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that his case is made-and especially not by the general reader who has read his scrupulously argued book attentively. Nor will even the most expert reader, fluent in the languages of genetics and statistics, deny that the author’s own analyses of the concepts of evolution, fitness and selection are considerably more rigorous than those offered by most workers in the field marked out by the original Wilsonian thesis that “Sociobiology is ...the systematic study of the biological basis of all social behaviour.” Oursimpleintuition of human freedom from the tyranny of nature, at least in high cultural and artistic life, is by no means sufficient to arm us against the powerful, scientifically reductivist thesis that even our altruism is assimilable to self-interest. If we are not to look increasingly sillyas the century turns, we shall need, at least, the support of Philip Kitchener’s penetrating scepticism. Of course, weshall need more than that if ourconventional wisdom isfinally to be supportable; and it is perhaps with unreasonable regret that we notice the brevity (but not the poverty!) of his mere dozen pageson the notion of freedom and the absence from the index of such key words as ‘art’,‘creation’, and ‘invention’. But to suppose this author capable of satisfying all of our most profound intellectual longings in a singletext would be to entertain on his behalf the very quality of ambition that he has sethisface against. THE WORKSHOPOF BARTOKAND KODALY by Ern3 Lendvai. Editio Musica, Budapest , Hungary, 1983. 762 pp. Reviewed by Jean-Bernard Condat, B.P. 8005,69351 Lyon Ctdex 08, France. For many musicians thename of Lendvai is immediately associated with the Golden Section and the music of Bart6k. In the late 1940s, Lendvai propounded the basic elements of a ‘system’ ranging over most of the parameters of music, which gained during the 1960s a much wider currency in the English-speaking world. Given such a lavish book of 762 pages, with a staggering 1,191 musical examples, Lendvai’s aim is, simply, to give “into the hands of the reader a practical method for comprehensive analysis of Bart6k’s music”. Numericaltricksareplayedby Lendvai, often connected with the assertion of Golden Section (GS) proportions. Many of these ‘inaccuracies’have been pointed out by Roy Howat [I], but Howat’s interpretation is, in my opinion, too kindly. Most of Lendvai’s ‘inaccuracies’ are attempts to trick the reader into thinking that the GS properties are more exact than is the case. His own recent comments [2] only reinforce this interpretation . In the opening section of the Sonata for Two Pianos and Percussion (1937) there are many intriguing GS proportions. The discussion of this section in The Workshop o f Bartdk and Kodbly (pp. 36-40) is not substantially different from that provided in Bartdk stilusa[3], and,importantly, its arithmetic is identical. What concerns me is the subterfuge of Lendvai’s arithmetic procedure . In performing his analysis he makes thefollowingseriesof calculations: A 46 XO.618=28 for 28.428 B 28 X0.618 = 17.3 for 17.304 C 17.3X 0.618 = 11 for 10.6914 Although the givenand real results donot differ greatly (one full unit here equalling a dotted crotchet), Lendvai is using the device of ‘rounding’, as well as different degrees of accuracy (integral versus fractional), to bring his theoretical GS results as closelyas possible into linewith the musical proportionsthat he wishes to highlight.Examiningtheaboveprocedure we see, in calculation A, Lendvai rounding down to the nearest whole number, which makes a differenceof only a little more than a quaver in duration but allows him to assert an exact correspondence . Looking within the section of 28 units as in calculation B, Lendvai prefers to keep his GS results in tenths (17.3),and not to round down this figure. For, rather than being a quaver out, this allowshim again to assert a coincidenceof theoretical and musical proportions. Indeed, as Howat [4] has pointed out, Lendvai miscalculated, but in nearly 40 years he has, for obvious reasons, not corrected the error. The dividing point that he wishes to identify is really after 18.3units! In calculation C, Lendvai rounds up his result, by approximatelya quaver’s worth...


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