Journal of the Optical Society of America/Volume 30/Issue 12/Spacing of the Munsell Colors

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Journal of the Optical Society of America, Volume 30, Issue 12 (1940)
Spacing of the Munsell Colors by Sidney Merritt Newhall
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4436802Journal of the Optical Society of America, Volume 30, Issue 12 — Spacing of the Munsell ColorsSidney Merritt Newhall
​

Preliminary Report of the O.S.A. Subcommittee on the Spacing of the Munsell Colors

Sidney M. Newhall[1]

Johns Hopkins University, Baltimore, Maryland


The spacing problem consists in the detection and correction of errors of allocation in surface color space of the regular 1929 Munsell samples. This amounts to the adjustment of imperfections in a real chromatic skeleton of 400 units so that it will more properly fit into an ideal chromatic body. For the last five years various observers have been making visual estimates of the color spacings and the accumulated data have been summarized and are presented herewith in tabular form. These data will provide a psychological basis for defining smooth contours of Munsell hue, value, and chroma in terms of the 1931 I.C.I. colorimetric coordinate system. The plan is to present those contours in the final report. The present report includes charts of a preliminary smoothing of chroma based on the earlier visual estimates.

Table of Contents

Introduction 617
Spacing problem and procedure 618
Historical note 618
Ratio method 620
Procedural details 622
Complications 624
Observers 625
Visual data and computation 626
Averaging the estimates 626
The averaged estimates 629
General indications 629
Preliminary smoothing of chroma 638
Procedure in smoothing 638
Charted results 638
Discussion 643
Summary 643

Introduction

THE familiar principle of specifying color by spatial location underlies the design of various color solids (10-14, 34, 39, 43-45, 53, 63, 64). The ideal of this investigation is a psychological color-solid in which cylindrical coordinates of Euclidean space represent the principal at tributes of colors perceived as belonging to surfaces and equal linear extents represent equal sense-distances. Along the color scales there is variation in but one attribute at a time, and the scalar graduations are perceptually uniform. Furthermore, any horizontal section through the solid would define a plane of constant lightness (Munsell value) while any vertical plane originating at the achromatic axis would be a plane of constant hue. Finally, a cylindrical section concentric with the axis would constitute a surface of constant saturation (Munsell chroma). Just how closely this psychological ideal can be realized in either theory or practice still remains somewhat conjectural.

One question arises at once. A marked influence of surrounding-field reflectance on surface-color perception has long been evident (1, 4, 25-28, 37, 58, 65, 71, p. 546; 82). Since the color perceived as belonging to a surface may vary with the background, there is the question of what ground to employ. Present views suggest grounds similar to samples for ideal viewing but continual changes in observational conditions seemed neither feasible nor desirable in the present study. Therefore, the subcommittee decided to have all observations made against three approximately neutral grounds of high, low, and intermediate reflectance (white, black and gray), and to decide later, by reference to the comparative data thus secured, what to do regarding this important problem of specifying an ideal or standard viewing ground.

The principal practical advantage of defining ​a close approximation to the psychological solid is that the resulting scales facilitate adequate interpolation among the adjacent members of a finite system of samples. For if the chromatic continua are equi-stepped variations in but one attribute at a time, an unknown color can be evaluated quite definitely and quickly by assigning to it the notational equivalent of its appropriate position in the color system (39, p. 362). In the absence of such psychological scales, on the contrary, a relatively haphazard and laborious succession of comparisons must be made. That is because close interpolation is then scarcely possible, and the system must include a far larger assortment of samples to permit the employment of the alternative method of evaluating the unknown by matching or approximately matching it.

A further practical advantage of uniform colorscales lies in the convenient assignment of color tolerances. Of course, “noticeability of color variations” is not the only important determinant of color tolerances (48, p. 416). On the other hand, the general population considers that visual appearance or “how it looks” is very often crucial, and so perceptual tolerances are correspondingly important for many scientific and industrial colorists (5, 9, 27, 35, 36, 39, 57, 59).

Spacing Problem and Procedure

Historical note

Long recognized as the outstanding practical device for color specification by pigmented-surface standards (38), the Munsell system of color (49, 52-54) has become the subject of several other recent studies (15, 16, 23, 61). As early as 1919, however, I. G. Priest, Gibson, and others were already making constructive proposals for its improvement with special emphasis on scientific specification and the value scale (68) of the Atlas colors (54). Subsequently, A. E. O. Munsell, Godlove, and Sloan markedly improved the neutral-scale value spacings (18, 50). When the original report of the Glenn-Killian data (16) was circulated in 1935, numerous irregularities became apparent. There were general irregularities which could be referred to the I.C.I. coordinate system in which the data were expressed, and there were local irregularities due to clerical or to measurement errors, as one might expect. A third class of irregularities could be ascribed to various field factors including spatial arrangement and background reflectance, but a fourth class seemed to be due to real errors in the Munsell samples themselves (49). Some of these irregularities are shown in Figs. 7 to 14, to be discussed later.

The idea of improving the Munsell system by visually smoothing it appears to have occurred independently to three people in 1935, viz., H. P. Gage, Dorothy Nickerson, and W. B. VanArsdel. In 1936 there appeared a mimeographed statement by D. B. Judd and Dorothy Nickerson entitled the “Review of the spacing of the Munsell colors” (40), which not only pointed out the desirability of smoothing irregularities but also outlined procedure for reviewing the constant-value charts and recording the observers’ estimates of the true notation for each sample. The procedural details employed in securing most of the present data will be described later. Suffice it to say here that the principal features were included in that original statement of 1936 and that the essential ratio method involved had been known as early as 1929 (73).

The smoothing process is designed, of course, to eliminate only those irregularities which represent real departures from psychological regularity in the samples themselves. Thus sweeping irregularities in the coordinate system of reference can be allowed to remain as a part of the normal baseline. Most of the clerical errors can be corrected by checking. Irregularities due to field factors can be controlled, in part at least, by the systematic employment of masks and backgrounds of varied form and reflectance (Fig. 4). The residual should lie largely in the Munsell notations assigned to the individual samples, and it is the smoothing out of these individual sample errors which constitutes the principal task of the subcommittee.

The subcommittee did not undertake to evolve a single scaling unit for the entire solid, or for any attributive dimension of it. As is well known, the Munsell scaling units for hue, value, and chroma are far from equivalent perceptually. The relation between these units is, and remains, roughly as follows: 1 value unit=2 chroma units=3 hue units (at /5 chroma) (59). Even were the three units equated at the /5 chroma ​level, the resultant probably would remain an unsuitable scaling unit for the solid as a whole. This is because the size of each unit seems to exhibit some tendency to vary from one part of the color solid to another (8, 12, 48, 66, 70). The best single scaling unit would seem to be some kind of equal-contrast unit like the National Bureau of Standards unit (36), but that is a consideration for the future. At present, it seems unwise to attempt any changes which would do away with the well-known and useful Munsell notation (52, 53).[2]

Incidentally, the spacing of the samples of nearly neutral colors on the constant-value charts of the Book of Color (49) is intentionally wider than that suggested by the psychological color solid; this distortion is a practical expedient to provide sufficient space for the inclusion of low-chroma samples.

As early as 1935, some chromatic smoothing was accomplished by Gage[3] and by VanArsdel.[4] The latter’s analysis was confined to yellowish hues but showed also a connection between the Munsell samples and samples of maximum chromatic efficiency (23, 44, 45).

In the same year, the 1929 Munsell constant-value samples were plotted in three different colorimetric-coordinate systems, and five years later in a fourth system. Illustrative charts of given (5/ value) data plotted in these several systems of coordinates are presented as Fig. 1. The location corresponding to Munsell neutral five (N 5/) is indicated by the open circle near the center of each chart, and that corresponding to I.C.I. Illuminant C (22, 33) by the small triangle. Of course, the constant-hue loci are oriented differently in each chart. These trials were made with original samples, unadjusted by any visual smoothing, the object being to discover a coordinate system which would effect minimum distortion of the concentric circular spacing proper to constant chroma loci at the various Munsell value levels. Such a system would facilitate the smoothing operation, partly because a circle is easy to draw and partly because departures from a circle are easy to estimate.

The Glenn-Killian determinations (16) for value 5/ are shown in Fig. 1 plotted on the I.C.I. (x, y) diagram. Decentering and elliptoid forms of distortion are obviously present and they persist in varied amounts at the other value levels. The U.C.S. (35) chart shows the spacing, if anything, to be less uniform than in the I.C.I. chart. A great improvement is evidently effected by the use of Judd’s modification of his U.C.S. system.[5] However, the fit was nearly optimum around value 5/ shown in Fig. 1 and there is considerable and increasing distortion toward the extreme value levels. The remaining diagram illustrates Adams’ (2) adaptation of the I.C.I. system in which X — Y is plotted against Z— Y.[6] This diagram yields the closest approximation to ​the centered circularity of chroma loci expected of a uniform chromaticity-scale system, and it was given due consideration in choosing the system for the final smoothing of the data. It was rejected, however, because the neutral point changes rapidly with the value level and there would be practical difficulties in combining the determinations made at the different levels. The adapted U.C.S. system was rejected because it did not eliminate distortion, especially near black and white. The points in favor of the I.C.I. system are its standard character and wide acceptance. There is also the essential fact that like the other three systems, it does not present sharp irregularities which would be confused with those to be smoothed out of the Munsell data.

Fig. 1. The unsmoothed Glenn-Killian measurements of the 5/ value samples as plotted in four different colorimetric-coordinate systems.


The present committee on the spacing of the Munsell colors was appointed by L. A. Jones in 1937 as a Subcommittee of the Colorimetry Committee of the Optical Society of America. The present personnel includes B. R. Bellamy, H. P. Gage, D. B. Judd, Dorothy Nickerson, W. B. VanArsdel, and S. M. Newhall.

Ratio method

The ratio method, which has been relied upon from the beginning in this survey, consists in the estimation by direct impression of the ratio of ​supraliminal sense magnitudes or intervals (17, 19, 21, 47, 57, 72-78).[7] The one magnitude or interval is taken as standard and the ratio of the other to it is then estimated directly.

Fig. 2. Recording of estimates made by the simple ratio method

The two forms of this method are applicable to color problems and both were applied in the present review. The first form may be referred to as the simple ratio or form and represented by the simple operational equation

in which , represents the color perceived as belonging to the chosen standard; , the color to be evaluated; , the estimate of the ratio; and the subscript , the attribute with respect to which the estimate is made. Thus, the given color , is judged equal to , with respect to . Suppose that and , represent two surface-color perceptions and the observer’s task were to estimate relative lightness. He would compare the two colors directly with each other and report a quantitative judgment concerning the fraction or multiple which the lightness of is of ;. In case of surface-color perception, as when one views the Munsell samples, may become either , or , according to whether hue, saturation, or lightness is the attribute being estimated. According to the existing O.S.A. definitions (31, p. 213) hue, saturation, and lightness correspond closely to Munsell hue, chroma, and value.

Fig. 3. Recording of estimates made by the difference ratio method.

The second, or difference ratio, method is designated by R’ and represented by the analogous equation

in which is the perceived standard difference or interval, is the difference to be evaluated, and R’ is the estimate of the ratio of intervals with respect to 4, the particular aspect under estimate.

The observer records his estimate either by numbers or by linear extents which seem to him to be in the ratio of the sense magnitudes in question. Perhaps the easiest method is to adjust the relative positions of the samples themselves until the space ratio represents the sense ratio. A more generally practicable recording method, however, is graphically to indicate rather than actually to make, the representative space adjustment. Figure 2 suggests the application of graphic recording to the form. The observer represents the attributive magnitude of ; by a line of convenient length. He then draws a second line, representing , of such length relative to the first line that the ratio formed by the two lines is the same as the estimated ratio. Figure 3 shows the same kind of recording in case of the form of the ratio method. Here the one line is drawn to represent the sense difference or sense distance between ; and , while the other line is so drawn that its length relative to the first will be the same as ; relative to .

The difference-form () of estimate is more reliable because the perceptual unit is defined by its beginning point () and its end point (), both presented to the observer during the estimate. The analytically simpler form () implies a beginning point corresponding to zero (zero lightness, or zero saturation), but no sample exemplifying this beginning point is present. Therefore greatest reliance was placed on estimates by the difference-form ().

The use of the ratio method seems peculiarly ​ significant because, as pointed out by Judd,[8] amounts to the direct application of the definitions of the attributes of color-perception. Until other methods are proved comparable, only the ratio method is strictly applicable. Then, too, precision psychophysical threshold methods of the traditional sort (20, p. 23) were not considered feasible, partly because of the great length of time required and partly because the inescapable preliminary problem of the equality of supraliminal magnitudes representing equal numbers of just noticeable differences still remains to be solved (5, p. 286; 20, p. 143).

Fig. 4. Examples of Munsell constant-value charts and constant-hue charts mounted on white, gray, and black grounds; shown (A) without and (B) with several types of masks used to facilitate visual estimates by exposing simultaneously only samples designed to differ in a single attribute.

Procedural details

The observers were instructed to use daylight or its equivalent, to illuminate the samples at 45°, and to view them along the perpendicular as recommended in 1931 by the International Commission on Illumination (33). They were also requested not to fixate a given sample for long but to keep the fixation relatively mobile; for preadaptation is an important factor (29, 37, 42, 55, 71, p. 544). They made visual estimates of hue, lightness, and saturation on the Munsell constant-value and constant-hue charts. All of these charts were mounted and viewed on three different, approximately neutral grounds of relatively high, medium, and low reflectance, respectively; see Fig. 4. The I.C.I. tristimulus specifications (33, 38) of these white, gray, and black (matt cardboard) surfaces were determined under artificial daylight illumination approximating 6500°K.[9] The daylight apparent reflectance relative to magnesium oxide (Y) and the trilinear coordinates (x,y) were, respectively, as follows: white, Y=0.852, x=0.3204, y=0.3292; gray, Y=0.253, x =0.3140, y=0.3244; black, Y=0.040, x=0.307, y=0.312. Masks of the same materials, Fig. 4, were made and used to expose separately the various rows, columns, and arcs of samples designed to yield colors constant in two attributes and regularly varying in the third. These grounds and masks were of some service in controlling the psychological phenom-​ena of contrast and end-effect (24-28, 37, 71, p. 546; 79, 82, 85, p. 567) due to field factors aforementioned. The manner of using the masks is indicated later.

The form of the ratio method here involved the direct comparison of several samples with respect to a given attribute while the or difference-ratio form called for the comparison of the attributive differences between samples. Thus, in the one case the observer asked himself, “How much does each of these colors differ in this attribute from my chosen standard?” And in the other case, “How much do the attributive intervals between these various pairs of adjacent colors differ from my standard interval?” In both cases, the estimates of the departures from the standards were recorded in vectorial notation. The record forms used by the observers are shown in Fig. 5 and are similar in shape and pattern to the color charts themselves.

Fig. 5. Examples of original forms for recording in vectorial notation visual estimates from a constant-value chart (left), and from a constant-hue chart (right).

The observers were instructed to represent their estimates of the kinds and degrees of departure by drawing vectors of appropriate directions and proportionate lengths. Outlines of the prescribed procedure for estimating hue, saturation and lightness differences are as follows.

Hue differences were estimated from the constant-value charts. The series of samples in a given radius of constant Munsell hue was isolated by masking the remainder of the chart, and the series was then examined for variations in hue. If such were observed, the effort was made to estimate a representative or average hue and indicate departures therefrom by tangential vector notation ( form). The same procedure was followed in turn for each radius of constant Munsell hue on the chart. Next, the hue spacings of the hue radii considered as wholes were examined, and if the hue differences seemed unequal, a tangential vector of length proportional to the estimated adjustment required was affixed to the end of the radius (R’ form).

Saturation differences, like hue differences, were estimated from the constant-value charts. The samples in a given constant-chroma ring were masked off, and the subject looked them over in an effort to select a sample of representative chroma to serve as standard. Any sample ​which seemed to differ in chroma from the standard was then evaluated in terms of it, and a suitable radial vector was drawn to indicate the displacement ( form). Subsequently, the masks were removed, and the radii of constant Munsell hue were examined for irregularities in the size of the saturation steps between adjacent colors. After selection of a representative saturation step, each of the other steps could be evaluated in terms of it ( form).

Saturation differences were estimated again, this time from the constant-hue charts. A constant-chroma column was masked off, and the form applied. After each column had been so studied, the masks were removed, and the equality of the chroma steps checked by the form. Incidentally, most subjects found the applications of the form to saturation the most difficult part of the entire procedure.

Lightness differences were also estimated from the constant-hue charts. Rows of constant Munsell value were masked off and deviations in lightness of each sample from the average lightness of the row were evaluated by the form, after which the masks were removed, and the size of the lightness difference between successive constant-value rows was estimated by the procedure. These estimates were recorded numerically as the ratio of the actual size to the average size of value step. It will be noted that two color attributes were estimated from both types of chart, and it frequently happened that two vectors, each for a different attribute, had to be recorded for a single sample. If, for a sample on a constant-value chart, a radial vector had been drawn already to indicate a chroma deviation, the tangential vector to indicate a hue deviation would be started from the end or arrow-head of the radial vector. Thus the resultant of the two vectors would be indicated by the position of the final arrow-head, and would represent the difference between the 1929 Munsell notation of the sample and that estimated by the observer to indicate the color. In case of constant-hue charts an analogous combination of horizontal and vertical vectors would be required to record combined saturation and lightness deviations.

