Journal of the Optical Society of America/Volume 30/Issue 12/Analysis of the Original

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Journal of the Optical Society of America, Volume 30, Issue 12 (1940)
John E. Tyler and Arthur C. Hardy
Analysis of the Original Munsell Color System
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4420961Journal of the Optical Society of America, Volume 30, Issue 12 — Analysis of the Original Munsell Color SystemJohn E. Tyler and Arthur C. Hardy
​

An Analysis of the Original Munsell Color System

John E. Tyler AND Arthur C. Hardy

Massachusetts Institute of Technology, Cambridge, Massachusetts

IN 1919, the Munsell Color System was subjected to a spectrophotometric examination by Priest, Gibson, and McNicholas,[1] who determined the spectral reflection characteristics of fifteen chromatic standards and nine neutral standards of the system. These spectrophotometric data have now been integrated in accordance with the 1931 I.C.I. standard observer and Illuminant C. The resulting tristimulus values and trichromatic coefficients are listed in Table I.


Table I. Tristimulus specifications (X, Y, Z) and trichromatic coefficients (x,y) of 15 Munsell Atlas colors computed from spectrophotometric data (1919) on the basis of the I.C.I. standard observer and coordinate system and for I.C.I. Illuminant C,

Munsell
Notation 		X Y Z x y
R 7/5 0.4951 0.4399 0.4305 0.3626 0.3221
5/5 .2768 .2140 .1713 .4101 .3276
3/2 .0977 .0878 .0809 .3667 .3295
Y 7/4 .4661 .4869 .2625 .3835 .4006
5/5 .2605 .2662 .1024 .4141 .4232
3/2 .0950 .0974 .0708 .3611 .3700
G 7/4 .4173 .4860 .4688 .3041 .3542
5/5 .1811 .2454 .1982 .2899 .3928
3/2 .0766 .0933 .0952 .2888 .3519
B 7/4 .4325 .4827 .6573 .2750 .3070
5/5 .2246 .2595 .4385 .2434 .2813
3/2 .0822 .0904 .1412 .1412 .2620
P 7/3 .5162 .4978 .6613 .3081 .2972
5/5 .2773 .2448 .4187 .2948 .2602
3/2 .0981 .0921 .1553 .2838 .2667

The instructions given by Professor Munsell for making a pigment color-solid are so complete that the entire color system can be constructed, given any five chromatic colors of the system which are unrelated in the sense that no two have either the same hue or complementary hues. The definitions of hue, value, and chroma are unambiguously established by the operations involved in constructing the system by means of additive mixtures on a Maxwell disk.[2] The hue, value, and chroma of such a mixture are related to those of the components of the mixture as follows:

Hue.—When a chromatic color is mixed additively with a neutral (white, gray, or black), the hue of the mixture is the same as that of the chromatic color.

Value.—When two colors whose values are and ; occupy relative areas a and b on a Maxwell disk, the value of the mixture is given by the equation .

Chroma.—When two complementary colors occupy areas on a Maxwell disk which are inversely proportional to the product of value by chroma, a neutral gray results.

By comparison of these quantities with the corresponding quantities in psychophysical systems, it is evident that hue is synonymous with dominant wave-length, that value is the square root of luminous apparent reflectance, , expressed in percent, and that, for a given hue and value, chroma is proportional[3] to colorimetric purity in psychophysical systems.

Table II. Tristimulus specifications (X,Y,Z) and trichromatic coefficients (x,y) of the five principal Munsell colors taken from Table I, each set of tristimulus specifications being multiplied by a factor to make Y=0.2500.

Munsell
Notation 		X Y Z x y
R 5/5 0.31298 0.25000 0.20018 0.4101 0.3276
Y 5/5 .21634 .25000 .09613 .4141 .4232
G 5/5 .24459 .25000 .20198 .2899 .3928
B 5/5 .18454 .25000 .42235 .2434 2813
P 5/5 .28326 .25000 .42761 .2948 .2602


When tristimulus specifications have been assigned to five unrelated colors in the Munsell system, the calculation of the tristimulus specifications for all other colors in the system involves no more than a hypothetical repetition of the procedure employed originally by Professor Munsell. In other words, the disk mixtures of Professor Munsell can be made hypothetically by the I.C.I. observer under carefully standard-​

TABLE III. Tristimulus specifications (X, Y, Z) and trichromatic coefficients (x, y) computed for 260 Munsell designations according to instructions by Professor Munsell for making a pigment color-solid. These computed specifications are based upon the five principal Munsell colors specified in Table II.

