Table I
Desirable and ambiguous intervals between colors (ω space).

Pleasing interval Displeasing interval Variation in z only Variation in r only+ Variation in θ only Identity 0 to 1 j.n.d. 0 to 1 j.n.d. 0 to ±1 j.n.d. 1st ambiguity 1 j.n.d. to 4* 1 j.n.d. to 3* ±1 j.n.d. to ±25° Similarity 4 to 12 3 to 5 ±25° to ±43° 2nd ambiguity 12 to 20 5 to 7 ±43° to ±100° Contrast 20 to 80 7→ ±100° to ±180° glare >80 — —

+ For simultaneous variation of

z and

r , see

Figs. 3 and

4 .

* Numbers refer to units of

z or

r in

ω space.

Table II
Desirable and ambiguous intervals between colors (Munsell system).

Pleasing intervals Displeasing intervals Variation in value only Variation in chroma only+ Variation in hue only Identity 0 to 1 j.n.d. 0 to 1 j.n.d. 0 to 1 j.n.d. 1st ambiguity 1 j.n.d. to
${\scriptstyle \frac{1}{2}}$ step 1 j.n.d. to 3 steps 1 j.n.d. to 7 steps* Similarity
${\scriptstyle \frac{1}{2}}$ to
$1{\scriptstyle \frac{1}{2}}$ 3 to 5 7 to 12 2nd ambiguity
$1{\scriptstyle \frac{1}{2}}$ to
$2{\scriptstyle \frac{1}{2}}$ 5 to 7 ±12 to ±28 Contrast
$2{\scriptstyle \frac{1}{2}}$ to 10 7→ ±28 to ±50 glare >10 — —

+ For simultaneous variation of value and chroma, see

Figs. 3 and

4 .

* One hue step is equal to 1/100 of the complete hue circle.

Table III
Ambiguity, similarity, and contrast in a plane of constant hue expressed in Munsell notation (see Fig. 4 ).

Region Chroma difference Value difference 1st ambiguity 2 0 Similarity 0 1 2 1 4 0 2nd ambiguity 0 2 2 2 4 1 4 2 6 1 6 0 Contrast 0 3, 4, ⋯ 10 2 3, 4, ⋯ 10 4 3, 4, ⋯ 10 6 2, 3, ⋯ 10 8 0, 1, 2, ⋯ 10 Glare Any >10

Table IV
Classification of harmonies.

Class I. One variable
1. Variable z

A. Achromatic

(a) Two color-points

(b) Three points

(c) More than three points

B. Chromatic

(a) Two points

(b) Three points

(c) More than three points

2. Variable r

(a) Two points

(b) Three points

(c) More than three points

3. Variable θ

(a) Two points

(b) Three points

(c) More than three points

Class II. Two variables
1. In a plane of constant θ

A. Points on a straight line

B. Triangles

C. Rectangles

D. Points on a circle

2. In a plane of constant z

(a) Two points

(b) Three points on isosceles triangle

(c) Five points on two triangles

(d) n points on a circle with center on neutral axis

(e) n points on a circle with center at a chromatic point

3. In a cylinder of constant r

(a) Two points

(b) n points on an ellipse with center on neutral axis

Class III. Three variables
1. With reference to planes of constant θ

2. With reference to planes of constant z

3. With reference to cylinders of constant r

4. With reference to tilted planes

Table V
Class I. Harmonies in one variable.

1A . Variable z , achromatic harmonies
(a) Two color-points

(1) Harmony of analogy. Difference in z is between 4 and 12 (
${\scriptstyle \frac{1}{2}}$ to
$1{\scriptstyle \frac{1}{2}}$ Munsell value steps).

Example: N 7, N 8.

(2) Harmony of contrast. Difference in z is between 20 and 80 (
$2{\scriptstyle \frac{1}{2}}$ to 10 Munsell value steps).

Examples: N 3, N 6; N 2, N 6; N 1, N 9.

(b) Three points

(1) Small equal steps. Difference in z is between 4 and 12.

Example: N 4, N 5, N 6.

(2) Large equal steps. Difference in z is between 20 and 80.

Example: N 2, N 5, N 8.

(3) Large and small steps.

