This paper will explore a small but potentially significant category of Homeric expression, the approximately 200 adjective-noun phrases which occur in each epic once and only once. A compact two-page handout will display the entire set, providing the audience with an overview of this phenomenon and allowing the speaker to focus on specific examples within the larger context. The paper will concentrate on two main questions. Is the size of this group consonant with statistical expectation, insofar as one can attempt to "predict" the occurrence and distribution of very-low-frequency formulae? Does this category have anything to contribute to the long-running dispute over unitary authorship of the two epics? Even if definitive conclusions do not emerge, the close examination of a hitherto neglected area yields worthwhile results which deserve to be added to the already complex picture of archaic epic, as may be seen by comparison with other aspects of lexical research.
The Homeric hapax legomena (i.e. individual words which occur only once in both epics) have been noted since antiquity, and the major modern work, Michael Kumpf's Four Indices of the Homeric Hapax Legomena, was published almost a quarter century ago. Kumpf's lists comprise 2040 non-capitalized forms--a surprisingly high number, given the generally formulaic nature of epic composition. At the other end of the frequency spectrum, scholars since Milman Parry have concentrated their efforts on analyzing the intricacies of repeated formula groups, which may be rigidly invariant or may exhibit multiple shapes and locations within the hexameter.
By contrast, hardly any attention has been paid to this particular subset of epic diction, which is admittedly small when compared with the much larger group of noun-adjective phrases that occur only once (about 3000) -- or even when compared with the noun-adjective phrases that occur twice in one poem and not in the other (about 400 in the Iliad, 250 in the Odyssey). Nonetheless, these expressions, which earn (just barely) the term "formula" by the fact of repetition, need explaining, since many of them seem quite "ordinary" and might easily have been used--at least judged in retrospect--much more often. The paper offers some observations on particular clusters, noting the presence or absence of parallels in the remainder of archaic epic and commenting on salient characteristics, e.g. semantic aspects and metrical placements.
Finally, there is the question of origins: assuming the chronological priority of the Iliad, should we regard these phrases as borrowed from the older work (whether by the same composer or another) or as coming independently from a hypothetical common source? I cite here an unpublished paper by W. M. Sale, which applies powerful statistical arguments to some highly frequent formulas, showing that Homer must have engaged in phrasal coining. That argument is extended to suggest that many of the 3000 unique phrases and at least some of the 200 in the once-each category must be innovations by the master poet himself.
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