Journal of the Optical Society of America/Volume 30/Issue 12/Analysis of the Munsell Color System

by Kasson S. Gibson and Dorothy Nickerson

An Analysis of the Munsell Color System Based on Measurements Made in 1919 and 1926

Kasson S. Gibson and Dorothy Nickerson

Introduction

THREE reports have been made by the National Bureau of Standards on papers representative of the Munsell color system: First, a very early report (No. 10,696) dated February 28, 1912, from P. G. Nutting to A. H. Munsell, giving dominant wave-length, percent white, and the reflection coefficient on six cards, which included the principal hues at 5/5, submitted to the Bureau by Mr. Munsell (1)^[1]; second, report No. 23,998 dated June, 1919, to the Munsell Color Company (later published as Bureau of Standards Technologic Paper No. 167 by Priest, Gibson, and McNicholas) (2) giving spectro-photometric data on nine neutral grays and three samples of each of the five principal hues; and third, report No. 46,045 (1), dated September 14, 1926, on “The spectral reflection of 70 representative colored cards from the Munsell color system.” This third report was made to the Munsell Research Laboratory as a part of the cooperative work then being carried on between the two laboratories under the supervision of I. G. Priest, at that time chief of the Colorimetry Section, National Bureau of Standards, and A. E. O. Munsell, Director of the Munsell Research Laboratory.

The first report is not based on spectrophotoetric data, and was made before publication of the complete Atlas of the Munsell Color System (3), but it is noted here because it indicates that from a very early date A. H. Munsell was intent upon standardization, particularly of the five basic “middle colors” around which his system was built. The second report has been published (2) and is therefore a matter of record. The data of the third report, obtained in 1926, are published for the first time in this paper.

For this 1926 test 70 samples were selected by A. E. O. Munsell for measurement, and submitted, not only as an exemplification of the Munsell system as it existed in 1926 but as an exemplification, as far as it was then possible, of the original system developed by A. H. Munsell. The samples were either the original paintings which had been kept unexposed in the files, or, where such were not available, duplicates that had been made to match the originals as accurately as possible whenever the supply of an original color was nearly exhausted. The samples were submitted in sheets 8 by 8 inches square, and were representative of the most highly saturated colors of the system as it then existed.^[2] Their Munsell notations are given in Table I.

Table 1. Notations of the 70 Munsell Atlas samples measured at the National Bureau of Standards in 1926, NBS test 46,045.

Hue
Name	Symbol	Value and Chroma V/C
Red	R	2/4	3/7	4/10	5/10	6/8	7/6	8/4
Yellow-red	YR	2/1	3/4	4/5	5/7	6/8	7/7	8/5
Yellow	Y	2/1	3/3	4/5	5/7	6/7	7/8	8/9
Green-yellow	GY	2/1	3/3	4/5	5/6	6/8	7/7	8/6
Green	G	2/1	3/4	4/7	5/7	6/7	7/7	8/5
Blue-green	BG	2/2	3/4	4/5	5/5	6/5	7/5	8/3
Blue	B	2/4	3/5	4/6	5/6	6/5	7/4	8/2
Purple-blue	PB	2/2	3/9	4/10	5/8	6/6	7/4	8/2
Purple	P	2/3	3/6	4/6	5/6	6/4	7/3	8/2
Red-purple	RP	2/2	3/6	4/6	5/6	6/4	7/4	8/2

Methods of Measurement in 1926 Test

Three instruments were used to obtain the spectrophotometric data given in the 1926 report, all of the values being expressed relative to freshly prepared magnesium oxide.

Diffuse illumination, normal reflection, visual method

The König-Martens spectrophotometer with auxiliary equipment (4) was used to obtain data under these conditions. Measurements were made at every 20 mμ from 420 to 720 mμ. In addition to the usual precautions to eliminate stray-light, wave-length, and slit-width errors, the order of wave-lengths chosen for measurement was such as to detect any change in the sample during measurement, so that if such change occurred the data could be corrected to apply as nearly as possible to the sample as it was at the start of the measurements. For these measurements and for those with the other instruments, small samples were cut for measurement from the large 8×8-inch sheets. A complete set of measurements was made on each of the 70 samples by W. Greenberg, research associate placed at the Bureau for this purpose by the Munsell Research Laboratory. Check measurements were later made by other observers, H. J. McNicholas, P. Rudnick and W. Greenberg, on different samples cut from the same large sheets. Such checks were made particularly for samples which changed during the first set of measurements.

Fig. 1. Work sheet of spectrophotometric data and adopted values for Munsell Atlas sample RP 3/6, as used in National Bureau of Standards Test No. 46045 (1926 data). This is typical of the work sheets used for each of the 70 samples of that test. Key: open circles, diffuse-normal visual data; larger closed circles, 45°-normal visual data; smaller closed circles, 45°-normal photographic data; continuous line, adopted diffuse-normal data; dashed line, adopted 45°-normal data: values below 0.10 are also magnified by 10.

45° illumination, normal reflection, visual method

The Martens photometer with filters was used with improvised equipment to obtain these data. Two light sources were used. The first was a quartz-mercury arc, with filters isolating in turn the light at 578 (577.0+579.1), 546.1, 435.8, and 405 (404.7+407.8) mμ. The efficiency of the filters was such that the light transmitted by the filter from the next most luminous line was not more than one percent of the light nominally being used. In addition, the red light from the arc was absorbed by a blue-green glass where the filter would otherwise transmit this. Plate glass prevented radiant energy of wave-length less than 320 mμ from reaching the sample. The second source was an incandescent lamp with filters isolating spectral regions centering at 501, 651, and 703 mμ for a white surface. The data obtained in this way, while meager with respect to wave-length, had the advantage of yielding values applying to 45°-normal illuminating-viewing conditions, and of being free from errors caused by fading during measurements. Polarization errors were eliminated by proper orientation of the Martens photometer, the plane of the sample, and the direction of illumination. Measurements were made by P. Rudnick and K. S. Gibson.

Fig. 2. One of ten figures given in the report on National Bureau of Standards Test 46045 (1926 data) showing adopted diffuse-normal (continuous lines) and 45°-normal (dashed lines) data for the eight samples of each of the ten hue designations of the Munsell Atlas colors. This illustration is for the eight samples of the blue-green (BG) series.

45° illumination, normal reflection, photographic method

Inasmuch as zinc oxide was understood to be an important constituent of many of the pigments of the Munsell samples it seemed desirable to obtain data from 380 to 420 mμ, rather than to estimate over this range solely on the basis of the values at 405 mμ, since the reflectance of zinc oxide was known to vary strongly between 405 and 365 mμ (5). Accordingly, measurements were made photographically on most of the samples,^[3] using the Hilger sector-photometer equipment (6) adapted to reflection measurements with incandescent lamps as source. All of the photographic measurements were made by H. J. McNicholas.

Reduction of the 1926 Spectrophotmetric Data

All of the data obtained by the above methods, to quote the 1926 report, “were plotted as a function of wave-length. A separate curve sheet was used for each sample. Values of $R_{x}/R_{0}$ (apparent reflectance of the sample relative to that of MgO) less than 0.10 were also magnified by 10 in plotting....

Table II. Trichromatic analysis of Munsell Atlas colors,1919 data. Values computed from spectrophotometric data in Bureau of Standards Technologic Paper No. 167 (B.S. test report 23,998) on the basis of the I.C.I. standard observer and coordinate system and for I.C.I. Illuminant C.

Munsell Notation		Tristimulus Specifcations			Trichromatic Coefficients		Dominant Wave-Length*	Excitation Purity*
		X	Y	Z	x	y	Λ	$P_{0}$
R	7/5	0.4951	0.4399	0.4305	0.3626	0.3221	605	15.7
	5/5	.2678	.2140	.1713	.4101	.3276	604	29.8
	3/2	.0977	.0878	.0809	.3667	.3295	597	18.8
Y	7/4	.4661	.4869	.2625	.3835	.4006	577.5	42.2
	5/5	.2605	.2662	.1024	.4141	.4232	577.3	56.7
	3/2	.0950	0974	.0708	.3611	.3700	577.0	28.2
G	7/4	.4173	.4860	.4688	.3041	.3542	542	9.0
	8/5	.1811	.2454	.1982	.2899	.3928	534	16.3
	3/2	.0766	.0933	.0952	.2888	.3519	513	7.5
R	7/4	.4325	.4827	.6573	.2750	.3070	487.7	13.8
	5/5	.2246	.2595	.4385	.2434	.2813	484.4	27.8
	3/2	.0822	.0904	.1412	.2620	.2881	483.5	20.5
P	7/3	.5162	.4978	.6613	.3081	.2972	555 c	7.2
	5/5	.2773	.2448	.4187	.2948	.2602	562 c	19.6
	3/2	.0981	.0921	.1553	.2838	.2667	453	16.8

* Reference point (heterogeneous stimulus): I.C.I. Iluminant C.

