Metric ambiguity is an important feature of 18th century music. Of particular interest is the occurrence of metrical ambiguity resulting from conflicting groupings occurring within a monophonic texture. This paper explores the perceptual and structural implications of these monophonic metrical ambiguities. Phenomenal accents suggesting nonconcurrent groupings can generate competing metric interpretations of a musical surface. Sometimes these conflicts continue for a relatively prolonged period. We use the term polymeter to describe such cases and perceived polymeter created by conflicting cues within a single melodic line is referred to as monophonic polymeter. Contributing factors and the perceptual effects of monophonic polymeter are described. In particular, we consider the cognitive implications of music that commences with monophonic polymeter. We propose that the modus operandi of processing incipiently ambiguous music is, by nature, quite different than that of music that commences with umabiguous metrical structure.