We present parametric studies of the loss cone instability of multi-harmonic electron cyclotron instabilities in a plasma consisting of a hot component with loss cone free energy source and a cold thermal component. We find that the cold upper hybrid frequency must exceed the wave frequency in order that a non-convective instability exist. When NC/NH~0.5, at least the first three harmonic bands can be simultaneously non-convective. However, the first harmonic band has large spatial growth rates over the widest parameter range; it should therefore be the most commonly observed harmonic, and except in certain circumstances should normally accompany the higher harmonics when they are observed.