“Smooth average curves were then drawn through the values obtained on the König-Martens spectrophotometer with diffuse illumination, the relative shape of the curves in the violet being influenced by the photographic data.

“With a relative shape following as closely as possible the curves for diffuse illumination just described, dotted curves were then plotted through the values obtained on the Martens photometer with approximately 45° illumination. . . . In some cases in the violet the shape of the curves was determined primarily by the Martens photometer values instead of by the König-Martens spectrophotometer values.

“In addition to the plotted values obtained photographically, the plates themselves were in most cases examined and the shape of the curves in the violet finally determined . . . from all of the data available. In general no attempt was made to keep the curves for diffuse and 45° illumination separated at 380 and 390 (mμ) where the reflection is varying rapidly.

Table III. Trichromatic analysis of Munsell Atlas colors, 1926 data, diffuse illumination. Values computed from spectrophotometric data given in Bureau of Standards Test Report 46,045 on the basis of the I.C.I. standard observer and coordinate system and for I.C.I. Illuminant C.

Munsell Notation		Tristimulus Specifcations			Trichromatic Coefficients		Dominant Wave-Length*	Excitation Purity*
		X	Y	Z	x	y	Λ	$P_{0}$
R	8/4	0.6796	0.6311	0.6388	0.3486	0.3237	599	12.1
	7/6	.5336	.4522	.4130	.3824	.3228	606	21.0
	6/8	.4347	.3368	-2726	.4164	.3226	600	30.1
	5/10	.3218	.2137	.1316	.4824	.3203	613	47.1
	4/10	.2543	.1363	.0894	.5086	.3126	620	52.2
	3/7	.1224	.0846	.0591	.4600	.3179	615	40.5
	2/4	.0543	.0439	.0435	.3831	.3100	640	18.0
YR	8/5	.6334	.6015	.3992	.3876	.3681	583.2	34.5
	7/7	.4999	.4567	.2535	.4131	.3774	584.8	44.0
	6/8	.4397	.3677	.0962	.4866	.4069	586.8	71.5
	5/7	.2637	.2253	.0920	.4539	.3878	587.4	57.5
	4/5	.1927	.1598	.0656	.4610	.3822	589.1	58.2
	3/4	.1028	.0937	.0622	.3972	.3623	586.5	35.8
	2/1	.0530	.0528	.0515	.3372	.3354	582.5	12.5
Y	8/9	.5478	.5717	.1222	.4411	.4604	576.3	73.8
	7/8	.4697	.4841	.1052	.4435	.4572	576.8	73.5
	6/7	.3523	.3627	.0970	.4339	.4467	576.9	68.2
	5/7	.2345	.2382	.0815	.4231	.4298	577.6	60.8
	4/5	.1719	.1214	.0639	.4220	.4210	578.5	58.1
	3/3	.0943	.0967	.0626	.3720	.3812	576.9	34.0
	2/1	.0544	.0556	.0503	.3393	.3470	577.0	16.1
GY	8/6	.5138	.6034	.3121	.3595	.4222	567.8	41.7
	7/7	.4058	.5004	.1844	.3721	.4588	567.0	55.0
	6/8	.3313	.4131	.1440	.3730	.4650	366.5	57.0
	5/6	.1676	.2009	.1062	.3531	.4232	566.2	40.1
	4/5	.1565	.1902	.0811	.3659	.4445	567.0	49.5
	3/3	.0935	.1056	.0729	.3439	.3881	567.8	28.3
	2/1	.0463	.0498	.0477	.3220	.3464	566.0	11.2
G	8/5	.5505	.6259	.6157	.3072	.3493	546	8.3
	7/7	.4208	.5241	.4650	.2984	.3718	538	12.3
	6/7	.3141	.4160	.3243	.2979	.3945	542	18.4
	5/7	.1812	.2873	.2118	.2663	.4224	523	20.5
	4/7	.1332	.2033	.1555	.2708	.4132	523	18.8
	3/4	.0792	.0946	.0964	.2931	.3501	518	6.8
	2/1	.0450	.0493	.0500	.3118	.3419	554	7.5
BG	8/3	.5836	.6383	.7236	.2964	.3298	504	4.5
	7/5	.4596	.5.359	.6168	.2851	.3324	499	8.4
	6/5	.3611	.4454	.5773	.2610	.3219	492	17.8
	5/5	.2119	.2726	.3227	.2625	.3378	496	16.4
	4/5	.1394	.1920	.2840	.2265	.3120	490	31.5
	3/4	.0741	.0875	.1477	.2396	.2828	485	29.3
	2/2	.0429	.0506	.0751	.2543	.3003	488	22.0
B	8/2	.6362	.6730	.8941	.2887	.3054	484.6	9.0
	7/4	.4840	.5341	.7490	.2739	.3023	486.3	14.7
	6/5	.3891	.4308	.7340	.2504	.2772	482.5	26.0
	5/6	.2431	.2824	.5431	.2275	.2643	483.0	35.5
	4/6	.1459	.1705	.3751	.2110	.2466	482.0	43.6
	3/5	.1054	.1161	.2676	.2154	.2374	480.2	43.0
	2/4	.0429	.0475	.1061	.2182	.2417	480.5	41.6
PB	8/2	.6433	.6589	.8758	.2954	.3025	478.4	7.0
	7/4	.4449	.4619	.7333	.2713	.2816	479.0	17.9
	6/6	.3845	.3966	.6989	.2598	.2680	478.1	23.7
	5/8	.2650	.2697	.5749	.2388	.2430	477.0	34.5
	4/10	.1865	.1797	.5388	.2060	.1986	475.3	51.5
	3/9	.1020	.0881	.3240	.1984	.1713	472.0	58.3
	2/2	.0458	.0444	.1072	.2319	.2252	474.7	39.5
P	8/2	.6343	.6197	.8163	.3064	.2993	560 c	6.0
	7/3	.5398	.5223	.6626	.3130	.3028	537 c	6.0
	6/4	.4248	.3948	.5721	.3052	.2837	558 c	12.2
	5/6	.2843	.2536	.4230	.2958	.2640	562 c	18.3
	4/6	.2115	.1799	.3159	.2990	.2543	559 c	23.0
	3/6	.1325	.1090	.2324	.2796	.2300	565 c	29.0
	2/3	.0540	.0461	.0893	.2850	.2435	565 c	24.7
RP	8/2	.6718	.6510	.7869	.3185	.3086	503	c 4.7
	7/4	.6142	.5594	.6765	.3320	.3024	499	c 9.8
	6/4	.4276	.3829	.4934	.3279	.2937	508 c	12.5
	5/6	.3055	.2597	.3438	.3361	.2857	506 c	17.0
	4/6	.2020	.1603	.2375	.3368	.2673	515 c	24.6
	3/6	1179	.0884	.1509	.3301	.2475	532 c	31.3
	2/2	.0545	.0466	.0686	3211	.2748	534 c	19.0

* Reference point (beterogeneous stimulus): I.C.I. Illuminant C.

“Values of $R/R_{0}$ were read at every 10 mμ from the curves as thus plotted.”

These values are tabulated in the original report, and the colorimetric data which follow are based upon them. It seems unnecessary to give these spectrophotometric data here in detail, but Figs. 1 and 2 are shown to illustrate the nature and extent of the work.

Figure 1 shows the working plot for RP 3/6. It includes the diffuse-normal, König-Martens spectrophotometric data, with some check points; the 45°-normal Martens photometer (with filters) data; the 45°-normal photographic data, 370 to 460 mμ, showing the absorption from the ZnO below 400 mμ; the plotting to a 10-times scale of values below 0.10; and the smooth curves drawn through the diffusenormal and the 45°-normal data. The final judgment as to the true course of all of the curves (representing the adopted values) was made by the senior author of the present paper.

Table IV. Trichromatic analysis of Munsell Atlas colors, 1926 data, 45° illumination. Values computed from spectrophotometric data given in Bureau of Standards Test Report 46,045 on the basis of the I.C.I. standard observer and coordinate system and for I.C.I. Illuminant C.