Complications

The unusual difficulties of the judgmental situation justify some account of the special problems reported by the observers.

(A) There was the problem of complex chromatic comparisons forcing, as it does, the abstraction of the attribute to be estimated. Attributive abstraction is peculiarly difficult in cases of strong association; for instance, when saturation is the judged attribute, hue being constant and lightness variable, there is a strong tendency to estimate darker colors as of higher saturation. This relation is often found in everyday life. A familiar related problem is that of comparing the lightness of colors differing in hue. A similar difficulty, especially for unsophisticated subjects, is that of comparing chromatic and achromatic colors in respect to lightness. The untrained observer usually perceives chromatic samples as lighter relative to achromatic samples than does the trained observer. Inspection of data from the constant-hue charts revealed the interesting fact that the vectorial lightness indications for the chromatic samples were rarely downward. The indication was usually that the chromatic sample seemed too light relative to the achromatic sample of the same Munsell value. (B) Observers making estimates of saturation difference by the method reported greater facility when all colors departed definitely from neutral gray than when one of the colors was perceived as gray. The trouble seemed to be that a first step extending from zero saturation appeared as a qualitative step and so tended to give the impression of an infinite quantitative step. The second step was, on the other hand, a definitely limited quantitative step. Seven of the observers made a written memorandum to the effect that the first step was or seemed definitely too great.

Possibly related to this was a certain change of attitude correlated with presence or absence of gray. When observing saturation differences from gray some observers reported that they “just look for any difference” whereas between two chromatic colors of the same hue they think more definitely in terms of saturation. Such a change of attitude might be expected to occur on the basis of least effort. Looking for a mere difference ​would be easier when the detection of saturation was difficult, whereas looking for a saturation difference would be easier when both colors are saturated to an obvious degree.

(C) The long recognized difficulties of spatial and temporal separation of compared samples were evidently present in this study where widely separated parts of a chart so often must be compared. Contrast and end-effects due to proximity of samples and terminal positions have already been mentioned.

(D) Finally, the visual estimates of the colors were all made with the samples in the regular positions and patterns of the Munsell system. This condition in itself would serve as a resistance to change. The untrained subject, or even the trained subject in a doubtful case, would tend to be affected or guided by the system (56); therefore, slight adjustments were probably not made and larger adjustments may not have been great enough. Still, this resistance to change might be considered advantageous in the sense of producing conservative estimates of the revisions required.

In the face of all of these difficulties what did the observers actually do? Only the more typical tendencies can be mentioned here. (a) The series of colors, or color differences, to be judged was first surveyed as a whole and the observer essayed a decision with respect to rank order for the attribute in question. Often no progressive graduation was found; and instead of arriving at an order, the observer was able to identify a few extreme colors and a number which seemed about equal with respect to the attribute in question. (b) After some such preliminary survey, the observer might proceed to the assignment of vectors. A common practice was to draw in vectors representing the more extreme displacements first, and then, partly on the basis of those, to fill in the shorter vectors indicating the lesser irregularities. (c) There was the tendency to "carry" a standard subjectively even though some particular perceptual standard had been chosen. Occasionally, the subject might refer to the standard sample for verification, but would often make many comparisons without doing so.

This "absolute" procedure (20, p. 205; 84) and the ranking procedure (20, p. 244; 81) mentioned above were both hit upon by many subjects without instruction, probably because they facilitated the subject's difficult task. Certainly it is easier to decide which of two sensory magnitudes is greater than to estimate how much greater; and it is sometimes easier when making numerous comparisons to carry a subjective standard than to refer back each time to a perceptual one.

Evidently, it would be a mistake to conclude that the ratio method has been applied to the spacing problem in anything like pure form. The actual procedure was so complex that if the ratio method were not pointed out it might pass unrecognized. An advantage of the complicated instructions is that they call for so thorough an examination of the charts that marked irregularities in spacing can scarcely be overlooked.

Observers

Since there were 7 constant-value charts and 20 constant-hue charts used in the survey, and since each of these 27 charts was prepared with the three backgrounds, a total of 81 charts were to be examined, each chart requiring about 100 judgments. The task was exacting, and those observers who returned complete sets of data from observation of the constant-value charts, the constant-hue charts, or both, usually took a year or more to do so. Without substantial contributions of this character, the successful completion of the investigation would have been impossible.

Data were received from forty-one subjects. Complete or nearly complete returns were secured from the following: W. H. Beck, Marion Belknap, B. R. Bellamy, Elizabeth Burris-Meyer, Claire Dimmick, F. L. Dimmick, Dean Farnsworth, Loraine Fawcett, F. A. Geldard, W. C. Granville, Paul Henry, M. M. Jackson, D. B. Judd, K. L. Kelly, D. L. MacAdam, S. M. Newhall, Dorothy Nickerson, R. W. Russell, Walter Scott, L. L. Sloan, W. T. Spry, Samuel Talbot, Irving Taylor, J. Weitz. Partial or supplementary observations which were summarized with the others were furnished by the following: Genevieve Becker, H. P. Gage, S. R. Gilmore, I. H. Godlove, G. W. Haupt, R. S. Hunter, H. E. Hussong, L. A. Jones, E. M. Lowry, Alexander Murray, P. Nutting, M. R. Paul, F. H. Rahr,R. H. Sawyer, Albert Smith, W. B. VanArsdel, K. S. Weaver.

​All subjects were similar in that they had some interest in color and passed the Ishihara test for color blindness (30),[10] but they differed widely in respect to the nature of their color interest and the character of their special training. In general they may be classified as follows: professional colorists in science or industry, 10; amateur or apprentice colorists, 8; professional physicists specialized or interested in color, 5; professional psychologists specially interested in color, 5; psychology students, 5; business executives with a broad or commercial interest in color, 3; specialists in dyes and pigments, 2; specialists in physiological optics, 2; graphic arts research, 1. There is much overlapping and this classification, like any other, is rather arbitrary.

The task of making visual estimates of colors and color differences is obviously a psychological one and the fact that one of our psychological observers, F. L. Dimmick, was opposed to the procedure as too demanding is duly noted. It should be noted, further, that the psychologists as a group were inevitably aware of numerous sources of error, technical imperfections, and general observational difficulty in the procedure. The various specific difficulties which seemed of any essential importance to the writer have been revealed in the preceding section on “complications.” Most of them appeared to bother the nonpsychological observers relatively little or not at all. But one of these, D. L.MacAdam, also objected on psychological grounds. The subcommittee is grateful to both of these subjects for carrying through their series of observations in spite of their objections.

The advantages of having such a diverse group of subjects are; first, that participation by a wide representation of the color-interested population yields correspondingly representative results and, second, tends toward wide application of results. A disadvantage of the fact that the data represent a heterogeneous sample of color-interested individuals is that they may not prove wholly satisfactory to any particular individual in the group. Lack of psychological training in scientific observation will tend to make the group results incorrect for the specialized sense-psychologist whose judgments in general might be assigned a higher validity than those of anyone else. Other observers would be more susceptible to the various recognized sources of error indicated in the section on “complications. Some of the sources of error are not even recognized by most of the untrained observers. These errors undoubtedly affect the results in ways not intended by the observers, but, on the other hand, they show various systematic tendencies which should correspond to the way the Munsell samples look to them. An example of the latter is the tendency to see chromatic colors as lighter than does the more experienced observer. As already indicated, there is something to be said for the view that what is really wanted here is a system of color which will seem right to the bulk of the population which will use it. Probably this population would never contain more than a minority who were specially trained in technical color observation. A desirable later step, perhaps, would be to produce a surface-color solid which would be as correct as the most rigorous technical training could make it. In the meantime, however, we shall hope to make some comparisons between results secured from sense-psychologists and conscientious colorists; possibly the differences in their results will not prove to be intolerably large after all.

Visual data and Computation

Averaging the estimates

Representative visual determinations were computed for the hue, value, and chroma of each of the standard Munsell colors as perceived against each of the three experimental grounds. Each of these determinations is an average of the individual estimates of the participating observers. The averaging procedure included two principal steps: (a) summarization of all of the available data, and (b) computation from the summary of the arithmetical means of hue, value, and chroma. A detailed description of these two principal steps is given below.

(a) The original vectorial records entered by the observers in the data sheets, of the form already illustrated in Fig. 5, were summarized on sheets of the form illustrated in Fig. 6. In this particular form, which was used in conjunction with the constant-value charts, the hori-​zontal dimension represents hue while the perpendicular dimension represents chroma. The dimensions of a similar form used with the constant-hue charts represent value and chroma. On these forms each observer’s estimate of the deviations of the particular color in respect to two of the attributes in question have been recorded by inserting his initials in the appropriate place. A total of 800 record sheets were required to summarize the color. judgments, roughly three million in number.

Fig. 6. Upper. Summarized visual estimates of hue and chroma of a particular Munsell sample (G 5/6) as presented on the three grounds. Lower. The corresponding numerical frequencies and averages.

The summarization forms are so similar that only the form for use with the data from the constant-value charts need be described in detail. Each vertical third contains data secured from the observations against a different background. In any third, entries falling in the central vertical column represent judgments that the Munsell hue notation is correct, while entries in parallel columns to the left or right represent, respectively, estimates of hue deviations in the counter-clockwise or clockwise direction around the hue circle. The recording unit of estimate is one Munsell hue-step. Similarly, the middle horizontal column represents the judgment that the Munsell chroma notation is correct, while the parallel columns above and below include respective estimates of “too strong” and “too weak.” The recorder’s unit of estimate is here 0.4 chroma-step. Of course, entries falling in the central rectangle, formed by the intersection of the central columns, represent judgments of correctness for both attributes. Preliminary estimates (encircled initials) by the method, and final or check estimates (unencircled initials) by the method, were made on each of the three grounds. Consequently the initials of a given observer usually appear several times on the summary sheet for a given color. Inspection of Fig. 6 shows at once that the particular color sample, G 5/6, was judged on the average to have a chroma higher than /6 and hue corresponding closely to the Munsell notation, regardless of background.[11]

The summarization process varied somewhat with the attribute. In case of hue, it will be recalled, the final instructions called for an unmasked inspection of the general spacing of the several hue radii in the constant-value charts, and the assignment of tangential vectors when adjacent hue radii, considered as wholes, seemed too close together or too far apart. The hue-shifts represented by such general radial adjustments were individually added to the results of the preliminary hue adjustments of the colors concerned. Incidentally, it may be noted, that only a minority of the subjects made any general adjustments.

In case of value, an analogous type of treatment was required. The instructions had called for an unmasked inspection of the spacings of the successive value rows in the constant-hue charts, and the indication of departures from perceptual uniformity by direct numerical estimates in terms of the standard value-step unit. The given observer estimated the eight spacings between values 1/ and 9/, and the results were added to his preliminary value estimates. If the ​spacing-estimates did not total eight, they were proportionally adjusted before application to the preliminary data.

Table I. Average value determinations derived from the estimates of general value spacing, exclusive of the preliminary estimates. The observations were made for samples of each value on white, gray, and black grounds.

MUNSELL
HUE 		MUNSELL VALUE
2/ 3/ 4/ 5/ 6/ 7/ 8/
Wh Gr Bl Wh Gr Bl Wh Gr Bl Wh Gr Bl Wh Gr Bl Wh Gr Bl Wh Gr Bl
R 1.8 1.8 2.3 2.8 2.8 3.7 3.8 3.8 4.8 4.8 4.7 5.6 5.9 6.2 6.6 6.9 7.2 7.4 8.0 8.1 8.2
10R 1.7 1.7 2.1 2.6 2.7 3.4 3.6 3.7 4.6 4.5 4.7 5.5 5.6 6.1 6.5 6.7 7.3 7.4 7.8 8.1 8.2
YR 1.7 1.7 2.2 2.6 2.7 3.6 3.6 3.6 4.7 4.5 4.6 5.6 5.6 6.0 6.6 6.7 7.2 7.5 7.8 8.1 8.3
10YR 1.8 1.8 2.2 2.8 2.8 3.6 3.8 3.6 4.7 4.7 4.7 5.6 5.7 6.2 6.5 6.7 7.3 7.4 7.9 8.1 8.2
Y 1.7 1.8 2.3 2.6 2.6 3.6 3.7 3.6 4.8 4.6 4.7 5.7 5.7 6.1 6.6 6.8 7.2 7.4 7.9 8.1 8.2
10Y 1.7 1.7 2.2 2.7 2.7 3.5 3.6 3.6 4.8 4.6 4.6 5.7 5.6 6.1 6.6 6.7 7.2 7.4 7.9 8.1 8.2
GY 1.7 1.7 2.2 2.7 2.7 3.7 3.7 3.5 4.8 4.6 4.5 5.7 5.7 6.0 6.7 6.8 7.2 7.5 7.9 8.1 8.2
10GY 1.7 1.8 2.2 2.6 2.7 3.7 3.6 3.7 4.8 4.6 4.7 5.7 5.6 6.1 6.6 6.7 7.3 7.4 7.8 8.2 8.2
G 1.8 1.8 2.2 2.7 2.7 3.7 3.6 3.7 4.9 4.6 4.6 5.7 5.6 6.1 6.7 6.7 7.3 7.6 7.8 8.1 8.3
10G 1.7 1.7 2.2 2.7 2.6 3.5 3.7 3.6 4.7 4.6 4.6 5.6 5.7 6.1 6.6 6.7 7.2 7.5 7.8 8.1 8.2
BG 1.8 1.8 2.3 2.8 2.8 3.8 3.7 4.8 4.8 4.8 4.8 5.6 5.8 6.2 6.6 6.9 7.3 7.4 8.0 8.1 8.2
10BG 1.7 1.7 2.2 2.6 2.7 3.4 3.6 3.7 4.5 4.6 4.7 5.5 5.6 6.1 6.5 6.7 7.2 7.3 7.8 8.1 8.2
B 1.7 1.7 2.2 2.6 2.7 3.6 3.6 3.7 4.7 4.6 4.6 5.7 5.6 6.0 6.6 6.7 7.2 7.5 7.8 8.1 8.2
10B 1.8 1.8 2.2 2.8 2.8 3.6 3.8 3.6 4.7 4.7 4.6 5.6 5.7 6.1 6.5 6.8 7.2 7.4 7.9 8.1 8.2
PB 1.8 1.8 2.3 2.6 2.7 3.6 3.6 3.7 4.7 4.6 4.7 5.6 5.7 6.1 6.6 6.8 7.3 7.4 7.9 8.1 8.2
10PB 1.7 1.7 2.2 2.7 2.7 3.7 3.7 3.6 4.9 4.7 4.6 5.8 5.7 6.0 6.7 6.8 7.2 7.5 7.9 8.1 8.2
P 1.7 1.7 2.2 2.7 2.7 3.7 3.6 3.5 4.8 4.6 4.5 5.7 5.7 6.0 6.7 6.8 7.2 7.5 7.9 8.1 8.2
10P 1.7 1.8 2.2 2.6 2.7 3.8 3.6 3.7 4.8 4.6 4.7 5.7 5.6 6.2 6.6 6.6 7.4 7.5 7.8 8.2 8.2
RP 1.8 1.8 2.2 2.7 2.7 3.7 3.6 3.7 4.9 4.6 4.6 5.8 5.6 6.1 6.7 6.7 7.3 7.6 7.8 8.1 8.2
10RP 1.7 1.8 2.2 2.7 2.6 3.5 3.7 3.6 4.8 4.6 4.6 5.7 5.7 6.1 6.6 6.7 7.2 7.5 7.8 8.1 8.2
Average 1.7 1.7 2.2 2.7 2.7 3.6 3.7 3.6 4.8 4.6 4.6 5.7 5.7 6.1 6.6 6.7 7.2 7.5 7.9 8.1 8.2

All of the observers of the constant-hue charts made the general spacing-estimates just referred to, and these modified the preliminary value estimates so substantially that it seemed well to provide some means of recovering the preliminary adjustments in case they should ever be wanted separately. This can be accomplished easily by subtracting out the grosser effects of the final step. The necessary constants for this purpose are supplied in Table I. Munsell value is indicated in the top row across the table while in the several columns below are presented mean spacing estimates corresponding to sample hue and background. To determine the magnitude of a preliminary adjustment, given the total estimate, all that is necessary is to find the difference between the total estimate recorded in Table II and the corresponding partial estimate in Table I. Thus, for instance, in the case of G 5/6 on the white ground, the total estimate is found in Table II to be 4.7; the corresponding figure for the final step in Table I is 4.6; and the difference, 0.1, represents the amount of the preliminary adjustment required. The averages for all hues given in the bottom row of Table I may be taken as approximate lightness estimates of the Munsell neutral samples.

Unlike hue and value, there was in the case of chroma no special problem in arriving at the summarized estimates, but only a simple averaging operation which will be mentioned presently.

(b) The other principal step in the averaging procedure was to enter the summarized final estimates (unencircled initials) as numerical frequencies in averaging sheets of the form shown at the bottom of Fig. 6. The arithmetical means[12] of the estimates of the given color on ​each of the three grounds were computed in the usual manner. These means were multiplied by the appropriate constants to transform them from the investigator’s recording scales to the Munsell attributive scales. These constants were 1.0, 0.1, and 0.4, respectively. In this way, averaged estimates of the hue of each color were secured from the constant-value chart data, and averaged estimates of the value of each color were secured from the constant-hue chart data. Since the estimates from both sets of charts included chroma, the two sets of chroma data were weighted in proportion to the numbers of observations and averaged together to yield a single representative chroma determination.

