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  1. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 46 (1944).
    [CrossRef]
  2. W. Ostwald, Die Harmonie der Farben (Leipzig, 1922); Farbkunde (Leipzig, 1923).
  3. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 270 (1943).
    [CrossRef]
  4. B. R. Bellamy and S. M. Newhall, J. Opt. Soc. Am. 32, 465 (1942).
    [CrossRef]
  5. George Field, Chromatics (London, 1845).
  6. A. H. Munsell, A Color Notation (Munsell Color Company, Baltimore, 1941).
  7. Tensor notation will be used. See J. A. Schouten and D. J. Struik, Einführung in die neueren Methoden der Differentialgeometrie (P. Noordhoff, Groningen, 1935). A tensor is represented by a letter with superscript or subscript, as ωκ; gij. Powers will be distinguished by numerals outside parehtheses, as (ωk)2; and if m tensors of the same kind are used, they are distinguished by subscripts outside the parentheses, as (ωk)1, (ωk)2,⋯(ωk)m. This notation is easier on the typesetter than the placement of a label beneath the letter, as done by Schouten and Struik.
  8. D. E. Spencer, “A tensor interpretation of Study’s Geometrie der Dynamen,” Ph.D. thesis, M.I.T. (1942); “Geometric figures in affine space,” “The tensor representation of Study’s Geometrie der Dynamen,” to be published in J. Math. Phys.; J. Frank. Inst.236, 293 (1943).
  9. A. H. Munsell, “An introduction to the Munsell color system,” in A Grammar of Color (Strathmore Paper Company, 1921), p. 9.
  10. T. M. Cleland, “A practical description of the Munsell color system,” in A Grammar of Color (Strathmore Paper Company, 1921), p. 22.

1944 (1)

1943 (1)

1942 (1)

Bellamy, B. R.

Cleland, T. M.

T. M. Cleland, “A practical description of the Munsell color system,” in A Grammar of Color (Strathmore Paper Company, 1921), p. 22.

Field, George

George Field, Chromatics (London, 1845).

Moon, P.

Munsell, A. H.

A. H. Munsell, A Color Notation (Munsell Color Company, Baltimore, 1941).

A. H. Munsell, “An introduction to the Munsell color system,” in A Grammar of Color (Strathmore Paper Company, 1921), p. 9.

Newhall, S. M.

Ostwald, W.

W. Ostwald, Die Harmonie der Farben (Leipzig, 1922); Farbkunde (Leipzig, 1923).

Schouten, J. A.

Tensor notation will be used. See J. A. Schouten and D. J. Struik, Einführung in die neueren Methoden der Differentialgeometrie (P. Noordhoff, Groningen, 1935). A tensor is represented by a letter with superscript or subscript, as ωκ; gij. Powers will be distinguished by numerals outside parehtheses, as (ωk)2; and if m tensors of the same kind are used, they are distinguished by subscripts outside the parentheses, as (ωk)1, (ωk)2,⋯(ωk)m. This notation is easier on the typesetter than the placement of a label beneath the letter, as done by Schouten and Struik.

Spencer, D. E.

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 34, 46 (1944).
[CrossRef]

P. Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 270 (1943).
[CrossRef]

D. E. Spencer, “A tensor interpretation of Study’s Geometrie der Dynamen,” Ph.D. thesis, M.I.T. (1942); “Geometric figures in affine space,” “The tensor representation of Study’s Geometrie der Dynamen,” to be published in J. Math. Phys.; J. Frank. Inst.236, 293 (1943).

Struik, D. J.

Tensor notation will be used. See J. A. Schouten and D. J. Struik, Einführung in die neueren Methoden der Differentialgeometrie (P. Noordhoff, Groningen, 1935). A tensor is represented by a letter with superscript or subscript, as ωκ; gij. Powers will be distinguished by numerals outside parehtheses, as (ωk)2; and if m tensors of the same kind are used, they are distinguished by subscripts outside the parentheses, as (ωk)1, (ωk)2,⋯(ωk)m. This notation is easier on the typesetter than the placement of a label beneath the letter, as done by Schouten and Struik.

J. Opt. Soc. Am. (3)

Other (7)

W. Ostwald, Die Harmonie der Farben (Leipzig, 1922); Farbkunde (Leipzig, 1923).

George Field, Chromatics (London, 1845).

A. H. Munsell, A Color Notation (Munsell Color Company, Baltimore, 1941).

Tensor notation will be used. See J. A. Schouten and D. J. Struik, Einführung in die neueren Methoden der Differentialgeometrie (P. Noordhoff, Groningen, 1935). A tensor is represented by a letter with superscript or subscript, as ωκ; gij. Powers will be distinguished by numerals outside parehtheses, as (ωk)2; and if m tensors of the same kind are used, they are distinguished by subscripts outside the parentheses, as (ωk)1, (ωk)2,⋯(ωk)m. This notation is easier on the typesetter than the placement of a label beneath the letter, as done by Schouten and Struik.

D. E. Spencer, “A tensor interpretation of Study’s Geometrie der Dynamen,” Ph.D. thesis, M.I.T. (1942); “Geometric figures in affine space,” “The tensor representation of Study’s Geometrie der Dynamen,” to be published in J. Math. Phys.; J. Frank. Inst.236, 293 (1943).

A. H. Munsell, “An introduction to the Munsell color system,” in A Grammar of Color (Strathmore Paper Company, 1921), p. 9.