Munsell Notation		Tristimulus Specifcations			Trichromatic Coefficients		Dominant Wave-Length*	Excitation Purity*
		X	Y	Z	x	y	Λ	$P_{0}$
R	8/4	0.6807	0.6318	0.6419	0.3483	0.3233	599	12.1
	7/6	.5399	.4598	.4122	.3824	.3256	603	22.
	6/8	.4406	.3430	.2697	.4183	.3256	606	31.5
	5/10	.3224	.2114	.1277	.4874	.3195	614	48.2
	4/10	.2536	.1557	.0844	.5138	.3153	617	54.1
	3/7	.1215	.0841	.0552	.4659	.3225	612	43.2
	2/4	.0518	.0420	.0385	.3914	.3175	615	22.0
YR	8/5	.6345	.6059	.4038	.3859	.3685	582.8	34.1
	7/7	.5026	.4616	.2480	.4146	.3808	584.5	45.2
	6/8	.4478	.3787	.0973	.4848	.4099	586.3	71.8
	5/7	.2666	.2273	.0880	.4581	.3906	587.2	59.8
	4/5	.1956	.1652	.0660	.4582	.3871	587.8	58.8
	3/4	.1002	.0920	.0578	.4009	.3680	585.8	38.0
	2/1	.0496	.0484	.0466	.3434	.3345	586.2	13.8
Y	8/9	.5514	.5833	.1199	.4395	.4649	575.7	74.4
	7/8	.4678	.4898	.1067	.4396	.4602	576.2	73.4
	6/7	.3524	.3673	.1000	.4299	.4481	576.3	67.5
	5/7	.2329	.2408	.0807	.4201	.4343	576.6	61.2
	4/5	.1681	.1688	.0612	.4223	.4240	578.2	59.2
	3/3	.0919	.0947	.0590	.3742	.3857	576.5	35.9
	2/1	.0519	.0532	.0492	.3365	.3446	576.5	14.7
GY	8/6	.5060	.5953	.3018	.3606	.4243	567.8	42.6
	7/7	.4010	.4952	.1750	.3743	.4623	567.1	56.5
	6/8	.3260	.4111	.1424	.3707	.4674	566.1	57.0
	5/6	.1615	.1929	.0991	.3562	.4253	566.6	41.8
	4/5	.1519	.1887	.0767	.3640	.4521	566.0	51.0
	3/3	.0868	.0982	.0666	.3449	.3902	567.8	29.2
	2/1	.0444	.0468	.0450	.3260	.3435	570.8	11.5
G	8/5	.5395	.6179	.5985	.3072	.3519	546	9.0
	7/7	.4129	.5181	.4600	.2968	.3725	536	12.2
	6/7	.3067	.4082	.3218	.2959	.3938	534	17.7
	5/7	.1782	.2862	.2080	.2650	.4256	523	21.2
	4/7	.1261	.1944	.1428	.2722	.4195	526	20.3
	3/4	.0748	.0900	.0902	.2934	.3529	520	7.2
	2/1	.0424	.0459	.0473	.3128	.3385	556	6.8
BG	8/3	.5594	.6229	.6971	.2977	.3314	507	4.1
	7/5	.4476	.5213	.5939	.2864	.3356	500	7.8
	6/5	.3489	.4343	.5531	.2611	.3250	493	17.8
	5/5	.2003	.2603	.3058	.2613	.3396	497	16.4
	4/5	.1272	.1748	.2637	.2249	.3089	490	32.2
	3/4	.0696	.0823	.1382	.2398	.2838	485	29.2
	2/2	.0391	.0457	.0709	.2512	.2935	486	23.9
B	8/2	.6321	.6679	.8731	.2909	.3074	485.1	7.9
	7/4	.4722	.5217	.7294	.2740	.3027	486.4	14.7
	6/5	.3778	.4202	.7241	.2482	.2761	482.7	26.9
	5/6	.2317	.2731	.5203	.2260	.2664	483.5	36.0
	4/6	.1437	.1661	.3646	.2131	.2463	481.7	42.9
	3/5	.0977	.1076	.2493	.2150	.2367	480.1	43.4
	2/4	.0398	.0447	.0981	.2180	.2448	480.9	41.3
PB	8/2	.6417	.6546	.8702	.2962	.3022	477.2	6.8
	7/4	.4477	.4261	.7350	.2722	.2809	478.6	17.6
	6/6	.3800	.3894	.6988	.2588	.2652	477.5	24.5
	5/8	.2616	.2653	.5699	.2385	.2419	476.8	34.7
	4/10	.1796	.1773	.5248	.2038	.2011	476.1	52.1
	3/9	.0993	.0859	.3191	.1969	.1703	472.2	59.0
	2/2	.0430	.0430	.0972	.2347	.2348	476.1	37.0
P	8/2	.6272	.6161	.7907	.3084	.3029	556 c	5.0
	7/3	.5324	.5110	.6536	.3137	.3011	535 c	6.7
	6/4	.4245	.3936	.5650	.3069	.2846	556 c	12.1
	5/6	.2785	.2480	.4076	.2982	.2655	561 c	18.2
	4/6	.2080	.1727	.3124	.3001	.2492	558 c	25.0
	3/6	.1271	.1022	.2216	.2819	.2266	564 c	30.9
	2/3	.0509	.0436	,0856	.2826	.2420	565 c	24.7
RP	8/2	.6710	.6525	.7599	.3221	.3132	494 c	3.5
	7/4	.6029	.5508	.6600	.3324	.3037	498 c	9.5
	6/4	.4223	.3776	.4834	.3291	.2942	506 c	12.5
	5/6	.2968	.2509	.3263	.3396	.2871	504 c	17.2
	4/6	.1991	.1555	.2311	.3399	.2655	513 c	26.0
	3/6	.1134	.0850	.1337	.3414	.2559	516 c	30.2
	2/2	.0514	.0436	.0606	.3302	.2802	514 c	18.3

TABLE V. Average values of Y for samples in 1919 and 1926 tests. These values are computed from the data of Tables II, III and IV, except for the neutral samples, for which the values are taken from Bureau of Standards Technologic Paper No. 167.

Munsell Value
	1919		1926 Chromatic Samples
	Chromatic Samples	Neutral Samples[4]	Illumination at
			45°	Diffuse
	Y	Y	Y	Y
9/		0.772
8/		.602	.0.6248	0.6274
7/	0.4787	.465	.4991	.5031
6/		.343	.3923	.3947
5/	.2460	.234	.2456	.2503
4/		-161	.1719	.1763
3/	.0922	.090	.0922	.0964
2/		041	.0457	0.487
1/		.018

Figure 2 is one of the ten illustrations in the original report which show the deviations between the data as adopted for the diffuse-normal and the 45°-normal conditions. These blue-green samples have been selected for illustration because they show the greatest variation in dominant wave-length. Figure 2 also illustrates the general tendency for the apparent reflectances for the diffuse-normal conditions to be higher than those for the 45°-normal conditions.

Colormetric Computations

Colorimetric computations were not made in 1919 nor in 1926, but have been completed during the past year, computations of the 1926 data being made for both the diffuse-normal and the 45°-normal conditions. These computations were made on the basis of the 1931 I.C.I. standard observer and coordinate system and for I.C.I. Illuminant C. The weighted ordinate method was used, summations being taken at every 10 mu. Values of dominant wave-length (A) and excitation purity (P.) have been read from the charts of the Hardy Handbook of Colorimetry (7). Values of X, Y, Z, of x, y, of A, and of P, are given in Tables II, III and IV.

It will be recalled that the values of Y represent the luminous apparent reflectances relative to MgO. Table V gives the average values of Y for the respective Munsell samples in Tables II, III and IV, and for the neutral samples given in the 1919 report (2).

Fig. 3. These data show the relation between luminous apparent reflectance (relative to magnesium oxide) and the square of Munsell value, as obtained in the 1919 and 1926 measurements on the Munsell Atlas samples.

Tests for Conformity of the 1919 and 1926
Data to the Psychophysical System
Described by A. H. Munsell

A. H. Munsell left two representations of his system, first, the charts of his Atlas, and second, statements concerning the method by which they might be tested. Without doubt he intended the charts to exemplify the laws of color sensation by illustrations of equally stepped scales of hue, value, and chroma. Also without doubt he intended these as “measured scales”, and described them as having been measured, value by the photometer, and chroma by matches made on Maxwell spinning disks. The rule used for measuring chroma is that colors of complementary or opposite hue balance to gray in areas that are in inverse proportion to the products of their values and chromas.

The Munsell color system was based upon five color standards so chosen as to appear to be of the same lightness, the same saturation, and equally separated in hue. From these five standards chosen to fulfill the purely psychological requirement of appearance, it is possible by application of the psychophysical rules given in the Atlas of the Munsell Color System to derive a whole system of color standards. This aspect of the original Munsell color system has been analyzed by Tyler and Hardy (11). It is probable that Mr. Munsell believed that a color system derived by these psychophysical rules would also conform to psychological requirements analogous to those met by the five basic standards, but we now know that the conformity is not exact. We propose therefore to inquire whether the papers measured in 1919 and 1926 represent more nearly the psychological system described by Mr. Munsell when he said (9) in 1911, “‘The solid having been built up by equal and decimal steps of sensation ...” or the psychophysical system which he implies in other places. To this end we shall compare the color specifications computed from the 1919 and 1926 measurements both with the psychophysical system and with the psychological system represented by the most adequate data that are available.

