I. INTRODUCTION The phase transition diagram in the ( µ$_{B}$ − T ) has attracted much attention. The crucial pieces in the phase transition diagram are the existence of the tri-critical point and the discovery of quark-gluon fluid besides the other predicted phenomena such as the color- conductivity and CFL phase. The phase transition diagram persists to be proved non- trivial and very rich. The ingredient element of any investigation is the equation of state and its thermodynamics. The density of states for the hadronic mass spectrum is essential for the thermodynamic description of strongly interacting hadronic matter as well as the deconfinement phase transition to the quark-gluon plasma. The deconfined quark-gluon plasma is represented by the colored SU ( N$_{c}$ ) symmetry group where quarks and gluons are liberated and attain the color degrees of freedom. They can also form colored quark-gluon bubbles It is recently argued that the hadronic matter that is populated by the discrete low- lying hadronic mass spectrum exhibits Gross-Witten transition to another hadronic matter that is dominated by the continuous high-lying hadronic mass spectrum when the nuclear matter is compressed or heated up [1, 2]. The broken chiral symmetry generates a discrete mass spectrum. When the chiral symmetry is restored under the extreme conditions, we expect a continuous mass spectrum to emerge in the system. It appears that both the color and flavor sectors support the discrete and the continuous mass spectrum hadronic phase transition scenario. The discrete low-lying hadronic mass spectrum consists all the known mesons, baryons, resonances and the exotic hadronic particles which are found in the data book [3] such as π, ω · · · and N, Λ , Σ , Ξ · · · etc. For instance, the non-strange discrete mass spectrum consists 76 mesons and 64 baryons. The continuous high-lying hadronic mass spectrum is the mass spectrum of the Hagedorn states and these states appear as gas/liquid of hadronic fireballs. The asymptotic continuous high-lying mass spectrum can be calculated using the canonical ensemble construction [4, 5]. These predicted states are fireballs or composite bags consisting of quarks and gluons with specific internal color and/or flavor symmetry. In order to ensure the confinement of the bag’s constituent quarks and gluons and subsequently the hadronic state, the composite bag is projected to the color-singlet state (i.e. the colorless state). Hence, in QCD, it is naturally to assume that the Hagedorn states is the mass spectrum of a composite bag that is projected into color-singlet state regardless of the bag’s internal symmetry. There nothing to prevent us to extrapolate the mass spectrum 2