Thus in the end, there became available one representative estimate for each attribute of each chromatic color on each ground. These 3500 determinations are presented in the body of Table II.

The averaged estimates

The first column of Table II shows the 1929 notation of hue, value, and chroma; the next three (double) columns to the right show the average hue estimates and uncertainties, corresponding to the observations with the three different viewing grounds; the next three columns present the corresponding value data; and the final three columns, the chroma data. All determinations are presented to the first decimal place of the respective Munsell attributive unit.

The measure of uncertainty or variability consists of the range within which the middle 80 percent of the individual estimates fall. This range could be found only approximately from our summary sheets; but it provides a consider ably more reliable and representative measure than would the full range. Where no measure is given, as is often true of the hue estimates, the fact is that the 80 percent fell within a single recording unit of estimate. Though expressed in tenths, the limits of the 80 percent attributive ranges are given only to the nearest unit of estimate. Thus, one may note, the hue ranges are expressed in full hue steps, chroma in 0.4 steps and value in 0.1 steps.

In certain rare instances the mean may be found to fall without the 80 percent range. This anomaly is possible because of the skewness of distributions and the fact that means are computed in smaller units than ranges.

Asterisks in the hue columns accent a few instances in which the hue means are absent because hue data could not be taken. These instances concern the /2 chroma intermediate colors which do not appear on the constant-value charts. Corresponding value and chroma data could be given in Table II, however, because they were secured from the constant-hue charts upon which the samples in question do appear.

Before pointing out some general results, one more technical detail concerning Table II must be mentioned. This is the marked variation in the number, n, of cases upon which any given mean and range depend. In general, the chroma data are based on the largest numbers of observations (around 35) because results from both types of charts could be combined. Only in the case of the /2 chroma intermediate colors, mentioned above, are the chroma data scanty, for here only the few observers of the constant-hue charts could contribute. The hue data are next most plentiful (n≐25), being based on the relatively numerous observations with the constant value charts. The lightness data, on the other hand, could be secured only from the 10 subjects who observed the constant-hue charts, and the results from one of these could not be used because of a failure to follow instructions. More lightness data had been expected and, unquestionably, more are desirable. Fortunately, however, lightness has been the most investigated attribute, and there are visual data on Munsell value in the laboratory files of the Munsell company as well as in the literature (18, 50, 68). These sources will be consulted in conjunction with the final smoothing operation.


General indications

A detailed analysis of Table II will constitute a part of the smoothing operation to be per formed in preparation for the final report, but ​

Table II. Average visual estimates of the 1929 Munsell samples as viewed on white, gray, and black grounds, together with the corresponding ranges of the central 80 percent of the estimates.

1929
Munsell
Notation 		Visual Estimates, Average and 80% Range
Hue Value Chroma
White Gray Black White Gray Black White Gray Black
H V/C Av. Range Av. Range Av. Range Av. Range Av. Range Av. Range Av. Range Av. Range Av. Range
R8/ 4 48R 4.5R 48R 8.1 8.0-8.3 8.1 8.0-8.2 8.2 8.1-8.5 4.2 4.0- 4.4 3.8 3.6- 4.4 3.9 8.6- 4.0
2 3.0R 1R-6R 4.1R 4R-5R 43R 2R-5R 8.1 8.1-8.3 8.1 8.0-8.3 8.2 7.9-8.3 2.0 1.6- 3.0 2.0 1.6- 2.0 1.9
7/8 4.9R 5.0R 4.7R 7.0 7.0-7.3 7.2 7.2-7.4 7.1 6.9-7.4 8.1 7.2-8.4 7.9 7.6-8.4 8.0 7.6-8.4
6 4.8R 4.9R 4.7R 7.0 7.0-7.3 7.3 7.0-7.4 7.4 7.2-7.7 6.0 6.0-6.4 5.8 5.2-6.4 5.8 5.6-6.4
4 4.6R 4.6R 4.8R 7.0 7.0-7.3 7.2 6.9-7.4 7.4 7.2-7.8 4.5 4.0-4.8 4.5 3.6-5.2 4.4 3.6-4.8
2 3.8R 2R-5R 4.7R 4.2R 8R-5R 7.0 6.9-7.3 7.3 7.0-7.4 7.4 7.2-7.8 1.9 1.6-2.0 2.0 1.6-2.0 2.3 1.6-2.8
6/10 4.7R 4.9R 4.9R 6.0 5.9-6.2 6.2 5.9-6.6 6.6 6.2-6.7 10.1 9.2-10.0 10.0 9.6-10.0 10.1 9.6-10.4
8 4.7R 4.8R 4.9R 6.0 5.7-6.2 6.2 5.9-6.4 6.6 6.2-7.0 7.8 7.6-8.0 7.9 7.6-8.0 7.9 7.6-8.4
6 4.7R 4R-5R 4.9R 4.9R 6.0 5.7-6.3 6.2 5.9-6.4 6.6 6.2-6.6 5.9 6.6-6.0 6.0 5.6-6.0 6.0 6.0-6.4
4 4.5R 4R-5R 4.8R 4.8R 5.9 5.7-6.3 6.2 5.9-6.4 6.6 6.3-7.1 4.0 3.9 3.6-4.0 4.0 3.6-4.0
2 4.0R 3R-5R 4.2R 4R-5R 4.7R 6.0 5.7-6.3 6.2 5.9-6.4 6.6 6.2-6.6 1.9 1.6-3.0 1.9 1.9
5/12 5.0R 5.1R 5.1R 4.9 4.7-5.3 4.8 4.2-5.1 5.7 5.1-5.9 12.3 12.0-12.8 12.3 12.0-12.8 12.3 12.0-12.8
10 5.0R 5.0R 5.1R 4.9 4.0-5.2 4.8 4.7-5.1 5.7 5.1-5.9 10.1 9.6-10.4 10.1 9.2-10.4 10.1 9.6-10.4
8 5.0R 5.0R 5.0R 49 4.7-5.2 4.8 4.5-6.0 5.7 6.1-5.9 8.3 7.6-8.8 8.5 8.0-8.8 8.3 8.0-8.8
6 4.7R 4.6R 4R-6R 4.8R 4R-5R 4.9 4.7-5.2 4.8 4.7-5.1 5.7 5.1-5.9 6.2 6.0-6.8 6.3 6.0-6.8 6.3 6.0-6.8
4 4.4R 4R-5R 4.4R 3R-5R 4.7R 4R-5R 4.9 4.7-5.2 4.8 4.7-5.1 5.7 5.1-6.3 4.3 4.0-4.8 4.2 4.0-4.4 4.2 4.0-4.8
2 4.1R 3R-5R 4.1R 2R-6R 4.0R 2R-5R 4.9 4.7-5.2 4.8 4.6-5.1 5.7 5.2-6.3 2.1 2.0-2.4 2.1 2.0-2.4 2.1 2.0-2.4
4/14 5.0R 5.0R 5.0R 3.9 3.7-4.3 3.8 3.7-4.2 4.8 4.2-5.4 13.9 13.2-14.4 13.9 13.6-14.4 13.9 13.6-14.4
12 5.0R 5.0R 5.0R 3.9 5.7-4.3 3.8 3.8-4.2 4.8 4.2-5.4 12.1 11.6-12.4 12.2 12.0-12.8 12.2 11.6-12.8
10 4.9R 4.9R 4R-6R 4.8R 3.9 3.8-4.8 3.8 3.4-4.1 4.8 4.2-5.4 10.1 10.0-10.4 10.1 9.6-10.4 10.2 9.6-10.4
8 4.9R 4.8R 4.9R 3.9 3.7-4.3 3.8 3.8-4.2 4.8 4.2-5.4 8.0 8.0-8.4 8.2 7.6-8.4 8.1 8.0-8.4
6 4.7R 5.0R 4.7R 3.9 3.7-4.3 3.8 3.6-4.1 4.8 4.2-5.4 6.0 6.1 6.0-6.4 6.0 6.0-6.4
4 4.3R 2R-5R 4.6R 4R-5R 4.2R 3R-5R 3.9 3.5-4.3 3.8 3.7-4.1 4.8 4.1-5.4 4.0 3.6-4.0 4.1 4.0-4.4 4.0 4.0-4.4
2 4.4R 3R-5R 4.6R 4.5R 4R-5R 3.9 3.5-4.3 3.8 3.8-4.2 4.8 4.2-5.4 2.0 1.6-2.0 2.0 1.6-2.4 2.0
3/10 4.9R 4.9R 5.0R 2.9 2.5-3.5 2.9 2.4-3.1 3.7 3.1-4.2 10.0 10.0-10.4 10.1 10.0-10.8 10.2 10.0-10.4
8 5.0R 4.7R 4.9R 2.9 2.5-3.3 2.9 2.8-3.1 3.7 3.3-4.2 7.9 7.0-8.4 8.0 7.0-8.4 8.2 8.0-8.4
6 4.7R 4R-6R 4.8R 4R-5R 4.8R 2.9 2.5-3.5 2.9 2.7-3.1 3.8 3.2-4.3 6.0 5.6-6.0 6.1 6.0- 6.4 6.1 6.0-6.4
4 4.7R 4.8R 4.9R 2.9 2.3-3.3 2.8 2.6-3.1 3.7 3.3-4.2 4.0 4.2 4.0-4.8 4.2 4.0-4.4
2 4.7R 3R-5R 4.7R 4.3R 3R-5R 2.9 2.3-3.3 2.8 2.8-3.1 3.8 3.3-4.3 1.9 1.6-2.0 2.0 1.6-2.0 2.1 2.0-2.4
2/6 4.8R 5.1R 4R-5R 5.0R 1.9 1.4-2.3 2.0 1.6-2.3 2.6 2.1-3.0 5.8 5.2-6.0 5.8 5.2-6.4 6.0 5.6-6.4
4 5.5R 5R-7R 5.0R 5.0R 3R-5R 2.0 1.6-2.3 2.0 1.7-2.2 2.4 2.0-2.9 3.7 3.6-4.0 3.7 3.6-4.0 4.0 3.6-4.8
2 5.1R 5R-7R 4.8R 2R-6R 4.9R 2R-5R 1.9 1.5-2.2 2.0 1.6-2.1 2.5 2.0-2.7 1.9 1.9 1.6-2.0 2.2 2.0-2.8
 