Munsell
Notation 		X Y Z x y
R 8/6 0.7598 0.6400 0.5569 0.3883 0.3271
4 .7185 .6400 .6013 .3666 .3266
2 .6771 .6400 .6459 .3449 .3260
7/8 .6315 .4900 .3729 .4226 .3279
6 .5953 .4900 .4118 .3977 .3273
4 .5591 .4900 .4507 .3728 .3267
2 .5229 .4900 .4896 .3480 .3261
6/10 .5128 .3600 .2215 .4686 .3290
8 .4817 .3600 .2549 .4393 .3283
6 .4507 .3600 .2882 .4101 .3276
4 .4197 .3600 .3216 .3811 .3269
2 .3886 .3600 .3550 .3522 .3262
5/14 .4293 .2500 .0751 .5690 .3314
12 .4034 .2500 .1029 .5334 .3308
10 .3776 .2500 .1307 .4979 .3297
8 .3517 .2500 .1585 .4627 .3288
6 .3259 .2500 .1863 .4276 .3280
2 .3000 .2500 .2141 .3927 .3272
10 .2742 .2500 .2419 .3579 .3263
4/12 .2830 .1600 .0392 .5869 .3318
10 .2624 .1600 .0614 .5423 .3307
8 .2417 .1600 .0836 .4980 .3297
6 .2210 .1600 .1059 .4539 .3286
4 .2003 .1600 .1281 .4101 .3276
2 .1796 .1600 .1503 .3666 .3266
3/10 .1670 .0900 .0137 .6169 .3325
8 .1515 .0900 .0304 .5572 .3311
6 .1359 .0900 .0470 .4980 .3297
4 .1204 .0900 .0637 .4393 .3283
2 .1049 0900 .0804 .3811 .3269
2/6 .0708 .0400 .0098 .5868 .3317
4 .0604 .0400 .0209 .4979 .3296
2 0501 .0400 0320 .4100 .3276
YR 8/6 0.6972 0.6400 0.3966 0.4021 0.3691
4 .6767 .6400 4945 .3736 .3534
2 .6562 .6400 .5924 .3475 .3389
7/8 .5585 .4900 .1863 .4523 .3968
6 5405 .4900 .2719 .4150 .3762
4 .5226 .4900 .3574 .3814 .3577
2 .5047 .4900 .4430 .3510 .3408
6/8 .4190 .3600 .0951 .4794 .4118
6 .4037 .3600 .1684 .4331 .3862
4 .3883 .3600 .2417 .3922 .3636
2 .3730 .3600 .3150 .3559 .3435
5/8 .2996 .2500 .0252 .5211 .4350
6 .2868 .2500 .0864 .4602 .4012
4 .2740 .2500 .1475 .4080 .3724
2 .2611 .2500 .2086 .3628 .3474
4/6 .1896 .1600 .0260 .5048 .4259
4 .1794 .1600 .0749 .4330 .3862
2 .1692 .1600 .1237 .3735 .3533
3/4 .1047 .0900 .0238 .4793 .4119
2 .0971 .0900 .0604 .3922 .3636
2/2 .0449 .0400 .0187 .4332 .3862
Y 8/12 0.6214 0.6400 0.0241 0.4834 0.4979
10 .6238 .6400 .1353 .4458 .4574
8 .6262 .6400 .2459 .4141 .4233
6 .6286 .6400 .3572 .3866 .3937
4 .6310 .6400 .4683 .3627 .3679
2 .6333 .6400 .5790 .3419 .3455
7/10 .4762 .4900 .4272 .4720 .4856
8 .4783 .4900 .1399 .4316 .4422
6 .4804 .4900 .2370 .3979 .4058
Y 7/4 0.4825 0.4900 0.3342 0.3693 0.3750
2 .4846 .4900 .4314 .3447 .3485
6/8 .3504 .3600 .0552 .4578 .4702
6 .3522 .3600 .1384 .4141 .4232
4 .3540 .3600 .2217 .3783 .3847
