		Observed scale difference	Computed color difference	Error	Ratio of computed lightness difference to total difference
1	1	2	2.311	2.388	0.077	0.14
2	1	3	2.608	2.909	0.301	0.24
3	2	3	2.176	2.210	0.034	0.17
4	2	5	2.160	2.251	0.091	0.02
5	2	6	1.818	2.189	0.371	0.27
8	3	4	2.569	2.059	−0.510	0.27
9	3	6	2.788	2.582	−0.206	0.09
10	3	7	2.038	2.188	0.150	0.23
11	4	7	1.877	2.136	0.259	0.02
13	4	8	2.127	1.981	−0.146	0.23
15	5	6	2.268	2.114	−0.154	0.31
16	5	10	2.602	2.560	−0.042	0.11
17	5	11	1.746	2.521	0.775	0.12
18	6	7	2.039	2.220	0.181	0.13
20	6	11	2.054	2.455	0.401	0.14
21	6	12	1.240	2.276	0.104	0.00
22	7	8	2.234	1.637	−0.597	0.30
23	7	12	1.560	2.539	0.979	0.11
25	7	13	1.957	2.068	0.111	0.23
26	8	9	2.944	2.359	−0.585	0.24
27	8	13	1.706	2.085	0.379	0.47
29	8	14	2.525	1.969	−0.556	0.38
31	9	14	2.133	2.481	0.348	0.08
32	9	15	2.727	2.061	−0.666	0.15
33	10	11	1.705	2.203	0.498	0.27
34	10	17	2.537	2.209	−0.328	0.33
35	10	18	2.177	2.320	0.143	0.07
36	11	12	2.122	2.053	−0.069	0.16
38	11	18	2.728	2.364	−0.364	0.32
39	11	19	1.655	2.287	0.632	0.08
40	12	13	1.943	2.097	0.154	0.09
42	12	19	2.279	2.489	0.210	0.21
44	12	20	1.972	2.115	0.143	0.23
45	13	14	2.122	1.766	−0.356	0.13
47	13	20	1.860	2.533	0.673	0.11
49	13	21	1.994	2.122	0.128	0.11
50	14	15	2.462	1.942	−0.520	0.06
51	14	21	1.689	2.486	0.797	0.18
53	14	22	2.391	2.004	−0.387	0.19
54	15	16	1.739	1.566	−0.173	0.04
56	15	22	2.312	2.326	0.014	0.11
57	15	23	2.436	2.154	−0.282	0.22
58	16	23	2.315	2.196	−0.119	0.19
60	16	24	2.538	1.818	−0.720	0.12
61	17	18	1.709	1.670	−0.039	0.34
62	17	25	3.399	2.472	−0.927	0.05
63	18	19	2.247	2.081	−0.166	0.28
64	18	25	3.345	2.628	−0.717	0.26
66	18	26	3.223	2.471	−0.752	0.21
67	19	20	2.342	1.967	−0.375	0.01
68	19	26	3.019	2.542	−0.477	0.44
70	19	27	2.588	2.241	−0.347	0.45
72	20	21	2.257	1.834	−0.423	0.03
73	20	27	2.459	2.394	−0.065	0.44
74	20	28	2.387	1.850	−0.537	0.02
76	21	22	1.599	1.986	0.387	0.04
77	21	28	1.792	2.037	0.245	0.01
79	21	29	2.358	2.007	−0.351	0.12
81	22	23	1.409	1.849	0.440	0.11
83.	22	29	1.643	2.261	0.618	0.14
84	22	30	2.160	1.895	−0.265	0.17
85	23	24	1.846	1.870	0.024	0.10
86	23	30	1.872	2.097	0.225	0.05
87	23	31	2.507	2.147	−0.360	0.10
88	24	31	2.907	2.295	−0.612	0.17
90	24	32	2.974	2.787	−0.187	0.42
91	25	26	2.232	1.992	−0.240	0.07
93	25	33	3.389	2.642	−0.747	0.18
95	26	27	2.126	2.093	−0.033	0.05
96	26	33	3.001	2.588	−0.413	0.24
97	26	34	2.740	2.173	−0.567	0.18
99	27	28	2.000	2.088	0.088	0.52
100	27	34	2.734	2.395	−0.339	0.21
102	27	35	2.513	1.885	−0.628	0.06
103	28	29	2.014	2.018	0.004	0.11
104	28	35	2.730	2.504	0.226	0.39
105	28	36	1.957	1.859	−0.098	0.34
107	29	30	1.369	1.645	0.276	0.01
109	29	36	2.071	2.090	0.019	0.20
110	29	37	1.496	1.479	−0.017	0.02
111	30	31	2.052	2.366	0.314	0.04
113	30	37	2.483	1.914	−0.569	0.02
115	30	38	2.039	2.246	0.207	0.18
117	31	32	1.218	1.905	0.687	0.41
118	31	38	2.519	2.181	−0.338	0.14
119	31	39	2.487	2.233	−0.254	0:32
120	32	39	2.564	2.094	−0.470	0.03
122	33	34	2.709	1.979	−0.730	0.11
124	34	35	1.805	1.792	−0.013	0.34
125	34	40	2.435	2.563	0.128	0.00
127	35	36	1.889	1.916	0.027	0.18
128	35	40	2.150	2.643	0.493	0.23
129	35	41	2.372	2.694	0.322	0.07
131	36	37	1.915	1.916	0.001	0.20
133	36	41	2.853	2.775	−0.078	0.20
134	36	42	2.024	3.296	1.272	0.15
135	37	38	1.489	2.253	0.764	0.17
137	37	42	2.436	3.057	0.621	0.29
138	37	43	2.525	3.294	0.769	0.21
139	38	39	1.457	2.002	0.545	0.20
141	38	43	2.945	2.795	−0.150	0.11
143	40	41	2.242	1.840	−0.402	0.22
144	41	42	2.093	2.236	0.143	0.02
147	42	43	1.275	1.386	0.111	0.14
151	R1	R2	1.611	1.431	−0.180	0.25
152	R1	R3	3.497	2.952	−0.545	0.82
153	R1	R4	3.150	2.732	−0.418	0.75
154	R2	R3	3.538	3.422	−0.116	0.82
155	R2	R4	2.590	2.728	0.138	0.89
156	R3	R4	3.253	3.090	−0.163	0.12
157	Y1	Y2	2.498	2.263	−0.235	0.04
158	Y1	Y3	3.365	3.262	−0.103	0.83
159	Y1	Y4	3.701	3.302	−0.399	0.82
160	Y2	Y3	2.773	2.808	0.035	0.93
161	Y2	Y4	2.610	2.700	0.090	0.97
162	Y3	Y4	2.253	1.395	−0.858	0.00
163	G1	G2	1.733	2.155	0.422	0.31
164	G1	G3	3.375	3.262	−0.113	0.88
165	G1	G4	2.804	2.975	0.171	0.85
166	G2	G3	3.803	3.814	0.011	0.93
167	G2	G4	3.375	3.429	0.054	0.93
168	G3	G4	2.508	2.088	−0.420	0.17
169	B1	B2	1.835	2.686	0.851	0.22
170	B1	B3	2.467	2.981	0.514	0.74
171	B1	B4	3.151	3.026	−0.125	0.65
172	B2	B3	2.641	3.203	0.562	0.88
173	B2	B4	2.936	3.057	0.121	0.84
174	B3	B4	3.008	2.654	−0.354	0.09
Weighted means			2.483	2.453
rms error					0.421

Abstract

Cited By

Figures (13)

Tables (5)

Equations (10)

Journal of the Optical Society of America