In recent work [emph{Quantum tunneling and black hole spectroscopy, Phys. Lett.} B686 (2010) 279, arXiv:0907.4271, by Banerjee et al.], it has been shown, in the tunneling mechanism, the area spacing parameter of a black hole horizon is given by $gamma=4$. In this paper, by carefully analyzing the tunneling process of the black hole radiation, we interestingly find that the most qualified candidate for a universal area gap in the tunneling mechanism is $gamma=8pi$. First, we develop the Banerjees treatment and the Kunstatters conjecture to revisit the black hole spectroscopy via quantum tunneling, and find for a real tunneling process, the area spacing parameter is given by the possible value $gammageq 4$. That is, the previous model-dependent area spacing parameters, i.e. $gamma=8pi, 4ln 3, 4$, are all possible in the tunneling mechanism. Finally, some discussions are followed to find, in the tunneling mechanism, $gamma=8pi$ is the most qualified candidate for a universal area spacing parameter.
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