T. M. Cleland, “A practical description of the Munsell color system,” in A Grammar of Color (Strathmore Paper Company, 1921), p. 22.

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Figures (4)

Fig. 1
Fig. 1

Coordinate systems in ω space. P and Q represent two colors of the same Munsell value and hue, P′ and Q′ two colors which differ in value and hue.

Fig. 2
Fig. 2

A plane of constant hue (θ=const.).

Fig. 3
Fig. 3

Outline of a poster design.

Fig. 4
Fig. 4

Gray harmony applied to the design of Fig. 3. The colors are (1) N 6, (2) N 3, (3) N 8, (4) N 9.

Tables (5)

Tables Icon

Table I Some experimental results on area balance. Neutral background (N 5).

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Table II Moment arms about N 5.

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Table III Psychological effect of the balance point.

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Table IV Examples of color harmony.

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Table V Color harmonies for Fig. 3.

Equations (22)

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S 1 r 1 = S 2 r 2 .
S 1 [ ( r 1 ) 2 + ( z 1 - z A ) 2 ] 1 2             and             S 2 [ ( r 2 ) 2 + ( z 2 - z A ) 2 ] 1 2 .
S 1 [ ( r 1 ) 2 + ( z 1 - z A ) 2 ] 1 2 = S 2 [ ( r 2 ) 2 + ( z 2 - z A ) 2 ] 1 2 .
n S 1 [ ( r 1 ) 2 + ( z 1 - z A ) 2 ] 1 2 = S 2 [ ( r 2 ) 2 + ( z 2 - z A ) 2 ] 1 2
n 1 S 1 [ ( r 1 ) 2 + ( z 1 - z A ) 2 ] 1 2 = n 2 S 2 [ ( r 2 ) 2 + ( z 2 - z A ) 2 ] 1 2 = = n m S m [ ( r m ) 2 + ( z m - z A ) 2 ] 1 2 ,
S [ ( chroma ) 2 + 64 ( value - 5 ) 2 ] 1 2 = area × moment arm .
( Area of P 3 / 8 ) / ( Area of P 6 / 8 ) = 11.31 / 17.89 = 0.63.
X = [ ( X 1 S 1 ) + ( X 2 S 2 ) ] / ( S 1 + S 2 ) , Y = [ ( Y 1 S 1 ) + ( Y 2 S 2 ) ] / ( S 1 + S 2 ) , Z = [ ( Z 1 S 1 ) + ( Z 2 S 2 ) ] / ( S 1 + S 2 ) .
x = X / ( X + Y + Z ) , y = Y / ( X + Y + Z ) .
ω k = Ω k / Ω 0 ,             or             Ω k = Ω 0 ω k .
x k = X k / X 0 ,             or             X k = X 0 x k .
M = [ g i j ( Ω 0 a i - Ω i ) ( Ω 0 a j - Ω j ) ] 1 2 = Ω 0 [ g i j ( a i - ω i ) ( a j - ω j ) ] 1 2 .
g i j = { 1 if i = j 0 if i j .
M = [ ( Ω 0 a i - Ω i ) 2 + ( Ω 0 a 2 - Ω 2 ) 2 + ( Ω 0 a 3 - Ω 3 ) 2 ] 1 2 = Ω 0 [ ( a 1 - ω 1 ) 2 + ( a 2 - ω 2 ) 2 + ( a 3 - ω 3 ) 2 ] 1 2 ,
( M ) i = ( n ) i Ω 0 [ [ a 1 - ( ω 1 ) 1 ] 2 + [ a 2 - ( ω 2 ) i ] 2 + [ a 3 - ( ω 3 ) i ] 2 ] 1 2 .
( n ) 1 ( M ) 1 = ( n ) 2 ( M ) 2 = ( n ) 3 ( M ) 3 = = ( n ) m ( M ) m .
( Ω 0 ) i ( Ω 0 ) j = ( n ) j [ [ a 1 - ( ω 1 ) j ] 2 + [ ( a 2 - ( ω 2 ) j ] 2 + [ a 3 - ( ω 3 ) j ] 2 ] 1 2 ( n ) i [ [ a 1 - ( ω 1 ) i ] 2 + [ a 2 - ( ω 2 ) i ] 2 + [ a 3 - ( ω 3 ) i ] 2 ] 1 2 .
( Ω 0 ) i = ( Ω 0 ) 1 ( n 1 ) [ [ a 1 - ( ω 1 ) 1 ] 2 + [ a 2 - ( ω 2 ) 1 ] 2 + [ a 3 - ( ω 3 ) 1 ] 2 ] 1 2 ( n ) i [ [ a 1 - ( ω 1 ) i ] 2 + [ a 2 - ( ω 2 ) i ] 2 + [ a 3 - ( ω 3 ) i ] 2 ] 1 2 .
( R ) j = ( Ω 0 ) 1 ( n ) 1 ( Ω 0 ) j ( n ) j [ [ a 1 - ( ω 1 ) 1 ] 2 + [ a 2 - ( ω 2 ) 1 ] 2 + [ a 3 - ( ω 3 ) 1 ] 2 ] 1 2 .
Z κ = X κ + Y κ .
z k = Z k / Z 0 = ( X k + Y k ) / Z 0 = ( X 0 x k + Y 0 y k ) / ( X 0 + Y 0 ) .
z k = 1 n ( X 0 x k ) i / 1 n ( X 0 ) i .