2 .3558 .3600 .3050 .3486 .3527
5/6 .2438 .2500 .0614 .4391 .4503
4 .2453 .2500 .1308 .3919 .3993
2 .2468 .2500 .2003 .3541 .3586
4/6 .1554 .1600 .0060 .4834 .4978
4 .1565 .1600 .0615 .4140 .4232
2 .1557 .1600 .1171 .3628 .3680
3/4 .0876 .0900 .0138 .4577 .4702
2 .0885 .0900 .0554 .3783 .3847
2/2 .0391 .0400 .0154 .4140 .4234
GY 8/6 0.5687 0.6400 0.3871 0.3564 0.4011
4 .5910 .6400 .4882 .3438 .3723
2 .6134 .6400 .5892 .3329 .3473
7/8 .4088 .4900 .1747 .3808 .4565
6 .4283 .4900 .2631 .3625 .4148
4 .4478 .4900 .3526 .3470 .3797
2 .4673 .4900 .4401 .3344 .3507
6/8 .2906 .3600 .0850 .3950 .4895
6 .3073 .3600 .1608 .3711 .4347
4 .3241 .3600 .2366 .3520 .3910
2 .3409 .3600 .3125 .3364 .3552
4/6 .2064 .2500 .0801 .3848 .4660
4 .2204 .2500 .1433 .3592 .4074
2 .2344 .2500 .2065 .3393 .3619
4/6 .1254 .1600 .0210 .4094 .5222
4 .1366 .1600 .0715 .3711 .4346
2 .1478 .1600 .1221 .3438 .3722
4/4 .0726 .0900 .0212 .3950 .4897
2 .0810 .0900 .0591 .3520 .3911
2/2 .0342 .0400 .0179 .3711 .4346
G 8/6 0.5133 0.6400 0.5608 0.2995 0.3734
4 .5541 .6400 .6039 .3082 .3559
2 .5949 .6400 .6471 .3161 .3401
7/8 .3438 .4900 .3769 .2840 .4047
6 .3796 .4900 .4148 .2955 .3815
4 .4153 .4900 .4527 .3058 .3608
2 .4510 .4900 .4906 .3150 .3423
6/8 .2351 .3600 .2583 .2755 .4218
6 .2657 .3600 .2908 .2899 .3928
4 .2964 .3600 .3233 .3025 .3675
2 .3270 .3600 .3558 .3136 .3452
5/10 .1207 .2500 .1343 .2391 .4950
8 .1463 .2500 .1614 .2623 .4484
6 .1718 .2500 1884 .2815 .4097
4 .1973 .2500 .2155 .2977 .3772
2 .2228 .2500 .2426 .3115 .3495
4/10 .0568 .1600 .0642 .2022 .5692
8 .0773 .1600 .0859 .2391 .4951
6 .0977 .1600 .1076 .2674 .4381
4 .1181 .1600 .1292 .2899 .3928
2 .1385 .1600 .1509 .3082 .3560
3/8 .0282 .0900 .0321 .1874 .5990
6 .0435 .0900 .0484 .2391 .4950
4 .0588 .0900 .0646 .2755 .4218
2 .0741 .0900 .0808 .3025 .3675
2/6 .0091 .0400 .0106 .1518 .6702
4 .0192 .0400 .0215 .2388 .4954
2 .0295 .0400 .0323 .2898 .3929 ​
BG 8/4 0.5530 0.6400 0.7792 0.2804 0.3245
2 .5944 .6400 .7348 .3019 .3250
7/6 .3782 .4900 .6452 .2499 .3238
4 .4144 .4900 .6063 .2743 .3244
2 .4506 .4900 .5674 .2988 .3249
6/6 .2645 .3600 .4884 .2377 .3235
4 .2956 .3600 .4550 .2661 .3242
2 .3266 .3600 .4216 .2947 .3248
5/10 .1191 .2500 .4086 .1531 .3215
8 .1449 .2500 .3808 .1868 .3223
6 .1708 .2500 .3530 .2207 .3231