Examples: N 2, N 3, N 7; N 3, N 7, N 8.

(c) More than three points

An obvious extension of the classification for three colors.

Table VI
Class I. Harmonies in one variable.

1B . Variable z , chromatic harmonies
(a) Two points

(1) Harmony of analogy

Examples: R 6/8, 5/8; B 6/6, 7/6.

(2) Harmony of contrast

Examples: P 6/8, 3/8; RP 8/6, 3/6.

(b) Three points

(1) Small steps

Examples: GY 7/8, 6/8, 5/8; Y 8/6, 7/6, 6/6.

(2) Large steps

Example: R 8/4, 5/4, 2/4.

(3) Large and small steps

Examples: BG 7/4, 6/4, 3/4; YR 8/4, 4/4, 3/4.

(c) More than three color-points

Table VII
Class I. Harmonies in one variable.

2. Variable r
(a) Two points

(1) Harmony of analogy

Examples: N 7, R 7/4; YR 4/4, YR 4/8.

(2) Harmony of contrast

Examples: GY 7/2, GY 7/10; N 4, P 4/12.

(b) Three points

(1) Small steps

Examples: RP 4/4, 4/8, 4/12; PB 5/2, 5/6, 5/10.

(2) Large steps

Example: N 4, R 4/7, R 4/14.

(3) Large and small steps

Example: N 8, Y 8/8, Y 8/12.

(c) More than three points

Table VIII
Class I. Harmonies in one variable.

3. Variable θ
(a) Two points

(1) Harmony of analogy

Examples: Y 8/8, YR 8/8; 10 RP 4/10, 10 P 4/10; YR 6/6, Y 6/6.

(2) Harmony of contrast

Examples: 5 R 7/8, 10 GY 7/8; 5 B 5/6, 10 R 5/6.

(b) Three points

(1) Small steps

Examples: RP 3/10, P 3/10, PB 3/10.

(2) Large steps

Example: G 7/2, YR 7/2, P 7/2.

(3) Large and small steps

Example: GY 6/6, G 6/6, P 6/6.

(c) More than three points

Table IX
Class II. Harmonies in two variables.

1A . In a plane of constant θ , points on a straight line
(a) Two points

(1) Harmony of analogy

Examples: (positive slope) BG 5/6, BG 4/4.

(negative slope) GY 6/6, GY 5/8.

(2) Harmony of contrast

Examples: (positive slope) YR 5/6, YR 2/2.

(negative slope) GY 7/4, GY 5/10.

(b) Three points

(1) Small steps

Examples: (positive slope) G 5/2, 6/4, 7/6.

(negative slope) P 6/8, 5/10, 4/12.

(2) Large steps

Examples: (positive slope) R 7/6, R 4/4, R 1/2.

(negative slope) RP 8/2, 5/6, 2/10.

(3) Large and small steps

Examples: (positive slope) GY 5/2, 7/8, 8/10.

(negative slope) PB 7/4, 6/6, 4/10.

(b) More than three points

Table X
Class II. Harmonies in two variables.

1B . In a plane of constant θ , triangles
(a) Isosceles triangle, horizontal base (z =const.)

(1) All sides constituting small steps

Example: R 5/6, 4/4, 4/8.

(2) All sides large

Example: PB 7/6, 4/2, 4/10.

(3) Equal sides large, third side small

Example: YR 7/4, 4/2, 4/6.

(b) Isosceles triangle, vertical base (r =const.)

(1) All sides small

Example: N 5.5, G 6/2, G 5/2.

(2) All sides large

Example: RP 5/2, 2/4, 8/4.

(3) Equal sides large, third side small

Example: N 4.5, BG 5/8, BG 4/8.

(c) Right triangles

(1) Two mutually perpendicular sides constituting small steps

Example: BG 6/6, 5/4, 5/6.

(2) Two sides large

Example: Y 8/4, 8/12, 5/4.

(3) One large and one small side

Example: B 7/2, 7/6, 3/6.

(d) More than three points arranged on a triangle

Table XI
Class II. Harmonies in two variables.

1C . In a plane of constant θ , rectangles
(a) All sides constituting small steps

Example: YR 7/6, 7/10, 6/6, 6/10.