Relation between Munsell value and apparent reflectance

The value scale was the first of the three “color dimensions” to be developed by Mr. Munsell; and because he found early in his studies the relation between reflectance and value (8), he developed the Munsell daylight photometer on which value was thereafter always measured in making up the Munsell Atlas papers. He selected the cat’s-eye form of shutter because it meant that a psychologically photometer scale.^[5] The amount of light (the photometric scale) of the Munsell photometer varies in proportion to the square of the diagonal of the diaphragm opening and, since Munsell Atlas papers were all measured on this photometer, it is to be expected that $V^{2}$ will equal point $Y=1.0$, $V^{2}=100.0$ is well representative of $k(100Y)$ where $V$ is Munsell value, $Y$ is the the data as a whole. The fact that this line luminous apparent reflectance relative to MgO (hereafter termed simply the reflectance), and $k$ is a constant close to unity. This was demonstrated in the 1919 report (2) and is also pointed out by Tyler and Hardy (11).

To test this relation further we have plotted in Fig. 3^[6]: A straight line with value of $k=1$; the straight line given in Bureau of Standards Technologic Paper No. 167 as representative of the relation derived from the nine neutral samples therein described; the average values of $Y$ for Munsell values 3/, 5/, and 7/, as derived from Bureau of Standards Technologic Paper No. 167 in accordance with Table II of the present paper (1919 data); the average values of $Y$ for the respective Munsell values from 2/ to 8/, for both diffuse-normal and 45°-normal conditions, 10 values of Y entering into each of the average values of Y for each of the two illuminating-viewing conditions, these data taken from Tables III and IV (1926 data); and the extreme individual values of Y for the respective Munsell values, taken from Tables II, III or IV.

From Fig. 3 we may draw several conclusions: The relation $V^{2}=k(100Y)$ is followed approximately by both the 1919 and 1926 data, although particular samples show large deviations. Both the 1919 and 1926 data indicate that $Y$ has a small positive value (0.005 to 0.01) when the Munsell value is zero; black, in the Munsell Atlas, therefore corresponds to a luminous apparent reflectance of 0.5 to 1.0 percent. While the straight line representing the neutral samples of the 1919 data falls under the line $k=1$, a majority of the points representing the chromatic samples of the 1926 data fall above this line, satisfactory scale could be read directly on the and it is obvious that a straight line passing through the point $Y=0.007$, $V^{2}=0.0$ and the $V^{2}=100$ passes through the point $Y=1.0$, $V^{2}=100$ indicates that white, in the Munsell Atlas, is represented by fresh magnesium oxide. There are slight indications that individual values of $Y$ for any given Munsell value may be high or low as a group. The data for $V=6$ are the most definite in this respect. The data also show that the colors of certain hues are uniformly different from others in Munsell value.

Relation between Munsell hue and dominant wave-length

If the samples representing the Munsell color system conform to the simple psychophysical definition of hue by disk mixture, the points representing all samples of the same Munsell hue designation and its complementary will plot on the Maxwell triangle along a straight line passing through the neutral point (11). To test this relation all of the 1919 and 1926 data for the chromatic samples have been plotted on the (x, y)-diagram shown in Fig. 4. To assist in an evaluation of any consistent or erratic differences among the data two straight lines are plotted for each Munsell hue designation: First, a dashed line passing from the 5/5 point for each of the five principal hues through the point representing I.C.I. Illuminant C and on to the complementary; and second, a continuous line passing from the same 5/5 point through the point (DM) which results from disk mixture of these five principal hues in equal proportions.^[7]

Fig. 4. Trichromatic coefficients (trilinear coordinates) of Munsell Atlas samples as obtained from measurements made in 1919 and 1926. Also shown in this figure are the complements of the 5/5 R, Y, G, B, and P colors derived from Eqs. [5], both with I.C.I. Illuminant C as the neutral point and with the disk-mixture (DM) color as the neutral point. Note the regularity of the ten-sided figure (continuous lines) resulting from use of the DM point as compared with that (dashed lines) based on C. Each pair of points representing the experimental data is connected to a point (X) on the line joining the DM and the respective 5/5 points, these X-points being computed by Eqs. [5] and [6] for the given values of V/C.

To assist the reader to correlate the plotted points representing the experimental data with the proper pair of these dominant wave-length lines, each pair of points (45° and diffuse illumination) is connected by a light continuous line to the respective line of dominant wave-length, using the lines through DM for this purpose. The points chosen for the contact of the line connecting the experimental data with the lines of dominant wave-length, designated by crosses in Fig. 4, were determined on the basis of the psychophysical system described below and are taken from Table III of the Tyler-Hardy paper.

Fig. 5. In this figure is shown the degree to which the dominant wave-length of each Munsell Atlas sample (1926 data) departs from the average dominant wave-length for all samples of that hue designation, as derived from Tables III and IV. In each case, the arrow shows the direction of the departure and its length indicates the proportional part of the dominant wave-length interval to the adjacent hue. It illustrates the relative constancy of the dominant wave-lengths of, for example, the yellow samples and the shift of dominant wave-length for the blue-green and red-purple samples from value 8/ to value 2/. These dominant wave-lengths are all derived with I.C.I. Illuminant C as the reference point; the results would in some cases be importantly different if DM (Fig. 4) were used as the reference point.

The 1926 data of Fig. 4 are plotted in different form in Fig. 5 in order to discover whether such variations as there may be in the relation between hue and dominant wave-length are random differences, or whether there may be some regularity in the pattern of variation. Each arrow point, at the value plotted, indicates the direction and magnitude of the difference between the dominant wave-length of that sample and the average dominant wave-length of all the samples of that hue designation, the length of arrow indicating the proportional part of the whole A interval. These average dominant wave-lengths were computed from Tables III and IV.

From an examination of Figs. 4 and 5 and reference to Tables II, III and IV, we may conclude that there are many deviations from dominant wave-length constancy among the samples for a single hue and its complementary. Some of the deviations are obvious from inspection of the samples, others are not. The hue which has the most constant dominant wave-length is yellow; the hue exhibiting the least constant dominant wave-length is blue-green, the deviation for this hue being nearly enough to extend to the average dominant wavelength of Munsell blue. In addition there is a very definite trend in some of the hues for the dominant wave-lengths of the samples of high Munsell value to be greater than those for the lower values. For example, with the blue-green samples, from values 8/ to 2/, dominant wavelength progresses from 506 through 500, 492, 496, 490 to 485 and 487 mμ. A reverse progression holds for the red series, the samples of high Munsell value being shorter in wave-length than those of low value, the progression being from a dominant wave-length of 599 mμ at value 8/ to 615 (or 640) mμ at value 2/. Such progressions are suggestive of the Bezold-Brücke phenomenon (12), the change in hue produced by an increase in luminance, but it must be recalled that the samples of each Munsell hue represented by Fig. 5 differ in purity as well as in luminous apparent reflectance. So the more or less regular departures from constant dominant wave-length shown in Fig. 5 for all but the yellow and green-yellow hues may exemplify the hue change by admixture of achromatic light (19) as well as the Bezold-Brücke phenomenon, and indeed the latter phenomenon would seem to be secondary for Munsell red and yellow-red because the direction of the departures from dominant wavelength constancy indicated in Fig. 5 for those hues is such as to accentuate the hue difference ascribable to the Bezold-Brücke phenomenon instead of compensate for it. Although detailed analysis by comparison with the Newhall (15) data has yet to be made, preliminary comparisons indicate that in general the departures shown in Fig. 5 are such as to make the samples of more nearly constant hue than they would be by keeping dominant wave-length constant.

On the other hand it is clear from Fig. 4 that most of the hues may be represented by lines, whether straight or slightly curved, which pass somewhere between the neutral gray point represented by Illuminant C and that represented by the disk mixture of the five principal hues. It is particularly noticeable that for the greens and complementary red-purples, and for the purples and complementary green-yellows, straight lines passing through the illuminant point do not properly represent the respective data, but that straight lines running through the point of disk mixture (DM) represent them more closely. The data for the yellows and complementary purple-blues may be represented by straight lines passing through either of the two neutral points, which themselves differ nearly in the yellow to purple-blue direction. Further discussion of the relative significance of these two neutral points is given in the following section.

