Architecture Transformed: A History of Photography of Buildings from 1839 to the Present by Cervin Robinson, Joel Herschman (review)

equal parts, instead of the 12-part division that became standard in Western music. Attracted to music theory, and 31-tone tuning in particular, Fokker began writing on the subject and composing short musical examples. After the war, he continued to pursue his musical interests alongside his activities in physics. In 1950 he had a pipe organ constructed with a special keyboard having 31 tones per octave; this organ remains in use today in Teyler ’s Museum in Haarlem. Fokker’s promotion of the 31-tone system led a number of composers from the Netherlands and other countries to use it. But although he published several books and articles regarding his theories of music, Fokker was most secretive about his own activities as a composer. The publication of the present volume of compositions therefore allows the world a new glimpse into the musical mind of the man with whose name the 31-tone tuning is most closely associated. The book should also be of interest to anyone studying connections between science and the arts, because rarely does an esteemed scientist take up musical composition, and there is clearly an interdisciplinary inspiration behind Fokker’s musical thought. The book is divided into two main parts. The first contains extensive editorial commentary and background material, and the second consists of the compositions. Part One evinces keen insight and meticulous research on the part of the editor, himself both a scientist (in the field of psychoacoustics ) and a musicologist (who has already published several volumes in this series by other composers, as well as some fine editions of historical treatises on tuning). This first part includes a brief biography, a list of works, an introduction to the 31-tone system, chapters on Fokker’s theories and compositions,and notes on the individual pieces included in Part Two. Chapter 3, “Fokker’sTheories of Music”,is an especially useful summary , for Fokker’s theories-which are essential to an understanding of his music-are scattered in his own writings over a number of articles and books in different languages. In this chapter, one learns how Fokker’s music is based on the representation of intervals as numerical ratios. This approach relates directly to the acoustical phenomenon of the harmonic series, a satisfying theoretical foundation for a physicist. Whereas the traditional intervals of Western music are based on numbers whose greatest prime is 5, Fokker wanted to augment the musical vocabulary by including numbers with 7 as a factor. The 31part division of the octave provides intervals that closely approximate some of these ‘septimal’ ratios. It also produces a major third that is virtually identical to the ‘pure’ major third (5:4),and in this respect improves upon the standard division of the octave into 12equal parts. Using 31 notes per octave rather than 12 permits an extension of the musical language into the realm of microtonality -that is, the use of intervals substantially smaller than the semitone (the smallest interval in traditional Western music). Thus Fokker’s approach is grounded in accoustics and the Western musical tradition, but extends the latter in a logical direction quite different from the mainstream of twentiethcentury musical development. Part Two consists, appropriately enough, of 31 musical scores by Fokker, the bulk of which are for the 31-tone organ or for two violins. That this composer was a scientist is evident throughout: his musical ideas are highly logical-if sometimes overly literalistic-and clarity and symmetry are of the utmost importance. It must be stated, however, that certain aspects of Fokker’s music are decidedly amateurish. His compositions often exhibit a characteristic squareness of rhythm and phrase structure, an awkwardly persistent motivic repetition , an absence of the ebb and flow that usually characterize musical discourse . Yet a number of the pieces are musically quite acceptable and not without charm, such as the tranquil “Bagatelle ‘Verstrengeling”’ for organ, and the epigrammatic “Hotelkamer 315”for two violins, in which the contrapuntal back-andforth between the two instruments culminates in an engaging chordal passage. In any case, it is unfair to judge Fokker by the same criteria as one would a professional composer, since he never presented himself as one. Rather, one...