10R 8/4 0.1YR 0.2YR 9.9R 8.0 7.4-8.2 8.2 8.0-8.3 8.3 8.1-8.6 4.0 4.0-4.4 4.2 4.0-4.4 4.0 4.0-4.4
7/8 9.8R 9R-10R 0.3YR 9.9R 6.7 5.8-7.2 7.2 7.0-7.3 7.4 7.1-7.5 8.2 7.6-8.4 8.1 7.6-8.4 8.0 7.2-8.4
6 9.6R 9R-10R 9.9R 9.8R 6.8 6.0-7.2 7.2 7.1-7.4 7.4 7.1-7.7 5.9 5.6-6.0 5.9 5.6- 6.4 5.8 5.6-6.4
4 9.5R 8R-10R 9.8R 9.6R 6.8 6.0-7.2 7.2 7.1-7.3 7.4 7.1-7.5 4.1 4.0-4.8 4.1 4.0-4.8 4.1 4.0-4.4
6/10 10.0R 10.0R 0.2YR 10R-1YR 5.8 4.9-6.1 5.9 5.5-6.4 6.5 6.2-6.6 10.4 10.0-10.8 10.6 10.0-10.8 10.2 10.0-10.8
8 0.1YR 0.1YR 10.0R 5.7 4.9-6.2 6.1 5.7-6.4 6.5 6.2-6.6 8.0 8.0-8.4 8.0 8.0-8.4 8.0 8.0-8.4
6 9.9R 10.0R 10.0R 5.7 4.9-6.2 6.2 5.8-6.4 6.5 6.2-6.7 6.0 6.0 6.0-6.4 6.0 6.0-6.4
4 9.3R 9R-10R 9.6R 9R-10R 9.7R 9R-10R 5.6 4.9-6.2 6.2 5.9-6.4 6.5 6.2-6.7 3.9 4.0 4.0
5/10 9.9R 0.1YR 10.0R 4.6 3.8-5.2 4.6 4.2-5.0 5.5 5.1-5.9 10.2 10.0-10.4 10.2 10.0-10.4 10.2 10.0-10.4
8 10.0R 10.0R 10.0R 4.6 3.8-5.0 4.7 4.2-5.1 5.6 5.1-5.9 8.1 8.1 8.0-8.4 8.0 8.0-8.4
6 10.0R 9.9R 9.9R 4.6 3.8-5.0 4.7 4.2-5.0 5.5 5.1-5.9 6.1 6.2 6.0-6.4 6.0
4 9.5R 9R-10R 94R 9R-10R 95R 9R-10R 4.5 3.8-5.2 4.7 4.8-5.0 5.5 5.0-5.7 4.0 3.6-4.0 4.0 4.0
4/10 9.9R 0.1YR 9.8R 3.7 2.8-4.1 3.7 3.5-4.1 4.6 4.2-4.9 10.0 9.2-10.0 10.2 9.6-10.4 10.2 10.0-10.4
8 10.0R 10.0R 9.8R 3.6 2.8-4.0 3.6 3.6-4.1 4.6 4.2-4.9 8.2 7.6- 8.4 8.3 8.0-8.8 8.2 7.6-8.4
6 10.0R 10.0R 99R 3.7 2.8-4.0 3.8 3.5-4.2 4.6 4.2-4.9 6.1 6.0-6.8 6.2 6.0-6.4 6.3 6.0-6.8
4 9.8R 9.8R 9R-10R 9.5R 9R-10R 3.6 2.8-4.0 3.7 3.6-4.0 4.6 4.1-4.9 4.0 4.0-4.4 4.1 4.1 3.6-4.4
3/6 9.9R 0.2YR O.1YR 2.8 2.0-3.2 2.8 2.4-3.1 3.4 29-4.0 6.0 5,6-6.0 6.1 6.0-6.4 6.1 6.0-6.4
4 10.0R 0.2YR 9.9R 2.7 2.0-3.2 2.8 2.4-8.2 3.4 2.9-3.9 4.0 4.1 4.0-4.4 4.1 4.0-4.4 ​
YR 8/4 4.4YR 4YR-5YR 5.0YR 4.8YR 7.9 7.5-8.4 8.1 8.0-8.2 8.3 8.0-8.5 4.0 3.6-4.0 4.0 4.0-4.4 4.0 3.6-4.0
2 3.6YR 2YR-5YR 3.9 YR 2YR-6YR 4.3YR 3YR-5YR 7.9 7.5-8.1 8.1 8.0-8.2 8.3 1.9 1.6-2.4 1.9 1.6-2.0 1.9
7/10 5.2YR 5.2YR 5.2YR 6.7 6.2-7.2 7.2 7.0-7.4 7.5 7.2-7.8 10.3 10.0-10.8 10.4 10.0-10.8 10.3 10.0-10.8
8 5.0YR 4.9YR 4.9YR 4YR-5YR 6.8 6.2-7.2 7.2 7.0-7.2 7.5 7.2-7.9 8.2 8.0-8.4 8.1 8.0-8.4 8.0 8.0-8.4
6 4.5YR 4YR-5YR 4.7 YR 4YR-5YR 4.7YR 4YR-5YR 6.7 6.2-7.1 7.2 7.0-7.2 7.5 7.2-8.0 6.1 6.0-6.4 6.0 6.0 5.6-6.4
4 4.2YR 3YR-5YR 4.4YR 4YR-5YR 4.2YR 3YR-5YR 6.8 6.2-7.1 7.2 7.0-7.3 7.5 7.2-8.0 4.0 4.0-4.4 3.9 4.0
2 3.9YR 2YR-5YR 4.6YR 3.7YR 2YR-5YR 6.7 6.2-7.1 7.2 7.0-7.3 7.5 7.2-8.0 2.0 1.6-2.0 2.0 1.9 1.6-2.0
6/12 5.1YR 5YR-6YR 5.0YR 5.0YR 5.7 5.1-6.4 6.0 5.7-6.3 6.6 6.2-7.0 12.0 12.0-12.4 11.9 10.8-12.4 11.9 11.2-18.4
10 5.0YR 5.2YR 5.0YR 5.7 5.1-6.3 6.0 5.7-6.2 6.6 6.2-7.1 10.1 10.0-10.4 10.2 10.0-10.4 10.1 10.0-10.4
8 5.0YR 5.2YR 4.9YR 5.7 5.1-6.2 6.0 5.7-6.2 6.6 6.1-7.1 8.1 8.0-8.4 8.2 8.0-8.4 8.0 8.0-8.4
6 4.7YR 5.0YR 4.7 YR 4YR-5YR 5.7 5.1-6.2 6.0 6.0-6.2 6.7 6.2-7.0 5.9 5.6-6.0 5.9 5.9 5.6-6.0
4 4.3YR 4YR-5YR 4.6YR 4YR-5YR 4.2YR 3YR-5YR 5.6 5.1-6.2 6.0 5.7-6.2 6.6 6.2-7.0 3.9 3.6-4.0 3.9 3.9 3.6-4.0
2 4.5YR 4.3YR 3YR-5YR 4.2YR 4YR-5YR 5.6 5.4-6.2 6.0 5.7-6.2 6.6 6.2-7.0 1.9 1.6-2.0 2.0 1.8 1.6-2.0
5/10 5.0YR 5.0YR 5.0YR 4.7 4.2-5.1 4.6 4.5-5.0 5.8 5.2-6.2 10.1 10.1 10.0-10.4 10.1 10.0-10.4
8 5.0YR 5.0YR 5.2YR 4.6 4.0-5.1 4.6 4.2-5.0 5.7 5.2-6.2 8.1 8.0-8.4 8.1 8.0-8.4 8.0 8.0-8.4
6 5.1YR 5.0YR 5.1YR 4.6 4.0-5.1 4.6 4.2-5.0 5.7 5.2-6.2 6.1 6.0 6.0-6.4 5.9 5.6-6.0
4 4.6YR 4YR-5YR 4.5YR 4YR-6YR 4.3YR 3YR-5YR 4.6 4.0-5.0 4.6 4.2-4.8 5.7 5.1-6.0 4.0 4.1 4.0-4.4 4.0 4.0-4.4
2 4.3YR 3.9YR 2YR-5YR 4.0YR 2YR-5YR 4.5 3.9-5.0 4.6 3.9-5.0 5.7 5.1-6.2 1.9 1.6-2.0 1.9 1.6-2.4 1.9 1.6-2.0
4/8 5.2YR 5.3YR 4.9YR 3.7 3.0-4.1 3.7 3.2-4.0 4.8 4.4-5.2 7.7 7.2-8.0 8.0 7.6-8.8 7.8 7.2-8.4
6 5.1YR 5.0YR 5.1YR 3.7 3.0-4.1 3.7 3.2-4.0 4.8 4.3-5.2 6.0 5.6-6.4 6.2 6.0-6.8 6.1 5.6-6.4
4 5.0YR 4.8YR 5.0YR 3.7 3.0-4.1 3.7 3.2-4.0 4.8 4.2-5.2 4.1 4.0-4.4 4.2 4.0-4.8 4.1 4.0-4.4
2 4.4YR 4.77YR 4YR-5YR 3.7YR 2YR-7YR 3.6 3.0-4.1 3.6 3.2-3.9 4.8 4.2-5.2 2.0 1.6-2.0 2.0 2.0-2.4 2.1 2.0-2.4
3/4 5.2YR 4.8YR 5.0YR 2.8 2.3-3.1 2.8 2.4-3.0 3.8 3.3-4.0 4.0 3.6-4.0 4.3 4.0-4.8 4.3 4.0-4.4
2 4.8YR 4.6YR 4.8YR 2.6 2.1-3.0 2.7 2.2-3.0 3.7 3.2-4.0 1.9 1.6-2.0 2.1 2.0-2.4 2.2 2.0-2.4
2/2 5.3YR 5.1YR 5.0YR 1.8 1.5-2.1 1.9 1.6-2.1 2.5 2.1-2.7 1.9 1.9 1.6-2.0 2.1 2.0-2.4
‍
10 YR8/6 9.8YR 9YR-10YR 10.0YR 10.0YR 8.0 8.0-8.3 8.1 7.9-8.2 8.2 8.0-8.5 6.3 6.0-6.8 6.3 6.0-6.8 6.1 5.2-6.4
4 9.8YR 9YR-10YR 9.8YR 9.8YR 8.0 8.0-8.2 8.1 8.0-8.1 8.0-8.4 4.0 3.6-4.0 3.8 3.6-4.0 3.9 3.6-4.0
7/10 10.0YR 0.1Y 9.9YR 6.8 6.6-7.0 7.3 7.1-7.4 7.4 7.2-7.5 10.2 10.0-10.4 10.2 10.0-10.8 10.2 10.0-10.4
8 10.0YR 10.0YR 9.9YR 6.8 6.6-7.0 7.3 7.2-7.4 7.4 7.2-7.7 8.0 8.0-8.4 8.0 7.6-8.0 8.0 7.6-8.0
6 10.00YR 10.0YR 9.8YR 6.8 6.4-7.0 7.3 7.2-7.3 7.4 7.2-7.7 6.0 6.0-6.4 5.9 5.6-6.0 5.9 5.6-6.0
4 9.5YR 9YR-10YR 9.3 YR 8YR-10YR 9.4YR 9YR-1OYR 6.8 6.6-7.2 7.3 7.2-7.4 7.4 7.2-7.4 3.9 3.6-4.0 3.8 3.6-4.0 4.0 3.6-4.0
6/10 0.1Y 0.1Y 0.1Y 5.8 5.8-6.0 6.3 6.1-6.5 6.6 6.3-6.7 10.0 9.8 9.2-10.0 10.2 10.0-10.4
8 10.00YR 0.2Y 0.1Y 5.8 5.8-6.0 6.3 6.1-6.4 6.6 8.0 7.6-8.0 8.0 8.0-8.4 8.0 7.6-8.4
6 9.9YR 0.2Y 10.0YR 5.8 5.8-6.0 6.3 6.1-6.5 6.6 6.3-6.6 6.1 6.0-6.4 6.2 6.0-6.4 6.1 6.0-6.4
4 9.7YR 10.0YR 9.9YR 5.7 5.6-6.0 6.2 6.0-6.4 6.5 6.3-6.8 3.9 3.6-4.0 3.8 3.6-4.4 3.9 3.2-4.0
5/8 10.00YR 10.0YR 10.0YR 4.8 4.7-5.1 4.8 4.2-5.0 5.6 5.4-5.9 8.0 8.0-8.4 8.1 8.0-8.4 8.1 8.0-8.4
6 10.00YR 10.0YR 10.0YR 4.8 4.6-5.1 4.8 4.2-5.0 5.6 5.4-5.9 5.9 5.6-6.4 5.9 5.6-6.4 5.8 5.6-6.0
4 10.0YR 9.8YR 9.8YR 4.8 4.6-5.1 4.8 4.2-5.0 5.6 5.4-5.9 3.9 3.6-4.0 4.0 4.0~4-5 4.0 4.0-4.4
4/4 9.9YR 9.8YR 9.9YR 3.9 3.7-4.2 3.7 3.2-4.0 4.8 4.3-5.2 4.0 3.6-4.8 4.3 4.0-4.8 4.3 4.0-4.8
‍
Y 8/12 5.3Y 5.3Y 5.2Y 7.8 7.5-8.1 8.0 8.0-8.1 8.2 8.0-8.2 11.8 11.2-12.4 11.9 11.2-12.4 12.0 11.2-12.4
10 5.2Y 5Y-6Y 5.4Y 5Y-6Y 5.2Y 7.9 7.9-8.3 8.0 8.0-8.1 8.2 8.1-8.4 10.2 10.0-10.8 10.3 9.6-10.8 10.4 10.0-10.8
8 5.5Y 5Y-6Y 5.6Y 5Y-6Y 5.3Y 5Y-6Y 7.9 7.8-8.2 8.1 8.0-8.1 8.2 8.0-8.3 8.0 7.6—8.0 8.1 8.0—8.4 8.0 7.6-8.4
6 4.8Y 4Y-5Y 4.9Y 4Y-6Y 4.6Y 4Y-5Y 7.9 7.5-8.1 8.1 8.0-8.1 8.2 8.0-8.2 5.8 5.6-6.0 5.9 6.6-6.0 5.8 5.2-6.0
4 4.8Y 4Y-6Y 4.6Y 3Y-5Y 4.5Y 3Y-5Y 7.9 7.6-8.2 8.1 8.0-8.1 8.2 8.0-8.2 3.8 3.6-4.0 3.9 3.2-4.0 3.8 3.2-4.0
2 5.1Y 4.8Y 5Y-7Y 4.5Y 3Y-5Y 7.9 7.9-8.1 8.1 8.0-8.1 8.2 8.0-8.2 1.6 1.6-2.0 1.8 1.6-2.0 1.9 1.6-2.0
7/10 5.2Y 5.2Y 5.3Y 6.7 6.3-7.1 7.2 7.0-7.3 7.4 6.9-7.5 9.8 9.6-10.4 9.8 9.6-10.4 9.9 9.2-10.0
8 5.5Y 5Y-6Y 5.5Y 5.8Y 5Y-7Y 6.8 6.4-7.3 7.2 7.1-7.4 7.4 7.2-7.8 8.4 8.0-8.8 8.4 8.0-8.8 8.6 8.0-9.2
6 5.2Y 5.3Y 5.3Y 5Y-6Y 6.7 6.2-7.1 7.1 7.0-7.3 7.4 7.2-7.8 5.9 5.6-6.0 6.1 6.0-6.4 6.1 6.0-6.4
4 5.1Y 4.8Y 4Y-5Y 4.8Y 6.7 6.5-7.1 7.3 7.1-7.3 7.4 7.1-8.0 3.8 3.6-4.4 4.0 3.6-4.4 3.9 3.6-4.0
2 5.0Y 4.6Y 5.2Y 6.7 6.4-7.1 7.2 7.0-7.4 7.4 7.0-7.6 1.6 1.2-2.0 1.8 1.2-2.0 1.8 1.2-2.0
6/8 5.4Y 5.4Y 5.3Y 5.6 5.4-6.2 6.1 5.7-6.3 6.6 6.2-7.3 8.0 7.6-8.4 8.0 8.0-8.4 8.2 8.0-8.8
6 5.4Y 5,5Y 5Y-6Y 5.2Y 5.6 5.4-6.2 6.0 5.7-6.3 6.5 6.2-7.2 6.3 6.0-6.8 6.4 6.0-7.2 6.5 6.0-6.8
4 5.2Y 5.4Y 5.0Y 5Y-6Y 5.7 5.6-6.2 6.0 5.6-6.3 6.6 6.2-7.3 4.0 3.6-4.0 4.0 3.6-4.4 3.8 3.2-4.0
2 5.0Y 5.1Y 4.8Y 5.7 5.2-6.1 6.1 5.7-6.2 6.6 6.2-7.4 1.8 1.2-2.0 1.9 1.6-2.0 1.8 1.6-2.0 ​
Y 5/6 5.5Y 5Y-7Y 5.5Y 5Y-6Y 5.4Y 5Y-6Y 4.6 4.2-5.2 4.7 4.2-5.1 5.7 5.2-6.3 6.0 5.6-6.4 6.2 5.6-6.4 6.3 6.0-6.8
4 5.3Y 5.2Y 5.3Y 4.6 4.2-5.2 4.7 4.2-5.0 5.7 5.1-6.2 3.9 3.6-4.4 3.9 3.6-4.4 3.9 3.6-4.4
2 5.2Y 5.1Y 4.9Y 4.7 4.6-5.2 5.1 4.7-5.3 5.6 5.1-6.3 1.9 1.6-2.4 1.7 1.2-2.0 1.8 1.2-2.0
4/4 5.6Y 5Y-6Y 5.1Y 5.2Y 3.7 3.2-4.3 3.6 3.2-4.1 4.8 4.0-5.3 4.1 3.6-4.4 4.3 4.0-4.8 4.2 4.0-4.8
2 5.2Y 5.0Y 5.0Y 3.8 3.4-4.3 3.7 3.2-4.2 4.8 4.1-5.5 1.9 1.2-2.0 2.0 1.6-2.4 2.0 1.6-2.4
3/2 5.3Y 5.2Y 5.2Y 2.6 2.2-2.9 2.6 2.4-3.0 3.7 3.0-4.3 1.6 1.2-2.0 1.6 1.2-2.0 1.8 1.6-2.0
2/2 5.2Y 5.4Y 5.1Y 1.9 1.5-2.2 1.9 1.7-2.0 2.6 2.2-3.1 1.9 1.9 1.6-2.8 1.9 1.2-2.0
‍
10Y 8/8 10.0Y 10.0Y 10.0Y 7.9 7.3-8.2 8.0 7.8-8.1 8.2 8.0-8.5 8.2 7.6-8.4 8.1 8.0-8.4 8.1 8.0-8.4
6 10.0Y 0.1GY 0.1GY 7.9 7.3-8.3 8.0 8.0-8.1 8.1 8.0-8.6 5.9 5.9 5.6-6.0 5.8 5.6-6.0
4 10.0Y 0.1GY 10.0Y 7.9 7.4-8.3 8.0 8.0-8.1 8.2 8.0-8.5 3.9 3.6-4.0 3.8 3.2-4.0 3.8 3.2-4.0
7/8 0.1GY 0.1GY 9.9Y 6.9 5.9-7.1 7.1 6.9-7.2 7.3 7.0-7.7 8.1 8.0-8.4 8.1 8.0-8.4 8.3 8.0-8.8
6 0.1GY 0.4GY 0.2GY 6.7 7.0-7.1 7.1 7.0-7.3 7.3 7.0-7.8 6.1 6.0-6.4 6.1 5.6-6.4 6.1 6.0-6.4
4 10.0Y 0.1GY 0.1GY 6.7 6.8-7.2 7.1 7.0-7.3 7.3 6.8-7.7 3.8 3.6-4.0 3.8 3.6-4.4 3.8 3.6-4.0
6/6 9.8Y 10.0Y 10.0Y 5.7 5.8-6.2 6.1 5.7-6.4 6.5 6.0-6.8 6.4 6.0-6.8 6.5 6.0-6.8 6.6 6.0-6.8
4 0.2GY 10.0Y 9.8Y 5.7 5.6-6.1 6.0 5.7-6.3 6.3 6.0-6.6 3.9 3.6-4.0 4.0 3.6-4.0 3.9 3.6-4.0
