  In a remarkable paper, Dienes discovered that the absence of physical
tachyons in closed string theory is intimately related to oscillations in the
net number of bosonic minus fermionic degrees of freedom, a pattern predicted
by an underlying misaligned supersymmetry. The average of these oscillations
was linked to an exponential growth controlled by an effective central charge
C_{eff} smaller than the expected inverse Hagedorn temperature. Dienes also
conjectured that C_{eff} should vanish when tachyons are absent. In this paper,
we revisit this problem and show that boson-fermion oscillations are realised
even when tachyons are present in the physical spectrum. In fact, we prove that
the average growth rate C_{eff} is set by the mass of the lightest state, be it
massless or tachyonic, and coincides with the effective inverse Hagedorn
temperature of the associated thermal theory. We also provide a general proof
that the necessary and sufficient condition for classical stability is the
vanishing of the sector averaged sum which implies C_{eff}=0, in agreement with
Dienes' conjecture.
