FIB and PHI in Music: The Golden Proportion in Musical Form (review)

FIB and PHI in Music: The Golden Proportion in Musical Form is a promising book by Charles Madden, a well-presented edition, hardcover, from High Art Press, the fourth volume of its InMusic series.

The initial pages of the book are the most engaging, providing interesting historical data on PHI and its uses by the Egyptians and the Greeks, and touching on Fibonacci numbers from the year 1200 on. Almost immediately, the reader encounters innumerable charts and tables where the majority of the cases under discussion are defined. To take one example: "Phi remains elusive in this music . . . as seen in tables 5.13 to 5.15 there is little evidence of Phi proportions . . . it seems clear that [the composer] was not an important user of phi proportions" (pp. 206–207). It seems that the writer has focused more on discussing examples where the proportions were not used, or even not approximated. Why bother?

There are some contradictions in the book. On page 247, the conclusion to the all-important Romantic chapter, one can read that "in the symphony the golden proportion was found in several movements of [Felix] Mendelssohn." Then, referring to the pages devoted to this composer, Mr. Madden starts with the Songs Without Words, finding that a few were "close to [Golden Section]" (GS). However, on the same page we read: "Some of these pieces are not close to phi and percentages are often poor . . . Nonetheless, it is hard to refrain from thinking that he must have had some awareness of phi." Then follows a not very convincing chart concerning these songs, where only a few are noted as close enough to be placed under the subheading "At GS or GS2" (p. 236), with the majority of these many songs included under the subheading "Too far [from GS]." Arriving at the paragraph concerning the symphonies, Mr. Madden criticizes another author—Michael Richard Adkins—in reference to the Symphony No. 3 by Mendelssohn: "our results were far from his." He proceeds to chart his own figures and concludes with "Not GS." In all fairness, Mr. Madden finally finds GS (or very near it) in two movements of the Symphony No. 3 and the same in the Symphony No. 4. However, he repeatedly classifies all other movements as "Not GS."

Nevertheless, the author provides a résumé of all Mendelssohn symphonies on Table 6.7, apparently with a fewer number of movements found to be GS. It is obvious that the greater number of movements in that classification are "Too far from GS." Mr. Madden asserts that based on the above tables "it seems that Mendelssohn must have known about phi." Hmm . . . not convincing at all.

Furthermore, it is baffling how anyone can dismiss Frédéric Chopin's Prelude No. 4, in E minor, in one short sentence, saying "[Michael Richard Rogers] said that the dramatic peak of Pr. #4 occurred at measure 16 of 25. This is correct, for the leap from a#1 to g2 is after beat 62, which is GS. He also correctly stated that the piece was structurally not phi, as shown in fig. 6.4."

Mr. Madden misses the opportunity of "re-enforcing" the notion that Chopin may have actually effectively used GS by adding that, (1) this prelude can be "perceived" as being slightly longer: there is the anacrusis on bar zero that should be accounted for, then fermatas on bars 23 and 25; and (2) there is the possibility that GS is actually an "area" and not just a "point"—this GS zone then, could be defined as comprising bars 16 and 17. An analytical mind should consider it important that Chopin had intentionally put into this GS zone (1...