5/6 10.0Y 9.9Y 10.0Y 4.6 4.4-5.1 4.6 4.2-5.0 5.6 5.2-6.3 6.0 6.1 6.0-6.4 6.1
4 0.1GY 10.0Y 0.1GY 4.6 3.7-5.0 4.6 4.2-5.0 5.6 5.0-6.1 4.2 4.0-4.4 4.2 4.0-4.8 4.2 4.0-4.4
4/4 0.2GY 0.1GY 10.0Y 3.7 3.5-4.2 3.6 3.2-4.0 4.7 3.8-5.4 4.2 4.0-4.4 4.2 4.0-4.8 4.3 4.0-4.8
‍
GY 8/8 5.0GY 4.8GY 4.7GY 4GY-5GY 8.0 7.2-8.4 8.1 8.0-8.4 8.1 8.0-8.3 8.4 8.0-8.8 8.3 8.0-8.8 8.3 8.0-8.8
6 5.0GY 5.0GY 5.0GY 7.9 7.9-8.3 8.0 8.0-8.2 8.2 8.0-8.3 6.2 6.0-6.4 6.2 6.0-6.8 6.1 6.0-6.8
4 5.2GY 5.1GY 5.0GY 7.9 7.4-8.2 8.0 8.0-8.2 8.2 8.0-8.4 4.0 4.0 4.0-4.4 3.9 3.2-4.0
2 5.6GY 4.9GY 5.3GY 7.9 7.6-8. 8.0 8.0-8.2 8.2 8.0-8.4 1.9 1.6-2.0 1.7 1.2-2.0 1.8 1.2-2.0
7/10 5.0GY 4.8GY 4.9GY 6.7 5.7-7.2 7.1 6.7-7.4 7.5 7.2-7.8 10.3 10.0-10.8 10.1 10.0-10.4 10.3 10.0-10.4
8 5.1GY 5.1GY 5.1GY 6.7 5.9-7.1 7.1 6.9-7.4 7.4 7.2-7.6 8.1 7.6-8.4 7.9 7.2-8.4 8.0 7.6-8.8
6 5.0GY 5.0GY 5.2GY 6.7 5.9-7.1 7.1 7.0-7.4 7.4 7.2-7.9 6.1 6.0-6.4 6.1 6.0-6.4 6.1 6.0-6.4
4 5.1GY 5.2GY 5.3GY 6.7 6.0-7.1 7.1 7.0-7.4 7.5 7.2-7.9 4.0 4.0-4.4 4.0 4.0-4.4 4.0 3.6-4.0
2 5.3GY 5.2GY 5.3GY 6.6 5.9-7.0 7.1 7.0-7.4 7.4 7.0-7.6 2.1 1.6-2.4 2.0 1.6-2.4 1.9 1.6-2.0
6/8 5.1GY 4.9GY 5.0GY 5.6 4.6-6.1 5.9 5.7-6.4 6.6 6.3-7.1 8.1 7.6-8.4 8.0 7.6-8.4 8.0 8.0-8.4
6 5.1GY 5.2GY 5.0GY 5.6 4.6-6.0 5.9 5.7-6.4 6.7 6.1-7.3 6.3 6.0-6.8 6.4 6.0-6.8 6.4 6.0-6.8
4 5.2GY 5.3GY 4.9GY 5.6 5.6-6.1 6.0 5.7-6.4 6.7 6.2-7.3 4.1 4.1 4.0-4.4 4.0
2 5.2GY 5.4GY 5.0GY 5.6 4.8-6.0 6.0 5.7-6.4 6.7 6.2-7.3 1.9 1.6-2.0 1.9 1.6-2.0 1.9 1.6-2.0
5/8 5.1GY 5.0GY 5.0GY 4.6 4.7-5.1 4.5 3.8-5.0 5.8 5.0-6.0 8.1 8.0-8.4 8.2 8.0-8.8 8.3 8.0-8.8
6 5.2GY 5.0GY 5.2GY 4.6 4.6-5.1 4.4 3.9-5.0 5.7 5.3-6.5 6.1 6.0-6.4 5.8 5.6-6.0 6.0 5.6-6.0
4 5.1GY 5.1GY 5.0GY 4.6 4.6-5.1 4.5 4.0-5.0 5.7 5.0-6.0 4.2 4.0-4.4 4.2 4.0-4.4 4.2 4.0-4.4
2 5.3GY 5.2GY 5.0GY 4.6 3.6-5.0 4.5 4.0-5.0 5.8 5.1-6.0 2.0 2.0-2.4 2.1 2.0-2.4 2.0 1.6-2.4
4/6 5.1GY 4.7GY 3GY-5GY 5.3GY 3.6 3.6-4.0 3.5 3.0-3.9 4.9 4.2-5.2 5.9 5.6-6.4 6.0 5.6-6.0 6.0 5.6-6.4
4 4.9GY 4.8GY 5.0GY 3.7 2.7-4.0 3.5 3.2-4.0 4.8 4.0-5.7 4.0 3.6-4.0 4.1 4.0-4.8 4.1 4.0-4.4
2 4.9GY 5.3GY 5.3GY 3.6 3.6-4.0 3.6 3.2-4.0 4.9 4.2-5.2 1.9 1.6-2.0 2.0 1.6-2.4 1.9 1.6-2.4
3/4 5.0GY 5.0GY 4.7GY 2.8 2.3-3.2 2.7 2.4-3.1 3.8 3.3-4.2 3.7 3.2-4.0 3.9 3.2-4.4 4.0 3.6-4.8
2 5.1GY 5.1GY 5.0GY 2.7 2.0-3.0 2.7 2.4-3.0 3.7 3.3-4.0 1.9 1.6-2.0 2.0 1.6-2.0 2.0 1.6-2.4
2/2 5.0GY 5.2GY 5.0GY 1.8 1.6-2.2 1.9 1.6-2.0 2.5 2.2-3.0 2.0 2.0-2.4 2.1 1.6-2.4 2.3 2.0-2.8
‍
10GY 8/6 10.0GY 10.0GY 10.0GY 7.8 7.4-8.0 8.2 8.0-8.4 8.2 8.0-8.3 6.1 6.0-6.8 5.9 5.6-6.4 5.9 5.2-6.0
4 10.0GY 10.0GY 10.0GY 7.8 7.6-8.1 8.2 8.0-8.2 8.3 8.1-8.4 4.4 4.0-4.8 4.1 4.0-4.4 4.2 4.0-4.8
7/8 9.9GY 9.8GY 9.8GY 9GY-10GY 6.7 6.3-7.1 7.3 7.2-7.4 7.4 7.1-7.9 8.4 8.0-8.8 8.3 8.0-8.8 8.2 8.0-8.8
6 10.0GY 10.0GY 10.0GY 6.7 6.6-7.1 7.3 7.2-7.5 7.4 7.1-7.5 6.3 6.0-6.8 6.1 6.0-6.8 6.1 6.0-6.8
4 10.0GY 9.9GY 0.1G 6.6 6.3-7.1 7.3 7.2-7.7 7.5 7.1-7.6 4.0 4.0-4.4 4.0 4.0-4.4 3.9 3.6-4.0
6/10 10.0GY 0.1G 9.9GY 5.6 5.4-6.0 6.2 6.0-6.9 6.6 6.4-7.3 10.3 10.0-10.8 10.2 10.0-10.4 10.3 10.0-10.8
8 9.8GY 10.0GY 9.9GY 5.6 5.4-6.1 6.2 5.8-6.4 6.6 6.0-6.6 8.5 8.0-9.2 8.4 8.0-8.8 8.3 7.6-8.8
6 0.1G 10.0GY 10.0GY 5.6 5.4-6.1 6.2 5.9-6.4 6.6 6.0-6.8 6.5 6.0-6.8 6.3 6.0-6.8 6.2 6.0-6.4
4 0.4G 0.2G 0.1G 5.6 5.4-6.1 6.1 5.8-6.4 6.6 6.2-7.3 4.2 4.0-4.8 4.2 4.0-4.4 4.1 3.6-4.8
5/8 0.1G 0.1G 9.8GY 4.6 4.2-5.1 4.7 4.2-5.1 5.7 5.2-6.3 8.4 8.0-8.8 8.4 8.0-8.8 8.5 8.0-8.8
6 9.9GY 9.8GY 9.7GY 4.6 4.2-5.2 4.7 4.2-5.1 5.7 5.0-5.9 6.5 6.0-6.8 6.5 6.0-6.8 6.7 6.0-6.8
4 0.3G 0.1G 0.1G 4.6 4.2-5.1 4.7 4.2-5.1 5.8 5.2-6.5 4.0 3.6-4.4 4.1 4.0 3.6-4.0 ​
10GY 4/6 0.3G 0.1G 0.4G 3.7 3.2-4.2 3.8 3.5-4.2 4.9 4.1-5.6 6.3 6.0-6.8 6.4 6.0-6.8 6.3 6.0-6.8
4 0.2G 0.2G 0.3G 3.6 3.2-4.1 3.8 3.5-4.2 4.8 4.2-6.6 4.2 4.0-4.4 4.2 4.0-4.4 4.2 4.0-4.4
3/4 10.00GY 9.9GY 9.7GY 2.7 2.3-4.2 2.8 2.4-3.3 3.9 3.0-4.0 4.5 4.0-4.8 4.7 4.0-4.8 4.7 4.0-5.2
‍
G 8/6 5.0G 5.2G 5.2G 7.8 7.5-8.2 8.1 8.0-8.2 8.2 8.0-8.4 6.3 6.0-6.8 6.2 6.0-6.8 6.0
4 5.2G 5.3G 5.2G 7.9 7.7-8.2 8.2 8.0-8.2 8.3 8.1-8.6 4.2 4.0-4.8 4.0 3.6-4.4 3.9 3.2-4.0
2 5.3G 5.3G 5.4G 7.9 7.9-8.2 8.1 8.0-8.3 8.3 8.1-8.6 2.3 2.0-2.4 2.1 2.0-2.4 2.1 2.0-2.8
7/6 5.0G 4.9G 5.1G 6.8 6.8-7.2 7.3 7.1-7.4 7.6 7.3-7.8 6.3 6.0-6.8 6.3 6.0-6.8 6.1 6.0-6.4
4 5.4G 5.0G 5.2G 6.8 6.6-7.2 7.2 7.0-7.3 7.5 7.2-7.7 4.2 4.0-4.4 4.2 4.0-4.8 4.1 4.0-4.4
2 5.3G 5.0G 5.2G 6.7 6.4-7.2 7.2 7.1-7.4 7.6 7.2-7.8 2.2 2.0-2.4 2.2 2.0-2.4 2.1 2.0-2.4
6/6 5.0G 4G-5G 5.2G 5.1G 5.7 5.5-6.3 6.1 5.7-6.5 6.7 6.4-7.2 6.6 6.4-7.2 6.8 6.0-7.2 6.6 6.0-6.8
4 5.2G 5.1G 5.1G 5.7 5.3-6.2 6.1 5.8-6.3 6.7 6.4-7.5 4.3 4.0-4.8 4.3 4.0-4.8 4.1 4.0-4.4
2 5.3G 5.6G 5.2G 5.6 5.3-6.2 6.1 5.8-6.3 6.7 6.2-6.9 2.3 2.0-2.4 2.3 2.0-2.8 2.1
5/8 5.0G 4.9G 5.0G 4.7 4.1-5.2 4.7 4.5-5.2 5.8 5.5-6.5 8.5 8.0-8.8 8.5 8.0-8.8 8.4 8.0-8.8
6 5.1G 5.0G 5.1G 4.7 4.1-5.2 4.6 4.2-5.0 5.8 5.5-6.5 6.4 6.0-6.8 6.4 6.0-6.8 6.3 6.0-6.8
4 5.2G 5.0G 5.2G 4.7 4.1-5.2 4.6 4.2-5.0 5.8 5.5-6.5 4.3 4.0-4.4 4.3 4.0-4.8 4.2 4.0-4.4
2 5.0G 5.0G 5.2G 4.6 4.2-5.2 4.6 4.2-5.0 5.8 5.4-6.7 2.1 2.2 2.0-2.4 2.0 2.0-2.4
4/4 5.1G 5.0G 5.2G 3.7 3.1-4.2 3.8 3.7-4.2 5.0 4.6-5.8 4.4 4.0-4.8 4.5 4.0-4.8 4.6 4.0-5.2
2 5.0G 5.0G 6.0G 5G-7G 3.7 3.1-4.1 3.7 3.2-4.0 4.9 4.4-6.8 2.2 2.0-2.4 2.3 2.0-2.4 2.2 2.0-2.8
3/4 5.0G 5.2G 4.9G 2.7 2.3-3.2 2.9 2.6-3.1 4.0 3.6-4.7 4.3 4.0-4.8 4.4 4.0-4.8 4.5 4.0-4.8
2 5.1G 5.0G 4.9G 2.7 2.2-3.1 2.8 2.4-2.9 3.8 3.4-4.6 2.3 2.0-2.8 2.4 2.0-2.8 2.3 2.0-2.8
2/2 5.1G 5.2G 5.4G 1.8 1.6-2.1 1.9 1.8-2.1 2.4 2.0-2.8 2.1 2.0-2.4 2.2 2.0-2.8 2.6 2.0-2.8
‍
10G 7/4 9.8G 10.0G 10.0G 6.8 6.6-7.1 7.3 7.2-7.4 7.5 7.2-8.1 4.0 4.0 4.1 3.6-4.4
6/6 10.0G 10.0G 0.2BG 5.8 5.2-6.2 6.2 6.0-6.4 6.7 6.3-7.3 6.0 5.6-6.0 6.0 5.6-6.0 6.0 5.6-6.0
4 0.1BG 0.1BG 0.3BG 5.7 5.3-6.2 6.2 5.7-6.3 6.7 6.3-7.3 4.2 4.0-4.4 4.0 4.0-4.4 4.0
5/6 10.0G 0.2BG 0.1BG 4.7 4.3-5.1 4.7 4.2-5.1 5.7 5.2-6.5 6.4 6.0-6.8 6.3 6.0-6.4 6.4 6.0-6.8
4 9.9G 0.3BG 10.0G 4.6 4.0-5.0 4.7 4.2-5.0 5.7 5.2-6.5 4.0 4.0 4.0
4/4 9.9G 10.0G 0.1BG 3.7 3.5-4.2 3.7 3.5-4.1 4.8 4.1-5.7 4.2 4.0-4.4 4.1 4.0-4.4 4.1 4.0-4.4
3/4 9.8G 0.1BG 9.9G 2.8 2.3-3.1 2.7 2.4-3.0 3.7 2.9-4.3 4.2 4.0-4.4 4.2 4.0-4.4 4.2 4.0-4.4
‍
BG 8/2 4.8BG 4.9BG 4.8BG 8.0 8.0-8.3 8.2 8.0-8.2 8.2 8.1-8.5 2.1 2.0 2.0-2.4 1.9 1.6-2.0
7/4 4.7BG 4.7BG 4.9BG 6.9 6.7-7.2 7.3 7.2-7.4 7.5 7.3-7.9 4.0 4.0-4.4 4.0 4.0-4.4 3.9 3.6-4.0
2 4.7BG 4.6BG 4.6BG 7.0 7.0-7.3 7.3 7.2-7.4 7.5 7.2-7.4 2.1 2.0-2.4 2.0 2.0-2.4 2.0
6/6 4.7BG 5.0BG 4.9BG 5.9 5.5-6.2 6.3 6.1-6.5 6.7 6.3-6.6 6.0 5.2-6.4 5.9 5.2-6.4 5.8 5.6-6.0
4 4.7BG 4.9BG 4.8BG 5.9 5.5-6.2 6.3 5.7-6.4 6.6 6.3-6.6 4.1 4.0-4.1 4.0 4.0
2 4.8BG 5.0BG 5.1BG 5.9 5.9-6.2 6.3 6.2-6.5 6.6 6.3-7.2 2.1 2.0-2.4 2.0 2.1
5/6 5.0BG 5.0BG 5.0BG 4.9 4.7-5.2 4.9 4.7-5.2 5.7 5.2-6.3 6.1 6.0-6.4 5.9 5.6-6.4 6.0 6.6-6.0
4 5.0BG 5.0BG 5.1BG 4.9 4.7-5.2 4.8 4.5-6.1 5.7 5.2-6.3 4.0 4.0-4.4 4.0 4.0-4.4 3.9 3.6-4.0
2 5.0BG 4.8BG 5.1BG 4.8 4.8-5.2 4.8 4.5-5.1 5.7 5.4-6.3 2.1 2.0-2.4 2.1 2.0-2.4 2.0 2.0-2.4
4/6 4.8BG 4BG-5BG 5.0BG 5.3BG 3.9 3.8-4.2 3.9 3.8-4.2 4.9 4.3-5.4 6.2 6.0-6.8 6.2 6.0-6.4 6.2 6.0-6.4
4 5.1BG 5.0BG 5.3BG 3.8 3.6-4.2 3.8 3.6-4.1 4.8 4-4-6.0 4.0 4.0-4.4 4.0 3.6-4.0 4.0 3.6-4.0
2 5.1BG 4.9BG 4.9BG 3.8 3.5-4.2 3.8 3.8-4.0 4.8 4.2-5.2 2.1 2.0-2.4 2.2 2.0-2.4 2.1 2.0-2.8
3/6 5.0BG 5.1BG 5.0BG 2.9 2.6-3.3 2.9 2.8-3.1 3.9 3.6-4.5 6.1 6.0-6.8 6.2 6.0-6.8 6.3 6.0-6.8
4 4.9BG 4.8BG 4.9BG 2.9 2.5-3.2 2.8 2.8-3.1 3.8 3.4-4.3 4.0 4.0-4.4 4.1 4.0-4.4 4.2 4.0-4.8
2 4.7BG 5.2BG 4.9BG 2.9 2.4-3.2 2.8 2.8-3.1 3.8 3.6-4.4 2.2 2.0-2.4 2.2 2.2-2.8 2.2 1.6-2.8
2/4 4.9BG 5.0BG 4.8BG 2.0 1.6-2.3 2.0 1.7-2.2 2.5 2.2-3.3 4.0 3.6-4.4 4.2 4.0-4.8 4.4 3.6-6.2
2 4.9BG 5.0BG 4.7BG 1.9 1.4-2.2 2.0 1.9-2.3 2.5 2.2-3.2 2.0 2.0-2.4 2.1 2.0-2.8 2.2 1.6-2.4
‍
10BG 7/4 10.0BG 10.0BG 9.9BG 6.8 6.0-7.2 7.3 7.2-7.6 7.5 7.3-7.9 4.1 4.0 4.0 3.6-4.4
6/6 10.0BG 9.8BG 9.9BG 5.8 4.9-6.2 6.2 5.9-6.4 6.6 6.2-6.9 6.1 6.0-6.4 6.0 5.6-6.0 6.1 6.0-6.4
4 10.0BG 9.7BG 9.9BG 5.7 4.9-6.1 6.2 6.0-6.4 6.5 6.1-6.8 4.1 4.1 4.0
5/6 0.1B 10.0BG 0.2B 4.8 4.0-5.3 4.8 4.3-5.1 5.6 5.1-5.9 6.2 6.0-6.4 6.2 6.0-6.8 6.1 6.0-6.4
4 0.1B 0.1B 10.0BG 4.7 3.9-5.0 4.7 4.2-5.0 5.5 5.0-5.7 4.0 4.0 4.0
4/6 9.5BG 9BG-10BG 9.8BG 10.0BG 3.7 2.9-4.0 3.8 3.3-4.0 4.6 4.1-5.2 6.0 5.6-6.0 6.0 6.0-6.4 6.0
4 9.6BG 9BG-10BG 10.0BG 9BG-10BG 10.0BG 9BG-10BG 3.7 2.8-4.0 3.7 3.2-4.0 4.5 4.0-5.2 4.0 3.6-4.0 4.1 4.0-4.4 4.0 ​
10BG 3/6 10.0BG 10.0BG 9BG-10BG 9.8BG 2.8 2.0-3.2 2.8 2.6-3.1 3.5 3.0-4.0 6.1 6.1 6.0-6.4 6.3 6.0-6.8
4 10.0BG 9.7BG 9.7BG 2.8 2.0-3.2 2.8 2.5-3.2 3.5 3.0-4.0 4.0 4.1 4.2 4.0-4.8
‍
B 8/4 4.8B 4.9B 4.8B 7.9 7.5-8.3 8.1 8.0-8.1 8.3 8.1-8.5 4.1 4.0-4.4 3.9 3.2-4.0 3.9 3.6-4.0
