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has more

interest than M., are as follows: For (1) I. + D. = D.; (2) I. = D. +

D.; (3) I. = D.; (4) I. = D.; (5) I. + D. = D.; etc. These are in

order of complete balance, but it will be seen that from (7) on, while

the factors are constant, the framework is not balanced; e.g. in (9)

both I. and D. work on the same side. For these groups, therefore, the

variations, if there is balance, will be more striking. Eliminating

the balancing elements in the framework, the tables for the ten groups

are:

 

(1) I. + D. = D. (2) I. = D. + D(M). (3) I. = D.

969. I. = Ms. 680. I. = D. 1094. Ms. + I. = I. + D.

601. I. = Ms. 735. I. = D. 33. I. = I. + D

49. I. = Ms. + I. 1121. I. = D.

634. I. = Ms. + I. 1035. I. = D. (4) I. = D.

584. I. = I. 333. I. = I. + D. 775. I. = D.

686. I. = I. 80. I. = I. + D. 746. I. = D.

794. I. = D. 753. I. = I. + D. 1106. I. = Ms. + D.

164. I. = D. 1114. I. = D. + L. 781. I. = Ms. + D.

368. I. = D. + V. 1131. I. = I. + D.

927. I. = V. 517. I. = I. + D.

273. I. = V. 327. I. + Ms. = D. + V.

951. I. + L. = D. + V.

715. Unbalanced.

 

(5) I. + D. = D. (6) I. = (7) I. + D. =

43. I. = I. 854. I. = Ms. 725. I. + D. = I. + L.

711. I. = I. 1148. I. = I. 206. I. + D. = I. + L.

447. I. = Ms. 709. I. = D. 155. I. + D. = D. + L.

643. I. = Ms. 907. I. = D. 739. I. + D. = L.

777. I. = Ms. + I. 586. I. = Ms. + I. 331. I. + D. = V.

637. I. = Ms. + I. 137. I. = Ms. + I. 980. Unbalanced.

187. Unbalanced.

 

(8) I. + D. = (9) I. + (D. + D.) = (10) 0.

57. I. + D. = Ms. 835. I. + D. = Ms + I.

979. I. + D. = I. + L. 724. I. + D. = Ms + L.

134. I. + D. = D. 495. I. + D. = Ms + L.

106. I. + D. = D. + V. 182. I. + D. = Ms + V.

220. I. + D. = L. 817. I. + D. = I.

118. I. + D. = V. + L. 662. I. + D. = I.

157. Unbalanced. 806. I. + D. = I.

1136. I. + D. = I. + L.

865. I. + D. = I. + V.

1023. I. + D. = V.

531. I. + D. = L.

553. I. + D. = L.

 

The most used element is I., in 100 per cent. of cases; the least

used, V., 13 per cent. D., in 91 per cent. of cases; Ms., 26 per

cent.; L., 19 per cent. 175, 433, unbalanced.

 

As seen in the table, a balance of elements is kept, except in four

cases which will be hereafter considered. In all cases the balance is

between the interest in C., sometimes plus D., (in the attention of

the figures to C.), on the one side, and other elements on the other.

Very seldom are other salient points found on the C. side. When the C.

side is especially ‘heavy,’ the number of opposing elements increases,

and especially takes the form of V. and L. [cf. (7), (8), (9)], which

were observed in the experimental chapter to be powerful in attracting

attention. For the fairly well-balancing framework—(i), (2), (3) and

(4)—Ms., I., and D. are much more often the opposing elements.

 

The pictures listed as unbalanced are, with one exception, among the

oldest examples given; conceived in the most slavish geometrical

symmetry in which, indeed, the geometrical outline almost hides the

fact that the slight variations are all toward a lack of balance.

 

There is but one S. & S. case (1054), Titian, _The Madonna of the

House of Pesaro_. In this, M. and C. are on a high throne on the

Right, other figures lower down on the Left bearing a flag that leans

back to the Left. All the lines of the figures and of the massive

architecture and the general direction of attention bear down so

strongly to Left that the importance of the Right figures is balanced.

We should have, then, I. = I. + L. + D. The D.C. cases, seven in

number, are remarkably alike. Six have a vista separating the two

groups, in five remarkably deep and beautiful, as if to fix the

oscillating attention there. In all, M. and C., either in position or

by the direction of their lines, are nearer the Cn. than the opposing

figures, which are naturally less interesting, thus giving an instance

of the mechanical balance. Their general equation, then, would be I. =

M. or M. + L. Having shown that the small variations from the general

symmetrical type of altarpieces are invariably, except in primitive

examples, in the direction of substitutional symmetry, or balance, we

may next study the Madonna pictures, using the same classifications

for purposes of comparison.

 

MADONNA WITH INFANT CHRIST.

 

(1) I. + D. = D. (2) I. = D. + D. (4) I. = D.

