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Highlights: [•] Humans hear ramped (slow attack and quick decay) sounds louder and longer than damped (quick attack and slow decay) sounds. [•] We found edge cells sensitive to the quick attack and decay and slope cells sensitive to the slow attack and decay in A1. [•] Integration time for evoking full responses is short for edge cells and long for slope cells, underlying the sensitivity. [•] Persistence of excitation after ramped sounds was longer than that after damped sounds caused mainly from the edge cell. [•] This supports psychological reports that persistence of perception is longer after ramped sounds than damped sounds. [ABSTRACT FROM AUTHOR]