The Collaborative International Dictionary of English v.0.48:

Inconcinnity \In`con*cin"ni*ty\, n. [L. inconcinnitas.]
   Lack of concinnity or congruousness; unsuitableness.
   [1913 Webster]

         There is an inconcinnity in admitting these words.
                                                  --Trench.
   [1913 Webster]