56. I. = L. 271. I. = D. + L. 668. I. = D. + Ms.

332. I. = L. 867. I. = D. + V. + D. 14. I. = D. + I.

633. I. = D. 91. I. = D. + V.

(3) I. = D. 1111. I. = D. + V.

144. I. = D. 1011. I. = D. = L.

521. I. = D. 915. I. = D. = L.

356. I. = L. + D. + D.

296. I. + Ms. = V. + L.

 

(5) I. + D. = D. (6) I. =

51. I. = D. 596. I. = Ms.

581. I. = D. 892. I. = Ms.

829. I. = D. + I. 224. I. = I. + D.

159. I. = I. + D. 908. I. = D. + L.

683. I. = D. + L.

1045. I. = I. + L. (7) I. + D. =

745. I. = I. + L. 344. I. + D. = Ms.

734. I. = D. + L. 949. I. + D. = Ms. + V. + L.

404. I. = D. + L. 608. I. + D. = L.

248. I. = L. 524. I. + D. = L.

37. I. = L.

97. I. = L. (8) 0.

363. I. = V. + L.

674. I. = V. + L. (9) I. + D. + D. =

62. I. = V. + L. 361. I. + D. = L.

1142. I. = V. + L.

1018. I. = V. + L. (10)

110. I. + V. = Ms. + L. 538. I. = D.

411. I. + V. = Ms. + L. 614. I. + Ms. = V.

771. I. + Ms. = V. + L. 34. D. = Ms. + L.

 

Most used element, I., 100 per cent.; least used, Ms., 21 per cent.

D., 96 per cent.; L., 64 per cent.; V., 27 per cent.

 

The first thing to be noted, on comparing this table with the

preceding, is the remarkable frequency of the use of the vista and the

line. Among the altarpieces, the direction of attention was the

element most often opposed to the interesting object; and next to

that, another object of interest. These two elements, however, here

sink into comparative insignificance. In general, balance is brought

about through the disposition of form rather than of interests. This

appears in comparing the numbers; against the use of L. in 19 per

cent. of the cases among the altarpieces, we have 64 per cent. among

the Madonna pictures; V. is used in the former cases 13 per cent. of

the times, in the latter 27 per cent. The reason for this would appear

to be that the lack of accessories in the person of saints,

worshippers, etc., and the consequent increase in the size of M. and

C. in the picture heightens the effect of any given outline, and so

makes the variations from symmetry greater. This being the case, the

compensations would be stronger—and as we have learned that V. and L.

are of this character, we see why they are needed. None of the M. and

C., S.C. pictures fails to give a complete balance of elements

according to hypothesis. There are no well-defined cases of S. & S. or

D.C.

 

Portraits.

 

A study of the Madonna pictures of all types, then, results in an

overwhelming confirmation of the hypothesis of substitutional

symmetry. It may be objected that the generally symmetrical framework

of these pictures suggests a complete balance, and the next step in

our analysis would, therefore, be a type of picture which is less

bound by tradition to the same form. The portrait would seem to

combine this desideratum with generally large and simple outlines, so

that the whole surface can be statistically reported with comparative

ease. A detailed analysis of a couple of portraits may justify the

classification adopted.

 

900. Anton Raphael Mengs, Self-Portrait. The head of the painter is

exactly in Cn., but is turned sharply to Right, while his shoulders

turn Left. His arm and hand are stretched out down to Right, while his

other hand, holding pencil, rests on his portfolio to Left. Hence, the

D. of attention plus that of L. on Right, balances I. in implements,

plus D. of body on Left, or D. + L. = D. + I.

 

438. B. van der Helst, Portrait of Paul Potter. The head of the

subject is entirely to Left of Cn., his easel on Right. His body is

turned sharply to Right, and both hands, one holding palette and

brushes, are stretched down to Right. His full face and frontward

glance are on Left. Hence, Ms. + I. in person balances I. in

implements + D. of L., or Ms. + I. = I. + L.

 

It is seen that the larger elements in these pictures are the

directions of the head and body, and the position of the head, with

reference to Cn. The following classification is based on this

framework.

 

CLASSIFICATION OF PORTRAITS.

 

A. Head in Cn.

I. Body front, head front, 6

II. Body turned, head turned other way, 7 D. = D.

III. Body turned, head front, 31 D. =

IV. Body front, head turned, 1 D. =

V. Body turned, head turned same way, 106 D. + D. =

 

B. Head not in Cn.

I. Body turned to empty side, head to same, 18 Ms.=D.

II. Body turned to empty side, head front, 23 Ms. = D.

III. Body turned to empty side, head to other, 3 Ms. + D. = D.

IV. Body front, head front, 2 Ms. =

V. Body turned from empty side, head same way, 10 Ms. + D. =

 

This is also in order of less complete balancing of the original

elements. The principal characteristics of the different divisions are

as follows:—

 

A.

I. (Symmetrical.) Most used element, L.; least used, V.

 

II. (Balanced, D. = D.) Most used element, L.; least used, V.

 

III. (D. = .) Most used element, Ms.,

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