4 .1966 .2500 .3252 .2548 .3239
2 .2225 .2500 .2974 .2890 .3247
4/10 .0555 .1600 .2837 .1112 .3205
8 .0762 .1600 .2615 .1531 .3215
6 .0969 .1600 .2393 .1953 .3225
4 .1176 .1600 .2170 .2377 .3235
2 .1383 .1600 .1948 .2804 .3245
3/10 .0119 .0900 .1805 .0420 .3188
8 .0274 .0900 .1638 .0973 .3201
6 .0429 .0900 .1471 .1531 .3215
4 .0584 .0900 .1304 .2094 .3228
2 .0739 .0900 .1137 .2661 .3242
2/6 .0087 .0400 .0765 .0695 .3196
4 .0191 .0400 .0653 .1532 .3215
2 .0294 .0400 .0542 .2377 .3235
B 8/4 0.5948 0.6400 0.8861 0.2804 0.3018
2 .6153 .6400 .7882 .3011 .3132
7/4 .4509 .4900 .6996 .2749 .2987
2 .4688 .4900 .6140 .2981 .3115
6/6 .3116 .3600 .6082 .2434 .2813
4 .3269 .3600 .5349 .2676 .2946
2 .3422 .3600 .4616 .2941 .3093
5/10 .1843 .2500 .5751 .1826 .2477
8 .1972 .2500 .5140 .2051 .2601
6 .2099 .2500 .4529 .2300 .2739
4 .2227 .2500 .3918 .2576 .2892
2 .2355 .2500 .3307 .2886 .3063
4/8 .1077 .1600 .4169 .1574 .2337
8 .1180 .1600 .3680 .1826 .2477
6 .1282 .1600 .3192 .2111 .2634
4 .1385 .1600 .2703 .2434 .2813
4 .1487 .1600 .2214 .2805 .3018
3/8 .0587 .0900 .2437 .1496 .2294
2/6 .0664 .0900 .2070 .1827 .2476
4 .0741 .0900 .1704 .2215 .2691
2 .0817 .0900 .1337 .2676 .2946
2/6 .0244 .0400 .1165 .1348 .2212
4 .0295 .0400 .0920 .1826 .2477
2 .0346 .0400 .0676 .2434 .2813
PB 8/4 0.6405 .0.6400 .0.9135 .0.2920 .0.2917
2 .6382 .6400 .8014 .3069 .3078
7/4 .4910 .4900 .7228 .2882 .2876
2 .4889 .4900 .6257 .3047 .3054
6/6 .3630 .3600 .6382 .2667 .2645
4 .3612 .3600 .5549 .2830 .2821
2 .3594 .3600 .4716 .3018 .3023
5/10 .2558 .2500 .6167 .2279 .2227
8 .2543 .2500 .5473 .2419 .2377
6 .2528 .2500 .4779 .2578 .2549
4 .2513 .2500 .4084 .2763 .2748
2 .2498 .2500 .3391 .2978 .2980
4/10 .1649 .1600 .4501 .2128 .2064
8 .1637 .1600 .3946 .2279 .2227
6 .1625 .1600 .3391 .2456 .2418
4 .1613 .1600 .2836 .2667 .2645
2 .1601 .1600 .2281 .2921 .2918
PB 3/10 0.0939 0.0900 0.3052 0.1920 0.1840
8 .0930 .0900 .2637 .2082 .2015
6 .0921 .0900 .2220 .2279 .2227
2 .0912 .0900 .1804 .2522 .2489
2 .0903 .0900 .1387 .2831 .2821
2/6 .0416 .0400 .1270 .1993 .1918
4 .0410 .0400 .0987 .2280 .2226
2 .0403 .0400 .0709 .2667 .2644
P 8/4 0.6804 .0.6400 .0.8924 .0.3075 .0.2892
2 .6581 .6400 .7914 .3150 .3063
7/4 .5258 .4900 .7063 .3053 .2845
2 .5063 .4900 .6170 .3138 .3037