Relation between Munsell chroma and colrimetric purity

In the constant hue charts of the Munsell Atlas we find statements such as the following, which is taken from the red and blue-green chart: “Any chosen steps of red and blue-green upon this chart may be balanced by noting their symbols: Thus light blue-green (BG 8/3) balances dark red (R 2/3) when the areas are inversely as the product of the symbols, viz.—six parts of light blue-green and twenty-four parts 7 of dark red.” Similar statements with illustrations may be found on the other charts.^[8] The general rule is stated by Tyler and Hardy (11) as follows: “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.” The consequences of this psychophysical relation may be evaluated by the well-known laws of additive combination of colors by Maxwell disks (7, p. 30). This evaluation has been made easier than might have been supposed by writing out, in accord with suggestions by Dr. Judd hereby gladly acknowledged, the equations which by this relation connect the tristimulus specifications of color $V/C$ (Munsell value, $V$, Munsell chroma, $C$) with those of color 5/5 of the same hue and of color 5/0 (Munsell N 5/).

The first step is to derive the equations for the complementary color $V/-C$. Let the tristimulus specifications of the two complementary colors be $(X_{1},Y_{1},Z_{1})$ and $(X_{2},Y_{2},Z_{2})$, respectively, and let $(X_{n},Y_{n},Z_{n})$ be those of the neutral gray resulting from their combination in the proportions, $a_{1}$ and $a_{2}$, respectively. From the Munsell psychophysical relation:

$a_{1}=C_{2}V_{2}/(C_{1}V_{1}+C_{2}V_{2}),\qquad \qquad \quad$,

and

$a_{2}=C_{1}V_{1}/(C_{1}V_{1}+C_{2}V_{2}).\qquad \qquad [1]$

From the laws of additive color combination (7, p. 30):

$a_{1}{X_{1}},+a_{2}{X_{2}}={X_{n}}$

$a_{1}{Y_{1}}+a_{2}{Y_{2}}={Y_{n}}$

$a_{1}{Z_{1}}+a_{2}{Z_{2}}={Z_{n}}.\qquad \qquad [2]$

From the definition of Munsell value, we have the relation:

$Y_{V/C}=V^{2}/100,\qquad \qquad$

and, in particular,

$Y_{V/C}=Y_{5/5}=25/100.\qquad \qquad [3]$

And from the fact that all Munsell neutral grays are taken as having identical trichromatic coefficients, we may write:

$X_{n}/X_{5/0}=Y_{n}/Y{5/0}=Z_{n}/Z{5/0}.\qquad \qquad [4]$

Now if the first color be 5/5, and the second be $V/-C$, then: $V_{1}=5$, $C_{1}=5$, $V2=V$, $C_{2}=C$,^[9] and we have from Eq. [1]:

$a_{1}=C_{V}/(C_{V}+25);\qquad$$a_{2}=25/(CV+25).$

By substituting these values in Eq. [2], and eliminating $X_{n},Y_{n},Z_{n},$ through Eqs. [3] and [4], we may solve explicitly for$X_{V/-C}$, $Y_{V/-C}$, and $Z_{V/-C}$:

$X_{V/-C}={\frac {V}{5}}\left[{\frac {V+C}{5}}X_{5/0}-{\frac {C}{5}}X_{5/5}\right]$

$Y_{V/-C}={\frac {V}{5}}\left[{\frac {V+C}{5}}Y_{5/0}-{\frac {C}{5}}Y_{5/5}\right]\qquad \qquad [5]$

$Z_{V/-C}={\frac {V}{5}}\left[{\frac {V+C}{5}}Z_{5/0}-{\frac {C}{5}}Y_{5/5}\right]$

Equation [5] expresses the color $V/-C$ in terms of the neutral 5/0 and of the complementary 5/5 color. A similar derivation for the color $V/C$ in terms of the 5/5 color of the same hue shows that it is necessary only to change the algebraic sign of C, thus:

$X_{V/C}={\frac {V}{5}}\left[{\frac {V-C}{5}}X_{5/0}+{\frac {C}{5}}X_{5/5}\right]$

$Y_{V/C}={\frac {V}{5}}\left[{\frac {V-C}{5}}Y_{5/0}+{\frac {C}{5}}Y_{5/5}\right]\qquad \qquad [6]$

$Z_{V/C}={\frac {V}{5}}\left[{\frac {V-C}{5}}Z_{5/0}+{\frac {C}{5}}Y_{5/5}\right]$

From these relations trichromatic coefficients may be derived, as follows:

$x_{V/C}={\frac {(V/C-1)x_{5/0}+(y_{5/0})/y_{5/5})x_{5/5}}{(V/C-1)+y_{5/0}/y_{5/5}}},\quad \quad [7]$

$y_{V/C}={\frac {(V/C)y_{5/0}}{(V/C-1)+y_{5/0}/y_{5/5}}}.$

Note that in Eqs. [7], $V/C$ is the only parameter; it follows that all samples of a given hue and for which $V/C$ is a constant will have the same trichromatic coefficients $(x,y)$. For example, R 2/2, R 3/3, R 4/4, and R 7/7 will have the same $(x,y)$ values as R 5/5; and G 8/4 will have the same $(x,y)$ values as G 4/2. The convention of writing Munsell value as the numerator of a fractional form whose denominator is Munsell chroma thus takes on an added meaning from the disk-mixture rule given in the Atlas apparently not foreseen at the time the convention was originated.

For a given dominant wave-length, excitation purity is proportional to distance on the Maxwell triangle, which, in turn may be measured by its projection either onto the x axis or the y axis of the $(x,y)$ diagram, or both. The relation between excitation purity and Munsell chroma on the basis of the psychophysical relation given by Munsell may be written out from Eqs. [7] as follows:

${\frac {P_{e(V/C)}}{P_{e(5/5)}}}={\frac {y_{V/C}-y_{5/0}}{y_{5/5}-y_{5/0}}}={\frac {y_{5/0}}{y_{5/5}(V/C-1)+y_{5/0}}}.\qquad \qquad [8]$

This derivation holds only for $y_{5/5}$, different from $y_{5/0}$, but if these two are equal, the same result may be obtained from the x differences.

As might be anticipated from the psychophysical definition of chroma by disk mixture, the relation with colorimetric purity is even simpler. From the known relation between excitation purity and colorimetric purity (7, p. 59), which in present terms is:

$P_{e}={\frac {y_{\lambda }}{P_{e}}}$

$P_{e5/5}={\frac {y_{\lambda }}{y_{5/5}}}P_{e(5/5)}.\qquad \qquad [9]$

combined with Eq. [8], we obtain

$P_{e(V/C)}=CP_{e(5/5)}/V\qquad \qquad [10]$

$C=VP_{e(v/c)}/P_{e(5/5)}\qquad \qquad \quad [11]$

Equation [8] enables us to test the psychophysical nature of the Munsell system as exemplified by the samples measured in 1919 and 1926; that is, to see if the actual samples conform to this relation derived on the basis of disk mixture according to the Atlas instructions.

Fig. 6. The second of the above diagrams (labeled 6700°K) is identical with the respective part of Fig. 4. The other diagrams above show that change of illuminant from 6700°K (I.C.I. Illuminant C) to 8000°K, 25000°K or 4800°K (I.C.I. Illuminant B) effects no appreciable improvement in the shape of the figure defined by complementaries derived by Eq. [5] using the illuminant as the reference point. In all four cases, the use of the equal-area disk-mixture point (DM) for computing the complementaries yields a much more regular figure.

Before carrying out this test, however, choice must be made of the trichromatic coefficients, $x_{5/0}$ and $y_{5/0}$. According to Fig. 4 there is considerable doubt whether I.C.I. Illuminant should be taken to represent Munsell neutral gray; should we perhaps instead use the point given by disk mixture of the five principal hues in equal proportions?

It is believed that a definite answer to this question is given by computing the complements of R 5/5, Y 5/5, G 5/5, B 5/5, and P 5/5 by expressions analogous to Eqs. [7] derived from Eqs. [5], first with I.C.I. Illuminant C^[10] and second with values obtained by equal-area disk mixture of the 5/5 samples.^[11] As already noted, this disk-mixture point is designated by the symbol, DM. In the first case an erratic outline is obtained, in the second case a regular elliptical outline is suggested, as shown in Fig. 4 and in that part of Eq. [6] marked 6700°K. In this second case the complementaries fall between the adjacent primaries at regular distances from the neutral (DM) point. From whatever cause, it is apparent that the ten principal and complementary hues space symmetrically about the DM point far better than they do about the point C.

