Roughness grows by a factor of three per 40 dB of level increase

Evidence

For an increase in sound pressure level by 40 dB roughness increases by a factor of about 3. This dependence of roughness on level is similar to the increase of fluctuation strength with level as displayed in Fig. 10.2. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1452