6/4 .3911 .3600 .5400 .3030 .2788
2 .3744 .3600 .4641 .3124 .3004
5/10 .3182 .2500 .5856 .2758 .2167
8 .3042 .2500 .5224 .2826 .2322
6 .2902 .2500 .4592 .2904 .2501
4 .2763 .2500 .3960 .2996 .2711
2 .2623 .2500 .3328 .3104 .2958
4/10 .2148 .1600 .4253 .2684 .2000
8 .2036 .1600 .3748 .2758 .2167
6 .1924 .1600 .3242 .2844 .2365
4 .1813 .1600 .2737 .2948 .2602
2 .1701 .1600 .2231 .3075 .2892
3/10 .1314 .0900 .2868 .2586 .1771
8 .1230 .0900 .2488 .2664 .1949
6 .1146 .0900 .2109 .2759 .2166
4 .1062 .0900 .1730 .2877 .2438
2 .0978 .0900 .1350 .3030 .2788
2/6 .0565 .0400 .1190 .2622 .1857
4 .0509 .0400 .0937 .2757 .2167
2 .0453 .0400 .0684 .2948 .2602
RP 8/4 0.7174 .0.6400 .0.7766 .0.3362 .0.2999
2 .6766 .6400 .7335 .3300 .3122
7/6 .5940 .4900 .6422 .3441 .2839
4 .5582 .4900 .6043 .3378 .2965
2 .5225 .4900 .5664 .3309 .3104
6/6 .4494 .3600 .4857 .3470 .2780
4 .4188 .3600 .4533 .3399 .2922
2 .3882 .3600 .4208 .3321 .3080
5/10 .3759 .2500 .4050 .3646 .2425
8 .3504 .2500 .3779 .3582 .2555
6 .3249 .2500 .3509 .3510 .2700
4 .2994 .2500 .3238 .3429 .2863
2 .2739 .2500 .2967 .3337 .3047
4/10 .2610 .1600 .2809 .3719 .2279
8 .2406 .1600 .2592 .3646 .2425
6 .2202 .1600 .2376 .3564 .2590
4 .1998 .1600 .2159 .3470 .2779
2 .1794 .1600 .1942 .3361 .2998
3/10 .1659 .0900 .1783 .3821 .2073
8 .1506 .0900 .1620 .3741 .2235
6 .1353 .0900 .1458 .3646 .2425
4 .1200 .0900 .1296 .3536 .2650
2 .1047 .0900 .1133 .3399 .2922
2/6 .0703 .0400 .0756 .3781 .2152
4 .0601 .0400 .0648 .3646 .2426
2 .0499 .0400 .0540 .3470 .2780
N 9 0.8046 0.8100 0.8737. 0.3234 0.3255
8 .6358 .6400 .6903 3234 .3255
7 .4868 .4900 .5285 .3234 .3255
6 .3576 .3600 .3883 .3234 .3255
5 .2483 .2500 .2697 3234 .3255
4 .1589 .1600 .1726 .3234 .3255
3 .0894 .0900 .0971 .3234 .3255
2 .0400 .0397 .0431 .3234 .3255
1 .0099 .0100 .0108 .3234 .3255
​
Table IV. Maximum Munsell chromas producible by real pigments.
Hue VALUE 2 VALUE 3 VALUE 4 VALUE 5 VALUE 6 VALUE 7 VALUE 8
R 7.7 11.6 15.4 17.8 16.8 13.5 9.6
YR 3.5 5.5 7.1 8.9 10.6 12.4 12.4
Y 3.7 4.0 7.0 8.0 10.0 12.4 13.4
GY 3.5 4.9 5.0 8.4 10.2 12.0 13.5
G 7.2 10.6 13.9 16.6 19.2 20.3 19.2
BG 6.6 9.5 12.0 13.6 14.7 14.7 13.3
B 9.1 12.9 14.0 17.5 18.6 15.3 10.0
PB 19.1 28.9 36.7 25.3 18.9 15.2 12.2
P 64.6 52.2 39.5 28.3 21.4 15.0 9.5
RP 17.3 23.5 27.2 26.2 24.3 19.6 12.8