In Table IV are given the tristimulus specifications, the trichromatic coefficients, the dominant wave-lengths, and the colorimetric and excitation purities, for the five principal 5/5 samples (1919 data) on which this psychophysical system is based. Corresponding data are also given for the neutral (DM) 5/0 sample resulting from equal-area disk mixture of these five principal samples and for the five 5/5 complementary samples computed relative to the DM point by Eqs. [5]. From these data in Table IV may be computed for each of the ten hues, the tristimulus specifications, the trichromatic coefficients, and the colorimetric and excitation purities for any other sample of desired V and C. Values of dominant wavelength remain unchanged for each hue. The values of X, Y, Z, x, and y given in Table III of the Tyler-Hardy paper (11) were computed in this way by using Eqs. [5], [6] and [7].

Before proceeding to compare the 1919 and 1926 data with the data resulting from the psychophysical system thus developed, the meaning of the shift of the neutral point from I.C.I. Illuminant C to the DM point may be considered. Three possibilities may be noted.

First, perhaps I.C.I. Illuminant C is not as blue as that used in building up the Munsell system; perhaps clear north sky was used in selecting the Atlas papers. This possibility has been explored by computing the trichromatic coefficients for the five principal hues and their complementaries, both for the spectral distribution for Planckian 8000°K and for a blue-sky distribution (one of those used by the authors (13)) having a color temperature of approximately 25,000°K. The result is shown in Fig. 6 which also shows a similar plot for I.C.I. Illuminant B (4800°K). None of these illuminants renders less irregular the shape of the area delimited by the five principal 5/5 colors and their 5/5 complementaries computed by Eqs. [5] when the tristimulus specifications of the illuminant are used for $X_{5/0}$, $Y_{5/0}$, and $Z_{5/0}$. It is concluded that the irregularity of the 5/5 locus computed about the illuminant point cannot be ascribed to a disparity between the illuminant used in the computations and that used in the selection of the colors of the Munsell Atlas.

Second, perhaps the Munsell gray samples are sufficiently nonselective in the yellowish sense to account for the difference. Some of those illustrated in Bureau of Standards Technologic Paper No. 167 (2) are slightly yellowish, but only N 7/, N 8/, and N 9/ show any important selectivity. Even the yellowest of these, N 9/ (x=0.3167, and y=0.3256 for I.C.I. Illuminant C), is not sufficiently selective to bridge the gap between the color of the illuminant and that of equal-area disk mixture of the five principal colors. Hence the average color of the Munsell neutral samples, at least in 1919, is not sufficiently different from that of the illuminant to account for the difference.^[12]

Third, it is possible that one or more of the five principal colors, by the time they were measured in 1919, may have changed sufficiently to shift the mixture point from the illuminant point to the DM point. If the five colors of the original system did spin to match a nonselective neutral at the time of their selection, then a regular system, of the sort represented here, would have resulted. The DM point would at that time have been identical with the illuminant point. There seems to be no way to test this possibility, but it is pointed out elsewhere that no certain changes in the samples have occurred between 1919 and 1926.

TABLE VI. Specifications of the five principal Munsell colors, for the Munsell N 5/ given by equal-area disk mixture of these five colors, and for the complements of these five colors at 5/5. The tristimulus specifications of each color have been multiplied by a factor to make Y=0.2500.

Munsell Not- ation	Trisimulus Specifications			Trichromatic Coefficients		Dominant Wave Length and Purities (Reference Point: z=0.3234, y=0.3255)
	X	Y	Z	x	y	A†	Pe‡	Pe§
R 5/5	0.31298	0.2500	0.20018	.0.41011	0.32759	610.6	25.7	25.3
Y 5/5	.24459	.25000	.09613	.41405	.42321	576.8	64.2	53.4
G 5/5	.18454	.25000	.20198	.28992	.39276	510.5	28.1	13.3
B 5/5	.21634	.25000	.42235	.24344	.28131	484.0	20.7	31.5
P 5/5	.28326	.25000	.42761	.29480	.26018	568.c	0.8	19.4
NDM 5/	.24834	.25000	.26965	.32336	.32553	—	0.0	0.0
BG 5/5	.18370	.25000	.33912	.23770	.32349	491.0	0.0	0.0
PB 5/5	.25208	.25000	.44318	.26668	.26448	476	9.1	25.4
RP 5/5	.31214	.25000	.33732	.34703	.27794	519 c	10.2	23.3
YR 5/5	.28034	.25000	.11694	.43311	.38623	585.8	56.9	48.9
GY 5/5	.21342	.25000	.11170	.37109	.43469	568	58.6	44.8

*r4 The reference point for this system is the neutral point N 5/ resulting from equal-area disk mixture of the five principal 5/5 samples; it differs slightly from the point representing I.C.I. Illuminant C.

†r5 Dominant wave-lengths were read from a large-scale (x,y)-plot of the spectrum locus by extending straight lines from the point representing the Nm mixture through the point representing the 5/5 sample in question to the spectrum locus.

†r6 Values of $P_{e}$ were calculated from the Judd (18) formula, except that for nonspectral colors the line connecting the extremes of the spectrum was taken to represent unit purity. With these values of Pc(5/5), Pe for all other samples in this psychophysical system can be calculated from Eq. [10].

§ Values of $P_{c}$. were calculated from a variation of the Hardy formula (7, p. 59) which results in: $P_{e}=Pc_{(y/y\lambda ,)}$. $P_{e}$ for all other samples in this psychophysical system can be calculated from Eq. [8].

We may now proceed by Eqs. [8] with a test of the psychophysical nature of the Munsell system exemplified by the papers measured in 1919 and 1926. The curves in Fig. 7 show C/V plotted against the ratio of excitation purities given by Eqs. [8] for the five principal Munsell hues and their complements.^[13] If the measurements of the papers had resulted in dominant wave-length constant for each hue, the desired comparison would be given by plotting, on the same graphs, $C/V$ for each color also against the ratio of excitation purities. Since, as shown in Fig. 5, considerable departure from dominant-wave-length constancy has been found, $C/V$ for each color is plotted instead against the ratio of distances from the neutral (DM) point on the (x, y)-diagram. This distance ratio is given by the expression:

$\left[{\frac {\left(x_{5/5}-x_{5/0}\right)^{2}+\left(x_{5/5}-x_{5/0}\right)^{2}}{\left(x_{V/C}-x_{5/0}\right)^{2}+\left(x_{V/C}-x_{5/0}\right)^{2}}}\right]^{\frac {1}{2}}$

all of whose terms are known (Tables II, III, IV and VI). For dominant wave-length constant, this ratio is the same as the ratio of excitation purities given in Eq. [8], and for minor deviations in dominant wave-length it is closely equivalent.

In Fig. 8 are plotted the "ideal" trichromatic coefficients of the colors, computed from Eqs. [7] and analogous equations derived from Eqs. [8]; data for Munsell values 2/, 4/, 6/, and 8/ are shown. In Fig. 8 are also plotted the 1926 data for the actual samples, these data being indicated by small triangles and circles (as in Fig. 4) The difference between the sample data and the psychophysical data for the same Munsell notation are shown by the dotted lines which connect these respective pairs of points.

Fig. 7. Comparison of the 1919 and 1926 experimental data with values computed from the psychophysical relations. For the five principal colors the relations are as expressed in Eqs. [7] and [8] and as given in the abscissa legend. For the five complementary colors, analogous relations for $x_{V/-C}$, $y_{v/-c}$ and $P_{e(V/-C)}$ were used, based also on $x_{5/5}$, $y_{5/5}$ and $P_{e(5/5)}$; this explains why the dashed curves do not pass through the point, 1, 1 as do the continuous curves. While there is rough agreement between data and curves, large individual deviations may be noted.

It may be seen from Fig. 7 that there is rough agreement between the curves and the plotted points, although the large erratic deviations in some cases make a mental averaging of the data difficult. For certain of the colors it is apparent that the 5/5 sample on which the curves are based is not too well representative of the other colors. It may be seen that there is no certain average difference between the 1919 and 1926 data. Reference to Fig. 8 shows certain trends not apparent from Fig. 7. Figure 8 shows the increasing departures of the experimental data from the psychophysical system as one departs from value 5/, either higher in value through 6/ and 8/, or lower in value through 4/ and 2/; a distinct tendency is shown for the chromas of the lowest Munsell value to be too weak to fit the psychophysical relation, and for the chromas of the highest Munsell value to be too strong to fit this relation.

It may therefore be concluded that the Atlas papers fail to follow the disk-mixture rule resulting in Eq. [11]. The deviations are not merely erratic, as would be expected from the technical difficulties of reproducing the colors by pigments; but also, for both high and low Munsell values, the deviations show consistent tendencies and indicate that selection of these colors was not made solely on the basis of disk mixture.