2 5.3B 5.0B 4.9B 8.0 7.5-8.3 8.1 8.0-8.2 8.4 8.1-8.7 2.1 2.0-2.4 2.0 2.0-2.4 2.0 2.0-2.4
7/6 4.9B 4.9B 4.8B 6.7 6.2-7.2 7.2 7.2-7.4 7.6 7.3-8.0 5.9 5.2-6.0 5.8 5.2-6.0 5.8
4 5.0B 4.9B 4.6B 6.8 6.2-7.3 7.2 7.2-7.4 7.7 7.3-8.0 4.0 3.6-4.0 4.0 4.0 4.0-4.4
2 5.0B 5.1B 4.7B 6.9 6.4-7.3 7.2 7.2-7.5 7.7 7.3-8.0 2.0 1.6-2.0 2.0 1.6-2.0 2.0 1.6-2.0
6/6 5.0B 4.8B 4.9B 5.8 5.3-6.4 6.1 5.7-6.3 6.8 6.4-7.0 6.5 6.0-6.8 6.4 6.0-6.8 6.3 6.0-6.8
4 5.0B 5.0B 5.0B 5.7 5.5-6.3 6.1 6.0-6.3 6.7 6.4-7.0 4.1 4.0-4.4 4.1 4.0-4.4 4.1 4.0-4.4
2 5.0B 5.1B 5.3B 5.7 5.5-6.2 6.1 6.0-6.4 6.7 6.4-7.1 2.1 2.0-2.4 2.0 2.0-2.4 2.2 2.0-2.4
5/6 4.9B 4.9B 5.0B 4.7 4.0-5.3 4.8 4.4-5.1 5.8 5.4-6.2 6.3 6.0-6.8 6.4 6.0-6.8 6.4 6.0-6.8
4 5.2B 4.8B 5.0B 4.6 4.0-5.1 4.7 4.5-5.3 5.7 5.3-6.2 4.1 4.0-4.4 4.4 4.0-4.8 4.4 4.0-4.8
2 5.2B 5.2B 5.3B 4.6 4.0-5.1 4.7 4.5-5.3 5.7 5.5-6.5 2.0 2.0 2.0-2.4 2.0 1.6-2.4
4/8 4.8B 5.1B 4.9B 3.7 3.0-4.2 3.8 3.3-4.1 4.9 4.5-5.9 8.1 8.0-8.4 8.2 8.0-8.8 8.3 8.0-8.8
6 4.6B 4B-5B 5.2B 5.0B 3.7 3.0-4.1 3.7 3.3-4.1 4.9 4.5-5.7 6.0 6.0-6.4 6.2 6.0-6.8 6.4 6.0-6.8
4 4.7B 5.0B 5.0B 3.7 3.1-4.1 3.8 3.4-4.1 4.9 4.3-5.2 4.1 3.6-4.4 4.2 4.0-4.8 4.3 4.0-4.8
2 4.9B 5.0B 5.3B 3.7 3.0-4.2 3.7 3.4-4.3 4.9 3.3-4.2 2.0 2.0-2.4 2.0 1.6-2.4 2.2 2.0-2.4
3/6 4.7B 4.6B 4B-5B 4.8B 2.8 2.1-3.3 2.8 2.5-3.1 3.8 3.3-4.0 6.0 6.0-6.4 6.3 6.0-6.8 6.3 6.0-6.8
4 5.0B 4.7B 4.9B 2.7 2.1-3.1 2.7 2.6-3.1 3.7 3.2-4.0 4.0 4.1 4.0-4.4 4.3 4.0-4.4
2 4.7B 4.8B 5.2B 2.7 2.1-3.1 2.7 2.6-3.1 3.7 3.2-4.0 2.0 1.6-2.0 2.0 1.6-2.0 2.0 2.0-2.4
2/2 4.5B 4.4B 3B-5B 4.5B 1.8 1.4-2.2 1.9 1.6-2.1 2.4 2.1-2.8 1.9 2.0 1.6-2.0 2.0 1.6-2.0
‍
10B 7/6 9.7B 9.9B 9.9B 6.9 6.9-7.2 7.3 7.1-7.4 7.4 7.3-7.7 6.3 6.0-6.4 6.1 5.6-6.4 6.1 6.0-6.4
4 9.7B 9.8B 9.8B 6.8 6.9-7.0 7.2 7.1-7.3 7.4 7.2-7.7 4.1 4.0-4.4 4.0 4.0 4.0-4.4
6/6 9.7B 9.6B 9.7B 5.9 5.8-6.2 6.2 6.1-6.4 6.6 6.3-6.8 6.2 6.0-6.4 6.1 6.0-6.4 6.0 6.0-6.4
/4 9.6B 9.7B 9.7B 5.8 5.8-6.1 6.2 6.1-6.3 6.6 6.3-6.8 4.1 4.0-4.4 3.9 4.0 4.0-4.4
5/6 9.9B 9.9B 9.9B 4.8 4.8-5.1 4.8 4.7-5.1 5.8 5.4-5.9 6.1 6.0-6.4 6.0 6.0-6.4 6.1
4 9.9B 9.9B 9.9B 4.8 4.7-5.1 4.7 4.7-5.1 5.7 5.4-5.9 4.0 4.0 3.6-4.0 4.0 3.6-4.0
4/8 9.8B 9.7B 9.6B 9B-10B 4.0 3.8-4.3 3.7 3.7-4.1 4.9 4.5-6.2 8.0 7.6-8.0 8.0 8.0-8.4 8.1 8.0-8.4
6 9.8B 9.9B 9.9B 3.9 3.7-4.2 3.7 3.3-4.0 4.9 4.5-6.2 6.0 6.0 6.2 6.0-6.8
4 9.9B 9.9B 10.0B 10B-2PB 3.9 3.7-4.2 3.7 3.6-4.1 4.8 4.4-5.2 3.9 3.6-4.0 3.9 3.6-4.0 3.9 3.6-4.0
3/8 9.7B 9B-10B 9.8B 9.7B 9B-10B 3.0 2.8-4.3 2.9 2.6-3.0 3.8 3.5-4.1 8.0 7.6-8.4 8.3 8.0-8.8 8.4 8.0-8.8
6 9.8B 9B-10B 9.8B 9.7B 3.0 2.7-3.2 2.9 2.5-3.0 3.8 3.5-5.1 6.0 6.0 6.0-6.4 6.2 6.0-6.8
4 9.9B 9B-10B 9.8B 9.8B 9B-10B 3.0 2.6-3.2 2.8 2.8-3.1 3.8 3.5-4.1 4.0 3.6-4.0 4.1 3.6-4.0 4.1 4.0-4.4
‍
PB 8/2 4.7PB 4.8PB 4.6PB 8.1 8.0-8.4 8.4 8.0-8.5 8.4 8.0-8.4 2.4 2.0-2.8 2.0 2.0-2.4 2.1 2.0-2.4
7/6 4.7PB 5.0PB 4.6PB 6.8 6.8-7.1 7.4 7.2-7.6 7.5 7.2-8.3 6.0 6.0-6.4 5.8 5.2-6.0 5.9 5.6-6.4
4 4.7PB 4.7PB 4.8PB 6.9 6.8-7.2 7.4 7.2-7.6 7.5 7.2-8.5 4.1 4.0-4.4 3.9 3.6-4.4 4.1 4.0-4.4
2 4.8PB 5.0PB 4.9PB 6.9 6.7-7.1 7.4 7.2-7.8 7.5 7.0-7.5 2.2 2.0-2.8 2.0 1.6-2.4 2.0
6/8 4.7PB 4.8PB 4.7PB 4PB-5PB 5.7 5.6-6.1 6.2 5.9-6.5 6.7 6.2-6.6 8.1 8.0-8.8 8.1 7.6-8.4 7.8 7.6-8.0
6 4.6PB 4.8PB 4.9PB 5.8 5.6-6.1 6.2 6.0-6.4 6.7 6.2-6.6 6.0 5.6-6.0 6.0 5.6-6.4 5.9 5.6-6.0
4 4.7PB 4.8PB 4.8PB 5.8 5.6-6.1 6.3 6.1-6.4 6.7 6.2-6.6 4.0 3.6-4.4 3.8 3.2-4.0 3.8 3.6-4.0
2 5.2PB 5.2PB 5.1PB 5.7 5.6-6.2 6.2 5.9-6.4 6.7 6.2-7.7 2.2 2.0-2.4 2.0 1.6-2.0 2.0 2.0-2.4
5/10 4.9PB 4.9PB 4.9PB 4.8 4.4-6.2 4.8 4.6-5.2 5.9 5.3-5.9 10.0 9.2-10.0 10.0 10.0-10.4 10.1 9.6-10.4
8 4.7PB 4.8PB 4.8PB 4.7 4.2-5.2 4.8 4.5-5.1 5.8 5.3-7.0 8.1 8.0-8.4 8.1 8.0-8.4 8.1 8.0-8.8
6 4.8PB 5.0PB 4.9PB 4.7 4.3-5.1 4.8 4.4-5.1 5.8 5.3-7.0 5.9 5.9 5.6-6.0 6.0 5.6-6.0
4 4.9PB 5.2PB 3PB-6PB 5.0PB 4.7 4.3-5.0 4.8 4.4-5.0 5.7 5.3-6.9 4.0 4.0 4.1 4.0-4.4
2 4.9PB 5.7PB 3PB-8PB 5.4PB 4.6 4.3-5.0 4.8 4.4-5.0 5.7 5.1-6.8 2.1 2.0-2.4 2.2 2.0-2.4 2.2 2.0-2.4
4/10 4.6PB 4.3PB 3PB-5PB 4.4PB 4PB-5PB 3.8 3.4-4.3 3.9 3.4-4.3 5.0 4.3-6.0 10.1 9.6-10.4 10.1 10.0-10.4 10.1 10.0-10.4
8 4.7PB 4.5PB 4PB-6PB 4.7PB 3.7 3.3-4.2 3.8 3.3-4.1 4.9 4.2-5.2 8.0 8.0-8.4 8.0 7.6-8.4 8.0 8.0-8.4
6 4.6PB 4.6PB 4PB-6PB 4.6PB 3.7 3.3-4.1 3.8 3.2-4.1 4.8 4.2-5.8 6.0 5.6-6.0 5.9 6.0 5.6-6.0
4 4.7PB 4.7PB 4PB-6PB 4.8PB 3.7 3.3-4.0 3.8 3.2-4.1 4.8 4.2-5.8 3.9 4.0 3.9 3.6-4.0
2 4.9PB 4.8PB 4.9PB 3.7 3.2-4.0 3.7 3.1-4.1 4.8 4.2-5.7 1.9 1.6-2.0 2.0 1.6-2.0 2.0 1.6-2.4 ​
PB 3/12 4.8PB 4.6PB 4PB-5PB 4.5PB 2.8 2.4-3.2 2.9 2.5-3.3 3.8 3.4-4.9 11.7 10.8-12.0 11.9 12.0-12.4 11.9 11.6-12.4
10 4.8PB 4.4PB 3PB-5PB 4.7PB 2.8 2.4-3.2 2.9 2.5-3.3 3.8 3.3-4.8 9.9 9.6-10.4 10.0 9.2-10.4 9.9 10.0-10.4
8 4.7PB 4.6PB 4PB-5PB 4.6PB 2.7 2.4-3.2 2.8 2.4-3.1 3.8 3.3-4.8 8.2 8.0-8.8 7.9 7.6-8.4 7.9 8.0-8.8
6 5.0PB 4.6PB 4PB-5PB 4.6PB 2.7 2.4-3.1 2.9 2.5-3.1 3.7 3.3-4.7 5.7 5.2-6.0 5.9 5.6-6.0 6.0 5.6-6.0
4 5.0PB 4.7PB 4.8PB 2.7 2.2-3.0 2.8 2.4-3.1 3.6 3.2-4.5 3.9 3.6-4.0 3.9 3.6-4.0 4.0 3.6-4.4
2 5.0PB 4.7PB 5.0PB 2.7 2.2-3.0 2.8 2.4-3.1 3.6 3.2-4.5 2.0 1.6-2.0 1.9 1.2-2.0 1.9 1.2-2.0
2/6 4.8PB 4.7PB 4.7PB 1.9 1.7-2.2 1.9 1.7-2.1 2.6 2.1-2.8 6.0 6.2 5.2-6.8 6.5 6.0-6.8
4 4.8PB 4.7PB 4.8PB 1.9 1.6-2.1 1.9 1.6-2.0 2.4 2.0-3.0 4.1 4.0-4.4 4.4 4.0-4.8 4.3 4.0-4.8
2 4.9PB 5.1PB 5.0PB 1.9 1.5-2.2 1.9 1.6-2.0 2.4 2.0-3.0 2.0 1.6-2.0 2.1 1.6-2.4 2.3 1.6-2.8
‍
10PB 7/6 0.2P 0.1P 10.0PB 6.8 6.2-7.1 7.2 7.0-7.3 7.6 7.2-8.0 5.8 5.2-6.0 5.7 5.2-6.0 5.6 5.2-6.0
4 10.0PB 0.1P 0.1P 6.8 6.2-7.1 7.2 7.0-7.3 7.6 7.2-8.0 3.9 3.6-4.0 3.7 3.2-4.0 3.8 3.2-4.0
6/8 10.0PB 0.1P 10.0PB 5.8 5.4-6.2 6.2 5.9-6.5 6.7 6.2-7.3 7.9 8.0-8.4 7.9 7.6-8.8 7.7 7.6-8.0
6 10.0PB 0.2P 10.0PB 5.8 5.3-6.2 6.2 5.9-6.4 6.7 6.3-7.3 6.0 5.6-6.4 5.8 5.6-6.4 5.8 5.6-6.0
4 10.0PB 0.2P 10.0PB 5.8 5.2-6.2 6.2 5.9-6.4 6.7 6.3-7.5 4.1 4.0-4.4 3.9 3.6-4.4 3.9 4.0-4.4
5/10 9.9PB 10.0PB 10.0PB 4.7 4.3-5.2 4.7 4.4-5.2 5.8 5.1-6.7 10.0 10.0-10.4 9.8 9.2-10.0 9.7 9.2-10.0
8 9.9PB 10.0PB 9.9PB 4.8 4.3-5.2 4.7 4.3-5.2 5.8 5.3-6.7 8.0 7.6-8.4 8.0 7.6-8.4 7.9 7.6-8.4
6 9.9PB 10.0PB 9.9PB 4.8 4.2-5.2 4.7 4.5-5.2 5.8 5.4-6.7 6.0 5.9 5.6-6.0 6.0 5.6-6.0
4 9.9PB 0.2P 9.9PB 4.7 4.1-5.2 4.7 4.4-5.2 5.8 5.4-6.7 4.0 4.1 4.0-4.4 4.1 4.0-4.4
4/10 10.0PB 9.6PB 10.0PB 3.8 3.0-4.2 3.7 3.4-4.1 4.9 4.3-5.8 10.0 10.0-10.4 10.0 10.0-10.4 10.0 10.0-10.4
8 0.1P 0.3P 10.0PB 3.8 3.7-4.3 3.7 3.5-4.2 4.9 4.5-5.9 8.1 8.0-8.4 8.1 8.0-8.4 8.1 8.0-8.4
6 0.1P 0.2P 10.0PB 3.8 3.1-4.2 3.8 3.4-4.2 4.9 4.3-5.7 6.1 6.0-6.4 6.1 6.0-6.4 6.1 6.0-6.8
4 0.2P 0.1P 9.9PB 3.8 3.0-4.2 3.6 3.2-3.9 4.9 4.3-5.6 4.0 4.1 4.0-4.4 4.1 4.0-4.4
3/10 0.1P 9.9PB 10.0PB 2.9 2.3-3.3 2.8 2.4-3.2 3.8 3.3-4.6 10.3 10.0-10.8 10.3 10.0-10.8 10.3 10.0-11.6
8 0.2P 9.9PB 10.0PB 2.9 2.2-3.3 2.8 2.4-3.2 3.8 3.3-4.2 7.9 7.6-8.0 8.0 7.6-8.0 8.1 7.6-8.8
6 0.2P 10.0PB 10.0PB 2.9 2.1-3.3 2.8 2.7-3.2 3.8 3.3-4.2 6.1 6.0-6.4 6.0 5.6-6.8 6.2 5.6-6.8
4 0.3P 10.0PB 0.1P 2.9 2.1-3.3 2.8 2.7-3.2 3.8 3.3-4.2 4.1 4.0-4.4 4.2 4.0-4.8 4.3 4.0-4.8
2/6 * * * 1.8 1.5-2.2 1.9 1.6-2.0 2.4 2.1-2.7 5.5 4.4-6.0 6.2 4.8-6.8 7.5 6.0-7.6
4 * * * 1.8 1.5-2.2 1.9 1.7-2.1 2.4 2.1-2.8 4.1 3.6-4.4 4.2 3.6-4.8 5.8 3.6-5.6
‍
P 8/4 5.2P 5.4P 5P-7P 5.4P 7.9 7.8-8.2 8.2 8.0-8.3 8.3 8.0-8.5 4.4 4.0-4.8 4.2 4.0-4.8 4.3 4.0-4.8
2 5.2P 5.3P 5.2P 8.1 7.9-8.4 8.1 8.0-8.2 8.3 8.1-8.5 2.1 2.0-2.4 1.9 1.6-2.0 2.0 2.0-2.4
7/6 5.2P 4.8P 5.1P 6.8 6.4-7.3 7.2 7.0-7.4 7.5 7.3-7.9 6.5 6.0-6.8 6.4 6.0-6.8 6.4 5.6-6.8
4 5.0P 4.8P 5.0P 6.8 6.8-7.2 7.2 7.0-7.4 7.5 7.2-7.8 4.2 4.0-4.8 4.1 3.6-4.8 4.1 4.0-4.8
2 4.9P 4.9P 5.0P 6.7 6.2-7.1 7.1 7.1-7.4 7.5 7.2-8.0 2.2 2.0-2.4 2.1 1.6-2.4 2.1 2.0-2.4
6/8 5.1P 5.2P 5.1P 5.7 5.5-6.2 6.0 5.7-6.4 6.7 6.3-7.2 8.3 8.0-8.8 8.1 8.0-8.8 8.0 7.2-8.4
6 5.0P 5.2P 5.0P 5.7 5.3-6.0 6.0 5.7-6.3 6.7 6.3-7.2 6.2 6.0-6.8 6.1 5.6-6.4 6.0 6.0-6.4
4 5.0P 5.2P 5.0P 5.7 5.3-6.0 6.0 5.7-6.3 6.7 6.2-7.2 4.1 4.0-4.4 4.1 4.0-4.8 4.0 3.6-4.4
2 4.8P 5.2P 5.2P 5.8 5.5-6.1 6.0 5.6-6.2 6.7 6.3-7.2 2.2 2.0-2.4 2.2 2.0-2.4 2.2 2.0-2.4
5/10 5.2P 5.0P 5.1P 4.8 4.6-5.2 4.5 4.2-5.0 5.8 5.2-6.5 10.2 10.0-10.8 10.1 10.0-10.4 10.1 10.0-10.4
8 5.1P 5.0P 5.0P 4.7 4.2-5.1 4.5 4.2-5.0 5.8 5.2-6.5 8.1 8.0-8.4 8.1 7.6-8.4 8.1 8.0-8.4
6 5.1P 5.0P 5.1P 4.7 4.7-5.1 4.5 4.2-5.0 5.8 5.2-6.5 6.1 6.0-6.4 6.2 6.0-6.8 6.1 6.0-6.8
4 5.1P 5.0P 5.0P 4.7 4.5-5.1 4.5 4.2-4.8 5.8 5.4-6.4 4.0 4.2 4.0-4.4 4.2 4.0-4.8
2 5.1P 5.0P 4.9P 4.7 4.5-5.1 4.5 4.2-5.0 5.7 5.3-6.5 2.0 2.2 2.0-2.4 2.1 2.0-2.4
4/12 5.3P 5P-6P 5.4P 5P-6P 5.3P 3.8 3.7-4.2 3.7 3.4-4.1 4.9 4.3-5.7 12.4 12.0-12.8 12.1 12.0-12.8 12.2 12.0-12.8
