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The idea that music profoundly affects behavior is part of the "Great Tradition." Begbie's discussion of Greek ideas about music is much better than many: he recognizes that what modern readers understand as "music" isn't necessarily what is meant when we read "music" in translations of ancient texts. Many times "music" refers to notions stemming from the mythology of divine number (divine because they are changeless) and has nothing to do with the world of musical pieces that is familiar to us (or to the Greeks themselves). But he slips in his understanding of the mechanics of Pythagorean intonation and fails to deal with its inherent contradictions (for instance, the tuning system is not concerned with pitch but instead with the intervals, and the system yields two differently sized half-steps, not one). While he gives a glance to the complaints musicians have leveled at the Pythagoreans since Aristoxenus, he fails to grasp that these complaints are not arguments between sensualists and intellectuals but between people of rival intellectual positions. (Begbie relies heavily for much of his argument about the legacy of the Pythagoreans on the work of Daniel Chua—perhaps best known for describing the opening chords of Beethoven's Eroica Symphony as "the testicles of the hero"—and his topic would have been better served with a more skeptical use of Chua's problematic analyses.)
The overtone series is an acoustic phenomenon. Produce any pitch, and that pitch will itself generate a series of pitches above it. It is for musicians what the color spectrum is for artists. Believing that a Christian theology of music should grow out of a "full-blooded doctrine of creation that recognizes our embeddedness in a given, common, physical environment," Begbie seeks to ground Christian music in the overtone series. But here he again missteps. He seems to believe that the overtone series produces the same tones as are constructed through Pythagorean tuning. It doesn't. The thirds are markedly different. While being careful not to argue that the harmonic language of Western Europe has a kind of theological superiority to music of other cultures, Begbie does suggest that there is direct relationship between the overtone series and the harmonic syntax of tonal music—that the tonic, dominant, and subdominant chords so important in harmonic tonality are implicit in the overtone series itself. But this is not at all the case. Put very simply, if C is our fundamental, a pitch a perfect fourth above that C, or F, isn't found within the first sixteen partials of the overtone series at all. Without that F, we have neither the dominant seventh chord (upon which the whole syntax of harmonic tonality is based), nor the subdominant chord. Instead of an F, we find an "out of tune" F sharp at the eleventh partial, flat from an equally tempered F sharp by almost a quartertone. In order for the pitches of the overtone series to be musically useful in tonal music, at least one very important pitch must be altered according to purely culturally derived aesthetic criteria. We have to flatten that eleventh partial. It's not too far off the mark to say that tonal music exists in spite of the harmonic series, not because of it.
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