ized conditions. The procedure need not be included here, since it is discussed in detail by Gibson and Nickerson in the paper[4] following this one.

If Priest, Gibson, and McNicholas had investigated only five chromatic colors instead of fifteen, there would have been no choice in the selection of data upon which to base these calculations. However, since an arbitrary choice of data must be made, it seemed appropriate to select the five principal colors R5/5, Y5/5, G5/5, B5/5, and P5/5. Use is also made of the rule that a mixture of the five principal colors in equal proportions yields N5/, which according to this definition is nearly but not quite the color of a nonselective surface.

Reference to Table I will disclose the fact that the five principal colors are not precisely of value 5 as intended by Professor Munsell. Instead, Y varies from a minimum of 0.2140 to a maximum of 0.2662. In view of the difficulties this paper may call attention to the fact that the involved in heterochromatic photometry, which were more serious then than now, it seemed reasonable to multiply each set of tristimulus principal color accurately to value 5. This procedure does not alter the hue of the principal colors, and it makes only a trifling change in the chroma. After this adjustment, the basic data relative to the principal colors are as listed in Table II.

The data in Table III indicate what the Munsell Atlas of Color would have been if, starting with the five basic colors as defined in Table II, the extension of the system had been entrusted to the standard I.C.I. observer working under Illuminant C. The first column indicates the Munsell designation. This is followed by three columns giving the corresponding tristimulus specifications. Columns 5 and 6 list the trichromatic coefficients, x and y.

Professor Munsell devoted much attention to speculations concerning the shape of the color solid that results from the representation of hue, value, and chroma in cylindrical coordinates. His speculations had, perforce, to be based on the color gamut obtainable with pigments that were then available, and he was obviously unable to predict what new pigments might result from chemical research. By application of the work of MacAdam on “The maximum visual efficiency of colored materials,”[5] it is now possible to establish the limits of the Munsell color solid which newly discovered pigments may approach but will never exceed. This gamut is expressed most conveniently in terms of the maximum chroma corresponding to a given hue and value, as in Table IV.

Since the Munsell Book of Color, which appeared in 1929, was intended to supplant the original Atlas of the Munsell Color System, it is not immediately obvious that the publication of this paper serves, at this time, a useful purpose. We believe that its publication is justified on the ground that it calls belated attention to the remarkable scientific insight of Professor A. H. Munsell. At a time when there was little to suggest such a procedure, he formulated rules for the construction of a psychophysical color system that could be used today without apology. We believe also that the publication of this paper may call attention to the fact that the psychophysical definitions of the terms hue, value, and chroma given in the Atlas of the original Munsell Color System differ from the specifications by a factor that would bring each purely psychological definitions used since the death of Professor Munsell.

The writers are indebted to Mrs. Blanche Bellamy, Manager of the Munsell Color Company, Inc., Baltimore, Maryland, for the loan of Professor Munsell’s Diary; to Dr. Walter Scott for valuable suggestions; and to Mrs. Arthur Howland for permission to review correspondence between her late husband and Professor Munsell. Miss Dorothy Nickerson has extended most gracious assistance in connection with the calculations.

  1. ↑ Tech. Paper No. 167, Bur. Stand. (1919).
  2. ↑ These operations are partly described in Chapter V of A Color Notation, by A. H. Munsell (Ellis, Boston, 1907), and the description is completed in the Atlas of the Munsell System (Wadsworth-Howland, Malden, Massachusetts,
  3. ↑ During his early work, Professor Munsell defined chroma in such a manner that when a chromatic color is mixed with a neutral on a Maxwell disk, the chroma of the mixture is less than that of the chromatic color in proportion to the fraction of the area of the disk occupied by the neutral. The type of color system to which this definition leads is discussed in a bachelor’s thesis by John E. Tyler on file in the Library at the Massachusetts Institute of Technology.
  4. ↑ J. Opt. Soc. Am. 30, 591 (1940).
  5. ↑ . D. L. MacAdam, J. Opt. Soc. Am. 25, 361 (1935).
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