Tests for Conformity to A
Pyschological System

Most people who have used the Munsell system have taken A. H. Munsell at his word, and have found the system to be a workable approximation of one "built up by equal and decimal steps of sensation." That it could be improved upon is indicated by the fact that the Munsell Research Laboratory was established to develop data upon which such an improvement could be based. Much work was done in the 1920's toward this end (1), with the result that in 1929 the Munsell Book of Color was published (14). Although individual papers of the Book of Color differ somewhat from those of the Atlas, the only important regular change is that the relation, $V^{2}=k(100Y)$, is replaced by a some what less simple relation.

Fig. 8. Illustration of the psychophysical system developed in this paper as expressed in Fig. 7, using the 5/5 R, Y, G, B, and P 1919 data as basic starting points and the equal-area disk-mixture data (DM) as the neutral point. The open circles are plotted at chromas 0, 2, 4, 6, 8, etc. Deviations of the 1926 Atlas data from this system are also shown. Corresponding charts for the 3/, 5/, and 7/ value levels are omitted.

Probably the most satisfactory way by which the data reported in this paper can be tested psychologically is to compare them with the data obtained by the Newhall subcommittee. These data, some of which are reported in the final paper of this series by Newhall (15), have been based upon observations made on samples of the Book of Color to see what changes, both in magnitude and direction, would be necessary to bring about a still better representation of the ideal psychological color system, in which the steps are truly representative of equally perceptible changes in any single color attribute.

Regarding value, we already know that a definite relationship between value and reflectance was intended by Munsell, and that the Munsell value scale was intended to represent equal sensation steps. In regard to hue, we know, from Fig. 5, that the dominant wave-lengths of certain hues tend to change in accord with the requirements of a psychological system when the illuminant point is taken for a reference point. In regard to chroma, we can compare the excitation purities for samples of the 70 Atlas colors measured in 1926, both with excitation purities obtained from the data of the psychophysical relation developed in an earlier portion of this paper, and with excitation purities obtained on a basis of the Glenn-Killian (16) data, modified by the Newhall (15) data. Table VII enables this comparison to be made.

As the comparison is made, we begin to realize that a psychophysical system such as developed in this paper and a psychological system may not be as far apart as might have been supposed. However, the 1926 data at the low Munsell values in most cases agree with the data indicated by the Newhall report better than with those indicated by the psychophysical system. At the other values the data of Table VII are not so conclusive, although, except for value 8/, the agreement of the 1926 data with the psychological

Table VII. Excitation purities for 70 Munsell notations: derived from the disk-mixture rule (psychophysical); computed from 1926 spectrophotometric data both for diffuse and 45° illumination (1926 data); and from the Glenn-Killian data on the papers of the Munsell Book of Color, with conformity to the Newhall psychological check indicated by direction of difference (psychological).

Munsell Notation		Excitation Purity
		Psycho- physical[14]	*[15]	1926 Data		*[15]	Psycho- logical[16]
				Dif- fuse[17]	45°[18]
R	2/4	50.7		18.0	22.0	n	19.8++
YR	2/1	24.5		12.5	13.8	n	15.4+
Y	2/1	26.7		16.1	14.7	n	10.0+
GY	2/1	22.4		11.2	11.5	n	07.8
G	2/1	6.6	n	7.5	6.8		4.5-
BG	2/2	23.2	n	22.0	23.9		15.5
B	2/4	62.9		41.6	41.3	n	40.2
PB	2/2	25.2		39.5	37.0	n	26.5
P	2/3	29.1		24.7	24.7	n	29.8--
RP	2/2	23.3		19.0	18.3	n	20.0
R	3/7	59.1		40.5	43.2	n	39.2
YR	3/4	65.3		35.8	38.0	n	47.9-
Y	3/3	53.4		34.0	35.9	n	23.7++
GY	3/3	44.9		28.3	29.2	n	20.6+
G	3/4	17.7		6.8	7.2	n	15.2-
BG	3/4	31.0		29.3	29.2		27.2-
B	3/5	52.4		43.0	43.4	n	45.6-
PB	3/9	75.6		58.3	59.0	n	54.7
P	3/6	38.8		29.0	30.9	n	36.1-
RP	3/6	61.2		31.3	30.2	n	33.0
R	4/10	63.3		52.2	54.1	n	51.2-
YR	4/5	61.2	n	58.2	58.8		50.8-
Y	4/5	66.8		58.1	59.2	n	58.5-
GY	4/5	56.1	n	49.5	51.0		35.8
G	4/7	23.2		18.8	20.3		25.0--
BG	4/5	29.1	n	31.5	32.2		27.0-
B	4/6	47.2		43.6	42.9	n	45.3-
PB	4/10	63.2		51.5	52.1	n	51.9-
P	4/6	29.1		23.0	25.0		28.7+
RP	4/6	35.0		24.6	26.0	n	27.8
R	5/10	50.7		47.1	48.2	n	47.0-
YR	5/7	68.6		57.5	59.8	n	59.6-
Y	5/7	74.8		60.8	61.2		75.6-
GY	5/6	53.8		40.1	41.8	n	46.0
G	5/7	18.6		20.5	21.2		19.2--
BG	5/5	23.3		16.4	16.4		24.0
B	5/6	37.8	n	35.5	36.0		41.4--
PB	5/8	40.3		34.5	34.7		40.1-
P	5/6	23.3		18.3	18.2		26.8--
RP	5/6	28.0		17.0	17.2	n	22.1+
R	6/8	33.8		30.1	31.5		30.0+
YR	6/8	65.3	n	71.5	71.8		59.6-
Y	6/7	62.3		68.2	67.5		69.0-
GY	6/8	59.8		57.0	57.0		55.5-
G	6/7	15.5		18.4	17.7		19.4---
BG	6/5	19.4		17.8	17.8		17.7
B	6/5	26.2		26.0	26.9		28.9--
PB	6/6	25.2	n	23.7	24.5		27.2
P	6/4	12.9	n	12.2	12.1		16.0—
RP	6/4	15.5		12.5	12.5	n	12.1+
R	7/6	21.7	n	21.0	22.0		17.4+
YR	7/7	49.0		44.0	45.2	n	46.1-
Y	7/8	61.1		73.5	73.4	n	75.2--
GY	7/7	44.9		55.0	56.5	n	50.7-
G	7/7	13.3		12.3	12.2		13.9--
BG	7/5	16.6		8.4	7.8	n	13.9-
B	7/4	18.0		14.7	14.7		17.4
PB	7/4	14.4		17.9	17.6	n	18.2
P	7/3	8.3	n	6.0	6.7		10.9-
RP	7/4	13.3		9.8	9.5	n	8.0+
R	8/4	12.7	n	12.1	12.1		9.1
YR	8/5	30.6	n	34.5	34.1		25.9
Y	8/9	60.1		73.8	74.4	n	70.6-
GY	8/6	33.6		41.7	42.6	n	40.6-
G	8/5	8.3	n	8.3	9.0		7.2-
BG	8/3	8.7		4.5	4.1		7.8
B	8/2	6.3	n	7.0	6.8		12.0-
PB	8/2	4.8		6.0	5.0		5.9
RP	8/2	5.8		4.7	3.5		3.7-

data appears somewhat better than with the psychophysical system. Before we can answer definitely, therefore, we shall need to study in further detail the preliminary report of the Newhall subcommittee (15), and may need also to wait for the final report which is expected to explore thoroughly the possibility of constructing a psychophysical color system based upon photometry and disk mixture which will be in satisfactory agreement with the requirements of an ideal psychological system. It would seem to be worth while to study the psychophysical color system resulting from five new principal colors chosen so that their equal-area disk mixture will have the same trichromatic coefficients (x,y) as the illuminant. When this is done, we should be able to decide with certainty not only whether the 1919, 1926, or 1929 series of Munsell colors more closely approach a psychological system or the psychophysical system dealt with here, but also the more important question whether or not a simply defined psychophysical color system similar to it can be made to meet the requirements of the ideal psychological system envisaged by A. H. Munsell.

Summary

An examination has been made of the Munsell color system as it existed in 1919 and 1926. This examination has been based on colorimetric data derived from published and unpublished spectrophotometric measurements made in those years on samples representative of the Munsell Atlas. The relation between Munsell value and luminous apparent reflectance, $V^{2}=100k(Y-0.007)$, closely similar to that found by others, has been confirmed in a general way. While there are large individual variations, it is found that the above relation, with k close to unity, adequately represents the data as a whole. The white point on this scale corresponds to magnesium oxide, the black point to a sample reflecting diffusely about 0.7 percent.

The relation between Munsell Atlas hue and dominant wave-length depends upon the neutral (reference) point adopted. At best there are significant deviations from one-to-one correspondence. Therefore the terms for dominant wave-length and for Munsell hue as illustrated by the original papers of the Munsell system cannot be used interchangeably.

