Letters

Leonardo, Vol. 12. pp. 349-352. Pergamon Press 1979. Printed in Great Britain LETTERS Readers’comments are welcomed on texts published in Leonardo. The Editors reserve the right to shorten letters. Letters should be written in English or in French PERCEPTION OF PERSPECTIVE PICTORIAL SPACE Richard Greene in his letter [Leonardo 11, 347 (1978)] has pointed out correctly and other respondents have similarlynoted that my recent paper on different viewing points [Leonardo 10, 283 (1977)]contains a serious violation of geometrical optics. I asserted that when observers,looking at a painting orthogonally, walk sideways, the changing views they receive will correspond optically to what they would see if, standing ‘really’ in the depicted space,they would rotate panoramically without changing their viewingpoint. What I said seems to be true for a family of orthogonals converging perspectively toward a vanishing point, but I neglected to see that it does not hold for a set of horizontals. (In the usual fashion, I am letting the two principal dimensions of a checkerboard floor stand here for the shape characteristics of the pictorial space as a whole.)This means that as viewers move sideways, the optical projection they receive does become distorted. What I regret most about my mistake is that quite understandably , it deflected the attention of readers from the challenging aesthetic problem offered by this state of affairs. A framed painting, I said, is composed in relation to its geometrical center and best understood when one actually stands before that center. If one stands elsewhere,one must neverthelesslook at the picture ‘asthough’ one were standing before the center, that is, one must try to allow for the displacement. If now the vanishing point of a picture done in central perspective lies off center and, if the viewers, obedient to the rules of geometry, place themselves opposite that point and accept it as the center of the picture, they overthrow the entire composition, displace the true center, falsify the relative weights of pictorial components-in short, they lose the picture. To mention just one side effect: the depth of the perspective vista seen from the geometrically ‘correct’ position will be much more compelling than is compatible with its function in the total composition. Therefore, any painting in which the vanishing point lies off center rejects the approximate coincidence of the pictorial space with the physical space of viewers,as it is suggested, forexample, by Leonardo da Vinci’s ‘Last Supper’. (I am discussing here onepoint perspective.) Instead, it presents the space of the picture as incompatible in principle with that of its viewer. (In my article I tried to save that unity but, helas, was found wanting.) The picture, when seen properly, projects a perspective viewers cannot share, and viewersproject a perspective not borne out by the picture. This discrepancy is much more serious than what is experienced when one faces an ‘actual’ space obliquely, because in the present case viewers are not only out of line with the framework of the pictorial space, but they are presented with a seen space they cannot see. The severity of this estrangement has not been sufficiently considered by historians. The use of the eccentric perspective is a stylistic feature whose perceptual and philosophical consequencesdeserve full appreciation. Rudolf Arnheim 1133South Seventh St. Ann Arbor, MI 48103, U.S.A. ON RELATIONSHIPS BETWEEN COLOUR AND MUSIC I would like to comment on James W. Davis’s response [Leoriurclo 12, 218 (1979)] to my paper on the relationship between colour and music in Leonardo 11, 225 (1978). I agree with much of what he says, but, as a scientist, I know that both colour and musical sounds can be described precisely and mathematically in terms of frequencies or of wavelengths. Each conceivable ‘pure’ colour can be described mathematically as occupying a precise point in a colour solid, such as that of Munsell. Each conceivable ‘pure’ musical tone can mathematically be described in terms of a fundamental plus harmonics. (Attemptsat producing a theoretical ‘sound solid’analogous to the ‘colour solid’ have so far failed.) My paper was merely intended to argue that, mathematically, that is, scientifically, there is no possible relationship between music and colour. However, as composer and...