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While quantitative and statistical genetic studies often invoke the "polygenicity" of traits and sometimes quantify it, the meaning of the term is not always clear. We propose a principled definition of polygenicity that encompasses a range of measures. We show that these measures satisfy mathematical properties that are sensible and, conversely, that measures that satisfy these properties meet our definition. We consider four specific measures in greater detail, describe how they differ, and show that three of them can be estimated from genome-wide association studies summary statistics using Fourier mixture regression. We then estimate these measures for 36 human traits. This analysis reveals a lack of traits with polygenicity values that fall in the large gap between Mendelian and highly polygenic traits. We discuss the generality of this finding and the evolutionary and cellular processes that may explain it.