A psychophysical system has been developed, based on the inverse $CV$ weighting indicated in the Atlas instructions for a disk mixture to yield neutral gray.

In this psychophysical system the trichromatic coefficients $(x,y)$ of a Munsell color of a given hue depend only upon the ratio of value to chroma $(V/C)$. The following relations between excitation purity and colorimetric purity on the one hand and Munsell chroma and value on the other are obtained from this derivation:

$P_{e(V/C)}={\frac {P_{e(5/5)}y_{5/0}}{y_{5/5}(V/C-1)+y_{5/0}}}$

$P_{c(V/C)}=(C/V)P_{c(5/5)}$

The 1919 and 1926 data indicate rough agreement with these relations, particularly for middle Munsell values; but there are consistent deviations from them, greater at low Munsell values than at high. Comparison of the data of this paper with the psychological data obtained by the Newhall subcommittee indicates that the above departures from the psychophysical system are in the direction to give chroma scales which are perceptually more uniform, and therefore that there has been an intentional departure from the psychophysical system.

Literature Cited

1. Dorothy Nickerson, “History of the Munsell color system, and its scientific application,” J. Opt. Soc. Am. 30, 575 (1940).

2. I. G. Priest, K. S. Gibson and H. J. McNicholas, “An examination of the Munsell color system. I. Spectral and total reflection and the Munsell scale of value,” Bur. Stand. Tech. Paper No. 167 (1920).

3. A. H. Munsell, Atlas of the Munsell Color System (Wadsworth-Howland & Co., Malden, Mass., 1915). (Preliminary charts A and B published in 1910.)

4. H. J. McNicholas, “Equipment for routine spectral transmission and reflection measurements,” J. Research Nat. Bur. Stand. 1, 793 (1928); RP30.

5. G. F. A. Stutz, “Observations of spectrophotometric measurement of paint vehicles and pigments in the ultraviolet,"” J. Frank. Inst. 200, 87 (1925).

6. K. S. Gibson, “Spectrophotometry at the Bureau of Standards,” J. Opt. Soc. Am. 21, 564 (1931).

7. A. C. Hardy, Handbook of Colorimetry (Technology Press, Cambridge, Mass., 1936).

8. A. H. Munsell, “On the relation of the intensity of chromatic stimulus (physical saturation) to chromatic sensation,” Psychol. Bull. 6, 238 (1909).

9. A. H. Munsell, “A pigment color system and notation,” Am. J. Psychol. 23, 236 (1912).

10. A. H. Munsell, Color Diary, Bibliofilm Document No. 1307 ($2.50) obtainable from the American Docu-mentation Institute, 2101 Constitution Ave., Washington, D. C.

11. E. Tyler and A. C. Hardy, “An analysis of the original Munsell color system,” J. Opt. Soc. Am. 30, 587 (1940).

12. T. Troland, The Principles of Psychophysiology, Vol. II. Sensation (D. Van Nostrand Co., Inc. New York, 1930).

13. K. S. Gibson, “Approximate spectral energy distribution of skylight,” J. Opt. Soc. Am. '30, 88A (1940); Dorothy Nickerson, “The illuminant in color matching and discrimination,” Illuminating Eng., to be published.

14. Munsell Book of Color (Munsell Color Co., Baltimore, 1939).

15. S. M. Newhall, “Preliminary report of the Optical Society of America Subcommittee on the spacing of the Munsell colors,” J. Opt. Soc. Am. 30, 617 (1940).

16. J. J. Glenn and J. T. Killian, “Trichromatic analysis of the Munsell Book of Color,” J. Opt. Soc. Am. 30, 609 (1940).

17. A. H. Munsell, “On a scale of color-values and a new photometer,” Technology Quarterly 18, 60 (1905).

18. D. B. Judd, “The 1931 I.C.I. standard observer and coordinate system for colorimetry,” J. Opt. Soc. Am. 23, 367 (1933).

19. W. de W. Abney, “On the change of hue of spectrum colors by dilution with white light,”’ Proc. Roy. Soc. London A83, 120 (1910); G. Révész, “Ueber die vom Weiss ausgehende Schwachung der Wirksamkeit farbiger Lichtreize (mit Anschluss einer Mitteilung des Herrn Prof. Dr. G. E. Miiller), Zeits. f. Sinnesphysiol. 41, 116 (1906).

1. Chief, Colorimetry and Spectrophotometry Section, National Bureau of Standards, Washington, D. C.
2. In 1929 the papers of the Atlas of the Munsell Color System were replaced with papers of the Munsell Book of Color in accordance with suggestions made in the Priest, Gibson, McNicholas 1919 report, reference 2. See reference 1 for details.
3. On all of the BG, B, PB, P, and RP samples and on the 2/, 4/, 6/, and 8/ value samples of the other colors.
4. Compound for noon sunlight. The Value of Y for neutral 9/ of which is the most selective of the neutral samples, is 0.763 for I.C.I. Illuminant C. Difference in illuminant therefore will not account for the differences between the values of Y for the neutral samples and the average values of Y for the chromatic samples.
5. In the Atlas there is a statement on several charts, to which Priest called attention in 1919, that is in error. says in effect that a sample of value 5/ reflects 50 percent “of the luminosity of white,” one of value 6/ reflects 60 percent, and so on. In footnote 17 of the Priest paper, reference 2, certain other excerpts from Mr. Munsell’s writings are quoted. From later reference to the diary, reference 10, and to other Munsell sources, reference 17, it is evident that during the development of the value scale, and the photometer, Mr. Munsell was entirely aware of the relation between value and reflectance. The wrong statement in the Atlas would seem to have been an oversight.
6. The authors are indebted to Marion A. Belknap for the preparation of Figs. 3 to 8.
7. Having first multiplied each (X, Y, Z)-triad by factors to make Y=0.25, as suggested by Tyler and Hardy, reference 11.
8. The authors have been unable to find any statement made by A. H. Munsell which definitely says that the color standards of the Atlas were chosen on the basis of this relation. After the system was partially completed, he found that colors used in areas inversely proportional to the product of their V and C numbers, often gave a neutral. Evidently he believed this relation to apply more rigorously than it may, for he notes it in several places. But the system was already well established, with chroma relations on a single value level being tested by disk mixture, before he found that this $V\times C$ relation seemed to exist.
9. Although the notation for a complementary color is taken as V/—C, the actual values of C for both the 5/5 and it) complementary color are positive in accord with Eq. [1].
10. $x_{5/0}=0.3101$, $y_{5/0}=0.3163$.
11. $x_{5/0}=0.3234$, $y_{5/0}=0.3255$; this point is slightly off the Planckian locus at approximately 6000°K.
12. It may be noted that equal-area disk mixture of the five principal colors without adjustment to Y=0.2500 yields $x{5/0}$=0.3213 and $y_{5/0}$=0.3262, not importantly different from the trichromatic coefficients obtained with this adjustment. It is curious, however, that the neutral point obtained by disk mixture of the five principal colors without adjustment, and the neutral point given by N 9/, both give better representative reference points for the dominant wave-length lines than do either I. C. I. Illuminant C or the disk-mixture (DM) point with the adjustment. The most symmetrical shape for the area defined by the five principal colors and their complementaries is, however, given by the DM point.
13. In preparing Fig. 7 the data and curves for the complements were based on equations analogous to Eqs. [7] and [8] (derived from Eqs. [5]) which express $(xv/-c)$, $y/-C$ and $P_{e(v/-c)}$ in terms of $x_{(5/5)}$, $y_{(5/5)}$ and $P_{e(5/5)}$. This explains why the dashed curves of Fig. 7 do not pass through the 1,1 point, and further illustrates that the whole psychophysical system can be expressed in terms of the five principal colors.
14. From Eq. [8].
15. The notations in these columns indicate whether the excitation purities for the 1926 data agree better with the psychophysical system or the psychological. An “n” between the first and second columns of excitation purities indicates “nearer to the psychophysical system,” while “nearer to the psychological system” is indicated by an “n” between the third and fourth columns. If the excitation purity found from the 1926 data does not agree significantly better with one than the other, no notation is given.
16. Read or interpolated from Table I of the next paper in this series (16) which gives the Glenn-Killian measurements of the papers in the 1929 Munsell Book of Color. The plus and minus signs indicate the directions of the changes necessary to improve agreement with the psychological requirements evaluated in the Newhall subcommittee report (15) forming the final paper of this series. For example, for R 6/8 the excitation purity given by Glenn and Killian is 30.0; but the Newhall data indicate that R 6/8, if it is to-fit into the ideal psychological system, should be slightly higher in excitation purity; so a plus sign is added. Two plus signs indicate that the difference is more than slight.
17. From Table III.
18. From Table IV.