Why do beryllium and magnesium not impart colour to the flame in the flame test?

Alkaline earth metals except Be and Mg impart a characteristic colour to the Bunsen burner flame in the flame test. The different colours arise due to the different energies (provided by heat in this case) for the states of electron excitation and de-excitation. Be and Mg electrons are tightly bound to the atom due to the small atomic and ionic size. The electrons do not gain excitation from the energy provided from the flame, hence they do not impart any colour to the flame.