his own mental forging of the numerical
ratios that generate musical concords (the three symphoniae of the octave,
fifth, and fourth); the relevance of these ratios to arithmetic, geometry, and
astronomy; and finally the ethical power of the Greek hupsilon (Υ), whose two
forking branches encapsulate the ethical choice we all must make, whether to
follow the wide path to vice or the narrow path to virtue.3 In the fourth cen-
tury, Macrobius had related the rebuke of the second-century Neopythagorean
Numenius, who had ventured to give an open account of the Eleusinian mys-
teries; in a dream, Numenius saw the Eleusinian goddesses dressed as pros-
titutes, ripped from their sacred shrine, now open and available to all. This,
Macrobius tells us, is a cautionary tale against publically denuding natura of
the careful, fabulous veils woven by Pythagoras, Empedocles, Parmenides and
Heraclitus.4 By the eleventh century, Numenius’ nightmare had become a real-
ity: the mysteries of Pythagoras, even his sacred oath ma ten tetraden (“by the
tetrad!”),5 had become the stuff of popular legend, sung and jauntily rhymed
in taverns by itinerant jongleurs to undeserving nobles and eavesdropping
commoners
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