In connection with conversion from energy class K_R (K_R = log₁₀E _R, where E_R — seismic energy, J) to the universal magnitude estimation of the Tien Shan crustal earthquakes the development of the self-coordinated correlation of the magnitudes (m_b , M_L, Ms ) and K_R with the seismic moment M₀ as the base scale became necessary. To this purpose, the first attempt to develop functional correlations in the magnitude—seismic moment system subject to the previous studies has been done. It is assumed that in the expression M (m_b , M_L , Ms) = K_i + z_i log₁₀M₀ , the coefficients k_i  and z_i  are controlled by the parameters of ratio (where ; f₀ —corner frequency, Brune, 1970, 1971; M₀, N×m). According to the new theoretical predictions common functional correlation of the advanced magnitudes M_m (m_bm = m_b , M_Lm = M_L , M_Sm = M_S ) from log₁₀M_0,  log₁₀t₀  and the elastic properties (C_i) can be presented as , where , and , for the averaged elastic properties of the Earth’s crust for thembmthe coefficients C_i= –11.30 and d_i = 1.0, for M_Lm: C_i = –14.12, di = 7/6; for M_Sm : C_i = –16.95 and d_i = 4/3. For theTien Shan earthquakes (1960-2012 years) it was obtained that , and on the basis of the above expressions we received that M_Sm = 1.59m_bm – 3.06. According to the instrumental data the correlation M_s = 1.57m_b – 3.05 was determined. Some other examples of comparison of the calculated and observed magnitude - seismic moment ratios for earthquakes of California, the Kuril Islands, Japan, Sumatra and South America are presented.