10 5.3P 5.1P 5.2P 5P-6P 3.7 3.2-4.0 3.6 3.2-4.0 4.9 4.3-5.7 10.0 9.6-10.0 9.9 9.6-10.0 9.9 9.2-10.0
8 5.2P 5.2P 5.1P 3.7 3.1-4.0 3.6 3.2-3.9 4.9 4.3-6.7 8.1 8.1 7.6-8.4 8.0 8.0-8.4
6 5.4P 5P-6P 5.1P 5.1P 3.7 3.6-4.0 3.6 3.2-4.0 4.8 4.2-5.7 5.9 5.6-6.0 5.9 5.6-6.0 5.8 5.6-6.0
4 5.1P 5.1P 5.2P 3.7 3.7-4.0 3.6 3.2-4.0 4.9 4.3-5.7 4.0 4.0 3.6-4.0 3.9
2 5.1P 4.6P 5.0P 3.7 3.6-4.0 3.5 3.2-4.0 4.9 4.3-5.7 1.9 2.0 1.6-2.4 2.1 2.0-2.8
3/10 5.2P 5.3P 5.5P 5P-6P 2.9 2.2-3.2 2.9 2.4-3.2 3.8 3.3-4.4 10.0 10.0-10.8 10.6 10.0-10.8 10.4 10.0-10.8
8 5.1P 5.2P 5.3P 2.8 2.2-3.1 2.7 2.4-3.0 3.7 3.2-4.0 8.1 8.0-8.4 8.1 8.0-8.4 8.1 8.0-8.8
6 5.0P 5.1P 5.2P 2.8 2.5-3.2 2.7 2.4-3.0 3.7 3.2-4.0 6.1 6.0-6.4 6.1 6.0 6.0-6.4
4 5.2P 5.2P 5.2P 2.8 2.5-3.2 2.7 2.4-3.0 3.7 3.2-4.0 4.1 4.0-4.4 4.2 4.0-4.4 4.1 4.0-4.4
2 5.1P 5.3P 5.3P 2.8 2.3-3.2 2.7 2.4-3.0 3.7 3.3-4.0 2.0 2.0-2.4 1.9 1.6-2.4 2.0 1.6-2.4
2/6 5.1P 5.2P 5.2P 1.9 1.6-2.2 1.9 1.6-2.1 2.5 1.9-2.7 6.2 6.0-6.4 6.7 6.0-6.8 6.6 6.0-6.8
4 5.1P 5.2P 5.1 1.9 1.6-2.1 1.8 1.6-2.1 2.5 2.2-2.8 4.1 3.2-4.0 4.1 4.0-4.8 4.0 3.2-4.8
2 5.0P 5.1P 5.1P 1.8 1.6-2.1 1.9 1.6-2.1 2.5 2.2-2.7 2.4 2.0-2.8 2.8 2.0-2.8 2.8 2.0-3.2 ​
10P 8/4 9.9P 0.4RP 0.2RP 7.9 7.8-8.1 8.3 8.0-8.4 8.3 8.1-8.5 4.0 3.9 3.8 3.2-4.0
7/8 0.3RP 0.2RP 0.2RP 6.7 6.4-7.2 7.4 7.2-7.8 7.5 7.2-7.9 7.9 7.6-8.8 7.8 6.4-8.4 7.6 7.2-8.0
6 0.2RP 0.3RP 0.1RP 6.7 6.6-7.1 7.4 7.2-7.4 7.6 7.2-7.9 5.7 5.2-6.0 5.6 5.2-6.0 5.7 6.2-6.0
4 0.3RP 0.3RP 0.2RP 6.7 6.6-7.1 7.4 7.2-7.4 7.6 7.2-7.9 4.1 4.0-4.4 4.0 3.6-4.4 3.9 3.6-4.0
6/8 0.2RP 0.2RP 10.0P 5.7 5.6-6.1 6.2 6.0-6.6 6.7 6.4-6.8 8.0 8.0-8.4 7.9 7.6-8.0 7.9 7.6-8.4
6 0.3RP 0.2RP 10.0P 5.6 5.4-6.1 6.2 6.0-6.4 6.7 6.4-7.3 5.9 5.6-6.0 5.9 5.6-6.0 5.9 6.0-6.4
4 0.1RP 0.1RP 10.0P 5.6 5.4-6.1 6.2 6.0-6.4 6.8 6.4-7.3 4.0 4.0 4.0 4.0-4.4
5/10 0.3RP 0.5RP 10P-1RP 0.4RP 10P-1RP 4.7 4.4-5.2 4.8 4.2-5.1 5.8 5.5-6.5 10.1 10.0-10.8 10.1 9.6-10.4 10.0 10.0-10.4
8 0.3RP 0.3RP 9P-1RP 0.3RP 4.7 4.4-5.1 4.7 4.2-5.1 5.8 5.4-6.5 8.0 8.0-8.4 8.1 8.0-8.4 8.0
6 0.2RP 0.3RP 10P-1RP 0.3RP 4.6 4.4-5.1 4.7 4.2-5.1 5.8 5.4-6.6 6.0 5.6-6.0 6.1 6.0-6.4 6.0 5.6-6.4
4 0.1RP 0.1RP 0.1RP 4.6 4.3-5.1 4.7 4.2-5.1 5.8 5.4-6.5 4.0 3.6-4.0 4.1 4.0-4.8 4.0 4.0-4.4
4/10 0.2RP 0.3RP 0.1RP 3.7 3.3-4.3 3.9 3.7-4.4 5.0 5.5-6.6 10.3 10.0-10.8 10.1 10.0-10.4 10.1 10.0-10.8
8 0.1RP 0.3RP 0.2RP 3.7 3.4-4.4 3.8 3.3-4.3 4.9 4.4-6.6 8.0 8.0-8.4 8.0 7.6-8.4 7.9 7.6-8.0
6 10.0P 0.2RP 0.2RP 3.8 3.2-4.2 3.9 3.6-4.4 4.9 4.4-5.6 6.0 5.6-6.0 6.0 5.9 5.6-6.4
4 10.0P 0.2RP 9.8P 3.6 3.2-4.1 3.8 3.6-4.4 4.9 4.4-5.6 4.0 4.0 3.9
3/10 01RP 10.0P 9.9P 2.7 2.3-3.1 2.9 2.4-3.3 4.0 3.5-4.8 10.0 9.6-10.4 10.1 9.6-10.4 10.1 9.6-10.8
8 0.1RP 0.1RP 0.2RP 2.7. 2.3-3.1 2.9 2.4-3.3 4.0 3.4-4.6 8.1 8.0-8.4 8.2 8.0-8.8 8.2 8.0-8.8
6 10.0P 0.1RP 9.9P 2.7 2.3-3.1 2.8 2.4-3.3 3.9 3.3-4.0 6.1 6.0-6.4 6.2 6.0-6.4 6.1 6.0-6.4
4 0.2RP 10P-2RP 10.0P 0.3RP 2.6 2.1-3.1 2.8 2.4-3.3 3.9 3.3-4.0 4.0 4.0-4.4 4.1 4.0-4.4 4.2 4.0-4.8
2/6 * * * 1.8 1.6-2.1 1.9 1.6-2.1 2.4 2.1-2.7 5.8 4.2-6.0 6.6 6.0-7.2 7.7 6.8-7.6
4 * * * 1.8 1.6-2.1 1.9 1.6-2.2 2.4 2.1-2.7 4.1 4.0-4.4 4.5 4.0-4.8 5.6 4.4-5.6
‍
RP 8/6 5.4RP 5RP-6RP 5.2RP 5RP-6RP 5.4RP 5RP-6RP 8.0 7.7-8.4 8.1 8.0-8.2 8.3 8.2-8.6 5.6 5.2-6.0 5.5 4.8-6.0 5.5 4.8- 6.0
4 5.4RP 3RP-7RP 5.2RP 5RP-7RP 5.3RP 5RP-7RP 7.9 7.7-8.2 8.0 8.0-8.3 8.3 8.1-8.7 3.8 3.2-4.0 3.7 2.8-4.0 3.8 2.8-4.0
2 5.6RP 5RP-7RP 5.2RP 5RP-6RP 5.4RP 5RP-6RP 8.1 7.9-8.5 8.3 8.1-8.5 8.3 8.1-8.6 2.1 2.0-2.4 2.2 2.0-2.8 1.9 1.6-2.4
7/8 5.3RP 5.3RP 5.2RP 6.8 6.4-7.2 7.4 7.1-7.6 7.6 7.3-7.7 7.6 7.2-8.0 7.4 6.8-8.4 7.4 6.8-8.0
6 5.3RP 5.3RP 5.2RP 6.8 6.4-7.2 7.3 7.2-7.5 7.6 7.3-8.0 5.7 5.2-6.0 5.7 5.2-6.0 5.7 5.2-6.4
4 5.4RP 5.3RP 5.1RP 6.8 6.5-7.2 7.4 7.2-7.6 7.6 7.3-7.9 3.8 3.6-4.0 3.8 3.2-4.0 3.8 3.2-4.0
2 5.0RP 5.2RP 4.9RP 5RP-6RP 6.8 6.6-7.2 7.4 7.2-7.5 7.6 7.3-7.9 1.8 1.6-2.0 1.9 1.6-2.0 1.8 1.2-2.0
6/10 5.3RP 5RP-6RP 5.4RP 5RP-6RP 5.2RP 5.7 5.3-6.2 6.1 5.8-6.3 6.7 6.4-7.2 9.6 9.2-10.0 9.7 8.8-10.0 9.8 9.2-10.0
8 5.3RP 5RP-6RP 5.4RP 5RP-6RP 5.2RP 5.7 5.8-6.3 6.2 5.8-6.3 6.7 6.4-7.2 7.9 7.2-8.0 7.8 7.2-8.0 7.9 7.2-8.0
6 5.3RP 5RP-6RP 5.4RP 5RP-6RP 5.2RP 5.6 5.3-6.2 6.1 5.8-6.3 6.8 6.4-7.4 5.9 5.6-6.0 5.8 5.2-6.0 5.9 5.6-6.0
4 5.2RP 5.3RP 5.1RP 5RP-6RP 5.6 5.4-6.0 6.1 5.8-6.3 6.7 6.3-7.5 3.9 3.9 3.6-4.0 3.9
2 4.9RP 5.3RP 5RP-7RP 5.0RP 5RP-6RP 5.6 5.4-6.2 6.1 6.0-6.3 6.8 6.3-7.6 1.9 1.6-2.0 1.9 1.6-2.0 1.9 1.6-2.0
5/10 5.2RP 5.3RP 5.1RP 4.7 4.1-5.3 4.7 4.2-5.2 5.9 5.4-6.5 10.0 9.6-10.8 9.9 9.6-10.0 9.9 9.6-10.4
8 5.1RP 5.2RP 5.1RP 4.7 4.1-5.2 4.7 4.2-5.1 5.8 5.4-6.5 7.9 7.9 8.0 8.0-8.4
6 5.1RP 5.2RP 5.0RP 4.7 4.1-5.2 4.7 4.2-5.1 5.8 5.4-6.5 5.9 5.6-6.0 5.9 5.6-6.0 6.0 5.6-6.0
4 5.0RP 5.1RP 5.1RP 4.6 4.1-5.2 4.7 4.2-5.1 5.8 5.4-6.5 3.9 4.0 3.6-4.0 4.1
2 4.5RP 4.6RP 5.0RP 4.6 4.2-5.2 4.7 4.2-5.1 5.9 5.4-6.7 1.9 1.6-2.0 2.0 1.6-2.4 2.0 1.6-2.0
4/12 5.1RP 5.3RP 5.1RP 3.8 3.1-4.2 3.8 3.5-4.3 5.0 4.6-5.8 11.9 11.6-12.0 11.9 11.6-12.4 12.1 12.0-12.8
10 5.1RP 5.3RP 5.1RP 3.7 3.1-4.1 3.7 3.5-4.3 5.0 4.6-5.8 10.0 9.6-10.4 9.9 9.6-10.4 10.0 9.6-10.8
8 5.1RP 5.1RP 5.1RP 3.7 3.1-4.1 3.7 3.2-4.1 5.0 4.5-5.8 8.0 7.6-8.0 7.9 7.6-8.4 8.0 7.6-8.4
6 5.0RP 5.1RP 5.0RP 3.7 3.2-4.1 3.8 3.5-4.1 5.0 4.5-5.8 6.0 6.0 5.6-6.0 6.0
4 4.9RP 5.0RP 4.9RP 3.7 3.2-4.1 3.7 3.2-4.1 5.0 4.5-5.8 4.0 3.6-4.0 4.0 3.6-4.0 4.0 4.0-4.4
2 4.7RP 4.9RP 4.8RP 3.7 3.2-4.1 3.7 3.2-4.1 5.0 4.4-6.2 1.9 1.6-2.0 2.0 1.6-2.0 2.0
3/10 5.5RP 5RP-6RP 5.4RP 5RP-6RP 5.3RP 2.8 2.4-3.3 2.9 2.5-3.1 4.0 3.5-4.8 10.0 9.6-10.0 10.1 9.6-10.4 10.2 9.6-10.8
8 5.5RP 5RP-6RP 5.3RP 5.1 RP 2.7 2.3-3.2 2.8 2.4-3.0 3.8 3.4-4.6 7.9 7.6-8.0 8.0 8.0-8.4 8.2 7.6-8.4
6 5.2RP 5RP-6RP 5.3RP 5.2RP 2.7 2.3-3.2 2.8 2.4-3.0 3.8 3.4-4.6 5.9 5.6-6.0 6.1 6.0-6.4 6.0 5.6-6.8
4 5.6RP 5RP-7RP 5.4RP 5.3RP 5RP-6RP 2.7 2.3-3.2 2.8 2.4-3.0 3.8 3.4-4.6 3.9 3.6-4.0 4.0 3.6-4.0 3.9 3.6-4.0
2 5.1RP 5.4RP 5RP-8RP 5.0RP 2.7 2.4-3.1 2.7 2.4-3.0 3.8 3.4-4.6 1.9 1.6-2.0 2.0 1.2-2.0 2.0
2/6 5.2RP 5.0RP 5.0RP 1.9 1.6-2.3 1.9 1.7-2.0 2.4 2.0-2.7 6.0 6.0-6.4 6.1 6.0-6.4 6.2 6.0-6.8
4 5.2RP 5.0RP 5.0RP 1.9 1.6-2.2 1.9 1.8-2.0 2.4 2.0-2.7 4.1 4.0-4.4 4.3 4.0-4.8 4.4 4.0-5.6
2 5.4RP 5.6RP 5RP-9RP 5.3RP 5RP-8RP 1.8 1.4-2.2 1.8 1.6-2.0 2.4 2.0-2.6 2.0 2.1 2.0-2.4 2.2 2.0-2.8 ​
10RP 8/6 10.0RP 9.9RP 10.0RP 8.0 7.9-8.3 8.2 8.0-8.2 8.3 8.1-8.6 5.7 5.2-6.0 5.6 5.2-6.0 5.7 5.2-6.4
4 9.7RP 9.8RP 9.7RP 7.9 7.8-8.1 8.2 8.0-8.2 8.3 8.1-8.6 3.7 3.2-4.0 3.8 3.2-4.0 3.8 3.2-4.0
7/8 9.8RP 0.2R 0.2R 6.8 6.6-7.2 7.2 7.1-7.3 7.5 7.3-7.9 7.7 7.2-8.0 7.7 7.2-8.0 7.8 7.2-8.4
6 9.9RP O.1R 0.2R 6.8 6.8-7.2 7.3 7.1-7.2 7.5 7.1-8.1 5.7 5.2-6.0 5.7 5.2-6.0 5.8 4.8-6.0
4 9.6RP 0.2R O.1R 6.7 6.6-7.2 7.2 7.1-7.2 7.5 7.1-7.9 3.9 3.6-4.0 3.9 3.6-4.0 3.9 3.2-4.0
6/10 10.0RP O.1R O.1R 5.8 5.6-6.5 6.2 5.9-6.4 6.7 6.2-7.3 9.9 9.6-10.4 9.9 9.2-10.4 9.9 9.2-10.4
8 9.9RP O.1R O.1R 5.7 5.3-6.3 6.1 6.0-6.3 6.7 6.1-7.1 7.8 7.6-8.0 7.8 7.2-8.0 7.8
6 9.9RP 10.0RP O.1R 5.7 5.3-6.3 6.1 6.0-6.3 6.6 6.1-7.1 5.8 5.2-6.0 5.7 5.6-6.0 5.8 5.6-6.0
4 9.5RP 9RP-10RP 9.8RP 10.0RP 5.7 5.1-6.3 6.1 6.0-6.3 6.6 6.1-7.1 3.8 3.6-4.0 3.9 3.6-4.0 3.9
5/10 10.0RP 9.9RP 9.9RP 4.8 4.4-6.3 4.8 4.2-5.2 5.8 5.3-6.3 10.1 10.0-10.8 10.1 10.0-10.8 10.0 9.6-10.4
8 9.9RP 9.8RP 9.8RP 4.8 4.3-5.3 4.7 4.2-5.1 5.7 5.1-6.5 8.0 7.6-8.0 8.1 8.0-8.4 8.0 7.6-8.0
6 9.9RP 9.9RP 9.8RP 4.7 4.2-5.2 4.7 4.2-5.0 5.7 5.2-6.5 6.0 5.6-6.0 6.0 5.6-6.0 6.0 5.6-6.0
4 9.6RP 9.8RP 9.8RP 4.7 4.0-5.2 4.7 4.2-5.0 5.7 5.1-6.2 3.8 3.2-4.0 3.8 3.2-4.0 3.9 3.2-4.0
4/10 9.7RP 9RP-1R 9.8RP 9RP-10RP 9.8RP 3.8 3.5-4.3 3.7 3.2-4.1 4.9 4.3-5.7 10.0 10.2 10.0-10.8 9.9 9.6-10.4
8 9.7RP 9RP-10RP 9.9RP 9RP-10RP 9.8RP 3.8 3.4-4.2 3.7 3.5-4.1 4.9 4.4-5.7 8.0 8.1 7.6-8.4 8.1 8.0-8.8
6 9.6RP 9RP-10RP 9.9RP 9RP-1RP 9.7RP 9RP-10RP 3.8 3.4-4.2 3.7 3.2-4.0 4.8 4.2-6.2 6.1 6.0-6.4 6.1 6.0-6.4 6.1 6.0-6.4
4 9.7RP 9RP-10RP 9.4RP 8RP-10RP 9.6RP 9RP-10RP 3.8 3.2-4.2 3.6 3.5-4.0 4.8 4.2-5.7 3.9 3.6-4.0 4.0 3.6-4.4 3.9 3.6-4.4
3/10 9.7RP 9RP-10RP 9.7RP 9RP-10RP 9.7RP 8RP-1R 2.8 2.4-3.1 2.8 2.4-3.0 3.7 3.2-4.3 10.1 9.6-10.4 10.3 10.0-10.8 10.3 10.0-10.8
8 9.7RP 9RP-10RP 9.7RP 9RP-10RP 9.6RP 9RP-10RP 2.8 2.3-3.1 2.7 2.4-3.1 3.6 3.0-4.3 7.9 7.6-8.0 8.1 7.6-8.0 8.2 8.0-9.2
6 9.7RP 9RP-10RP 9.7RP 9RP-10RP 9.6RP 9RP-10RP 2.8 2.3-3.1 2.8 2.4-2.9 3.6 3.0-4.3 6.0 5.6-6.4 6.1 6.0-6.4 6.1 6.0-6.8
4 9.8RP 9RP-10RP 9.6RP 9RP-10RP 9.5RP 9RP-10RP 2.8 2.1-3.1 2.7 2.4-3.0 3.6 3.0-4.3 3.8 3.6-4.0 3.9 3.6-4.0 3.9 3.2-4.0
2/6 * * * 1.8 1.6-2.2 2.0 1.7-2.2 2.4 2.1-2.5 5.8 5.6-6.8 6.7 5.6-6.8 7.0 6.0-6.8
4 * * * 2.0 1.6-2.1 2.0 1.9-2.1 2.5 2.1-3.0 5.2 4.0-6.4 4.6 3.6-4.8 5.2 4.4-5.6