(b) All sides constituting large steps

Example: N 6, B 6/8, N 3, B 3/8.

(c) Large and small sides

Example: B 7/2, 7/6, 4/2, 4/6.

1D . In a plane of constant θ , any number of points spaced on a circleExample: R 6/6, 4/2, 4/10, 2/6.

Table XII
Class II. Harmonies in two variables.

2. In a plane of constant z
(a) Two points

Example: RP 7/4, R 7/8.

(b) Three points on isosceles triangle with a vertex on the neutral axis

Example: N 7, BG 7/4, G 7/4.

(c) Five points at the vertices of two triangles of the type considered in (b )

Example: G 5/4, BG 5/4, N 5, RP 5/4, R 5/4.

(d) n points spaced on a circle whose center is on the neutral axis

Example: YR 6/6, RP 6/6, PB 6/6, BG 6/6, GY 6/6.

(e) n points spaced on a circle whose center is at a chromatic point

Example: R 5/6, P 5/4, BG 5/2, Y 5/4.

Table XIII
Class II. Harmonies in two variables.

3. In a cylinder of constant r
(a) Two points

(1) Small steps in θ and z

Example: GY 7/6, G 6/6.

(2) Large steps in θ and z

Example: G 3/2, P 7/2.

(3) Small step in θ and large step in z

Example: R 7/8, RP 3/8.

(4) Large step in θ and small step in z

Example: YR 7/4, BG 6/4.

(b) n points on an ellipse whose center is on the neutral axis

Three points, Example: R 2/4, G 7/4, B 7/4.

Four points, Example: GY 8/6, R 4/6, PB 4/6, P 2/6.

Table XIV
Class II. Harmonies in three variables.

1. With reference to planes of constant θ

(a) n points in a plane of constant θ , one related point in another plane, difference in θ is a small step.

Example: P 6/8, P 3/8, RP 6/8.

(b) n points in a plane of constant θ , one related point in another plane, difference in θ is a large step.

Examples: R 8/4, 5/4, 2/4, BG 5/4;

BG 7/4, 6/4, 3/4, R 7/4.

(c) n points in a plane of constant θ , similar arrangement of points in another plane.

Examples: P 6/8, P 3/8, B 6/8, B 3/8;

Y 7/4, Y 6/2, N 5, PB 4/2, PB 3/4.

(d) n points in a plane of constant θ , one point or similar arrangement of points in two or more other planes.

Example: N 4, R 7/6, R 6/4, B 7/6, G 7/6.

2. With reference to planes of constant z

(a) n points in one plane, one related point in another plane, difference in z is a small step.

Example: N 6, R 6/4, BG 6/4, BG 5/4.

(b) n points in one plane, one related point in another plane, difference in z is a large step.

Example: RP 7/4, R 7/8, R 3/8.

(c) n points in one plane, similar arrangement of points in another plane.

Example: BG 6/2, R 6/10, BG 2/2, R 2/10.

(d) n points in one plane, one point or similar arrangement of points in two or more other planes.

Example: RP 3/2, R 3/10, RP 7/2, RP 6/2.

3. With reference to cylinders of constant r

(a) n points on one cylinder, one related point on another cylinder, difference in r is a small step.

Example: GY 8/6, R 4/6, PB 4/6, P 2/6, R 4/10.

(b) n points on one cylinder, one related point on another cylinder, difference in r is a large step.

Example: N 5.5, B 6/4, R 5/4, R 5/12.

(c) n points on one cylinder, similar arrangement of points on another cylinder.

Example: G 3/2, P 7/2, G 3/6, P 7/6.

(d) n points on one cylinder, one point or similar arrangement of points on two or more other cylinders.

Example: R 7/8, RP 3/8, R 7/4, N 7.

4. With reference to tilted planes

(a) n points on an ellipse with center on the neutral axis, plus neutral point in the same plane.

Examples: N 5.5, G 5/4, BG 6/4;

N 5, GY 2/2, PB 8/2;

N 4.5, P 6/8, PB 3/8.

(b) n points on an ellipse whose center is at a chromatic point.

Example: P 3/10, PB 4/8, RP 4/8, GY 7/4.