Cardozo, B.L., van Lieshout, R.A.J.M. (1981). Estimates of annoyance of sounds of different character. Appl. Acoust. 14, 323-329
The character of a sound is defined as the weighted combination of all acoustic factors, not contained in $L_A$, contributing to its annoyance.
From this definition it follows that differences in annoyance due to sounds with equal $L_A$ are differences in sound character. For the concept of sound character to have real significance it is necessary that listeners agree on the annoyance due to sounds with equal $L_A$.
This paper describes a listening experiment with a variety of sounds of equal $L_A$. The annoyance due to the sounds was rated by twelve subjects. Their individual ratings show significant agreement. Moreover, their average rating correlates well (0.90) with the ratings obtained by Terhardt and Stoll  in a similar experiment.