are fairly apparent from inspection

Comparison with the 1929 notation of a given estimate of any attribute, is accomplished by looking along the appropriate row of the table. Wherever a difference is found it means that the consensus of the observers placed that particular sample at the new indicated position in Munsell color space. Thus G 5/6, as viewed on the white ground, appears somewhat misplaced in all dimensions and is better located by the notation 5.1G 4.7/6.4, as entered in the respective “white” columns. The notation of this sample on the gray ground was found to fall at 5.0G 4.6/6.4, as taken from the respective “gray” columns; and the notation for the black ground is 5.1G 5.8/6.3. The general indication from the table as a whole is that the averaged estimates usually approximate rather closely the 1929 Munsell notation and so support the validity of the latter. Still, minor adjustments of many samples may be expected to affect the final smoothing.

Inter-comparisons of the mean estimates from the different viewing grounds are facilitated by the arrangement of all relevant data in three adjacent columns. Thus in the case of G 5/6, the hue estimates from the three grounds are adjacently tabled in the same row, the figures being 5.1G, 5.0G, and 5.1G. Similarly, and further to the right in this same row, the comparative value estimates are 4.7, 4.6, and 5.8; and still further to the right, the chroma estimates are 6.4, 6.4, and 6.3. Comparisons of this character disclose no systematic differential influence of background on either hue or saturation, but it must be noted that such an influence could be reduced by the relativity of the judgments and the influence of color constancy (25-28, 37, 41, 85, p. 595). Briefly, that is because all the samples on a given chart are always seen in relation to each other and never on more than one background at a time. There is, however, a relatively marked and consistent effect in the case of value, and this effect is in the expected direction of simultaneous lightness ​contrast (58, 71, p. 546; 79, 82). Lightness variations are revealed which range in magnitude up to a full value step and more.

The variabilities, or 80 percent ranges, of the data in this table yield some idea of the spread of the individual estimates. The latter suggests, in conjunction with the size of n, that differences of a tenth or two in the means are usually not significant.

The several attributive units are so far from equivalent perceptually, that interattributive comparisons of variability are not valid psychologically; and intercomparisons of variability are best confined to the data of a given attribute. In regard to the influence of background on variability, for the given attribute, there seems to be no indication obvious on inspection. Little more can be said in advance of detailed analysis.

The reader should be cautioned that although the estimates in Table II are average estimates, they are not sufficiently reliable to be taken as standards at their face value. They remain to be smoothed and therefore should not be considered or used as standard data in their present form.

Preliminary Smoothing of Chroma

Preliminary smoothed data were made available by Nickerson in 1938 (60). These results are based on observations with charts on grounds of all three reflectances by about one-quarter of the subjects who eventually contributed to the review. Only the constant-value charts were used and only chroma was smoothed. Nevertheless, these earlier estimates are of considerable interest because they indicate some important adjustments in chroma, and they give the best definition of the ideal Munsell system yet available.

Procedure in smoothing

The samples at each of the seven value levels represented by the 1929 chromatic samples were plotted in the (x,y)-diagram of the I.C.I. coordinate system, utilizing for that purpose the Glenn-Killian data (16). The saturation estimates available at that date were summarized relative to each individual Munsell sample, and were plotted on the same diagram. Thus discrepancies between the 1929 Munsell notation and this 1938 visual consensus were revealed as spatial differences between plotted points at each value level.

Next, representative chroma contours were established by drawing smooth free-hand curves through the scattered Glenn-Killian points.

Wherever such a point was not confirmed by the consensus of visual estimates the contour was correspondingly deflected. Not infrequently the average visual estimate was found to fall in the path of a smooth curve and to justify the drawing of a contour different from that suggested by the unadjusted data alone.

The chroma smoothing was affected by two further considerations both of which involved considerable judgment or freedom of choice on the part of the investigator. In drawing the isochroma contours at the given value level, limited concessions were made to the form of the concentric pattern of curves at that level, taken as a whole, according to the principle that the individual curves must bear a systematic relation to each other. Thus, if the chroma /6 contour has a shape differing from that of chroma /2, the chroma /4 contour must be transitionally related to them.

The other consideration involved the interrelationships between similar chroma contours on adjacent value levels. By drawing the several curves of each value level on a large separate sheet of translucent paper and by properly superposing these sheets, a guide was arranged to this intervalue-level smoothing. Here the changes seemed to be transitional from one level to the next, and especially marked in progressing from the middle levels toward either extreme. The end result of applying these two considerations was the desired tridimensionally smoothed system of iso-chroma contours.

Charted results

Greatly reduced reproductions of the final charts are shown in Figs. 7 to 14. In each figure, the small circles represent the plotted Glenn-Killian points and they bear the 1929 Munsell notations. The heavy elliptoid curves are the smooth iso-chroma contours corresponding to chroma /2, /4, /6, and so on. The origin of these concentric curves is the point representing I.C.I. Illuminant C which approximately represents the achromatic axis of the Munsell solid. Radiating ​

Fig. 7.
Fig. 8.
Figs. 7-8. Representative iso-chroma contours at value levels 2/ and 3/ based on preliminary visual estimates of the constant-value charts.
​
Fig. 9.
Fig. 10.
Figs. 9-10. Representative iso-chroma contours at value levels 4/ and 5/ based on preliminary visual estimates of the constant-value charts.
​
Fig. 11.
Fig. 12.
Figs. 11-12. Representative iso-chroma contours at value levels 6/ and 7/ based on preliminary visual estimates of the constant-value charts.
​
Fig. 13.
Fig. 14.
Figs. 13-14. Representative iso-chroma contours at value levels 8/ and 9/ based on preliminary visual estimates of the constant-value charts.
​from this origin are 100 lighter lines of average dominant wave-length. Twenty of these indicate approximately the average dominant wavelengths of the 20 Munsell hues, while the remaining 80 are spaced arbitrarily at equal angles between them. Wave-length is shown for reference only, the relation between hue and dominant wave-length not being simple. Figure 14 differs from the others in that it is not based directly on data but simply represents at the 9/ value level the results of the intervalue smoothing.

Discussion

The iso-chroma contours at all value levels evince several distinctive characteristics. They are of a definitely elliptoid form with the major axis approximately coinciding with the Y to PB hue plane. There is an obvious broadening out of the contours in the first (10GY to R) as compared with the third (10P to B) quadrant, a tendency which is especially marked for higher chroma. Sections of contours lying in the first quadrant (10GY to R) show the greatest separation while those in the second quadrant (R to 10P) lie closest together. These sweeping departures from uniformly spaced concentric circles, may be ascribed reasonably to the I.C.I. system itself. They constitute a preliminary indication of the nature and magnitude of the general departures of the I.C.I. (x, y)-diagram from a uniform-chromaticity-scale system. This interpretation is admissible on the ground that our table of visual estimates has revealed no such irregularities in the Munsell system. On the other hand, the fact that the /2 chroma contour exhibits a tendency to a wider separation from the neutral point than the chroma contours do from each other, may represent a real irregularity in the Munsell spacing. As already. mentioned, a number of observers had specially reported that the /0 to /2 chroma interval seemed too great. Other data on the relation of chroma to purity may be found elsewhere (12, 32, 62, 67, 69).

The experience gained in this preliminary smoothing of the chroma estimates from the constant-value charts should, for the final report, prove useful in the tridimensional smoothing of hue, value, and chroma from both the constantvalue and constant-hue charts. Visual data for tridimensional smoothing are now available in Table II above.

Summary

This paper reports to date the work of the Optical Society of America subcommittee on the spacing of the Munsell colors. The ideal of this study is to produce a psychophysical specification of a system of surface colors corresponding as closely as possible to the true psychological color solid, but all along the general attitude of the subcommittee has been simply that any substantial improvement in spacing which might prove possible would be well worth while. The work of the subcommittee consists in revaluation by visual observations of the regular 400 Munsell samples of 1929, in order that they may conform more closely to the regular contours of the ideal solid. All samples were viewed against white, gray, and black grounds, independently.

A table is presented containing the averaged visual estimates of the numerous subjects who participated in the revaluation procedure. The unsmoothed corrections in the spacings are evident from a direct comparison of these data with the 1929 Munsell notation. The approximate validity of the latter is in general confirmed by the smallness and the distribution of the deviations.

Background reflectance is found to exert upon the lightness estimates a significant and systematic influence which is in the expected direction of simultaneous lightness contrast. There is evident from inspection no comparable general influence of background on either hue or saturation.

The plan is to smooth these averaged visual estimates in the I.C.I. colorimetric coordinate system for presentation in the final report. The smoothing operation is here illustrated by preliminary results for chroma, based on incomplete visual estimates with the constant-value charts.


Acknowledgment

The writer is particularly indebted to the staff of the color measurements laboratory of the Agricultural Marketing Service, United States Department of Agriculture, for substantial aid in the preparation of tables and figures.

​

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  1. ↑ Chairman of the Subcommittee. This subcommittee is a part of the O.S.A. committee on colorimetry, L. A Jones, Chairman.
  2. ↑ This notation is briefly described here for the convenience of any reader who does not happen to be familiar with it. In general the notation correlates with the coordinates of the surface-color solid described in the first paragraph of this paper. Thus, hue is indicated by angle about the neutral axis, value corresponds to distance above the base plane containing the point representing black, and chroma corresponds to distance from the neutral axis. A number and one or two letters indicate location of the given color in the hue circuit which is divided into 100 hue steps. Each of the 10 principal Munsell hues (R, YR, Y, GY, G, BG, B, PB, P, RP) may be accompanied by any number from 1 to 10 to indicate the lesser variations or steps in the circuit. The principal hues are understood to fall at positions indicated by the number 5, and it is conventional to omit this number in the hue notation. Any hue with a designation greater than 5 lies farther along in the above hue series (clockwise direction) while designations less than 5 indicate counter-clockwise departures from the principal hue. Thus, 9R is a yellowish red, for it departs from R (or 5R) by four hue steps in the direction of yellow-red (YR). On the other hand, 2R is a somewhat purplish red because it lies three steps in the counterclockwise direction toward RP. Numbers ranging from 0 to 10 indicate location on the value scale. Thus, value 1/ indicates a near black, 5/ indicates middle gray, and 9/ a near white. The extreme values or ideal limits, 0 and 10, are not realized in practice. Numbers ranging upward toward theoretical limits (23) represent degrees of chroma. Upper limits in practice depend upon the availability of suitable pigments. Zero chroma means an achromatic or gray color in which hue is absent. In the complete notation of a color, the hue designation is given first, followed by a fractional form of which the numerator is the value designation and the denominator is the chroma designation. Thus, for instance, 7R 3/8 specifies a color which is predominantly red in hue with a minor yellow component, somewhat low in value, and only moderately high in chroma.
  3. ↑ Reported in a memorandum to D. Nickerson (1935).
  4. ↑ Reported to the Research Department of the Brown Company (1935).
  5. ↑   The transformation from Judd’s U.C.S. system (R, G, B) to the modified system (R′, G′, B′):
    R′= R-0.2G+1.6B
    G′= 0.3R+0.7G+0.5B
    B′= 1.5B
  6. ↑ After E. Q. Adams, from data received by D. Nickerson. The near-coincidence of points 10GY 5/6 and 10GY 5/8 appears to constitute a real peculiarity of this plot; at least, it is not due to error in plotting the Glenn-Killian data.
  7. ↑ Reference 57 contains a detailed discussion of the ratio method and its application to the spacing problem; and much of that material has been adapted and included in the present report. Figs. 2 and 3 of the earlier paper have been reproduced as Figs. 2 and 3 herein.
  8. ↑ From an unpublished manuscript entitled “Color measurement and the just noticeable difference,” (March 30, 1935).
  9. ↑ Nat. Bur. Stand. test No. 81810 (1937).
  10. ↑ A limited number of observations were made by an individual known to be deuteranopic, and these are available for reference.
  11. ↑ These data were not complete and checked when Fig. 6 was made; and they differ (insignificantly) from the correct figures which are presented in Table II.
  12. ↑ Often the distributions proved to be violently skewed, so the question arose as to the most appropriate central representation to employ. Were the median chosen there would be less weighting of the extreme cases. On the other hand, there is some reason to believe that the extreme cases should be weighted. The reason is that there is a tendency to make “O.K.” judgments (estimates of zero displacement) unless there is somewhat clear evidence that displacement should be indicated. As a result one may reasonably suppose that the mode and median fall in the “O.K.” division more frequently than they should. Displacement estimates are especially significant, and so should, if any thing, be weighted more heavily rather than taken simply at their face value. If the extreme judgments, which are usually displacement judgments, are more heavily weighted, a closer approximation to “true” averages may be expected. Thus in a measure, the use of the mean in dealing with these skewed distributions may be justified.
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